pyrolite
pyrolite is a set of tools for making the most of your geochemical data.
The python package includes functions to work with compositional data, to transform geochemical variables (e.g. elements to oxides), functions for common plotting tasks (e.g. spiderplots, ternary diagrams, bivariate and ternary density diagrams), and numerous auxiliary utilities.
On this site you can browse the API, or look through some of the usage examples.
There’s also a quick installation guide, a list of recent changes and some notes on where the project is heading in the near future.
If you’re interested in contributing to the project, there are many potential avenues, whether you’re experienced with python or not.
Note
pyrolite has been published in the Journal of Open Source Software, and a recent publication focusing on using lambdas and tetrads to parameterise Rare Earth Element patterns has been published in Mathematical Geosciences!
Why pyrolite?
The name pyrolite is an opportunistic repurposing of a term used to describe an early model mantle composition proposed by Ringwood [Ringwood1962], comprised principally of pyr-oxene & ol-ivine. While the model certainly hasn’t stood the test of time, the approach optimises the aphorism “All models are wrong, but some are useful” [Box1976]. It is with this mindset that pyrolite is built, to better enable you to make use of your geochemical data to build and test geological models.
- Ringwood1962
Ringwood, A.E. (1962). A model for the upper mantle. Journal of Geophysical Research (1896-1977) 67, 857–867. doi: 10.1029/JZ067i002p00857
- Box1976
Box, G.E.P. (1976). Science and Statistics. Journal of the American Statistical Association 71, 791–799. doi: 10.1080/01621459.1976.10480949
Installation
pyrolite is available on PyPi, and can be downloaded with pip:
pip install --user pyrolite
Note
With pip, a user-level installation is generally recommended (i.e. using the
--user flag), especially on systems which have a system-level
installation of Python (including *.nix, WSL and MacOS systems); this can
avoid some permissions issues and other conflicts. For detailed information
on other pip options, see the relevant
docs.
pyrolite is not yet packaged for Anaconda, and as such
conda install pyrolite will not work.
Upgrading pyrolite
New versions of pyrolite are released frequently. You can upgrade to the latest edition
on PyPi using the --upgrade flag:
pip install --upgrade pyrolite
See also
Optional Dependencies
Optional dependencies (dev, skl, spatial, db, stats, docs) can be specified during pip installation. For example:
pip install --user pyrolite[stats]
pip install --user pyrolite[dev,docs]
Getting Started
Note
This page is under construction. Feel free to send through suggestions or questions.
Getting Set Up
Before you can get up and running with pyrolite, you’ll need to have a distribution of
Python installed. If you’re joining the scientific Python world, chances are that the
Anaconda distributions
are a good match for you *. Check PyPI for the most up to date information regarding
pyrolite compatibility, but as of writing this guide, pyrolite is
known to work well with Python 3.5, 3.6 and 3.7.
When it comes to how you edit files and interact with Python, there are now many
different choices (especially for editors), and choosing something which allows
you to work the way you wish to work is the key aspect. While you can certainly edit
python files (.py) in any text editor, choosing an editor designed for the task
makes life easier. Choosing one is subjective - know that many exist, and perhaps try a
few. Integrated Development Environments (IDEs) often allow you to
quickly edit and run code within the same window (e.g.
Spyder, which is typically included in the default
Anaconda distribution). Through notebooks and related ideas the
Jupyter ecosystem has broadened how people are interacting
with code across multiple languages, including Python. For reference,
pyrolite has been developed principally in Atom,
leveraging the Hydrogen package to provide
an interactive coding environment using Jupyter.
Finally, consider getting up to speed with simple Git practises for your projects and code such that you can keep versioned histories of your analyses, and have a look at hosted repository services (e.g. GitHub, GitLab). These hosted repositories together with integrated services are often worth taking advantage of (e.g. hosting material and analyses from papers, posters or presentation, and linking this through to Zenodo to get an archived version with a DOI).
- *
If you’re strapped for space, or are bloat-averse, you could also consider using Anaconda’s miniconda distributions.
Installing pyrolite
There’s a separate page dedicated to pyrolite installations, but for most purposes, the best way to install pyrolite is through opening a terminal (an Anaconda terminal, if that’s the distribution you’re using) and type:
pip install pyrolite
To keep pyrolite up to date (new versions are released often), periodically run the following to update your local version:
pip install --upgrade pyrolite
Writing Some Code
If you’re new to Python †, or just new to pyrolite, checking out some of the
examples is a good first step. You should be able to copy-paste or download
and run each of these examples as written on your own system, or alternatively you
can run them interatively in your browser thanks to
Binder and
sphinx-gallery
(check for the links towards the bottom of each page). Have a play with these, and
adapt them to your own purposes.
- †
If you’re completely new to Python, check out some of the many free online courses to get up to scratch with basic Python concepts, data structures and get in a bit of practice writing code (e.g. the basic Python course on Codecademy). Knowing your way around some of these things before you dive into applying them can help make it a much more surmountable challenge. Remember that the pyrolite community is also around to help out if you get stuck, and we all started from a similar place! There are no ‘stupid questions’, so feel free to ping us on Gitter with any questions or aspects that are proving particularly challenging.
Importing Data
A large part of the pyrolite API is based around pandas DataFrames.
One of the first hurdles for new users is importing their own data tables.
To make this as simple as possible, it’s best to organise - or ‘tidy’ - your data
tables ‡. Minimise unnecessary whitespace, and
where possible make sure your table columns are the first row of your table.
In most cases, where these data are in the form of text or Excel files,
the typical steps for data import are similar. A few simple examples are given
below.
To import a table from a .csv file:
from pathlib import Path
import pandas as pd
filepath = Path('./mydata.csv')
df = pd.read_csv(filepath)
In the case of an excel table:
filepath = Path('./mydata.xlsx')
df = pd.read_excel(filepath)
There is also a pyrolite function which abstracts away these differences by making a few assumptions, and enables you to import the table from either a csv or excel file:
from pyrolite.util.pd import read_table
df = read_table(filepath)
- ‡
Where each variable is a column, and each observation is a row. If you’re unfamiliar with the ‘Tidy Data’ concept, check out [Wickham2014].
- Wickham2014
Wickham, H., 2014. Tidy Data. Journal of Statistical Software 59, 1–23. doi: doi.org/10.18637/jss.v059.i10
Gitter Community
A Gitter Community has been set up to serve as a landing page for conversations, questions and support regarding the pyrolite python package and related activities. Here we hope to capture questions and bugs from the community such that these can be addressed quickly, and we can ensure pyrolite and its documentation are as useful as possible to the community. Please feel free to use this space to:
Ask questions or seek help about getting started with pyrolite or particular pyrolite features
Get tips for troubleshooting
Discuss the general development of pyrolite
Ask about contributing to pyrolite
Items which are related to specific aspects of pyrolite development (requesting a feature, or reporting an identified bug) are best coordinated through GitHub, but feel free to touch base here first. See below and the contribution and development guides for more information.
Note that users and contributors in online spaces (including Gitter) are expected to adhere to the Code of Conduct of this project (and any other guidelines of the relevant platform).
Bugs, Debugging & Bug Reporting
This section provides some guidance for what to do when things don’t work as expected,
and some tips for debugging issues and common errors associated with
pyrolite. Note that the scope of these suggestions is necessarily limited, and specific
issues which relate more to matplotlib.pyplot, pandas, and numpy
are often well documented elsewhere online.
Checked the documentation, had a look for FAQ and examples here and still stuck?
The maintainers are happy to answer questions and help you solve small bugs. It’s useful to know where people get stuck so we can modify things where useful, and this is an easy way to contribute to the project. Consider posting a question on Gitter, and if you think it’s something others may run into or could be a problem related to use of another package, perhaps also consider posting a question on stackoverflow for visibility.
Think it’s a bug or problem with pyrolite specifically?
Some guidelines for reporting issues and bugs are given in the contributing guide.
See also
Examples
This example gallery includes a variety of examples for using pyrolite which you can copy, download and alter, or run on Binder.
Plotting Examples
pyrolite provides some functionality for basic plotting of geochemical data in the form of spidergrams (pyrolite.plot.spider), ternary diagrams (pyrolite.plot.tern) and density diagrams (i.e. 2D histograms, pyrolite.plot.density).
Stem Plots
Stem plots are commonly used to visualise discrete distributions of data, and are useful to highlight discrete observations where the precision of values along one axis is high (e.g. an independent spatial measure like depth) and the other is less so (such that the sampling frequency along this axis is important, which is not emphasised by a scatter plot).
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from pyrolite.plot import pyroplot
from pyrolite.plot.stem import stem
np.random.seed(82)
First let’s create some example data:
x = np.linspace(0, 10, 10) + np.random.randn(10) / 2.0
y = np.random.rand(10)
df = pd.DataFrame(np.vstack([x, y]).T, columns=["Depth", "Fe3O4"])
A minimal stem plot can be constructed as follows:
ax = df.pyroplot.stem(color="k", figsize=(5, 3))
Stem plots can also be used in a vertical orientation, such as for visualising discrete observations down a drill hole:
ax = df.pyroplot.stem(
orientation="vertical",
s=12,
linestyle="--",
linewidth=0.5,
color="k",
figsize=(3, 5),
)
# the yaxes can then be inverted using:
ax.invert_yaxis()
# and if you'd like the xaxis to be labeled at the top:
ax.xaxis.set_ticks_position("top")
ax.xaxis.set_label_position("top")
Total running time of the script: (0 minutes 0.487 seconds)
Ternary Plots
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from pyrolite.plot import pyroplot
np.random.seed(82)
Let’s first create some example data:
df = pd.DataFrame(data=np.exp(np.random.rand(100, 3)), columns=["SiO2", "MgO", "CaO"])
df.loc[:, ["SiO2", "MgO", "CaO"]].head()
Now we can create a simple scatter plot:
ax = df.loc[:, ["SiO2", "MgO", "CaO"]].pyroplot.scatter(c="k")
plt.show()
If the data represent some continuous series, you could also plot them as lines:
ax = df.loc[:, ["SiO2", "MgO", "CaO"]].pyroplot.plot(color="k", alpha=0.5)
plt.show()
The plotting axis can be specified to use exisiting axes:
fig, ax = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(12, 5))
df.loc[:, ["SiO2", "MgO", "CaO"]].sample(20).pyroplot.scatter(ax=ax[0], c="k")
df.loc[:, ["SiO2", "MgO", "CaO"]].sample(20).pyroplot.scatter(ax=ax[1], c="g")
ax = fig.orderedaxes # creating scatter plots reorders axes, this is the correct order
plt.tight_layout()
Total running time of the script: (0 minutes 14.120 seconds)
REE Radii Plots
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from pyrolite.plot import pyroplot
Here we generate some example data, using the
example_spider_data() function (based on EMORB,
here normalised to Primitive Mantle);
from pyrolite.util.synthetic import example_spider_data
df = example_spider_data(noise_level=0.1, size=20)
Where data is specified, the default plot is a line-based spiderplot:
ax = df.pyroplot.REE(color="0.5", figsize=(8, 4))
plt.show()
This behaviour can be modified (see spiderplot docs) to provide e.g. filled ranges:
df.pyroplot.REE(mode="fill", color="0.5", alpha=0.5, figsize=(8, 4))
plt.show()
The plotting axis can be specified to use exisiting axes:
fig, ax = plt.subplots(1, 2, sharey=True, figsize=(12, 4))
df.pyroplot.REE(ax=ax[0])
# we can also change the index of the second axes
another_df = example_spider_data(noise_level=0.2, size=20) # some 'nosier' data
another_df.pyroplot.REE(ax=ax[1], color="k", index="radii")
plt.tight_layout()
plt.show()
If you’re just after a plotting template, you can use
REE_v_radii() to get a formatted axis which can be used
for subsequent plotting:
from pyrolite.plot.spider import REE_v_radii
ax = REE_v_radii(index="radii") # radii mode will put ionic radii on the x axis
plt.show()
See also
Total running time of the script: (0 minutes 4.711 seconds)
Ternary Color Systems
pyrolite includes two methods for coloring data points and polygons in
a ternary system, ternary_color() and
color_ternary_polygons_by_centroid() which work
well with some of the plot templates (pyrolite.plot.templates) and
associated classifiers (pyrolite.util.classification).
import numpy as np
import matplotlib.pyplot as plt
Colors by Ternary Position
The ternary_color() function serves to generate
the color which correpsonds the the mixing of three colours in proportion
to the components in a ternary system. By default these colours are red, green
and blue (corresponding to the top, left, and right components in a terarny diagram).
The function returns colours in the form of an RGBA array:
from pyrolite.util.plot.style import ternary_color
from pyrolite.util.synthetic import normal_frame
# generate a synthetic dataset we can use for the colouring example
df = normal_frame(
columns=["CaO", "MgO", "FeO"],
size=100,
seed=42,
cov=np.array([[0.8, 0.3], [0.3, 0.8]]),
)
colors = ternary_color(df)
colors[:3]
array([[0.18902861, 0.54222697, 0.26874443, 0.999999 ],
[0.5097609 , 0.16739226, 0.32284684, 0.999999 ],
[0.08310658, 0.37115312, 0.54574029, 0.999999 ]])
These can then be readily used in a ternary diagram (or eleswhere):
ax = df.pyroplot.scatter(c=colors)
plt.show()
ax = df[["MgO", "CaO"]].pyroplot.scatter(c=colors)
plt.show()
You can use different colors for each of the verticies if you so wish, and
mix and match named colors with RGB/RGBA represntations (note that the alpha will
be scaled, if it is passed as a keyword argument to
ternary_color()):
colors = ternary_color(df, alpha=0.9, colors=["green", "orange", [0.9, 0.1, 0.5, 0.9]])
ax = df.pyroplot.scatter(c=colors)
plt.show()
Colors by Centroid Position
We can also colour polygons within one of these templates by the ternary combination of colours (defaulting to red, green and blue) at the polygon centroid:
from pyrolite.util.classification import USDASoilTexture
from pyrolite.util.plot.style import color_ternary_polygons_by_centroid
clf = USDASoilTexture()
ax = clf.add_to_axes(ax=None, add_labels=True, figsize=(8, 8))
color_ternary_polygons_by_centroid(ax)
plt.show()
There are a range of options you can pass to this function to control the ternary colors (as above), change the scaling coefficients for ternary components and change the opacity of the colors:
color_ternary_polygons_by_centroid(
ax, colors=("red", "green", "blue"), coefficients=(1, 1, 1), alpha=0.5
)
plt.show()
See also
- Examples:
Total running time of the script: (0 minutes 12.978 seconds)
Parallel Coordinate Plots
Parallel coordinate plots are one way to visualise data relationships and clusters in higher dimensional data. pyrolite now includes an implementation of this which allows a handy quick exploratory visualisation.
import matplotlib.axes
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
import numpy as np
import pandas as pd
import pyrolite.data.Aitchison
import pyrolite.plot
To start, let’s load up an example dataset from Aitchison
df = pyrolite.data.Aitchison.load_coxite()
comp = [
i for i in df.columns if i not in ["Depth", "Porosity"]
] # compositional data variables
ax = df.pyroplot.parallel()
plt.show()
By rescaling this using the mean and standard deviation, we can account for scale differences between variables:
ax = df.pyroplot.parallel(rescale=True)
plt.show()
We can also use a centred-log transform for compositional data to reduce the effects of spurious correlation:
from pyrolite.util.skl.transform import CLRTransform
cmap = "inferno"
compdata = df.copy()
compdata[comp] = CLRTransform().transform(compdata[comp])
ax = compdata.loc[:, comp].pyroplot.parallel(color=compdata.Depth.values, cmap=cmap)
divider = make_axes_locatable(ax)
cax = divider.append_axes('right', size='5%', pad=0.05)
# we can add a meaningful colorbar to indicate one variable also, here Depth
sm = plt.cm.ScalarMappable(cmap=cmap)
sm.set_array(df.Depth)
plt.colorbar(sm, cax=cax, orientation='vertical')
plt.show()
ax = compdata.loc[:, comp].pyroplot.parallel(
rescale=True, color=compdata.Depth.values, cmap=cmap
)
divider = make_axes_locatable(ax)
cax = divider.append_axes('right', size='5%', pad=0.05)
plt.colorbar(sm, cax=cax, orientation='vertical')
plt.show()
Total running time of the script: (0 minutes 1.168 seconds)
Heatscatter Plots
While density() plots are useful summary visualizations
for large datasets, scatterplots are more precise and retain all spatial information
(although they can get crowded).
A scatter plot where individual points are coloured by data density in some respects
represents the best of both worlds. A version inspired by similar existing
visualisations is implemented with heatscatter().
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from pyrolite.plot import pyroplot
np.random.seed(12)
First we’ll create some example data
from pyrolite.util.synthetic import normal_frame, random_cov_matrix
df = normal_frame(
size=1000,
cov=random_cov_matrix(sigmas=np.random.rand(4) * 2, dim=4, seed=12),
seed=12,
)
We can compare a minimal heatscatter() plot to other
visualisations for the same data:
from pyrolite.util.plot.axes import share_axes
fig, ax = plt.subplots(3, 4, figsize=(12, 9))
ax = ax.flat
share_axes(ax[:4], which="xy")
share_axes(ax[4:8], which="xy")
share_axes(ax[8:], which="xy")
contours = [0.95, 0.66, 0.3]
bivar = ["SiO2", "MgO"]
trivar = ["SiO2", "MgO", "TiO2"]
# linear-scaled comparison
df.loc[:, bivar].pyroplot.scatter(ax=ax[0], c="k", s=10, alpha=0.3)
df.loc[:, bivar].pyroplot.density(ax=ax[1])
df.loc[:, bivar].pyroplot.density(ax=ax[2], contours=contours)
df.loc[:, bivar].pyroplot.heatscatter(ax=ax[3], s=10, alpha=0.3)
# log-log plots
df.loc[:, bivar].pyroplot.scatter(ax=ax[4], c="k", s=10, alpha=0.3)
df.loc[:, bivar].pyroplot.density(ax=ax[5], logx=True, logy=True)
df.loc[:, bivar].pyroplot.density(ax=ax[6], contours=contours, logx=True, logy=True)
df.loc[:, bivar].pyroplot.heatscatter(ax=ax[7], s=10, alpha=0.3, logx=True, logy=True)
# ternary plots
df.loc[:, trivar].pyroplot.scatter(ax=ax[8], c="k", s=10, alpha=0.1)
df.loc[:, trivar].pyroplot.density(ax=ax[9], bins=100)
df.loc[:, trivar].pyroplot.density(ax=ax[10], contours=contours, bins=100)
df.loc[:, trivar].pyroplot.heatscatter(ax=ax[11], s=10, alpha=0.3, renorm=True)
fig.subplots_adjust(hspace=0.4, wspace=0.4)
titles = ["Scatter", "Density", "Contours", "Heatscatter"]
for t, a in zip(titles + [i + " (log-log)" for i in titles], ax):
a.set_title(t)
plt.tight_layout()
See also
Total running time of the script: (0 minutes 17.975 seconds)
Plot Templates
pyrolite includes some ready-made templates for well-known plots. These can
be used to create new plots, or add a template to an existing
matplotlib.axes.Axes.
import matplotlib.pyplot as plt
Bivariate Templates
First let’s build a simple total-alkali vs silica (
TAS()) diagram:
from pyrolite.plot.templates import TAS, SpinelFeBivariate
from pyrolite.util.plot.axes import share_axes
ax = TAS(linewidth=0.5, add_labels=True)
plt.show()
A few different variants are now available, with slightly different positioning of field boundaries, and with some fields combined:
fig, ax = plt.subplots(1, 3, figsize=(12, 3))
TAS(ax=ax[0], linewidth=0.5, add_labels=True, which_model=None) # Middlemost's TAS
TAS(ax=ax[1], linewidth=0.5, add_labels=True, which_model="LeMaitre") # LeMaitre's TAS
TAS(ax=ax[2], linewidth=0.5, add_labels=True, which_model="LeMaitreCombined")
for a in ax[1:]:
a.set(yticks=[], ylabel=None)
For distinguishing Fe-rich variants of spinel phases, the bivariate spinel diagram can be useful:
ax = SpinelFeBivariate(linewidth=0.5, add_labels=True)
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/util/plot/axes.py:219: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`). Consider using `matplotlib.pyplot.close()`.
fig, ax = plt.subplots(1, **subkwargs(kwargs, plt.subplots, plt.figure))
pyrolite contains templates for the Pearce diagrams, used to discriminate mafic rocks
(and particularly basalts) based on their whole-rock geochemistry. Two templates are
included: pearceThNbYb() and
pearceTiNbYb().
We can create some axes and add these templates to them:
from pyrolite.plot.templates import pearceThNbYb, pearceTiNbYb
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
share_axes(ax, which="x") # these diagrams have the same x axis
pearceThNbYb(ax=ax[0])
pearceTiNbYb(ax=ax[1])
plt.tight_layout() # nicer spacing for axis labels
pyrolite also now includes some diagram templates for discrimination of sandstones
based on their whole-rock geochemistry (Pettijohn(),
Herron()):
from pyrolite.plot.templates import Herron, Pettijohn
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
share_axes(ax, which="x") # these diagrams have the same x axis
Pettijohn(ax=ax[0], add_labels=True)
Herron(ax=ax[1], add_labels=True)
plt.tight_layout()
Ternary Templates
pyrolite now also includes ternary classification diagrams inlcuding
the QAP() and
USDASoilTexture() diagrams:
from pyrolite.plot.templates import (
QAP,
FeldsparTernary,
JensenPlot,
SpinelTrivalentTernary,
USDASoilTexture,
)
ax = QAP(linewidth=0.4)
plt.show()
ax = USDASoilTexture(linewidth=0.4)
plt.show()
For the feldspar ternary diagram, which is complicated by a miscibility gap, there are two modes: ‘default’ and ‘miscibility-gap’. The second of these provides a simplified approximation of the miscibility gap between k-feldspar and plagioclase, wheras ‘default’ ignores this aspect (which itself is complicated by temperature):
fig, ax = plt.subplots(1, 2, figsize=(12, 6))
FeldsparTernary(ax=ax[0], linewidth=0.4, add_labels=True, mode="default")
FeldsparTernary(ax=ax[1], linewidth=0.4, add_labels=True, mode="miscibility-gap")
plt.tight_layout()
plt.show()
For general spinel phase discrimination, a ternary classification diagram can be used to give labels based on trivalent cationic content (\(\mathrm{Cr^{3+}}\), \(\mathrm{Al^{3+}}\), \(\mathrm{Fe^{3+}}\)):
SpinelTrivalentTernary(linewidth=0.4, add_labels=True, figsize=(6, 6))
plt.show()
The Jensen plot is another cationic ternary discrimination diagram (Jensen, 1976), for subalkaline volcanic rocks:
JensenPlot(linewidth=0.4, add_labels=True, figsize=(7, 7))
plt.show()
References and other notes for diagram templates can be found within the docstrings and within the pyrolite documentation:
help(TAS)
Help on function TAS in module pyrolite.plot.templates.TAS:
TAS(ax=None, add_labels=False, which_labels='ID', relim=True, color='k', which_model=None, **kwargs)
Adds the TAS diagram to an axes. Diagram from Middlemost (1994) [#pyrolite.plot.templates.TAS.TAS_1]_,
a closed-polygon variant after Le Bas et al (1992) [#pyrolite.plot.templates.TAS.TAS_2]_.
Parameters
----------
ax : :class:`matplotlib.axes.Axes`
Axes to add the template on to.
add_labels : :class:`bool`
Whether to add labels at polygon centroids.
which_labels : :class:`str`
Which labels to add to the polygons (e.g. for TAS, 'volcanic', 'intrusive'
or the field 'ID').
relim : :class:`bool`
Whether to relimit axes to fit the built in ranges for this diagram.
color : :class:`str`
Line color for the diagram.
which_model : :class:`str`
The name of the model variant to use, if not Middlemost.
Returns
-------
ax : :class:`matplotlib.axes.Axes`
References
-----------
.. [#pyrolite.plot.templates.TAS.TAS_1] Middlemost, E. A. K. (1994).
Naming materials in the magma/igneous rock system.
Earth-Science Reviews, 37(3), 215–224.
doi: `10.1016/0012-8252(94)90029-9 <https://dx.doi.org/10.1016/0012-8252(94)90029-9>`__
.. [#pyrolite.plot.templates.TAS.TAS_2] Le Bas, M.J., Le Maitre, R.W., Woolley, A.R. (1992).
The construction of the Total Alkali-Silica chemical
classification of volcanic rocks.
Mineralogy and Petrology 46, 1–22.
doi: `10.1007/BF01160698 <https://dx.doi.org/10.1007/BF01160698>`__
See also
- Examples:
- Modules:
- Classes:
Total running time of the script: (0 minutes 23.109 seconds)
Density and Contour Plots
While individual point data are useful, we commonly want to understand the the distribution of our data within a particular subspace, and compare that to a reference or other dataset. Pyrolite includes a few functions for visualising data density, most based on Gaussian kernel density estimation and evaluation over a grid. The below examples highlight some of the currently implemented features.
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from pyrolite.comp.codata import close
from pyrolite.plot import pyroplot
from pyrolite.plot.density import density
np.random.seed(82)
First we create some example data :
oxs = ["SiO2", "CaO", "MgO", "Na2O"]
ys = np.random.rand(1000, len(oxs))
ys[:, 1] += 0.7
ys[:, 2] += 1.0
df = pd.DataFrame(data=close(np.exp(ys)), columns=oxs)
A minimal density plot can be constructed as follows:
ax = df.loc[:, ["SiO2", "MgO"]].pyroplot.density()
df.loc[:, ["SiO2", "MgO"]].pyroplot.scatter(ax=ax, s=10, alpha=0.3, c="k", zorder=2)
plt.show()
A colorbar linked to the KDE estimate colormap can be added using the colorbar boolean switch:
ax = df.loc[:, ["SiO2", "MgO"]].pyroplot.density(colorbar=True)
plt.show()
density by default will create a new axis, but can also be plotted over an existing axis for more control:
fig, ax = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(12, 5))
df.loc[:, ["SiO2", "MgO"]].pyroplot.density(ax=ax[0])
df.loc[:, ["SiO2", "CaO"]].pyroplot.density(ax=ax[1])
plt.tight_layout()
plt.show()
There are two other implemented modes beyond the default density: hist2d and hexbin, which parallel their equivalents in matplotlib. Contouring is not enabled for these histogram methods.
fig, ax = plt.subplots(1, 3, sharex=True, sharey=True, figsize=(14, 5))
for a, mode in zip(ax, ["density", "hexbin", "hist2d"]):
df.loc[:, ["SiO2", "CaO"]].pyroplot.density(ax=a, mode=mode)
a.set_title("Mode: {}".format(mode))
plt.show()
For the density mode, a vmin parameter is used to choose the lower
threshold, and by default is the 99th percentile (vmin=0.01), but can be
adjusted. This is useful where there are a number of outliers, or where you wish to
reduce the overall complexity/colour intensity of a figure (also good for printing!).
fig, ax = plt.subplots(1, 3, figsize=(14, 4))
for a, vmin in zip(ax, [0.01, 0.1, 0.4]):
df.loc[:, ["SiO2", "CaO"]].pyroplot.density(ax=a, bins=30, vmin=vmin, colorbar=True)
plt.tight_layout()
plt.show()
plt.close("all") # let's save some memory..
Density plots can also be used for ternary diagrams, where more than two components are specified:
fig, ax = plt.subplots(
1,
3,
sharex=True,
sharey=True,
figsize=(15, 5),
subplot_kw=dict(projection="ternary"),
)
df.loc[:, ["SiO2", "CaO", "MgO"]].pyroplot.scatter(ax=ax[0], alpha=0.05, c="k")
for a, mode in zip(ax[1:], ["hist", "density"]):
df.loc[:, ["SiO2", "CaO", "MgO"]].pyroplot.density(ax=a, mode=mode)
a.set_title("Mode: {}".format(mode), y=1.2)
plt.tight_layout()
plt.show()
Contours are also easily created, which by default are percentile estimates of the underlying kernel density estimate.
Note
As the contours are generated from kernel density estimates, assumptions around e.g. 95% of points lying within a 95% contour won’t necessarily be valid for non-normally distributed data (instead, this represents the approximate 95% percentile on the kernel density estimate). Note that contours are currently only generated; for mode=”density”; future updates may allow the use of a histogram basis, which would give results closer to 95% data percentiles.
ax = df.loc[:, ["SiO2", "CaO"]].pyroplot.scatter(s=10, alpha=0.3, c="k", zorder=2)
df.loc[:, ["SiO2", "CaO"]].pyroplot.density(ax=ax, contours=[0.95, 0.66, 0.33])
plt.show()
You can readily change the styling of these contours by passing cmap (for different colormaps), colors (for bulk or individually specified colors), linewidths and linestyles (for bulk or individually specified linestyles). You can also use ‘label_contours=False` to omit the contour labels. For example, to change the colormap and omit the contour labels:
ax = df.loc[:, ["SiO2", "CaO"]].pyroplot.density(
contours=[0.95, 0.66, 0.33], cmap="tab10", label_contours=False
)
plt.show()
You can specify one styling value for all contours:
ax = df.loc[:, ["SiO2", "CaO"]].pyroplot.density(
contours=[0.95, 0.66, 0.33], linewidths=2, linestyles="--", colors="k"
)
plt.show()
Or specify a list of values which will be applied to the contours in the order given in the contours keyword argument:
ax = df.loc[:, ["SiO2", "CaO"]].pyroplot.density(
contours=[0.95, 0.66, 0.33],
linewidths=[1, 2, 3],
linestyles=["-", "--", "-."],
colors=["0.5", "g", "k"],
)
plt.show()
If for some reason the density plot or contours are cut off on the edges, it may be that the span of the underlying grid doesn’t cut it (this is often the case for just a small number of points). You can either manually adjust the extent ( extent = (min_x, max_x, min_y, max_y) ) or adjust the coverage scale ( e.g. coverage_scale = 1.5 will increase the buffer from the default 10% to 25%). You can also adjust the number of bins in the underlying grid (either for both axes with e.g. bins=100 or individually with bins=(<xbins>, <ybins>)):
ax = df.loc[:, ["SiO2", "CaO"]].pyroplot.density(
contours=[0.95, 0.66, 0.33], coverage_scale=1.5, bins=100
)
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/util/plot/density.py:202: UserWarning: The following kwargs were not used by contour: 'coverage_scale'
cs = contour(
Geochemical data is commonly log-normally distributed and is best analysed and visualised after log-transformation. The density estimation can be conducted over logspaced grids (individually for x and y axes using logx and logy boolean switches). Notably, this makes both the KDE image and contours behave more naturally:
# some assymetric data
from scipy import stats
xs = stats.norm.rvs(loc=6, scale=3, size=(200, 1))
ys = stats.norm.rvs(loc=20, scale=3, size=(200, 1)) + 5 * xs + 50
data = np.append(xs, ys, axis=1).T
asym_df = pd.DataFrame(np.exp(np.append(xs, ys, axis=1) / 25.0))
asym_df.columns = ["A", "B"]
grids = ["linxy", "logxy"] * 2 + ["logx", "logy"]
scales = ["linscale"] * 2 + ["logscale"] * 2 + ["semilogx", "semilogy"]
labels = ["{}-{}".format(ls, ps) for (ls, ps) in zip(grids, scales)]
params = list(
zip(
[
(False, False),
(True, True),
(False, False),
(True, True),
(True, False),
(False, True),
],
grids,
scales,
)
)
fig, ax = plt.subplots(3, 2, figsize=(8, 8))
ax = ax.flat
for a, (ls, grid, scale) in zip(ax, params):
lx, ly = ls
asym_df.pyroplot.density(ax=a, logx=lx, logy=ly, bins=30, cmap="viridis_r")
asym_df.pyroplot.density(
ax=a,
logx=lx,
logy=ly,
contours=[0.95, 0.5],
bins=30,
cmap="viridis",
fontsize=10,
)
asym_df.pyroplot.scatter(ax=a, s=10, alpha=0.3, c="k", zorder=2)
a.set_title("{}-{}".format(grid, scale), fontsize=10)
if scale in ["logscale", "semilogx"]:
a.set_xscale("log")
if scale in ["logscale", "semilogy"]:
a.set_yscale("log")
plt.tight_layout()
plt.show()
plt.close("all") # let's save some memory..
Note
Using alpha with the density mode induces a known and old matplotlib bug,
where the edges of bins within a pcolormesh image (used for plotting the
KDE estimate) are over-emphasized, giving a gridded look.
Total running time of the script: (0 minutes 11.582 seconds)
Spiderplots & Density Spiderplots
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
Here we’ll set up an example which uses EMORB as a starting point. Typically we’ll
normalise trace element compositions to a reference composition
to be able to link the diagram to ‘relative enrichement’ occuring during geological
processes, so here we’re normalising to a Primitive Mantle composition first.
We’re here taking this normalised composition and adding some noise in log-space to
generate multiple compositions about this mean (i.e. a compositional distribution).
For simplicility, this is handled by
example_spider_data():
from pyrolite.util.synthetic import example_spider_data
normdf = example_spider_data(start="EMORB_SM89", norm_to="PM_PON")
See also
Basic spider plots are straightforward to produce:
import pyrolite.plot
ax = normdf.pyroplot.spider(color="0.5", alpha=0.5, unity_line=True, figsize=(10, 4))
ax.set_ylabel("X / $X_{Primitive Mantle}$")
plt.show()
Index Ordering
The default ordering here follows that of the dataframe columns, but we typically
want to reorder these based on some physical ordering. A index_order keyword
argument can be used to supply a function which will reorder the elements before
plotting. Here we order the elements by relative incompatibility (using
pyrolite.geochem.ind.by_incompatibility() behind the scenes):
from pyrolite.geochem.ind import by_incompatibility
ax = normdf.pyroplot.spider(
color="k",
alpha=0.1,
unity_line=True,
index_order="incompatibility",
figsize=(10, 4),
)
ax.set_ylabel("X / $X_{Primitive Mantle}$")
plt.show()
Similarly, you can also rearrange elements to be in order of atomic number:
from pyrolite.geochem.ind import by_number
ax = normdf.pyroplot.spider(
color="k",
alpha=0.1,
unity_line=True,
index_order="number",
figsize=(10, 4),
)
ax.set_ylabel("X / $X_{Primitive Mantle}$")
plt.show()
Color Mapping
We can also specify either continuous or categorical values to use for the colors, and even map categorical values to specific colors where useful:
fig, ax = plt.subplots(3, 1, sharex=True, sharey=True, figsize=(10, 8))
ax[0].set_title("Continuous Values")
normdf.pyroplot.spider(
ax=ax[0],
unity_line=True,
index_order="incompatibility",
cmap="plasma",
alpha=0.1,
color=np.log(normdf["Li"]), # a range of continous values
)
ax[1].set_title("Boolean/Categorical Values")
normdf.pyroplot.spider(
ax=ax[1],
alpha=0.1,
unity_line=True,
index_order="incompatibility",
color=normdf["Cs"] > 3.5, # a boolean/categorical set of values
)
ax[2].set_title("Boolean/Categorical Values with Color Mapping")
normdf.pyroplot.spider(
ax=ax[2],
alpha=0.1,
unity_line=True,
index_order="incompatibility",
color=normdf["Cs"] > 3.5, # a boolean/categorical set of values
color_mappings={ # mapping the boolean values to specific colors
"color": {True: "green", False: "purple"}
},
)
[a.set_ylabel("X / $X_{Primitive Mantle}$") for a in ax]
plt.show()
Legend Proxies for Spiderplots
While it’s relatively straightforward to style spider plots as you wish, for the moment can be a bit more involved to create a legend for these styles. Where you’re creating styles based on a set of categories or labels, a few of pyrolite’s utility functions might come in handy. Below we’ll go through such an example, after creating a few labels (here based on a binning of the Cs abundance):
labels = pd.cut(
np.log(normdf["Cs"]), bins=4, labels=["Low", "Mid. Low", "Mid High", "High"]
)
pd.unique(labels)
['Mid. Low', 'Mid High', 'Low', 'High']
Categories (4, object): ['Low' < 'Mid. Low' < 'Mid High' < 'High']
Below we’ll use process_color() and
proxy_line() to construct a set of legend proxies.
Note that we need to pass the same configuration to both
spider() and process_color()
in order to get the same results, and that the order of labels in the legend
will depend on which labels appear first in your dataframe or series (and hence the
ordering of the unique values which are returned).
from pyrolite.plot.color import process_color
from pyrolite.util.plot.legend import proxy_line
ax = normdf.pyroplot.spider(
unity_line=True,
index_order="incompatibility",
color=labels, # a categorical set of values
cmap="Paired",
alpha=0.5,
figsize=(11, 4),
)
legend_labels = pd.unique(labels) # process_color uses this behind the scenes
proxy_colors = process_color(color=legend_labels, cmap="Paired", alpha=0.5)["c"]
legend_proxies = [proxy_line(color=c, marker="D") for c in proxy_colors]
ax.legend(legend_proxies, legend_labels)
plt.show()
If the specific order of the labels in your legend is important or you only want to include some of the legend entries for some reason, you could use a dictionary to store the key-value pairs and remap the order of the legend entries manually:
proxies = {
label: proxy_line(color=c, marker="D")
for label, c in zip(legend_labels, proxy_colors)
}
ordered_labels = ["High", "Mid High", "Mid. Low", "Low"]
ax.legend([proxies[l] for l in ordered_labels], ordered_labels)
plt.show()
Split Configuration
If you have potential conflicts between desired configurations for the lines and
markers of your plots, you can explictly separate the configuration using the
scatter_kw and line_kw keyword arguments:
fig, ax = plt.subplots(1, 1, sharex=True, sharey=True, figsize=(10, 4))
ax.set_title("Split Configuration")
normdf.pyroplot.spider(
ax=ax,
unity_line=True,
index_order="incompatibility",
scatter_kw=dict(cmap="magma_r", color=np.log(normdf["Li"])),
line_kw=dict(
color=normdf["Cs"] > 5,
color_mappings={"color": {True: "green", False: "purple"}},
),
alpha=0.2, # common alpha config between lines and markers
s=25, # argument for scatter which won't be passed to lines
)
plt.show()
Filled Ranges
The spiderplot can be extended to provide visualisations of ranges and density via the various modes. We could now plot the range of compositions as a filled range:
ax = normdf.pyroplot.spider(
mode="fill",
color="green",
alpha=0.5,
unity_line=True,
index_order="incompatibility",
figsize=(10, 4),
)
ax.set_ylabel("X / $X_{Primitive Mantle}$")
plt.show()
Spider Density Plots
Alternatively, we can plot a conditional density spider plot:
fig, ax = plt.subplots(2, 1, sharex=True, sharey=True, figsize=(10, 6))
normdf.pyroplot.spider(
ax=ax[0], color="k", alpha=0.05, unity_line=True, index_order=by_incompatibility
)
normdf.pyroplot.spider(
ax=ax[1],
mode="binkde",
vmin=0.05, # 95th percentile,
resolution=10,
unity_line=True,
index_order="incompatibility",
)
[a.set_ylabel("X / $X_{Primitive Mantle}$") for a in ax]
plt.show()
We can now assemble a more complete comparison of some of the conditional density modes for spider plots:
modes = [
("plot", "plot", [], dict(color="k", alpha=0.01)),
("fill", "fill", [], dict(color="k", alpha=0.5)),
("binkde", "binkde", [], dict(resolution=5)),
(
"binkde",
"binkde contours specified",
[],
dict(contours=[0.95], resolution=5), # 95th percentile contour
),
("histogram", "histogram", [], dict(resolution=5, bins=30)),
]
down, across = len(modes), 1
fig, ax = plt.subplots(
down, across, sharey=True, sharex=True, figsize=(across * 8, 2 * down)
)
[a.set_ylabel("X / $X_{Primitive Mantle}$") for a in ax]
for a, (m, name, args, kwargs) in zip(ax, modes):
a.annotate( # label the axes rows
"Mode: {}".format(name),
xy=(0.1, 1.05),
xycoords=a.transAxes,
fontsize=8,
ha="left",
va="bottom",
)
ax = ax.flat
for mix, (m, name, args, kwargs) in enumerate(modes):
normdf.pyroplot.spider(
mode=m,
ax=ax[mix],
vmin=0.05, # minimum percentile
fontsize=8,
unity_line=True,
index_order="incompatibility",
*args,
**kwargs
)
plt.tight_layout()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:211: UserWarning: No data for colormapping provided via 'c'. Parameters 'vmin' will be ignored
ax.scatter(
REE Density Plots
Note that this can also be used for REE-indexed plots, in both configurations. Here we first specify a set of common keyword-argument configurations and use them for both plots:
REE_config = dict(unity_line=True, mode="binkde", vmin=0.05, resolution=10)
fig, ax = plt.subplots(1, 2, sharey=True, figsize=(12, 4))
normdf.pyroplot.REE(ax=ax[0], **REE_config)
normdf.pyroplot.REE(ax=ax[1], index="radii", **REE_config)
[a.set_ylabel("X / $X_{Primitive Mantle}$") for a in ax]
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
See also
Total running time of the script: (0 minutes 11.800 seconds)
Geochemistry Examples
Mineral Database
pyrolite includes a limited mineral database which is useful for looking up endmember compositions.
import pandas as pd
from pyrolite.mineral.mindb import (
get_mineral,
get_mineral_group,
list_formulae,
list_groups,
list_minerals,
)
pd.set_option("display.precision", 3) # smaller outputs
From the database, you can get the list of its contents using a few utility functions:
list_groups()
['olivine', 'amphibole', 'epidote', 'pyroxene', 'garnet', 'mica', 'feldspar', 'spinel']
list_minerals()
['majorite', 'taramite', 'hastingsite', 'winchite', 'ferrotschermakite', 'magnesioarfvedsonite', 'spinel', 'kosmochlor', 'polylithionite', 'eckermanite', 'anthopyllite', 'spessartine', 'liebenbergite', 'eastonite', 'diopside', 'katophorite', 'clinozoisite', 'spodumene', 'ferrorichterite', 'ferrokaersutite', 'tremolite', 'andradite', 'magnesioreibeckite', 'celadonite', 'aegirine', 'uvarovite', 'ferrosilite', 'jadeite', 'clintonite', 'tschermakite', 'glaucophane', 'trilithionite', 'forsterite', 'ferrokatophorite', 'ferroeckermanite', 'piemontite', 'esseneite', 'microcline', 'magnesiohornblende', 'chromoceladonite', 'manganiceladonite', 'almandine', 'magnesioferrite', 'namansilite', 'magnesiohastingsite', 'allanite', 'chromphyllite', 'ferropargasite', 'ferroaluminoceladonite', 'richterite', 'kaersutite', 'riebeckite', 'paragonite', 'ferroceladonite', 'fayalite', 'hedenbergite', 'chromite', 'magnetite', 'muscovite', 'margarite', 'pyrope', 'enstatite', 'morimotoite', 'siderophyllite', 'annite', 'tephroite', 'epidote', 'phlogopite', 'magnesiochromite', 'ferrohornblende', 'barroisite', 'albite', 'pargasite', 'arvedsonite', 'gedrite', 'edenite', 'anorthite', 'hercynite', 'ferroedenite', 'phengite', 'aluminoceladonite', 'johannsenite', 'grossular']
list_formulae()
['Na(Na2)(Fe{2+}4Fe{3+})(Si8)O22(OH)2', 'K2(Fe{3+}2Fe{2+}2)(Si8)O20(OH)4', '(Na2)(Mg3Al2)(Si8)O22(OH)2', 'Mg3(MgSi)(SiO4)3', 'Fe2SiO4', 'MgCr{3+}2O4', 'K2(Al3Mg)(Si7Al)O20(OH)4', 'Ca3Cr2(SiO4)3', 'Na(Na2)(Fe4Al)(Si8)O22(OH)2', 'Ca2(Mg4Al2)(Si2Al6)O20(OH)4', 'Na(Ca2)(Fe4Ti)(Si6Al2)O22(OH)2', 'KAlSi3O8', 'Ca3(TiFe{2+})(SiO4)3', 'K2(Mg4)(Si4Al6)O20(OH)4', 'K2(Fe{2+}2Al2)(Si8)O20(OH)4', '(Ca2)(Fe4Al)(Si7Al)O22(OH)2', 'LiAlSi2O6', '(Ca2)(Mg5)(Si8)O22(OH)2', 'Na(NaCa)(Mg5)(Si8)O22(OH)2', 'NaFe{3+}Si2O6', 'K2(Mg2Al2)(Si8)O20(OH)4', 'NaCrSi2O6', 'K2(Fe{2+}4)(Si4Al6)O20(OH)4', 'K2(Cr{3+}4)(Si6Al2)O20(OH)4', 'Na(NaCa)(Mg4Al)(Si7Al)O22(OH)2', 'Na(Ca2)(Mg4Al)(Si6Al2)O22(OH)2', 'Mn2SiO4', 'NaAlSi2O6', 'NaAlSi3O8', 'CaMgSi2O6', '(NaCa)(Mg3Al2)(Si7Al)O22(OH)2', 'Ca2Al3(Si2O7)(SiO4)O(OH)', 'K2(Al3Li3)(Si6Al2)O20(OH)4', 'CaAlFe{3+}SiO6', 'K2(Fe{3+}2Mg2)(Si8)O20(OH)4', 'K2(Al2Li2)(Si8)O20(OH)4', 'Fe{2+}Cr{3+}2O4', 'K2(Fe{2+}6)(Si6Al2)O20(OH)4', 'CaFeSi2O6', 'MgFe{3+}2O4', 'Mg2SiO4', '(Mg2)(Mg3Al2)(Si6Al2)O22(OH)2', 'NaMn{3+}Si2O6', 'CaMnSi2O6', 'Na(Ca2)(Mg4Ti)(Si6Al2)O22(OH)2', 'Ca3Al2(SiO4)3', 'Ni1.5Mg0.5SiO4', 'Na(Na2)(Mg4Al)(Si8)O22(OH)2', 'Na(Ca2)(Fe4Al)(Si6Al2)O22(OH)2', 'Ca3Fe{3+}2(SiO4)3', 'K2(Al4)(Si6Al2)O20(OH)4', 'Na2(Al4)(Si6Al2)O20(OH)4', 'K2(Mn{3+}2Mg2)(Si8)O20(OH)4', 'Ca2Al2Mn{3+}(Si2O7)(SiO4)O(OH)', '(Na2)(Fe3Fe{3+}2)(Si8)O22(OH)2', 'Ca2(Al4)(Si4Al4)O20(OH)4', 'Na(Ca2)(Mg4Fe{3+})(Si6Al2)O22(OH)2', 'Fe{2+}Al2O4', 'Na(NaCa)(Fe4Al)(Si7Al)O22(OH)2', 'Fe{2+}Fe{3+}2O4', 'Na(NaCa)(Mg3Al2)(Si6Al2)O22(OH)2', 'MgAl2O4', 'Ca2Al2Fe{3+}(Si2O7)(SiO4)O(OH)', '(Mg2)(Mg5)(Si8)O22(OH)2', 'Na(Ca2)(Fe{2+}4Fe{3+})(Si6Al2)O22(OH)2', 'Na(Ca2)(Fe5)(Si7Al)O22(OH)2', 'Fe2Si2O6', 'K2(Mg6)(Si6Al2)O20(OH)4', 'Fe{2+}3Al2(SiO4)3', 'Mg3Al2(SiO4)3', 'CaAl2Si2O8', 'Na(NaCa)(Fe5)(Si8)O22(OH)2', '(Ca2)(Fe3Al2)(Si6Al2)O22(OH)2', 'Mn3Al2(SiO4)3', '(Na2)(Mg3Fe{3+}2)(Si8)O22(OH)2', 'Mg2Si2O6', '(Ca2)(Mg4Al)(Si7Al)O22(OH)2', 'Na(Ca2)(Mg5)(Si7Al)O22(OH)2', 'K2(Mg2Cr{3+}2)(Si8)O20(OH)4', '(Ca2)(Mg3Al2)(Si6Al2)O22(OH)2', '(NaCa)(Mg4Al)(Si8)O22(OH)2', 'CaCe{3+}Al2Fe{2+}(Si2O7)(SiO4)O(OH)', 'Na(Na2)(Mg4Fe{3+})(Si8)O22(OH)2']
You can also directly get the composition of specific minerals by name:
get_mineral("forsterite")
name forsterite
group olivine
formula Mg2SiO4
Mg 0.346
Si 0.2
O 0.455
Fe 0.0
Mn 0.0
Ni 0.0
Ca 0.0
Al 0.0
Fe{3+} 0.0
Na 0.0
Mn{3+} 0.0
Cr 0.0
Li 0.0
Cr{3+} 0.0
Fe{2+} 0.0
K 0.0
H 0.0
Ti 0.0
Ce{3+} 0.0
dtype: object
If you want to get compositions for all minerals within a specific group, you can
use get_mineral_group():
get_mineral_group("olivine")
Total running time of the script: (0 minutes 0.018 seconds)
Element-Oxide Transformation
One of pyrolite’s strengths is converting mixed elemental and oxide data to a new
form. The simplest way to perform this is by using the
convert_chemistry() function. Note that by default
pyrolite assumes that data are in the same units.
import pandas as pd
import pyrolite.geochem
pd.set_option("display.precision", 3) # smaller outputs
Here we create some synthetic data to work with, which has some variables in Wt% and some in ppm. Notably some elements are present in more than one column (Ca, Na):
from pyrolite.util.synthetic import normal_frame
df = normal_frame(columns=["MgO", "SiO2", "FeO", "CaO", "Na2O", "Te", "K", "Na"]) * 100
df.pyrochem.elements *= 100 # elements in ppm
df.head(2)
As the units are heterogeneous, we’ll need to convert the data frame to a single set of units (here we use Wt%):
df.pyrochem.elements = df.pyrochem.elements.pyrochem.scale("ppm", "wt%") # ppm to wt%
We can transform this chemical data to a new set of compositional variables. Here we i) convert CaO to Ca, ii) aggregate Na2O and Na to Na and iii) calculate mass ratios for Na/Te and MgO/SiO2. Note that you can also use this function to calculate mass ratios:
df.pyrochem.convert_chemistry(
to=["MgO", "SiO2", "FeO", "Ca", "Te", "Na", "Na/Te", "MgO/SiO2"]
).head(2)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[3.67297884 3.50325632 3.66224102 3.25764225 3.52937765 3.9315398
3.84124843 3.39657993 4.14447134 3.84324796]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
You can also specify molar ratios for iron redox, which will result in multiple iron species within the single dataframe:
df.pyrochem.convert_chemistry(to=[{"FeO": 0.9, "Fe2O3": 0.1}]).head(2)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.66875538 0.6503792 0.68473922 0.63454072 0.59756727 0.67044164
0.69027087 0.70640098 0.70099976 0.66848851]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
Total running time of the script: (0 minutes 0.147 seconds)
Normalization
A selection of reference compositions are included in pyrolite, and can be easily
accessed with pyrolite.geochem.norm.get_reference_composition() (see the list
at the bottom of the page for a complete list):
import matplotlib.pyplot as plt
import pandas as pd
import pyrolite.plot
from pyrolite.geochem.ind import REE
from pyrolite.geochem.norm import all_reference_compositions, get_reference_composition
chondrite = get_reference_composition("Chondrite_PON")
To use the compositions with a specific set of units, you can change them with
set_units():
CI = chondrite.set_units("ppm")
The normalize_to() method can be used to
normalise DataFrames to a given reference (e.g. for spiderplots):
fig, ax = plt.subplots(1)
for name, ref in list(all_reference_compositions().items())[::2]:
if name != "Chondrite_PON":
ref.set_units("ppm")
df = ref.comp.pyrochem.REE.pyrochem.normalize_to(CI, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=name)
ax.set_ylabel("X/X$_{Chondrite}$")
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
See also
Currently available models include:
- LCC_McLennan2001
- LCC_McLennan2001 Model of LowerContinentalCrust from McLennan (2001).
- LCC_RG2003
- LCC_RG2003 Model of LowerContinentalCrust from Rudnick & Gao (2003).
- LCC_RG2014
- LCC_RG2014 Model of LowerContinentalCrust from Rudnick & Gao (2014).
- PRS_Condie1993
- PRS_Condie1993 Model of ProterozoicCratonicShale from Condie (1993).
- Chondrite_MS95
- Chondrite_MS95 Model of Chondrite from McDonough & Sun (1995).
- Chondrite_PON
- Chondrite_PON Model of Chondrite from Palme and O'Neill (2014).
- ChondriteREE_ON
- ChondriteREE_ON Model of Chondrite from O'Neill (2016).
- Chondrite_SM89
- Chondrite_SM89 Model of Chondrite from Sun & McDonough (1989).
- BCC_McLennan2001
- BCC_McLennan2001 Model of BulkContinentalCrust from McLennan (2001).
- BCC_RG2003
- BCC_RG2003 Model of BulkContinentalCrust from Rudnick & Gao (2003).
- BCC_RG2014
- BCC_RG2014 Model of BulkContinentalCrust from Rudnick & Gao (2014).
- NMORB_Gale2013
- NMORB_Gale2013 Model of NMORB from Gale et al. (2013).
- NMORB_SM89
- NMORB_SM89 Model of NMORB from Sun & McDonough (1989).
- MCC_RG2014
- MCC_RG2014 Model of MidContinentalCrust from Rudnick & Gao (2014).
- MORB_Gale2013
- MORB_Gale2013 Model of MORB from Gale et al. (2013).
- DMORB_Gale2013
- DMORB_Gale2013 Model of DMORB from Gale et al. (2013).
- NASC_Gromet1984
- NASC_Gromet1984 Model of NorthAmericanShaleComposite from Gromet et al. (1984); Taylor and McLennan (1985); Condie (1993); McLennan (2001).
- Pyrolite_MS95
- Pyrolite_MS95 Model of BSE from McDonough & Sun (1995).
- PM_PON
- PM_PON Model of PrimitiveMantle from Palme and O'Neill (2014).
- PM_SM89
- PM_SM89 Model of PrimitiveMantle from Sun & McDonough (1989).
- MUQ_Kamber2005
- MUQ_Kamber2005 Model of MudFromQueensland from Kamber et al. (2005).
- DMM_WH2005
- DMM_WH2005 Model of DepletedMORBMantle from Workman & Hart (2005).
- D-DMM_WH2005
- D-DMM_WH2005 Model of DepletedDepletedMORBMantle from Workman & Hart (2005).
- PHS_Condie1993
- PHS_Condie1993 Model of PhanerozoicCratonicShale from Condie (1993).
- ARS_Condie1993
- ARS_Condie1993 Model of ArcheanCratonicShale from Condie (1993).
- DM_SS2004
- DM_SS2004 Model of DepletedMantle from Salters & Strake (2004).
- OIB_SM89
- OIB_SM89 Model of OIB from Sun & McDonough (1989).
- EUS_Bau2018
- EUS_Bau2018 Model of EuropeanShale from Bau et al. (2018).
- GLOSS2_P2014
- GLOSS2_P2014 Model of GLOSS from Plank (2014).
- GLOSS_P2014
- GLOSS_P2014 Model of GLOSS from Plank (2014).
- EMORB_Gale2013
- EMORB_Gale2013 Model of EMORB from Gale et al. (2013).
- EMORB_SM89
- EMORB_SM89 Model of EMORB from Sun & McDonough (1989).
- E-DMM_WH2005
- E-DMM_WH2005 Model of EnrichedDepletedMORBMantle from Workman & Hart (2005).
- PAAS_Pourmand2012
- PAAS_Pourmand2012 Model of PostArcheanAustralianShale from Pourmand et al. (2012).
- PAAS_TM1985
- PAAS_TM1985 Model of PostArcheanAustralianShale from Taylor & McLennan (1985); McLennan (2001).
- UCC_McLennan2001
- UCC_McLennan2001 Model of UpperContinentalCrust from McLennan (2001).
- UCC_RG2003
- UCC_RG2003 Model of UpperContinentalCrust from Rudnick & Gao (2003).
- UCC_RG2014
- UCC_RG2014 Model of UpperContinentalCrust from Rudnick & Gao (2014).
Total running time of the script: (0 minutes 2.354 seconds)
Geochemical Indexes and Selectors
import pandas as pd
import pyrolite.geochem
pd.set_option("display.precision", 3) # smaller outputs
from pyrolite.util.synthetic import normal_frame
df = normal_frame(
columns=[
"CaO",
"MgO",
"SiO2",
"FeO",
"Mn",
"Ti",
"La",
"Lu",
"Y",
"Mg/Fe",
"87Sr/86Sr",
"Ar40/Ar36",
]
)
df.head(2).pyrochem.oxides
df.head(2).pyrochem.elements
df.head(2).pyrochem.REE
df.head(2).pyrochem.REY
df.head(2).pyrochem.compositional
df.head(2).pyrochem.isotope_ratios
df.pyrochem.list_oxides
['CaO', 'MgO', 'SiO2', 'FeO']
df.pyrochem.list_elements
['Mn', 'Ti', 'La', 'Lu', 'Y']
df.pyrochem.list_REE
['La', 'Lu']
df.pyrochem.list_compositional
['CaO', 'MgO', 'SiO2', 'FeO', 'Mn', 'Ti', 'La', 'Lu', 'Y']
df.pyrochem.list_isotope_ratios
['87Sr/86Sr', 'Ar40/Ar36']
All elements (up to U):
from pyrolite.geochem.ind import REE, REY, common_elements, common_oxides
common_elements() # string return
['H', 'He', 'Li', 'Be', 'B', 'C', 'N', 'O', 'F', 'Ne', 'Na', 'Mg', 'Al', 'Si', 'P', 'S', 'Cl', 'Ar', 'K', 'Ca', 'Sc', 'Ti', 'V', 'Cr', 'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn', 'Ga', 'Ge', 'As', 'Se', 'Br', 'Kr', 'Rb', 'Sr', 'Y', 'Zr', 'Nb', 'Mo', 'Tc', 'Ru', 'Rh', 'Pd', 'Ag', 'Cd', 'In', 'Sn', 'Sb', 'Te', 'I', 'Xe', 'Cs', 'Ba', 'La', 'Ce', 'Pr', 'Nd', 'Pm', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Ho', 'Er', 'Tm', 'Yb', 'Lu', 'Hf', 'Ta', 'W', 'Re', 'Os', 'Ir', 'Pt', 'Au', 'Hg', 'Tl', 'Pb', 'Bi', 'Po', 'At', 'Rn', 'Fr', 'Ra', 'Ac', 'Th', 'Pa', 'U']
All elements, returned as a list of ~periodictable.core.Formula:
common_elements(output="formula") # periodictable.core.Formula return
[H, He, Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, I, Xe, Cs, Ba, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, At, Rn, Fr, Ra, Ac, Th, Pa, U]
Oxides for elements with positive charges (up to U):
common_oxides()
['TmO', 'Tm2O3', 'Be2O', 'BeO', 'Ti2O', 'TiO', 'Ti2O3', 'TiO2', 'Tc2O', 'TcO', 'Tc2O3', 'TcO2', 'Tc2O5', 'TcO3', 'Tc2O7', 'Ba2O', 'BaO', 'Co2O', 'CoO', 'Co2O3', 'CoO2', 'Co2O5', 'Tb2O', 'TbO', 'Tb2O3', 'TbO2', 'EuO', 'Eu2O3', 'As2O', 'AsO', 'As2O3', 'AsO2', 'As2O5', 'Sb2O', 'SbO', 'Sb2O3', 'SbO2', 'Sb2O5', 'Nb2O', 'NbO', 'Nb2O3', 'NbO2', 'Nb2O5', 'Li2O', 'Ac2O3', 'C2O', 'CO', 'C2O3', 'CO2', 'Te2O', 'TeO', 'Te2O3', 'TeO2', 'Te2O5', 'TeO3', 'Rb2O', 'K2O', 'Fr2O', 'U2O', 'UO', 'U2O3', 'UO2', 'U2O5', 'UO3', 'N2O', 'NO', 'N2O3', 'NO2', 'N2O5', 'Bi2O', 'BiO', 'Bi2O3', 'BiO2', 'Bi2O5', 'Rh2O', 'RhO', 'Rh2O3', 'RhO2', 'Rh2O5', 'RhO3', 'Mn2O', 'MnO', 'Mn2O3', 'MnO2', 'Mn2O5', 'MnO3', 'Mn2O7', 'NdO', 'Nd2O3', 'NdO2', 'Cu2O', 'CuO', 'Cu2O3', 'CuO2', 'Y2O', 'YO', 'Y2O3', 'SmO', 'Sm2O3', 'Au2O', 'AuO', 'Au2O3', 'Au2O5', 'Sn2O', 'SnO', 'Sn2O3', 'SnO2', 'CeO', 'Ce2O3', 'CeO2', 'RnO', 'RnO3', 'Th2O', 'ThO', 'Th2O3', 'ThO2', 'RaO', 'Cl2O', 'ClO', 'Cl2O3', 'ClO2', 'Cl2O5', 'ClO3', 'Cl2O7', 'Zr2O', 'ZrO', 'Zr2O3', 'ZrO2', 'Ni2O', 'NiO', 'Ni2O3', 'NiO2', 'Gd2O', 'GdO', 'Gd2O3', 'I2O', 'I2O3', 'IO2', 'I2O5', 'IO3', 'I2O7', 'PmO', 'Pm2O3', 'V2O', 'VO', 'V2O3', 'VO2', 'V2O5', 'LuO', 'Lu2O3', 'P2O', 'PO', 'P2O3', 'PO2', 'P2O5', 'PoO', 'PoO2', 'Po2O5', 'PoO3', 'Os2O', 'OsO', 'Os2O3', 'OsO2', 'Os2O5', 'OsO3', 'Os2O7', 'OsO4', 'Pd2O', 'PdO', 'Pd2O3', 'PdO2', 'Pd2O5', 'PdO3', 'ErO', 'Er2O3', 'Hg2O', 'HgO', 'HgO2', 'H2O', 'At2O', 'At2O3', 'At2O5', 'At2O7', 'Ge2O', 'GeO', 'Ge2O3', 'GeO2', 'HoO', 'Ho2O3', 'Tl2O', 'TlO', 'Tl2O3', 'In2O', 'InO', 'In2O3', 'S2O', 'SO', 'S2O3', 'SO2', 'S2O5', 'SO3', 'DyO', 'Dy2O3', 'DyO2', 'Fe2O', 'FeO', 'Fe2O3', 'FeO2', 'Fe2O5', 'FeO3', 'Fe2O7', 'Pt2O', 'PtO', 'Pt2O3', 'PtO2', 'Pt2O5', 'PtO3', 'Al2O', 'AlO', 'Al2O3', 'Ir2O', 'IrO', 'Ir2O3', 'IrO2', 'Ir2O5', 'IrO3', 'Ir2O7', 'IrO4', 'Ir2O9', 'Sr2O', 'SrO', 'Na2O', 'Pa2O3', 'PaO2', 'Pa2O5', 'Zn2O', 'ZnO', 'Ga2O', 'GaO', 'Ga2O3', 'Si2O', 'SiO', 'Si2O3', 'SiO2', 'Mo2O', 'MoO', 'Mo2O3', 'MoO2', 'Mo2O5', 'MoO3', 'Pb2O', 'PbO', 'Pb2O3', 'PbO2', 'Mg2O', 'MgO', 'Ca2O', 'CaO', 'B2O', 'BO', 'B2O3', 'Se2O', 'SeO', 'Se2O3', 'SeO2', 'Se2O5', 'SeO3', 'Cr2O', 'CrO', 'Cr2O3', 'CrO2', 'Cr2O5', 'CrO3', 'PrO', 'Pr2O3', 'PrO2', 'Pr2O5', 'Br2O', 'Br2O3', 'BrO2', 'Br2O5', 'Br2O7', 'YbO', 'Yb2O3', 'Hf2O', 'HfO', 'Hf2O3', 'HfO2', 'Cs2O', 'Cd2O', 'CdO', 'Ta2O', 'TaO', 'Ta2O3', 'TaO2', 'Ta2O5', 'Sc2O', 'ScO', 'Sc2O3', 'W2O', 'WO', 'W2O3', 'WO2', 'W2O5', 'WO3', 'La2O', 'LaO', 'La2O3', 'Ru2O', 'RuO', 'Ru2O3', 'RuO2', 'Ru2O5', 'RuO3', 'Ru2O7', 'RuO4', 'Re2O', 'ReO', 'Re2O3', 'ReO2', 'Re2O5', 'ReO3', 'Re2O7', 'Ag2O', 'AgO', 'Ag2O3', 'AgO2', 'FeOT', 'Fe2O3T', 'LOI']
REE()
['La', 'Ce', 'Pr', 'Nd', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Ho', 'Er', 'Tm', 'Yb', 'Lu']
REY()
['La', 'Ce', 'Pr', 'Nd', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Y', 'Ho', 'Er', 'Tm', 'Yb', 'Lu']
Total running time of the script: (0 minutes 0.294 seconds)
Mineral Endmember Decomposition
A common task when working with mineral chemistry data is to take measured compositions and decompose these into relative proportions of mineral endmember compositions. pyrolite includes some utilities to achieve this and a limited mineral database for looking up endmember compositions.
import numpy as np
import pandas as pd
from pyrolite.mineral.mindb import get_mineral
from pyrolite.mineral.normative import endmember_decompose
First we’ll start with a composition of an unknown olivine:
comp = pd.Series({"MgO": 42.06, "SiO2": 39.19, "FeO": 18.75})
We can break this down into olivine endmebmers using the
endmember_decompose() function:
ed = endmember_decompose(
pd.DataFrame(comp).T, endmembers="olivine", order=1, molecular=True
)
ed
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.57294068 nan nan 0.10480888]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.42705932 0.29485884 0.29750712 0.31249035]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan 0.70514116 nan nan]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
Equally, if you knew the likely endmembers beforehand, you could specify a list of endmembers:
ed = endmember_decompose(
pd.DataFrame(comp).T, endmembers=["forsterite", "fayalite"], order=1, molecular=True
)
ed
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.57294068 nan]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.42705932 0.29485884]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan 0.70514116]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
We can check this by recombining the components with these proportions. We can first lookup the compositions for our endmembers:
em = pd.DataFrame([get_mineral("forsterite"), get_mineral("fayalite")])
em.loc[:, ~(em == 0).all(axis=0)] # columns not full of zeros
First we have to convert these element-based compositions to oxide-based compositions:
emvalues = (
em.loc[:, ["Mg", "Si", "Fe"]]
.pyrochem.to_molecular()
.fillna(0)
.pyrochem.convert_chemistry(to=["MgO", "SiO2", "FeO"], molecular=True)
.fillna(0)
.pyrocomp.renormalise(scale=1)
)
emvalues
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[66.66666667 nan]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[33.33333333 33.33333333]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan 66.66666667]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
These can now be used with our endmember proportions to regenerate a composition:
recombined = pd.DataFrame(ed.values.flatten() @ emvalues).T.pyrochem.to_weight()
recombined
To make sure these compositions are within 0.01 percent:
assert np.allclose(recombined.values, comp.values, rtol=10**-4)
Total running time of the script: (0 minutes 0.214 seconds)
Ionic Radii
pyrolite incldues a few sets of reference tables for ionic radii in aangstroms
(Å) from [Shannon1976] and [WhittakerMuntus1970], each with tables indexed
by element, ionic charge and coordination. The easiset way to access these is via
the get_ionic_radii() function. The function can be used
to get radii for individual elements:
from pyrolite.geochem.ind import REE, get_ionic_radii
Cu_radii = get_ionic_radii("Cu")
print(Cu_radii)
index
Cu2+IV 0.57
Cu2+IVSQ 0.57
Cu2+V 0.65
Cu2+VI 0.73
Name: ionicradius, dtype: float64
Note that this function returned a series of the possible radii, given specific charges and coordinations of the Cu ion. If we completely specify these, we’ll get a single number back:
Cu2plus6fold_radii = get_ionic_radii("Cu", coordination=6, charge=2)
print(Cu2plus6fold_radii)
0.73
You can also pass lists to the function. For example, if you wanted to get the Shannon ionic radii of Rare Earth Elements (REE) in eight-fold coordination with a valence of +3, you should use the following:
shannon_ionic_radii = get_ionic_radii(REE(), coordination=8, charge=3)
print(shannon_ionic_radii)
[1.16, 1.143, 1.126, 1.109, 1.079, 1.066, 1.053, 1.04, 1.027, 1.015, 1.004, 0.994, 0.985, 0.977]
The function defaults to using the Shannon ionic radii consistent with [Pauling1960],
but you can adjust to use the set you like with the pauling boolean argument
(pauling=False to use Shannon’s ‘Crystal Radii’) or the source argument
(source='Whittaker' to use the [WhittakerMuntus1970] dataset):
shannon_crystal_radii = get_ionic_radii(REE(), coordination=8, charge=3, pauling=False)
whittaker_ionic_radii = get_ionic_radii(
REE(), coordination=8, charge=3, source="Whittaker"
)
We can see what the differences between these look like across the REE:
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1)
ax.plot(shannon_ionic_radii, label="Shannon Ionic Radii")
ax.plot(shannon_crystal_radii, label="Shannon Crystal Radii")
ax.plot(whittaker_ionic_radii, label="Whittaker & Muntus\nIonic Radii")
{a: b for (a, b) in zip(REE(), whittaker_ionic_radii)}
ax.set_xticks(range(len(REE())))
ax.set_xticklabels(REE())
ax.set_ylabel("Ionic Radius ($\AA$)")
ax.set_title("Rare Earth Element Ionic Radii")
ax.legend()
plt.show()
See also
- Examples:
- Functions:
get_ionic_radii(),pyrolite.geochem.ind.REE(),lambda_lnREE(),
References
- Shannon1976
Shannon RD (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A 32:751–767. doi: 10.1107/S0567739476001551.
- WhittakerMuntus1970(1,2)
Whittaker, E.J.W., Muntus, R., 1970. Ionic radii for use in geochemistry. Geochimica et Cosmochimica Acta 34, 945–956. doi: 10.1016/0016-7037(70)90077-3.
- Pauling1960
Pauling, L., 1960. The Nature of the Chemical Bond. Cornell University Press, Ithaca, NY.
Total running time of the script: (0 minutes 0.344 seconds)
Unit Scaling
import numpy as np
import pandas as pd
import pyrolite.geochem
pd.set_option("display.precision", 3) # smaller outputs
Here we create an example dataframe to work from, containing some synthetic data in the form of oxides and elements, each with different units (wt% and ppm, respectively).
from pyrolite.util.synthetic import normal_frame
df = normal_frame(
columns=["CaO", "MgO", "SiO2", "FeO", "Ni", "Ti", "La", "Lu"], seed=22
)
df.pyrochem.oxides *= 100 # oxides in wt%
df.pyrochem.elements *= 10000 # elements in ppm
In this case, we might want to transform the Ni and Ti into their standard oxide equivalents NiO and TiO2:
df.pyrochem.convert_chemistry(to=["NiO", "TiO2"]).head(2)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[1235.19505234 1301.09283284 1297.67084898 1332.78130758 1231.28287236
1223.09485893 1213.13011719 1220.86333288 1269.99495233 1193.1419757 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[2388.2200631 2164.62285792 2286.2934774 2443.58980729 2245.75825742
2269.68007197 2130.01547469 2282.00522338 2257.57443799 2515.3361174 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
But here because Ni and Ti have units of ppm, the results are a little non-sensical, especially when it’s combined with the other oxides:
df.pyrochem.convert_chemistry(to=df.pyrochem.list_oxides + ["NiO", "TiO2"]).head(2)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[1235.19505234 1301.09283284 1297.67084898 1332.78130758 1231.28287236
1223.09485893 1213.13011719 1220.86333288 1269.99495233 1193.1419757 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[2388.2200631 2164.62285792 2286.2934774 2443.58980729 2245.75825742
2269.68007197 2130.01547469 2282.00522338 2257.57443799 2515.3361174 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
There are multiple ways we could convert the units, but here we’re going to first
convert the elemental ppm data to wt%, then perform our oxide-element conversion.
To do this, we’ll use the built-in function scale():
from pyrolite.util.units import scale
df.pyrochem.elements *= scale("ppm", "wt%")
We can see that this then gives us numbers which are a bit more sensible:
df.pyrochem.convert_chemistry(to=df.pyrochem.list_oxides + ["NiO", "TiO2"]).head(2)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.12351951 0.13010928 0.12976708 0.13327813 0.12312829 0.12230949
0.12131301 0.12208633 0.1269995 0.1193142 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.23882201 0.21646229 0.22862935 0.24435898 0.22457583 0.22696801
0.21300155 0.22820052 0.22575744 0.25153361]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
Dealing with Units in Column Names
Often our dataframes will start containing column names which pyrolite doesn’t recognize
natively by default (work in progress, this is an item on the roadmap). Here we can
create an example of that, and go through some key steps for using this data in
pyrolite:
df = normal_frame(
columns=["CaO", "MgO", "SiO2", "FeO", "Ni", "Ti", "La", "Lu"], seed=22
)
df.pyrochem.oxides *= 100 # oxides in wt%
df.pyrochem.elements *= 10000 # elements in ppm
df = df.rename(
columns={
**{c: c + "_wt%" for c in df.pyrochem.oxides},
**{c: c + "_ppm" for c in df.pyrochem.elements},
}
)
df.head(2)
If you just wanted to rescale some columns, you can get away without renaming your columns, e.g. converting all of the ppm columns to wt%:
df.loc[:, [c for c in df.columns if "_ppm" in c]] *= scale("ppm", "wt%")
df.head(2)
However, to access the full native capability of pyrolite, we’d need to rename
these columns to use things like convert_chemistry():
units = { # keep a copy of the units, we can use these to map back later
c: c[c.find("_") + 1 :] if "_" in c else None for c in df.columns
}
df = df.rename(
columns={c: c.replace("_wt%", "").replace("_ppm", "") for c in df.columns}
)
df.head(2)
We could then perform our chemistry conversion, rename our columns to include units, and optionally export to e.g. CSV:
converted_wt_pct = df.pyrochem.convert_chemistry(
to=df.pyrochem.list_oxides + ["NiO", "TiO2"]
)
converted_wt_pct.head(2)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.12351951 0.13010928 0.12976708 0.13327813 0.12312829 0.12230949
0.12131301 0.12208633 0.1269995 0.1193142 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[0.23882201 0.21646229 0.22862935 0.24435898 0.22457583 0.22696801
0.21300155 0.22820052 0.22575744 0.25153361]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
Here we rename the columns before we export them, just so we know explicitly what the units are:
converted_wt_pct = converted_wt_pct.rename(
columns={c: c + "_wt%" for c in converted_wt_pct.pyrochem.list_oxides}
)
converted_wt_pct.head(2)
converted_wt_pct.to_csv("converted_wt_pct.csv")
Total running time of the script: (0 minutes 0.330 seconds)
Lattice Strain Calculations
Note
This example follows that given during a Institute of Advanced Studies Masterclass with Jon Blundy at the University of Western Australia on the 29th April 2019, and is used here with permission.
Pyrolite includes a function for calculating relative lattice strain 1, which together with the tables of Shannon ionic radii and Young’s modulus approximations for silicate and oxide cationic sites enable relatively simple calculation of ionic partitioning in common rock forming minerals.
This example below uses previously characterised calcium and sodium partition coefficients between plagioclase (\(CaAl_2Si_2O_8 - NaAlSi_3O8\)) and silicate melt to estimate partitioning for other cations based on their ionic radii.
A model parameterised using sodium and calcium partition coefficients 2 is then used to estimate the partitioning for lanthanum into the trivalent site (largely occupied by \(Al^{3+}\)), and extended to other trivalent cations (here, the Rare Earth Elements). The final section of the example highlights the mechanism which generates plagioclase’s hallmark ‘europium anomaly’, and the effects of variable europium oxidation state on bulk europium partitioning.
import matplotlib.pyplot as plt
import numpy as np
from pyrolite.geochem.ind import REE, get_ionic_radii
from pyrolite.mineral.lattice import strain_coefficient
First, we need to define some of the necessary parameters including temperature, the Young’s moduli for the \(X^{2+}\) and \(X^{3+}\) sites in plagioclase (\(E_2\), \(E_3\)), and some reference partition coefficients and radii for calcium and sodium:
D_Na = 1.35 # Partition coefficient Plag-Melt
D_Ca = 4.1 # Partition coefficient Plag-Melt
Tc = 900 # Temperature, °C
Tk = Tc + 273.15 # Temperature, K
E_2 = 120 * 10**9 # Youngs modulus for 2+ site, Pa
E_3 = 135 * 10**9 # Youngs modulus for 3+ site, Pa
r02, r03 = 1.196, 1.294 # fictive ideal cation radii for these sites
rCa = get_ionic_radii("Ca", charge=2, coordination=8)
rLa = get_ionic_radii("La", charge=3, coordination=8)
We can calculate and plot the partitioning of \(X^{2+}\) cations relative to \(Ca^{2+}\) at a given temperature using their radii and the lattice strain function:
fontsize = 8
fig, ax = plt.subplots(1)
site2labels = ["Na", "Ca", "Eu", "Sr"]
# get the Shannon ionic radii for the elements in the 2+ site
site2radii = [
get_ionic_radii("Na", charge=1, coordination=8),
*[get_ionic_radii(el, charge=2, coordination=8) for el in ["Ca", "Eu", "Sr"]],
]
# plot the relative paritioning curve for cations in the 2+ site
site2Ds = D_Ca * np.array(
[strain_coefficient(rCa, rx, r0=r02, E=E_2, T=Tk) for rx in site2radii]
)
ax.scatter(site2radii, site2Ds, color="g", label="$X^{2+}$ Cations")
# create an index of radii, and plot the relative paritioning curve for the site
xs = np.linspace(0.9, 1.3, 200)
curve2Ds = D_Ca * strain_coefficient(rCa, xs, r0=r02, E=E_2, T=Tk)
ax.plot(xs, curve2Ds, color="0.5", ls="--")
# add the element labels next to the points
for l, r, d in zip(site2labels, site2radii, site2Ds):
ax.annotate(
l, xy=(r, d), xycoords="data", ha="left", va="bottom", fontsize=fontsize
)
fig
<Figure size 640x480 with 1 Axes>
When it comes to estimating the partitioning of \(X^{3+}\) cations, we’ll need a reference point - here we’ll use \(D_{La}\) to calculate relative partitioning of the other Rare Earth Elements, although you may have noticed it is not defined above. Through a handy relationship, we can estimate \(D_{La}\) based on the easier measured \(D_{Ca}\), \(D_{Na}\) and temperature 2:
D_La = (D_Ca**2 / D_Na) * np.exp((529 / Tk) - 3.705)
D_La # 0.48085
0.48084614946362086
Now \(D_{La}\) is defined, we can use it as a reference for the other REE:
site3labels = REE(dropPm=True)
# get the Shannon ionic radii for the elements in the 3+ site
site3radii = [get_ionic_radii(x, charge=3, coordination=8) for x in REE(dropPm=True)]
site3Ds = D_La * np.array(
[strain_coefficient(rLa, rx, r0=r03, E=E_3, T=Tk) for rx in site3radii]
)
# plot the relative paritioning curve for cations in the 3+ site
ax.scatter(site3radii, site3Ds, color="purple", label="$X^{3+}$ Cations")
# plot the relative paritioning curve for the site
curve3Ds = D_La * strain_coefficient(rLa, xs, r0=r03, E=E_3, T=Tk)
ax.plot(xs, curve3Ds, color="0.5", ls="--")
# add the element labels next to the points
for l, r, d in zip(site3labels, site3radii, site3Ds):
ax.annotate(
l, xy=(r, d), xycoords="data", ha="right", va="bottom", fontsize=fontsize
)
ax.set_yscale("log")
ax.set_ylabel("$D_X$")
ax.set_xlabel("Radii ($\AA$)")
fig
<Figure size 640x480 with 1 Axes>
As europium is commonly present as a mixture of both \(Eu^{2+}\) and \(Eu^{3+}\), the effective partitioning of Eu will be intermediate between that of \(D_{Eu^{2+}}\). Using a 60:40 mixture of \(Eu^{3+}\) : \(Eu^{2+}\) as an example, this effective partition coefficient can be calculated:
X_Eu3 = 0.6
# calculate D_Eu3 relative to D_La
D_Eu3 = D_La * strain_coefficient(
rLa, get_ionic_radii("Eu", charge=3, coordination=8), r0=r03, E=E_3, T=Tk
)
# calculate D_Eu2 relative to D_Ca
D_Eu2 = D_Ca * strain_coefficient(
rCa, get_ionic_radii("Eu", charge=2, coordination=8), r0=r02, E=E_2, T=Tk
)
# calculate the effective parition coefficient
D_Eu = (1 - X_Eu3) * D_Eu2 + X_Eu3 * D_Eu3
# show the effective partition coefficient relative to the 2+ and 3+ endmembers
radii, ds = (
[get_ionic_radii("Eu", charge=c, coordination=8) for c in [3, 3, 2, 2]],
[D_Eu3, D_Eu, D_Eu, D_Eu2],
)
ax.plot(radii, ds, ls="--", color="0.9", label="Effective $D_{Eu}$", zorder=-1)
ax.legend(bbox_to_anchor=(1.05, 1))
fig
<Figure size 640x480 with 1 Axes>
- 1
Blundy, J., Wood, B., 1994. Prediction of crystal–melt partition coefficients from elastic moduli. Nature 372, 452. doi: 10.1038/372452A0
- 2(1,2)
Dohmen, R., Blundy, J., 2014. A predictive thermodynamic model for element partitioning between plagioclase and melt as a function of pressure, temperature and composition. American Journal of Science 314, 1319–1372. doi: 10.2475/09.2014.04
See also
- Examples:
- Functions:
strain_coefficient(),youngs_modulus_approximation(),get_ionic_radii()
Total running time of the script: (0 minutes 0.943 seconds)
CIPW Norm
The CIPW (W. Cross, J. P. Iddings, L. V. Pirsson, and H. S. Washington) Norm was introducted as a standard procedure for the estimation of rock-forming mineral assemblages of igneous rocks from their geochemical compositions [Cross1902] . This estimation process enables the approximate classificaiton of microcrystalline and partially crystalline rocks using a range of mineralogically-based classificaiton systems (e.g. most IUGS classifications), and the generation of normative-mineral modifiers for geochemical classificaiton systems.
A range of updated, modified and adjusted Norms were published in the century
following the original publication of the CIPW Norm, largely culminating in
Surendra Verma’s 2003 paper “A revised CIPW norm” which enumerates an
algorithm for the estimation of an anhydrous Standard Igenous Norm (SIN)
[Verma2003] .
This was subsequently updated with the publication of IgRoCS [Verma2013] .
A version of this algorithm has now been implemented in
pyrolite (CIPW_norm()), and an overview
of the implementation and the currently available options is given below.
For the purposes of testing, pyrolite includes a file containing the outputs from
Verma’s SINCLAS/IgRoCS program. Here we can use this file to demonstrate the use
of the CIPW Norm and verify that the results should generally be comparable
between Verma’s original implementation and the pyrolite implementation.
We import this file and do a little cleaning and registration of geochemical
components so we can work with it in the sections to follow:
import warnings
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pyrolite.geochem
from pyrolite.util.meta import pyrolite_datafolder
# silence a pandas warning
warnings.simplefilter("ignore", category=pd.errors.PerformanceWarning)
df = (
pd.read_csv(pyrolite_datafolder() / "testing" / "CIPW_Verma_Test.csv")
.dropna(how="all", axis=1)
.pyrochem.parse_chem()
)
df.pyrochem.compositional = df.pyrochem.compositional.apply(
pd.to_numeric, errors="coerce"
).fillna(0)
df.loc[:, [c for c in df.columns if "NORM" in c]] = df.loc[
:, [c for c in df.columns if "NORM" in c]
].apply(pd.to_numeric, errors="coerce")
The CIPW Norm can be accessed via pyrolite.mineral.normative.CIPW_norm(),
and expects a dataframe as input containing major element oxides (in wt%) and
can also use a select set of trace elements (in ppm).
from pyrolite.mineral.normative import CIPW_norm
NORM = CIPW_norm(df.pyrochem.compositional)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
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nan nan nan nan nan 0.006872
0.00369052 0.01018074 0.00025452 0.00114533 0.00012726 0.00101807
0.0006363 0.00101807 0.00127259 0.0006363 0.00089081 0.00101807
0.00101807 0.00127259 0.00114533 0.00101807 nan nan
nan 0.00649022 0.00445407 0.00547215 0.0075083 0.00585393
0.00636296 nan 0.0004645 0.0001718 0.00052176 0.00085645
nan nan 0.01488934 0.01718 0.00483585 0.03550534
0.01628919 0.03779601 0.00725378 0.02825156 0.02799704 0.02634267
0.01807082 0.02150682 0.01705274 0.00572667 0.00152711 0.04237734
0.04746771 nan nan nan nan nan
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nan nan nan nan nan nan
0.003436 0.00432682 0.00229067 0.00152711 0.00089081]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
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nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.74007099
0.79991055 0.40823347 0.99728646 0.71133382 0.50295972 0.88210124
0.65468728 1.03122708 0.84816062 1.62087137 1.31836233 1.2019945
1.2019945 0.74858571 0.55251066 0.31244288 0.28642569 0.24964683
0.19548376 0.41804905 0.10832615 0.08822195 0.11293829 0.11707739
0.06941861 0.05380829 0.07166555 0.12571037 0.04032666 0.04292838
nan nan 0.12902165 0.2024611 0.12618341 0.19205422
0.1646179 0.1995046 0.09153323 0.13493464 0.13245118 0.15007192
0.1758526 0.12582863 0.11530349 0.18306646 0.60111551 0.11033657
0.13020424 nan 0.17153611 0.18566818 0.13712245 0.09372104
0.08842299 0.14463196 0.12884426 0.1018727 0.11991563 nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.03287628 0.02235114 0.0266085 0.02459808 0.017739 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.18679143
0.2200633 0.59398112 0.0849661 0.07033987 0.06096122 0.19449532
0.09847582 0.08909717 0.14715547 0.08373794 0.08284473 0.06833016
0.08898552 0.05180587 0.05616024 0.59911704 nan 0.00223301
0.01462623 0.55155389 0.10003892 0.04588839 0.03014566 0.05113597
0.03260197 nan 0.00840952 0.00204209 0.00281025 0.00136325
nan nan 0.25590314 0.4677043 0.1992963 0.3140731
0.28783521 0.39033045 0.11466515 0.31630611 0.28817016 0.30268474
0.21515068 0.19315551 0.24429148 0.27131092 0.37737898 0.39200521
0.36487411 nan 0.20443222 0.23820652 0.17367249 0.11533506
0.09330528 0.10178737 0.16792248 0.11416272 0.076944 nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.07167968 0.03673304 0.07648065 0.07357774 0.05191752]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
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nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 6.56159396e-04
3.28079698e-04 3.28079698e-04 1.09359899e-04 1.96847819e-03
1.09359899e-04 3.28079698e-04 1.09359899e-04 1.42167869e-03
5.46799496e-04 5.46799496e-04 6.56159396e-04 6.56159396e-04
4.37439597e-04 6.56159396e-04 1.09359899e-04 5.46799496e-04
nan nan 1.64039849e-03 2.65744555e-02
1.89192626e-02 9.95175083e-03 8.74879194e-03 6.56159396e-03
8.09263255e-03 8.08169656e-04 3.25236340e-03 3.33547693e-04
3.24798901e-03 nan nan nan
4.06818825e-02 4.25410008e-02 2.60276560e-02 2.37310981e-02
2.55902164e-02 3.45577282e-02 3.70730059e-02 3.93695637e-02
4.25410008e-02 3.95882835e-02 2.05596611e-02 1.05751023e-01
1.73882240e-02 4.36345998e-02 1.14390455e-01 1.78256636e-02
9.29559144e-03 nan 1.32106758e-02 8.00514463e-03
1.24342205e-02 1.03673185e-02 1.25862308e-02 8.69848639e-03
1.77381757e-02 1.54295882e-02 6.72016581e-03 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 2.26374992e-02 2.79961342e-02
2.66838154e-02 2.74493347e-02 3.08394916e-02]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
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nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan 4.24076364e-05 1.74931500e-04 2.65047728e-05
1.91894555e-04 7.42133637e-06 nan nan
1.37824818e-03 1.07079282e-03 1.31463673e-03 7.52735546e-04
1.03898709e-03 8.26948910e-04 1.55848064e-03 2.69288491e-03
2.54445818e-03 2.89432118e-03 1.22982146e-03 1.53727682e-03
1.18741382e-03 2.90492309e-03 2.31121618e-03 4.24076364e-04
3.39261091e-04 nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 1.69630546e-03 8.48152728e-04
9.54171819e-04 8.48152728e-04 2.54445818e-03]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.03357944 0.03551672 0.03487096 0.03185742 0.03078116]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 1.35077173e-04
7.83447602e-03 6.75385863e-03 1.21569455e-03 1.35077173e-04
5.94339560e-03 1.35077173e-04 1.75600324e-03 2.43138911e-03
1.35077173e-04 1.35077173e-04 1.35077173e-04 4.14686920e-02
1.35077173e-04 6.20004223e-02 3.03923639e-02 4.05231518e-04
nan nan nan 1.08061738e-02
2.16123476e-02 1.91809585e-02 1.74249553e-02 1.79652640e-02
1.86406498e-02 5.69215206e-01 3.51200649e-03 1.48584890e-03
4.32246953e-03 2.97169780e-03 nan nan
6.45668885e-02 5.52465636e-02 2.99871323e-02 7.13207472e-02
4.16037692e-02 6.76736635e-02 3.71462225e-02 4.21440779e-02
4.18739235e-02 4.25493094e-02 3.90373029e-02 3.76865312e-02
3.05274410e-02 4.86277822e-02 4.53859300e-02 1.33456247e-01
1.21164224e-01 nan 8.32332030e-02 1.94011343e-02
6.37010439e-02 3.55279980e-02 5.18210065e-02 9.48836092e-02
1.01915727e-01 1.63848610e-01 9.63843166e-02 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 4.52508528e-02 4.28194637e-02
3.93074572e-02 3.84969942e-02 2.93117465e-02]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 2.19233366e-03
7.30777885e-04 3.21542270e-03 1.46155577e-04 1.46155577e-04
1.46155577e-04 4.38466731e-04 4.38466731e-04 2.92311154e-04
2.92311154e-04 2.92311154e-04 5.84622308e-04 7.30777885e-04
4.38466731e-04 5.84622308e-04 4.38466731e-04 2.92311154e-04
nan nan nan 9.50011251e-03
1.12539794e-02 1.16924462e-02 1.11078239e-02 1.06693571e-02
1.18386017e-02 5.33467856e-04 8.97395243e-04 3.25926937e-04
7.32239441e-04 6.95700547e-04 nan nan
4.18004950e-02 2.10464031e-02 8.62317905e-03 6.02160977e-02
2.61618483e-02 5.14467631e-02 9.50011251e-03 4.51620733e-02
4.75005625e-02 4.89621183e-02 2.42618258e-02 3.81466056e-02
4.07774060e-02 1.85617583e-02 2.48464481e-03 6.32853649e-02
6.50392318e-02 nan 8.57787082e-02 2.29464256e-01
8.00201784e-02 1.98771585e-01 1.84156027e-01 2.14848698e-01
4.25020418e-02 1.20066807e-01 1.68078914e-01 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 1.03770460e-02 1.09616683e-02
9.20780135e-03 6.72315654e-03 5.11544520e-03]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.00014711
0.027804 0.003972 0.00044133 0.04280933 0.02648 0.00014711
0.00823822 0.00559022 0.01279867 0.00029422 0.00720844 0.00382489
0.01412267 0.01162178 0.02044844 0.00823822 nan nan
nan 0.01324 0.01368133 0.01206311 0.01015067 0.01044489
0.010592 nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.014564 0.01162178 0.00941511 0.01088622 0.00647289]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
We can quickly check that this includes mineralogical data:
NORM.columns
Index(['quartz', 'zircon', 'potassium metasilicate', 'anorthite',
'sodium metasilicate', 'acmite', 'thenardite', 'albite', 'orthoclase',
'perovskite', 'nepheline', 'leucite', 'dicalcium silicate',
'kaliophilite', 'apatite', 'fluroapatite', 'fluorite', 'pyrite',
'chromite', 'ilmenite', 'calcite', 'corundum', 'rutile', 'magnetite',
'hematite', 'forsterite', 'fayalite', 'clinoferrosilite',
'clinoenstatite', 'ferrosilite', 'enstatite', 'wollastonite',
'cancrinite', 'halite', 'titanite', 'diopside', 'hypersthene',
'olivine'],
dtype='object')
The function accepts a few keyword arguments, all to do with the iron compositions and related adjustment/corrections:
Fe_correction = "LeMaitre" | "Middlemost"For specifying the Fe-correction method/function. Currently includes LeMaitre’s correction method [LeMaitre1976] (the default) and Middlemost’s TAS-based correction [Middlemost1989] .
Fe_correction_mode = 'volcanic'For specificying the Fe-correction mode, for LeMaitre’s correction.
adjust_all_Fe = FalseSpecifying whether you want to adjust all iron compositions, or only those which are partially specified (i.e. only have a singular value for one of FeO, Fe2O3, FeOT, Fe2O3T).
NORM = CIPW_norm(df.pyrochem.compositional, Fe_correction="Middlemost")
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.006872
0.00369052 0.01018074 0.00025452 0.00114533 0.00012726 0.00101807
0.0006363 0.00101807 0.00127259 0.0006363 0.00089081 0.00101807
0.00101807 0.00127259 0.00114533 0.00101807 nan nan
nan 0.00649022 0.00445407 0.00547215 0.0075083 0.00585393
0.00636296 nan 0.0004645 0.0001718 0.00052176 0.00085645
nan nan 0.01488934 0.01718 0.00483585 0.03550534
0.01628919 0.03779601 0.00725378 0.02825156 0.02799704 0.02634267
0.01807082 0.02150682 0.01705274 0.00572667 0.00152711 0.04237734
0.04746771 nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.003436 0.00432682 0.00229067 0.00152711 0.00089081]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.74007099
0.79991055 0.40823347 0.99728646 0.71133382 0.50295972 0.88210124
0.65468728 1.03122708 0.84816062 1.62087137 1.31836233 1.2019945
1.2019945 0.74858571 0.55251066 0.31244288 0.28642569 0.24964683
0.19548376 0.41804905 0.10832615 0.08822195 0.11293829 0.11707739
0.06941861 0.05380829 0.07166555 0.12571037 0.04032666 0.04292838
nan nan 0.12902165 0.2024611 0.12618341 0.19205422
0.1646179 0.1995046 0.09153323 0.13493464 0.13245118 0.15007192
0.1758526 0.12582863 0.11530349 0.18306646 0.60111551 0.11033657
0.13020424 nan 0.17153611 0.18566818 0.13712245 0.09372104
0.08842299 0.14463196 0.12884426 0.1018727 0.11991563 nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.03287628 0.02235114 0.0266085 0.02459808 0.017739 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.18679143
0.2200633 0.59398112 0.0849661 0.07033987 0.06096122 0.19449532
0.09847582 0.08909717 0.14715547 0.08373794 0.08284473 0.06833016
0.08898552 0.05180587 0.05616024 0.59911704 nan 0.00223301
0.01462623 0.55155389 0.10003892 0.04588839 0.03014566 0.05113597
0.03260197 nan 0.00840952 0.00204209 0.00281025 0.00136325
nan nan 0.25590314 0.4677043 0.1992963 0.3140731
0.28783521 0.39033045 0.11466515 0.31630611 0.28817016 0.30268474
0.21515068 0.19315551 0.24429148 0.27131092 0.37737898 0.39200521
0.36487411 nan 0.20443222 0.23820652 0.17367249 0.11533506
0.09330528 0.10178737 0.16792248 0.11416272 0.076944 nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.07167968 0.03673304 0.07648065 0.07357774 0.05191752]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 6.56159396e-04
3.28079698e-04 3.28079698e-04 1.09359899e-04 1.96847819e-03
1.09359899e-04 3.28079698e-04 1.09359899e-04 1.42167869e-03
5.46799496e-04 5.46799496e-04 6.56159396e-04 6.56159396e-04
4.37439597e-04 6.56159396e-04 1.09359899e-04 5.46799496e-04
nan nan 1.64039849e-03 2.65744555e-02
1.89192626e-02 9.95175083e-03 8.74879194e-03 6.56159396e-03
8.09263255e-03 8.08169656e-04 3.25236340e-03 3.33547693e-04
3.24798901e-03 nan nan nan
4.06818825e-02 4.25410008e-02 2.60276560e-02 2.37310981e-02
2.55902164e-02 3.45577282e-02 3.70730059e-02 3.93695637e-02
4.25410008e-02 3.95882835e-02 2.05596611e-02 1.05751023e-01
1.73882240e-02 4.36345998e-02 1.14390455e-01 1.78256636e-02
9.29559144e-03 nan 1.32106758e-02 8.00514463e-03
1.24342205e-02 1.03673185e-02 1.25862308e-02 8.69848639e-03
1.77381757e-02 1.54295882e-02 6.72016581e-03 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 2.26374992e-02 2.79961342e-02
2.66838154e-02 2.74493347e-02 3.08394916e-02]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan 4.24076364e-05 1.74931500e-04 2.65047728e-05
1.91894555e-04 7.42133637e-06 nan nan
1.37824818e-03 1.07079282e-03 1.31463673e-03 7.52735546e-04
1.03898709e-03 8.26948910e-04 1.55848064e-03 2.69288491e-03
2.54445818e-03 2.89432118e-03 1.22982146e-03 1.53727682e-03
1.18741382e-03 2.90492309e-03 2.31121618e-03 4.24076364e-04
3.39261091e-04 nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 1.69630546e-03 8.48152728e-04
9.54171819e-04 8.48152728e-04 2.54445818e-03]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.03357944 0.03551672 0.03487096 0.03185742 0.03078116]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 1.35077173e-04
7.83447602e-03 6.75385863e-03 1.21569455e-03 1.35077173e-04
5.94339560e-03 1.35077173e-04 1.75600324e-03 2.43138911e-03
1.35077173e-04 1.35077173e-04 1.35077173e-04 4.14686920e-02
1.35077173e-04 6.20004223e-02 3.03923639e-02 4.05231518e-04
nan nan nan 1.08061738e-02
2.16123476e-02 1.91809585e-02 1.74249553e-02 1.79652640e-02
1.86406498e-02 5.69215206e-01 3.51200649e-03 1.48584890e-03
4.32246953e-03 2.97169780e-03 nan nan
6.45668885e-02 5.52465636e-02 2.99871323e-02 7.13207472e-02
4.16037692e-02 6.76736635e-02 3.71462225e-02 4.21440779e-02
4.18739235e-02 4.25493094e-02 3.90373029e-02 3.76865312e-02
3.05274410e-02 4.86277822e-02 4.53859300e-02 1.33456247e-01
1.21164224e-01 nan 8.32332030e-02 1.94011343e-02
6.37010439e-02 3.55279980e-02 5.18210065e-02 9.48836092e-02
1.01915727e-01 1.63848610e-01 9.63843166e-02 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 4.52508528e-02 4.28194637e-02
3.93074572e-02 3.84969942e-02 2.93117465e-02]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 2.19233366e-03
7.30777885e-04 3.21542270e-03 1.46155577e-04 1.46155577e-04
1.46155577e-04 4.38466731e-04 4.38466731e-04 2.92311154e-04
2.92311154e-04 2.92311154e-04 5.84622308e-04 7.30777885e-04
4.38466731e-04 5.84622308e-04 4.38466731e-04 2.92311154e-04
nan nan nan 9.50011251e-03
1.12539794e-02 1.16924462e-02 1.11078239e-02 1.06693571e-02
1.18386017e-02 5.33467856e-04 8.97395243e-04 3.25926937e-04
7.32239441e-04 6.95700547e-04 nan nan
4.18004950e-02 2.10464031e-02 8.62317905e-03 6.02160977e-02
2.61618483e-02 5.14467631e-02 9.50011251e-03 4.51620733e-02
4.75005625e-02 4.89621183e-02 2.42618258e-02 3.81466056e-02
4.07774060e-02 1.85617583e-02 2.48464481e-03 6.32853649e-02
6.50392318e-02 nan 8.57787082e-02 2.29464256e-01
8.00201784e-02 1.98771585e-01 1.84156027e-01 2.14848698e-01
4.25020418e-02 1.20066807e-01 1.68078914e-01 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 1.03770460e-02 1.09616683e-02
9.20780135e-03 6.72315654e-03 5.11544520e-03]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.00014711
0.027804 0.003972 0.00044133 0.04280933 0.02648 0.00014711
0.00823822 0.00559022 0.01279867 0.00029422 0.00720844 0.00382489
0.01412267 0.01162178 0.02044844 0.00823822 nan nan
nan 0.01324 0.01368133 0.01206311 0.01015067 0.01044489
0.010592 nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.014564 0.01162178 0.00941511 0.01088622 0.00647289]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
For the purpose of establishing the congruency of our algorithm with Verma’s,
we’ll use adjust_all_Fe = True and LeMaitre’s correction. Notably, this
won’t make too much difference to the format of the output, but it will adjust
the estimates of normative mineralogy depending on oxidation state.
NORM = CIPW_norm(
df.pyrochem.compositional,
adjust_all_Fe=True,
Fe_correction="LeMaitre",
Fe_correction_mode="volcanic",
)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.006872
0.00369052 0.01018074 0.00025452 0.00114533 0.00012726 0.00101807
0.0006363 0.00101807 0.00127259 0.0006363 0.00089081 0.00101807
0.00101807 0.00127259 0.00114533 0.00101807 nan nan
nan 0.00649022 0.00445407 0.00547215 0.0075083 0.00585393
0.00636296 nan 0.0004645 0.0001718 0.00052176 0.00085645
nan nan 0.01488934 0.01718 0.00483585 0.03550534
0.01628919 0.03779601 0.00725378 0.02825156 0.02799704 0.02634267
0.01807082 0.02150682 0.01705274 0.00572667 0.00152711 0.04237734
0.04746771 nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.003436 0.00432682 0.00229067 0.00152711 0.00089081]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan
nan nan nan nan nan nan nan nan nan nan nan]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.74007099
0.79991055 0.40823347 0.99728646 0.71133382 0.50295972 0.88210124
0.65468728 1.03122708 0.84816062 1.62087137 1.31836233 1.2019945
1.2019945 0.74858571 0.55251066 0.31244288 0.28642569 0.24964683
0.19548376 0.41804905 0.10832615 0.08822195 0.11293829 0.11707739
0.06941861 0.05380829 0.07166555 0.12571037 0.04032666 0.04292838
nan nan 0.12902165 0.2024611 0.12618341 0.19205422
0.1646179 0.1995046 0.09153323 0.13493464 0.13245118 0.15007192
0.1758526 0.12582863 0.11530349 0.18306646 0.60111551 0.11033657
0.13020424 nan 0.17153611 0.18566818 0.13712245 0.09372104
0.08842299 0.14463196 0.12884426 0.1018727 0.11991563 nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.03287628 0.02235114 0.0266085 0.02459808 0.017739 ]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.18679143
0.2200633 0.59398112 0.0849661 0.07033987 0.06096122 0.19449532
0.09847582 0.08909717 0.14715547 0.08373794 0.08284473 0.06833016
0.08898552 0.05180587 0.05616024 0.59911704 nan 0.00223301
0.01462623 0.55155389 0.10003892 0.04588839 0.03014566 0.05113597
0.03260197 nan 0.00840952 0.00204209 0.00281025 0.00136325
nan nan 0.25590314 0.4677043 0.1992963 0.3140731
0.28783521 0.39033045 0.11466515 0.31630611 0.28817016 0.30268474
0.21515068 0.19315551 0.24429148 0.27131092 0.37737898 0.39200521
0.36487411 nan 0.20443222 0.23820652 0.17367249 0.11533506
0.09330528 0.10178737 0.16792248 0.11416272 0.076944 nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.07167968 0.03673304 0.07648065 0.07357774 0.05191752]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 6.56159396e-04
3.28079698e-04 3.28079698e-04 1.09359899e-04 1.96847819e-03
1.09359899e-04 3.28079698e-04 1.09359899e-04 1.42167869e-03
5.46799496e-04 5.46799496e-04 6.56159396e-04 6.56159396e-04
4.37439597e-04 6.56159396e-04 1.09359899e-04 5.46799496e-04
nan nan 1.64039849e-03 2.65744555e-02
1.89192626e-02 9.95175083e-03 8.74879194e-03 6.56159396e-03
8.09263255e-03 8.08169656e-04 3.25236340e-03 3.33547693e-04
3.24798901e-03 nan nan nan
4.06818825e-02 4.25410008e-02 2.60276560e-02 2.37310981e-02
2.55902164e-02 3.45577282e-02 3.70730059e-02 3.93695637e-02
4.25410008e-02 3.95882835e-02 2.05596611e-02 1.05751023e-01
1.73882240e-02 4.36345998e-02 1.14390455e-01 1.78256636e-02
9.29559144e-03 nan 1.32106758e-02 8.00514463e-03
1.24342205e-02 1.03673185e-02 1.25862308e-02 8.69848639e-03
1.77381757e-02 1.54295882e-02 6.72016581e-03 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 2.26374992e-02 2.79961342e-02
2.66838154e-02 2.74493347e-02 3.08394916e-02]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
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nan nan nan nan
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nan nan nan nan
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nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan 4.24076364e-05 1.74931500e-04 2.65047728e-05
1.91894555e-04 7.42133637e-06 nan nan
1.37824818e-03 1.07079282e-03 1.31463673e-03 7.52735546e-04
1.03898709e-03 8.26948910e-04 1.55848064e-03 2.69288491e-03
2.54445818e-03 2.89432118e-03 1.22982146e-03 1.53727682e-03
1.18741382e-03 2.90492309e-03 2.31121618e-03 4.24076364e-04
3.39261091e-04 nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 1.69630546e-03 8.48152728e-04
9.54171819e-04 8.48152728e-04 2.54445818e-03]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.03357944 0.03551672 0.03487096 0.03185742 0.03078116]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 1.35077173e-04
7.83447602e-03 6.75385863e-03 1.21569455e-03 1.35077173e-04
5.94339560e-03 1.35077173e-04 1.75600324e-03 2.43138911e-03
1.35077173e-04 1.35077173e-04 1.35077173e-04 4.14686920e-02
1.35077173e-04 6.20004223e-02 3.03923639e-02 4.05231518e-04
nan nan nan 1.08061738e-02
2.16123476e-02 1.91809585e-02 1.74249553e-02 1.79652640e-02
1.86406498e-02 5.69215206e-01 3.51200649e-03 1.48584890e-03
4.32246953e-03 2.97169780e-03 nan nan
6.45668885e-02 5.52465636e-02 2.99871323e-02 7.13207472e-02
4.16037692e-02 6.76736635e-02 3.71462225e-02 4.21440779e-02
4.18739235e-02 4.25493094e-02 3.90373029e-02 3.76865312e-02
3.05274410e-02 4.86277822e-02 4.53859300e-02 1.33456247e-01
1.21164224e-01 nan 8.32332030e-02 1.94011343e-02
6.37010439e-02 3.55279980e-02 5.18210065e-02 9.48836092e-02
1.01915727e-01 1.63848610e-01 9.63843166e-02 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 4.52508528e-02 4.28194637e-02
3.93074572e-02 3.84969942e-02 2.93117465e-02]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
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nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan 2.19233366e-03
7.30777885e-04 3.21542270e-03 1.46155577e-04 1.46155577e-04
1.46155577e-04 4.38466731e-04 4.38466731e-04 2.92311154e-04
2.92311154e-04 2.92311154e-04 5.84622308e-04 7.30777885e-04
4.38466731e-04 5.84622308e-04 4.38466731e-04 2.92311154e-04
nan nan nan 9.50011251e-03
1.12539794e-02 1.16924462e-02 1.11078239e-02 1.06693571e-02
1.18386017e-02 5.33467856e-04 8.97395243e-04 3.25926937e-04
7.32239441e-04 6.95700547e-04 nan nan
4.18004950e-02 2.10464031e-02 8.62317905e-03 6.02160977e-02
2.61618483e-02 5.14467631e-02 9.50011251e-03 4.51620733e-02
4.75005625e-02 4.89621183e-02 2.42618258e-02 3.81466056e-02
4.07774060e-02 1.85617583e-02 2.48464481e-03 6.32853649e-02
6.50392318e-02 nan 8.57787082e-02 2.29464256e-01
8.00201784e-02 1.98771585e-01 1.84156027e-01 2.14848698e-01
4.25020418e-02 1.20066807e-01 1.68078914e-01 nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan nan nan
nan nan 1.03770460e-02 1.09616683e-02
9.20780135e-03 6.72315654e-03 5.11544520e-03]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/geochem/transform.py:351: FutureWarning: Setting an item of incompatible dtype is deprecated and will raise in a future error of pandas. Value '[ nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
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nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan 0.00014711
0.027804 0.003972 0.00044133 0.04280933 0.02648 0.00014711
0.00823822 0.00559022 0.01279867 0.00029422 0.00720844 0.00382489
0.01412267 0.01162178 0.02044844 0.00823822 nan nan
nan 0.01324 0.01368133 0.01206311 0.01015067 0.01044489
0.010592 nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
nan nan nan nan nan nan
0.014564 0.01162178 0.00941511 0.01088622 0.00647289]' has dtype incompatible with int64, please explicitly cast to a compatible dtype first.
_df.loc[:, targetnames] = subsum.values[:, np.newaxis] @ coeff[np.newaxis, :]
Now we have the normative mineralogical outputs, we can have a look to see how these compare to some relevant geochemical inputs:
ax = NORM[["ilmenite", "magnetite"]].pyroplot.scatter(clip_on=False, c=df["TiO2"])
plt.show()
ax = NORM[["orthoclase", "albite", "anorthite"]].pyroplot.scatter(
clip_on=False, c=df["K2O"]
)
plt.show()
Coherency with SINCLAS / IgRoCS
Given we’re reproducting an existing algorithm, it’s prudent to check how closely the results match for a specific dataset to check whether there might be any numerical or computational errors. Below we go through this exercise for the test dataset we loaded above (which already includes the output of SINCLAS), comparing the original software to the pyrolite implementation.
Note
Currently there are inconsistent results for a small number or samples (deviations colormapped, and inconsistent results shown in red below), likely related to the handling of iron components and their conversion.
The output of SINCLAS has slightly different column naming that that of
pyrolite, which provides full mineral names in the output dataframe
columns. For this reason, we’ll need to translate our NORM output columns
to the SINCLAS column names. For this we can use the dictionary of minerals
used in the CIPW Norm (NORM_MINERALS)
from pyrolite.mineral.normative import NORM_MINERALS
translation = {
d["name"]: (d.get("SINCLAS_abbrv", None) or k.upper()) + "_NORM"
for k, d in NORM_MINERALS.items()
if (d.get("SINCLAS_abbrv", None) or k.upper()) + "_NORM" in df.columns
}
translation
{'quartz': 'Q_NORM', 'zircon': 'ZIR_NORM', 'potassium metasilicate': 'KS_NORM', 'anorthite': 'AN_NORM', 'sodium metasilicate': 'NS_NORM', 'acmite': 'AC_NORM', 'thenardite': 'TH_NORM', 'albite': 'AB_NORM', 'orthoclase': 'OR_NORM', 'perovskite': 'PER_NORM', 'nepheline': 'NE_NORM', 'leucite': 'LC_NORM', 'dicalcium silicate': 'CS_NORM', 'kaliophilite': 'KP_NORM', 'apatite': 'AP_NORM', 'fluorite': 'FR_NORM', 'pyrite': 'PYR_NORM', 'chromite': 'CHR_NORM', 'ilmenite': 'IL_NORM', 'calcite': 'CC_NORM', 'corundum': 'C_NORM', 'rutile': 'RU_NORM', 'magnetite': 'MT_NORM', 'forsterite': 'FO_NORM', 'fayalite': 'FA_NORM', 'clinoferrosilite': 'DIF_NORM', 'clinoenstatite': 'DIM_NORM', 'ferrosilite': 'HYF_NORM', 'enstatite': 'HYM_NORM', 'wollastonite': 'WO_NORM', 'cancrinite': 'CAN_NORM', 'halite': 'HL_NORM', 'titanite': 'SPH_NORM', 'diopside': 'DI_NORM', 'hypersthene': 'HY_NORM', 'olivine': 'OL_NORM'}
First we’ll collect the minerals which appear in both dataframes, and then iterate through these to check how close the implementations are.
minerals = {
k: v for (k, v) in translation.items() if (df[v] > 0).sum() and (NORM[k] > 0).sum()
}
To compare SINCLAS and the pyrolite NORM outputs, we’ll construct a grid
of plots which compare the respective mineralogical norms relative to a 1:1 line,
and highlight discrepancies. As we’ll do it twice below (once for samples labelled as
volanic, and once for everything else), we may as well make a function of it.
After that, let’s take a look at the volcanic samples in isolation, which are the the key samples for which the NORM should be applied:
from pyrolite.plot.color import process_color
def compare_NORMs(SINCLAS_outputs, NORM_outputs, name=""):
"""
Create a grid of axes comparing the outputs of SINCLAS and `pyrolite`'s NORM,
after translating the column names to the appropriate form.
"""
ncols = 4
nrows = len(minerals.keys()) // ncols + (1 if len(minerals.keys()) % ncols else 0)
fig, ax = plt.subplots(nrows, ncols, figsize=(ncols * 2.5, nrows * 2))
fig.suptitle(
" - ".join(
["Comparing pyrolite's CIPW Norm to SINCLAS/IgRoCS"] + [name]
if name
else []
),
fontsize=16,
y=1.01,
)
ax = ax.flat
for ix, (b, a) in enumerate(minerals.items()):
ax[ix].set_title("\n".join(b.split()), y=0.9, va="top")
if a in SINCLAS_outputs.columns and b in NORM_outputs.columns:
# colour by deviation from unity
c = process_color(
np.abs((SINCLAS_outputs[a] / NORM_outputs[b]) - 1),
cmap="RdBu_r",
norm=plt.Normalize(vmin=0, vmax=0.1),
)["c"]
ax[ix].scatter(SINCLAS_outputs[a], NORM_outputs[b], c=c)
# add a 1:1 line
ax[ix].plot(
[0, SINCLAS_outputs[a].max()],
[0, SINCLAS_outputs[a].max()],
color="k",
ls="--",
)
for a in ax:
a.set(xticks=[], yticks=[]) # turn off the ticks
if not a.collections: # turn off the axis for empty axes
a.axis("off")
return fig, ax
volcanic_filter = df.loc[:, "ROCK_TYPE"].str.lower().str.startswith("volc")
fig, ax = compare_NORMs(df.loc[volcanic_filter, :], NORM.loc[volcanic_filter])
And everything else:
fig, ax = compare_NORMs(df.loc[~volcanic_filter, :], NORM.loc[~volcanic_filter])
plt.show()
These normative mineralogical components could be input into mineralogical classifiers, as mentioned above. For example, the IUGS QAP classifier:
from pyrolite.util.classification import QAP
clf = QAP() # build a QAP classifier
qap_data = NORM.loc[:, ["quartz", "orthoclase"]] #
qap_data["plagioclase"] = NORM.loc[:, ["albite", "anorthite"]].sum(axis=1)
# predict which lithological class each mineralogical composiiton belongs in
# we add a small value to zeros here to ensure points fit in polygons
predicted_classes = clf.predict(qap_data.replace(0, 10e-6).values)
predicted_classes.head()
0 monzodiorite-monzogabbro
1 diorite-gabbro-anorthosite
2 monzodiorite-monzogabbro
3 monzodiorite-monzogabbro
4 monzodiorite-monzogabbro
dtype: object
We can use these predicted classes as a color index also, within the QAP diagram or elsewhere:
ax = clf.add_to_axes()
qap_data.pyroplot.scatter(ax=ax, c=predicted_classes, axlabels=False, cmap="tab20c")
plt.show()
We could also compare how these mineralogical distinctions map into chemical ones like the TAS diagram:
from pyrolite.plot.templates import TAS
ax = TAS()
components = df.loc[:, ["SiO2"]]
components["alkali"] = df.loc[:, ["Na2O", "K2O"]].sum(axis=1)
# add the predictions from normative mineralogy to the TAS diagram
components.pyroplot.scatter(ax=ax, c=predicted_classes, cmap="tab20c", axlabels=False)
plt.show()
References
- Cross1902
Cross, W., Iddings, J. P., Pirsson, L. V., & Washington, H. S. (1902). A Quantitative Chemico-Mineralogical Classification and Nomenclature of Igneous Rocks. The Journal of Geology, 10(6), 555–690. doi: 10.1086/621030
- Verma2003
Verma, S. P., Torres-Alvarado, I. S., & Velasco-Tapia, F. (2003). A revised CIPW norm. Swiss Bulletin of Mineralogy and Petrology, 83(2), 197–216.
- Verma2013
Verma, S. P., & Rivera-Gomez, M. A. (2013). Computer Programs for the Classification and Nomenclature of Igneous Rocks. Episodes, 36(2), 115–124.
- LeMaitre1976
Le Maitre, R. W (1976). Some Problems of the Projection of Chemical Data into Mineralogical Classifications. Contributions to Mineralogy and Petrology 56, no. 2 (1 January 1976): 181–89. doi: doi.org/10.1007/BF00399603
- Middlemost1989
Middlemost, Eric A. K. (1989). Iron Oxidation Ratios, Norms and the Classification of Volcanic Rocks. Chemical Geology 77, 1: 19–26. doi: doi.org/10.1016/0009-2541(89)90011-9.
Total running time of the script: (0 minutes 11.311 seconds)
lambdas: Parameterising REE Profiles
Orthogonal polynomial decomposition can be used for dimensional reduction of smooth function over an independent variable, producing an array of independent values representing the relative weights for each order of component polynomial. This is an effective method to parameterise and compare the nature of smooth profiles.
In geochemistry, the most applicable use case is for reduction Rare Earth Element (REE) profiles. The REE are a collection of elements with broadly similar physicochemical properties (the lanthanides), which vary with ionic radii. Given their similar behaviour and typically smooth function of normalised abundance vs. ionic radii, the REE profiles and their shapes can be effectively parameterised and dimensionally reduced (14 elements summarised by 3-4 shape parameters).
Note
A publication discussing this implementation of lambdas together with fitting tetrads for REE patterns has been published in Mathematical Geosciences!
Here we generate some example data, reduce these to lambda values, and visualise the results.
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pyrolite.plot
np.random.seed(82)
First we’ll generate some example synthetic data based around Depleted MORB Mantle:
from pyrolite.util.synthetic import example_spider_data
df = example_spider_data(
noise_level=0.05,
size=100,
start="DMM_WH2005",
norm_to="Chondrite_PON",
offsets={"Eu": 0.2},
).pyrochem.REE.pyrochem.denormalize_from("Chondrite_PON")
df.head(2)
Let’s have a quick look at what this REE data looks like normalized to Primitive Mantle:
df.pyrochem.normalize_to("PM_PON").pyroplot.REE(alpha=0.05, c="k", unity_line=True)
plt.show()
From this REE data we can fit a series of orthogonal polynomials, and subsequently used the regression coefficients (‘lambdas’) as a parameterisation of the REE pattern/profile:
ls = df.pyrochem.lambda_lnREE(degree=4)
ls.head(2)
So what’s actually happening here? To get some idea of what these λ coefficients
correspond to, we can pull this process apart and visualise our REE profiles as
the sum of the series of orthogonal polynomial components of increasing order.
As lambdas represent the coefficients for the regression of log-transformed normalised
data, to compare the polynomial components and our REE profile we’ll first need to
normalize it to the appropriate composition (here "ChondriteREE_ON") before
taking the logarithm.
With our data, we’ve then fit a function of ionic radius with the form \(f(r) = \lambda_0 + \lambda_1 f_1 + \lambda_2 f_2 + \lambda_3 f_3...\) where the polynomial components of increasing order are \(f_1 = (r - \beta_0)\), \(f_2 = (r - \gamma_0)(r - \gamma_1)\), \(f_3 = (r - \delta_0)(r - \delta_1)(r - \delta_2)\) and so on. The parameters \(\beta\), \(\gamma\), \(\delta\) are pre-computed such that the polynomial components are indeed independent. Here we can visualise how these polynomial components are summed to produce the regressed profile, using the last REE profile we generated above as an example:
from pyrolite.util.lambdas.plot import plot_lambdas_components
ax = (
df.pyrochem.normalize_to("ChondriteREE_ON")
.iloc[-1, :]
.apply(np.log)
.pyroplot.REE(color="k", label="Data", logy=False)
)
plot_lambdas_components(ls.iloc[-1, :], ax=ax)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/util/plot/axes.py:219: RuntimeWarning: More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`). Consider using `matplotlib.pyplot.close()`.
fig, ax = plt.subplots(1, **subkwargs(kwargs, plt.subplots, plt.figure))
Now that we’ve gone through a brief introduction to how the lambdas are generated, let’s quickly check what the coefficient values themselves look like:
fig, ax = plt.subplots(1, 3, figsize=(9, 3))
for ix in range(ls.columns.size - 1):
ls[ls.columns[ix : ix + 2]].pyroplot.scatter(ax=ax[ix], alpha=0.1, c="k")
plt.tight_layout()
But what do these parameters correspond to? From the deconstructed orthogonal polynomial above, we can see that \(\lambda_0\) parameterises relative enrichment (this is the mean value of the logarithm of Chondrite-normalised REE abundances), \(\lambda_1\) parameterises a linear slope (here, LREE enrichment), and higher order terms describe curvature of the REE pattern. Through this parameterisation, the REE profile can be effectively described and directly linked to geochemical processes. While the amount of data we need to describe the patterns is lessened, the values themselves are more meaningful and readily used to describe the profiles and their physical significance.
The visualisation of \(\lambda_1\)-\(\lambda_2\) can be particularly useful where you’re trying to compare REE profiles.
We’ve used a synthetic dataset here which is by design approximately normally distributed, so the values themeselves here are not particularly revealing, but they do illustrate the expected mangitudes of values for each of the parameters.
Dealing With Anomalies
Note that we’ve not used Eu in this regression - Eu anomalies are a deviation from
the ‘smooth profile’ we need to use this method. Consider this if your data might also
exhibit significant Ce anomalies, you might need to exclude this data. For convenience
there is also functionality to calculate anomalies derived from the orthogonal
polynomial fit itself (rather than linear interpolation methods). Below we use the
anomalies keyword argument to also calculate the \(\frac{Ce}{Ce*}\)
and \(\frac{Eu}{Eu*}\) anomalies (note that these are excluded from the fit):
ls_anomalies = df.pyrochem.lambda_lnREE(anomalies=["Ce", "Eu"])
ax = ls_anomalies.iloc[:, -2:].pyroplot.scatter(color="0.5")
plt.show()
Coefficient Uncertainties and Fit Quality
In order to determine the relative significance of the parameterisation and ‘goodness of fit’, the functions are able to estimate uncertainties on the returned coefficients (lambdas and taus) and will also return the chi-square value (\(\chi^2\); equivalent to the MSWD) where requested. This will be appended to the end of the dataframe. Note that if you do not supply an estimate of observed value uncertainties a default of 1% of the log-mean will be used.
To append the reduced chi-square for each row, the keyword argument
add_X2=True can be used; here we’ve estimated 10% uncertainty on the
REE:
ls = df.pyrochem.lambda_lnREE(add_X2=True, sigmas=0.1, anomalies=["Eu", "Ce"])
ls.columns
Index(['λ0', 'λ1', 'λ2', 'λ3', 'X2', 'Eu/Eu*', 'Ce/Ce*'], dtype='object')
We can have a quick look at the \(\chi^2\) values look like for the synthetic dataset, given the assumed 10% uncertainties. While the fit appears reasonable for a good fraction of the dataset (~2 and below), for some rows it is notably worse:
fig, ax = plt.subplots(1, figsize=(5, 3))
ax = ls["X2"].plot.hist(ax=ax, bins=40, color="0.5")
ax.set(xlabel="$\chi^2$")
ax.axvline(1, color="k", ls="--")
plt.show()
We can also examine the estimated uncertainties on the coefficients from the fit
by adding the keyword argument add_uncertainties=True (note: these do not
explicitly propagate observation uncertainties):
ls = df.pyrochem.lambda_lnREE(add_uncertainties=True)
ls.columns
Index(['λ0', 'λ1', 'λ2', 'λ3', 'λ0_σ', 'λ1_σ', 'λ2_σ', 'λ3_σ'], dtype='object')
Notably, on the scale of natural dataset variation, these uncertainties may end up being smaller than symbol sizes. If your dataset happened to have a great deal more noise, you may happen to see them - for demonstration purposes we can generate a noiser dataset and have a quick look at what these uncertainties could look like:
ls = (df + 3 * np.exp(np.random.randn(*df.shape))).pyrochem.lambda_lnREE(
add_uncertainties=True
)
With this ‘noisy’ dataset, we can see some of the errorbars:
fig, ax = plt.subplots(1, 3, figsize=(9, 3))
ax = ax.flat
dc = ls.columns.size // 2
for ix, a in enumerate(ls.columns[:3]):
i0, i1 = ix, ix + 1
ax[ix].set(xlabel=ls.columns[i0], ylabel=ls.columns[i1])
ax[ix].errorbar(
ls.iloc[:, i0],
ls.iloc[:, i1],
xerr=ls.iloc[:, i0 + dc] * 2,
yerr=ls.iloc[:, i1 + dc] * 2,
ls="none",
ecolor="0.5",
markersize=1,
color="k",
)
plt.tight_layout()
plt.show()
Fitting Tetrads
In addition to fitting orothogonal polynomial functions, the ability to fit tetrad functions has also recently been added. This supplements the \(\lambda\) coefficients with \(\tau\) coefficients which describe subtle electronic configuration effects affecting sequential subsets of the REE. Below we plot four profiles - each describing only a single tetrad - to illustrate the shape of these function components. Note that these are functions of \(z\), and are here transformed to plot against radii.
from pyrolite.util.lambdas.plot import plot_profiles
# let's first create some synthetic pattern parameters
# we want lambdas to be zero, and each of the tetrads to be shown in only one pattern
lambdas = np.zeros((4, 5))
tetrads = np.eye(4)
# putting it together to generate four sets of combined parameters
fit_parameters = np.hstack([lambdas, tetrads])
ax = plot_profiles(
fit_parameters,
tetrads=True,
color=np.arange(4),
)
plt.show()
In order to also fit these function components, you can pass the keyword argument
fit_tetrads=True to lambda_lnREE() and
related functions:
lts = df.pyrochem.lambda_lnREE(degree=4, fit_tetrads=True)
We can see that the four extra \(\tau\) Parameters have been appended to the right of the lambdas within the output:
lts.head(2)
from pyrolite.geochem.ind import REE
Below we’ll look at some of the potential issues of fitting lambdas and tetrads together - by examining the effects of i) fitting tetrads where there are none and ii) not fitting tetrads where they do indeed exist using some synthetic datasets.
from pyrolite.util.synthetic import example_patterns_from_parameters
ls = np.array(
[
[2, 5, -30, 100, -600, 0, 0, 0, 0], # lambda-only
[3, 15, 30, 300, 1500, 0, 0, 0, 0], # lambda-only
[1, 5, -50, 0, -1000, -0.3, -0.7, -1.4, -0.2], # W-pattern tetrad
[5, 15, 50, 400, 2000, 0.6, 1.1, 1.5, 0.3], # M-pattern tetrad
]
)
# now we use these parameters to generate some synthetic log-scaled normalised REE
# patterns and add a bit of noise
pattern_df = pd.DataFrame(
np.vstack([example_patterns_from_parameters(l, includes_tetrads=True) for l in ls]),
columns=REE(),
)
# We can now fit these patterns and see what the effect of fitting and not-Fitting
# tetrads might look like in these (slightly extreme) cases:
fit_ls_only = pattern_df.pyrochem.lambda_lnREE(
norm_to=None, degree=5, fit_tetrads=False
)
fit_ts = pattern_df.pyrochem.lambda_lnREE(norm_to=None, degree=5, fit_tetrads=True)
We can now examine what the differences between the fits are. Below we plot the four sets of synthetic REE patterns (lambda-only above and lamba+tetrad below) and examine the relative accuracy of fitting some of the higher order lambda parameters where tetrads are also fit:
from pyrolite.util.plot.axes import share_axes
x, y = 2, 3
categories = np.repeat(np.arange(ls.shape[0]), 100)
colors = np.array([str(ix) * 2 for ix in categories])
l_only = categories < 2
ax = plt.figure(figsize=(12, 7)).subplot_mosaic(
"""
AAABBCC
DDDEEFF
"""
)
share_axes([ax["A"], ax["D"]])
share_axes([ax["B"], ax["C"], ax["E"], ax["F"]])
ax["B"].set_title("lambdas only Fit")
ax["C"].set_title("lambdas+tetrads Fit")
for a, fltr in zip(["A", "D"], [l_only, ~l_only]):
pattern_df.iloc[fltr, :].pyroplot.spider(
ax=ax[a],
label="True",
unity_line=True,
alpha=0.5,
color=colors[fltr],
)
for a, fltr in zip(["B", "E"], [l_only, ~l_only]):
fit_ls_only.iloc[fltr, [x, y]].pyroplot.scatter(
ax=ax[a],
alpha=0.2,
color=colors[fltr],
)
for a, fltr in zip(["C", "F"], [l_only, ~l_only]):
fit_ts.iloc[fltr, [x, y]].pyroplot.scatter(
ax=ax[a],
alpha=0.2,
color=colors[fltr],
)
true = pd.DataFrame(ls[:, [x, y]], columns=[fit_ls_only.columns[ix] for ix in [x, y]])
for ix, a in enumerate(["B", "C", "E", "F"]):
true.iloc[np.array([ix < 2, ix < 2, ix >= 2, ix >= 2]), :].pyroplot.scatter(
ax=ax[a],
color=np.array([str(ix) * 2 for ix in np.arange(ls.shape[0] // 2)]),
marker="X",
s=100,
)
plt.tight_layout()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
More Advanced Customisation
Above we’ve used default parameterisations for calculating lambdas, but
pyrolite allows you to customise the parameterisation of both the orthogonal
polynomial components used in the fitting process as well as what data and algorithm
is used in the fit itself.
To exclude some elements from the fit (e.g. Eu which is excluded by default, and and potentially Ce), you can either i) filter the dataframe such that the columns aren’t passed, or ii) explicitly exclude them:
# filtering the dataframe first
target_columns = [i for i in df.columns if i not in ["Eu", "Ce"]]
ls_noEuCe_filtered = df[target_columns].pyrochem.lambda_lnREE()
# excluding some elements
ls_noEuCe_excl = df.pyrochem.lambda_lnREE(exclude=["Eu", "Ce"])
# quickly checking equivalence
np.allclose(ls_noEuCe_excl, ls_noEuCe_filtered)
True
While the results should be numerically equivalent, pyrolite does provide
two algorithms for fitting lambdas. The first follows almost exactly the original
formulation (algorithm="ONeill"; this was translated from VBA), while the
second simply uses a numerical optimization routine from scipy to achieve the
same thing (algorithm="opt"; this is a fallback for where singular matricies
pop up):
# use the original version
ls_linear = df.pyrochem.lambda_lnREE(algorithm="ONeill")
# use the optimization algorithm
ls_opt = df.pyrochem.lambda_lnREE(algorithm="opt")
To quickly demonstrate the equivalance, we can check numerically (to within 0.001%):
np.allclose(ls_linear, ls_opt, rtol=10e-5)
True
Or simply plot the results from both:
fig, ax = plt.subplots(1, figsize=(5, 5))
ax.set_title("Comparing $\lambda$ Estimation Algorithms", y=1.1)
ls_linear.iloc[:, 1:3].pyroplot.scatter(
ax=ax, marker="s", c="k", facecolors="none", s=50, label="Linear Algebra"
)
ls_opt.iloc[:, 1:3].pyroplot.scatter(
ax=ax, c="purple", marker="x", s=50, label="Optimization"
)
ax.legend()
plt.show()
You can also use orthogonal polynomials defined over a different set of REE, by specifying the parameters using the keyword argument params:
# this is the original formulation from the paper, where Eu is excluded
ls_original = df.pyrochem.lambda_lnREE(params="ONeill2016")
# this uses a full set of REE
ls_fullREE_polynomials = df.pyrochem.lambda_lnREE(params="full")
Note that as of pyrolite v0.2.8, the original formulation is used by default,
but this will cease to be the case as of the following version, where the full set of
REE will instead be used to generate the orthogonal polynomials.
While the results are simlar, there are small differences. They’re typically less than 1%:
np.abs((ls_original / ls_fullREE_polynomials) - 1).max() * 100
λ0 8.265e-01
λ1 4.306e-01
λ2 7.584e-01
λ3 1.322e-06
dtype: float64
This can also be visualised:
fig, ax = plt.subplots(1, figsize=(5, 5))
ax.set_title("Comparing Orthogonal Polynomial Bases", y=1.1)
ls_original.iloc[:, 1:3].pyroplot.scatter(
ax=ax, marker="s", c="k", facecolors="none", s=50, label="Excluding Eu"
)
ls_fullREE_polynomials.iloc[:, 1:3].pyroplot.scatter(
ax=ax, c="purple", marker="x", s=50, label="All REE"
)
ax.legend()
plt.show()
References & Citation
For more on using orthogonal polynomials to describe geochemical pattern data, dig into the paper which introduced the method to geochemists:
O’Neill, H.S.C., 2016. The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57, 1463–1508. doi: 10.1093/petrology/egw047.
If you’re using pyrolite’s implementation of lambdas in your research,
please consider citing a recent publication directly related to this:
Anenburg, M., & Williams, M. J. (2021). Quantifying the Tetrad Effect, Shape Components, and Ce–Eu–Gd Anomalies in Rare Earth Element Patterns. Mathematical Geosciences. doi: 10.1007/s11004-021-09959-5
See also
- Examples:
- Functions:
lambda_lnREE(),get_ionic_radii(),pyrolite.plot.pyroplot.REE()
Total running time of the script: (0 minutes 19.157 seconds)
Compositional Data Examples
Log-transforms
pyrolite includes a few functions for dealing with compositional data, at the heart of
which are i) closure (i.e. everything sums to 100%) and ii) log-transforms to deal with
the compositional space. The commonly used log-transformations include the
Additive Log-Ratio (ALR()), Centred Log-Ratio
(CLR()), and Isometric Log-Ratio
(ILR()) 1 2.
This example will show you how to access and use some of these functions in pyrolite.
First let’s create some example data:
from pyrolite.util.synthetic import normal_frame, random_cov_matrix
df = normal_frame(
size=100,
cov=random_cov_matrix(sigmas=[0.1, 0.05, 0.3, 0.6], dim=4, seed=32),
seed=32,
)
df.describe()
Let’s have a look at some of the log-transforms, which can be accessed directly from
your dataframes (via pyrolite.comp.pyrocomp), after you’ve imported
pyrolite.comp. Note that the transformations will return new dataframes,
rather than modify their inputs. For example:
import pyrolite.comp
lr_df = df.pyrocomp.CLR() # using a centred log-ratio transformation
The transformations are implemented such that the column names generally make it evident which transformations have been applied (here using default simple labelling; see below for other examples):
lr_df.columns
Index(['CLR(SiO2/G)', 'CLR(CaO/G)', 'CLR(MgO/G)', 'CLR(FeO/G)', 'CLR(TiO2/G)'], dtype='object')
To invert these transformations, you can call the respective inverse transform:
back_transformed = lr_df.pyrocomp.inverse_CLR()
Given we haven’t done anything to our dataframe in the meantime, we should be back
where we started, and our values should all be equal within numerical precision.
To verify this, we can use numpy.allclose():
import numpy as np
np.allclose(back_transformed, df)
True
In addition to easy access to the transforms, there’s also a convenience function
for taking a log-transformed mean (log-transforming, taking a mean, and inverse log
transforming; logratiomean()):
df.pyrocomp.logratiomean()
SiO2 0.241
CaO 0.395
MgO 0.094
FeO 0.104
TiO2 0.166
dtype: float64
While this function defaults to using clr(),
you can specify other log-transforms to use:
df.pyrocomp.logratiomean(transform="CLR")
SiO2 0.241
CaO 0.395
MgO 0.094
FeO 0.104
TiO2 0.166
dtype: float64
Notably, however, the logratio means should all give you the same result:
np.allclose(
df.pyrocomp.logratiomean(transform="CLR"),
df.pyrocomp.logratiomean(transform="ALR"),
) & np.allclose(
df.pyrocomp.logratiomean(transform="CLR"),
df.pyrocomp.logratiomean(transform="ILR"),
)
True
To change the default labelling outputs for column names, you can use the label_mode parameter, for example to get nice labels for plotting:
import matplotlib.pyplot as plt
df.pyrocomp.ILR(label_mode="latex").iloc[:, 0:2].pyroplot.scatter()
plt.show()
Alternatively if you simply want numeric indexes which you can use in e.g. a ML
pipeline, you can use label_mode="numeric":
df.pyrocomp.ILR(label_mode="numeric").columns
Index(['ILR0', 'ILR1', 'ILR2', 'ILR3'], dtype='object')
- 1
Aitchison, J., 1984. The statistical analysis of geochemical compositions. Journal of the International Association for Mathematical Geology 16, 531–564. doi: 10.1007/BF01029316
- 2
Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barceló-Vidal, C., 2003. Isometric Logratio Transformations for Compositional Data Analysis. Mathematical Geology 35, 279–300. doi: 10.1023/A:1023818214614
See also
- Examples:
- Tutorials:
- Modules and Functions:
Total running time of the script: (0 minutes 0.741 seconds)
Spherical Coordinate Transformations
While logratio methods are typically more commonly used to deal with with compositional data, they are not infallible - their principal weakness is being able to deal with true zeros like we have the example dataset below. True zeros are common in mineralogical datasets, and are possible in geochemical datasets to some degree (at least at the level of atom counting..).
An alternative to this is to use a spherical coordinate transform to handle our compositional data. This typically involves treating each covariate as a separate dimension/axis and each composition as a unit vector in this space. The transformation invovles the iterative calculation of an angular representeation of these vectors. \(N\)-dimensional vectors transformed to \(N-1\) dimensional angular equivalents (as the first angle is that between the first axis and the second). At least two variants of this type of transformation exist - a spherical cosine method and a spherical sine method; these are complementary and the sine method is used here (where angles close to \(\pi / 2\) represent close to zero abundance, and angles closer to zero/aligning with the repsective component axis represent higher abundances). See below for an example of this demonstrated graphically.
First let’s create some example mineralogical abundance data, where at least one of the minerals might occasionally have zero abundance:
import numpy as np
from pyrolite.util.synthetic import normal_frame
comp = normal_frame(
columns=["Ab", "Qtz", "Ms", "Sch"],
mean=[0.5, 1, 0.3, 0.05],
cov=np.eye(3) * np.array([0.02, 0.5, 0.5]),
size=10000,
seed=145,
)
comp += 0.05 * np.random.randn(*comp.shape)
comp[comp <= 0] = 0
comp = comp.pyrocomp.renormalise(scale=1)
We can quickly visualise this to see that it does indeed have some true zeros:
import matplotlib.pyplot as plt
comp[["Qtz", "Ms", "Sch"]].pyroplot.scatter(alpha=0.05, c="k")
plt.show()
The spherical coordinate transform functions can be found within
pyrolite.comp.codata, but can also be accessed from the
pyrocomp dataframe accessor:
import pyrolite.comp
angles = comp.pyrocomp.sphere()
angles.head()
The inverse function can be accessed in the same way:
inverted_angles = angles.pyrocomp.inverse_sphere()
inverted_angles.head()
We can see that the inverted angles are within precision of the original composition we used:
np.isclose(inverted_angles, comp.values).all()
True
To better understand what’s going on here, visualising our data is often
the best first step. Below we use a helper fucntion from
pyrolite.util.plot.helpers to create a 3D axis on which to plot our
angular data.
from pyrolite.plot.color import process_color
from pyrolite.util.plot.helpers import init_spherical_octant
ax = init_spherical_octant(labels=[c[2:] for c in angles.columns], figsize=(6, 6))
# here we can color the points by the angle from the Schorl axis
colors = process_color(angles["θ_Sch"], cmap="RdBu", alpha=0.1)["c"]
ax.scatter(*np.sqrt(comp.values[:, 1:]).T, c=colors)
plt.show()
We can compare this to the equivalent ternary projection of our data; note we need to reorder some columns in order to make this align in the same way:
tcolumns = np.array([c[2:] for c in angles.columns])[[2, 0, 1]]
comp[tcolumns].pyroplot.scatter(c=colors)
plt.show()
Total running time of the script: (0 minutes 7.233 seconds)
Log Ratio Means
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pyrolite.comp
from pyrolite.comp.codata import ILR, close, inverse_ILR
from pyrolite.plot import pyroplot
from pyrolite.util.synthetic import random_cov_matrix
np.random.seed(82)
def random_compositional_trend(m1, m2, c1, c2, resolution=20, size=1000):
"""
Generate a compositional trend between two compositions with independent
variances.
"""
# generate means intermediate between m1 and m2
mv = np.vstack([ILR(close(m1)).reshape(1, -1), ILR(close(m2)).reshape(1, -1)])
ms = np.apply_along_axis(lambda x: np.linspace(*x, resolution), 0, mv)
# generate covariance matricies intermediate between c1 and c2
cv = np.vstack([c1.reshape(1, -1), c2.reshape(1, -1)])
cs = np.apply_along_axis(lambda x: np.linspace(*x, resolution), 0, cv)
cs = cs.reshape(cs.shape[0], *c1.shape)
# generate samples from each
samples = np.vstack(
[
np.random.multivariate_normal(m.flatten(), cs[ix], size=size // resolution)
for ix, m in enumerate(ms)
]
)
# combine together.
return inverse_ILR(samples)
First we create an array of compositions which represent a trend.
m1, m2 = np.array([[0.3, 0.1, 2.1]]), np.array([[0.5, 2.5, 0.05]])
c1, c2 = (
random_cov_matrix(2, sigmas=[0.15, 0.05]),
random_cov_matrix(2, sigmas=[0.05, 0.2]),
)
trend = pd.DataFrame(
random_compositional_trend(m1, m2, c1, c2, resolution=100, size=5000),
columns=["A", "B", "C"],
)
We can visualise this compositional trend with a density plot.
ax = trend.pyroplot.density(mode="density", bins=100)
plt.show()
First we can see where the geometric mean would fall:
geomean = trend.mean(axis=0).to_frame().T
ax = geomean.pyroplot.scatter(ax=ax, marker="o", color="r", zorder=2, label="GeoMean")
plt.show()
Finally, we can also see where the logratio mean would fall:
ILRmean = trend.pyrocomp.logratiomean(transform="ILR")
ax = ILRmean.pyroplot.scatter(ax=ax, color="k", label="LogMean")
plt.show()
See also
- Examples:
- Tutorials:
- Modules and Functions:
Total running time of the script: (0 minutes 10.465 seconds)
Compositional Data?
pyrolite comes with a few datasets from Aitchison (1984) built in which we can use as examples:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from pyrolite.plot import pyroplot
from pyrolite.data.Aitchison import load_kongite
df = load_kongite()
For compositional data, everything is relative (thanks to the closure property), so we tend to use ratios to express differences or changes between things. However, if we make incorrect assumptions about the nature of our data, we can get some incorrect answers. Say you want to know the average ratio between A and B:
A_on_B = df["A"] / df["B"]
A_on_B.mean() # 2.8265837788402983
2.8265837788402983
Equally, you could have chosen to calculate the average ratio between B and A
B_on_A = df["B"] / df["A"]
B_on_A.mean() # 0.4709565704852008
0.4709565704852008
You expect these to be invertable, such that A_on_B = 1 / B_on_A; but not so!
A_on_B.mean() / (1 / B_on_A.mean()) # 1.3311982026717262
1.3311982026717262
Similarly, the relative variances are different:
np.std(A_on_B) / A_on_B.mean() # 0.6295146309597085
np.std(B_on_A) / B_on_A.mean() # 0.5020948201979953
0.5020948201979953
This improves when using logratios in place of simple ratios, prior to exponentiating means
logA_on_B = (df["A"] / df["B"]).apply(np.log)
logB_on_A = (df["B"] / df["A"]).apply(np.log)
The logratios are invertible:
np.exp(logA_on_B.mean()) # 2.4213410747400514
1 / np.exp(logB_on_A.mean()) # 2.421341074740052
2.421341074740052
The logratios also have the same variance:
(np.std(logA_on_B) / logA_on_B.mean()) ** 2 # 0.36598579018127086
(np.std(logB_on_A) / logB_on_A.mean()) ** 2 # 0.36598579018127086
0.36598579018127086
These peculiarities result from incorrect assumptions regarding the distribution of the data: ratios of compositional components are typically lognormally distributed, rather than normally distributed, and the compositional components themselves commonly have a Poisson distribution . These distributions contrast significantly with the normal distribution at the core of most statistical tests. We can compare distributions with similar means and variances but different forms, and note that the normal distribution has one immediate failure, in that it has non-zero probability density below 0, and we know that you can’t have negative atoms!
from scipy.stats import norm, poisson, lognorm
means = [[10, 10], [10, 20], [20, 100], [1000, 50]]
fig, ax = plt.subplots(len(means), 4, figsize=(11, 8))
ax[0, 0].set_title("A")
ax[0, 1].set_title("B")
ax[0, 2].set_title("Normal Fit to B/A")
ax[0, 3].set_title("Lognormal Fit to B/A")
ax[-1, 0].set_xlabel("A")
ax[-1, 1].set_xlabel("B")
ax[-1, 2].set_xlabel("B/A")
ax[-1, 3].set_xlabel("B/A")
for ix, (m1, m2) in enumerate(means):
p1, p2 = poisson(mu=m1), poisson(mu=m2)
y1, y2 = p1.rvs(2000), p2.rvs(2000)
ratios = y2[y1 > 0] / y1[y1 > 0]
y1min, y1max = y1.min(), y1.max()
y2min, y2max = y2.min(), y2.max()
ax[ix, 0].hist(
y1,
color="0.5",
alpha=0.6,
label="A",
bins=np.linspace(y1min - 0.5, y1max + 0.5, (y1max - y1min) + 1),
)
ax[ix, 1].hist(
y2,
color="0.5",
alpha=0.6,
label="B",
bins=np.linspace(y2min - 0.5, y2max + 0.5, (y2max - y2min) + 1),
)
# normal distribution fit
H, binedges, patches = ax[ix, 2].hist(
ratios, color="Purple", alpha=0.6, label="Ratios", bins=100
)
loc, scale = norm.fit(ratios, loc=0)
pdf = norm.pdf(binedges, loc, scale)
twin2 = ax[ix, 2].twinx()
twin2.set_ylim(0, 1.1 * np.max(pdf))
twin2.plot(binedges, pdf, color="k", ls="--", label="Normal Fit")
# log-normal distribution fit
H, binedges, patches = ax[ix, 3].hist(
ratios, color="Green", alpha=0.6, label="Ratios", bins=100
)
s, loc, scale = lognorm.fit(ratios, loc=0)
pdf = lognorm.pdf(binedges, s, loc, scale)
twin3 = ax[ix, 3].twinx()
twin3.set_ylim(0, 1.1 * np.max(pdf))
twin3.plot(binedges, pdf, color="k", ls="--", label="Lognormal Fit")
for a in [*ax[ix, :], twin2, twin3]:
a.set_yticks([])
plt.tight_layout()
The form of these distributions is a reflection of the fact that geochemical data is at is core a measure of relative quantities of atoms. Quantities of atoms have discrete distributions (i.e. you can have precisely 0, 1 or 6.02 x 10^23 atoms, but 1.23 atoms is not a sensible state of affairs); if you were to count them in a shiny machine, the amount of atoms you might measure over a given period will have a Poisson distribution. If you measure two components, the probability density distribution of the ratio is well approximated by a lognormal distribution (note this doesn’t consider inherent covariance):
from pyrolite.util.plot.axes import share_axes, subaxes
from pyrolite.util.distributions import lognorm_to_norm, norm_to_lognorm
# starting from a normal distribution, then creating similar non-normal distributions
mean, sd = 2.5, 1.5 #
logmu, logs = norm_to_lognorm(mean, sd) # parameters for equival
normrv = norm(loc=mean, scale=sd)
lognormrv = lognorm(s=logs, scale=logmu)
poissonrv = poisson(mu=mean)
We can visualise the similarities and differences between these distributions:
fig, ax = plt.subplots(2, 3, figsize=(8, 4))
ax = ax.flat
for a in ax:
a.subax = subaxes(a, side="bottom")
share_axes(ax[:3], which="x")
share_axes(ax[3:], which="x")
ax[0].set_xlim(-2, 10)
ax[3].set_xscale("log")
ax[3].set_xlim(0.1, 10)
for a in ax:
a.axvline(0, color="k", lw=0.5, ls="--")
# xs at which to evaluate the pdfs
x = np.linspace(-5, 15.0, 1001)
for ix, dist in enumerate([normrv, lognormrv, poissonrv]):
_xs = dist.rvs(size=10000) # random sample
_ys = -0.05 + np.random.randn(10000) / 100 # random offsets for visualisation
for a in [ax[ix], ax[ix + 3]]:
a.annotate(
"mean={:.2f}, var={:.2f}".format(np.mean(_xs), np.var(_xs)),
xy=(0.05, 1.05),
ha="left",
va="bottom",
xycoords=a.transAxes,
)
a.subax.scatter(_xs, _ys, s=2, color="k", alpha=0.01)
if dist != poissonrv: # cont. distribution
a.plot(x, dist.pdf(x), color="Purple", alpha=0.6, label="pdf")
else: # discrete distribution
a.vlines(
x[x >= 0],
0,
dist.pmf(x[x >= 0]),
color="Purple",
alpha=0.6,
label="pmf",
)
fig.suptitle("Data Distributions: Normal, Lognormal, Poisson", y=1.1)
plt.tight_layout()
Accounting for these inherent features of geochemical data will allow you to
accurately estimate means and variances, and from this enables the use of
standardised statistical measures - as long as you’re log-transforming your data.
When performing multivariate analysis, use log-ratio transformations (including the
additive logratio alr(), centred logratio
clr() and isometric logratio
ilr()). In this case, the logratio-mean is implemented for
you:
from pyrolite.comp.codata import logratiomean
import itertools
fig, ax = plt.subplots(2, 2, figsize=(12, 12), subplot_kw=dict(projection="ternary"))
ax = ax.flat
for columns, a in zip(itertools.combinations(["A", "B", "C", "D"], 3), ax):
columns = list(columns)
df.loc[:, columns].pyroplot.scatter(
ax=a, color="k", marker=".", label=df.attrs["name"], no_ticks=True
)
df.mean().loc[columns].pyroplot.scatter(
ax=a,
edgecolors="red",
linewidths=2,
c="none",
s=50,
label="Arithmetic Mean",
no_ticks=True,
)
logratiomean(df.loc[:, columns]).pyroplot.scatter(
ax=a,
edgecolors="k",
linewidths=2,
c="none",
s=50,
label="Geometric Mean",
axlabels=True,
no_ticks=True,
)
a.legend(loc=(0.8, 0.5))
See also
- Examples:
- Tutorials:
- Modules and Functions:
Total running time of the script: (0 minutes 18.705 seconds)
Utility Examples
pyrolite includes a range of utilities for everything from dealing with the web to plotting, synthetic data and machine learning. While most of these are used as part of the core functions of pyrolite, you may also find other uses for them, and this section provides some simple examples for some of these.
Using Manifolds for Visualisation
Visualisation of data which has high dimensionality is challenging, and one solution
is to provide visualisations in low-dimension representations of the space actually
spanned by the data. Here we provide an example of visualisation of classification
predictions and relative prediction certainty (using entropy across predicted
probability for each individual class) for a toy sklearn dataset.
import matplotlib.pyplot as plt
import numpy as np
import sklearn.datasets
from pyrolite.util.plot import DEFAULT_DISC_COLORMAP
from pyrolite.util.skl.pipeline import SVC_pipeline
from pyrolite.util.skl.vis import plot_mapping
np.random.seed(82)
wine = sklearn.datasets.load_wine()
data, target = wine["data"], wine["target"]
# data = data[:, np.random.random(data.shape[1]) > 0.4] # randomly remove fraction of dimensionality
svc = SVC_pipeline(probability=True)
gs = svc.fit(data, target)
Fitting 10 folds for each of 1 candidates, totalling 10 fits
fig, ax = plt.subplots(1, 2, figsize=(8, 4))
a, tfm, mapped = plot_mapping(data, gs.best_estimator_, ax=ax[1], s=50, init="pca")
ax[0].scatter(*mapped.T, c=DEFAULT_DISC_COLORMAP(gs.predict(data)), s=50)
ax[0].set_title("Predicted Classes")
ax[1].set_title("With Relative Certainty")
for a in ax:
a.set_xticks([])
a.set_yticks([])
Total running time of the script: (0 minutes 3.162 seconds)
TAS Classifier
Some simple discrimination methods are implemented, including the Total Alkali-Silica (TAS) classification.
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from pyrolite.util.classification import TAS
from pyrolite.util.synthetic import normal_frame, random_cov_matrix
We’ll first generate some synthetic data to play with:
df = (
normal_frame(
columns=["SiO2", "Na2O", "K2O", "Al2O3"],
mean=[0.5, 0.04, 0.05, 0.4],
size=100,
seed=49,
)
* 100
)
df.head(3)
We can visualise how this chemistry corresponds to the TAS diagram:
df["Na2O + K2O"] = df["Na2O"] + df["K2O"]
cm = TAS()
fig, ax = plt.subplots(1)
cm.add_to_axes(ax, alpha=0.5, linewidth=0.5, zorder=-1, add_labels=True)
df[["SiO2", "Na2O + K2O"]].pyroplot.scatter(ax=ax, c="k", alpha=0.2, axlabels=False)
plt.show()
We can now classify this data according to the fields of the TAS diagram, and add this as a column to the dataframe. Similarly, we can extract which rock names the TAS fields correspond to:
df["TAS"] = cm.predict(df)
df["Rocknames"] = df.TAS.apply(lambda x: cm.fields.get(x, {"name": None})["name"])
df["Rocknames"].sample(10) # randomly check 10 sample rocknames
78 [Phonotephrite, Foid Monzodiorite]
2 [Phonotephrite, Foid Monzodiorite]
56 [Phonotephrite, Foid Monzodiorite]
41 [Phonotephrite, Foid Monzodiorite]
93 [Phonotephrite, Foid Monzodiorite]
60 [Phonotephrite, Foid Monzodiorite]
61 [Phonotephrite, Foid Monzodiorite]
47 [Phonotephrite, Foid Monzodiorite]
4 [Trachy-\nandesite, Monzonite]
12 [Trachy-\nandesite, Monzonite]
Name: Rocknames, dtype: object
We could now take the TAS classes and use them to colorize our points for plotting on the TAS diagram, or more likely, on another plot. Here the relationship to the TAS diagram is illustrated, coloring also the populated fields:
fig, ax = plt.subplots(1)
cm.add_to_axes(ax, alpha=0.5, linewidth=0.0, zorder=-2, add_labels=False,
which_ids=np.unique(df["TAS"]), fill=True, facecolor=[0.9, 0.8, 1.0])
cm.add_to_axes(ax, alpha=0.5, linewidth=0.5, zorder=-1, add_labels=True)
df[["SiO2", "Na2O + K2O"]].pyroplot.scatter(ax=ax, c=df["TAS"], alpha=0.7, axlabels=False)
<Axes: xlabel='SiO$_2$', ylabel='Na$_2$O + K$_2$O'>
Variations of the Diagram
To use a different variation of the TAS diagram, you can pass the relevant keyword
which_model allowing you to access the other available variants.
Currently, the Le Bas/Le Maitre alternative and a T1-T2 combined variant of it are available as alternatives to the Middlemost version. Each of these can be used as a classifier model as for the default above.
fig, ax = plt.subplots(1, 3, figsize=(20, 4))
for a, model in zip(ax, ["Middlemost", "LeMaitre", "LeMaitreCombined"]):
a.set_title(model if model is not None else "")
cm = TAS(which_model=model)
cm.add_to_axes(a, alpha=0.5, linewidth=0.5, add_labels=True)
plt.show()
References & Citation
For a few references on the TAS diagram as used here:
Middlemost, E. A. K. (1994).Naming materials in the magma/igneous rock system. Earth-Science Reviews, 37(3), 215–224. doi: 10.1016/0012-8252(94)90029-9.
Le Bas, M.J., Le Maitre, R.W., Woolley, A.R. (1992). The construction of the Total Alkali-Silica chemical classification of volcanic rocks. Mineralogy and Petrology 46, 1–22. doi: 110.1007/BF01160698.
Le Maitre, R.W. (2002). Igneous Rocks: A Classification and Glossary of Terms : Recommendations of International Union of Geological ciences Subcommission on the Systematics of Igneous Rocks. Cambridge University Press, 236pp. doi: 10.1017/CBO9780511535581.
Total running time of the script: (0 minutes 1.330 seconds)
Geological Timescale
pyrolite includes a simple geological timescale, based on a recent verion
of the International Chronostratigraphic Chart 1. The
Timescale class can be used to look up names for
specific geological ages, to look up times for known geological age names
and to access a reference table for all of these.
- 1
Cohen, K.M., Finney, S.C., Gibbard, P.L., Fan, J.-X., 2013. The ICS International Chronostratigraphic Chart. Episodes 36, 199–204.
First we’ll create a timescale:
from pyrolite.util.time import Timescale
ts = Timescale()
From this we can look up the names of ages (in million years, or Ma):
ts.named_age(1212.1)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/util/time.py:261: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
max([ix for (ix, r) in enumerate(counts) if r == counts[0]])
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/util/time.py:54: FutureWarning: Series.__getitem__ treating keys as positions is deprecated. In a future version, integer keys will always be treated as labels (consistent with DataFrame behavior). To access a value by position, use `ser.iloc[pos]`
nameguess = agenamelist[-1]
'Ectasian'
As geological age names are hierarchical, the name you give an age depends on what level you’re looking at. By default, the timescale will return the most specific non-null level. The levels accessible within the timescale are listed as an attribute:
ts.levels
['Eon', 'Era', 'Period', 'Superepoch', 'Epoch', 'Age']
These can be used to refine the output names to your desired level of specificity (noting that for some ages, the levels which are accessible can differ; see the chart):
ts.named_age(1212.1, level="Epoch")
'Ectasian'
The timescale can also do the inverse for you, and return the timing information for a given named age:
ts.text2age("Holocene")
(0.0117, 0.0)
We can use this to create a simple template to visualise the geological timescale:
import pandas as pd
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, figsize=(5, 10))
for ix, level in enumerate(ts.levels):
ldf = ts.data.loc[ts.data.Level == level, :]
for pix, period in ldf.iterrows():
ax.bar(
ix,
period.Start - period.End,
facecolor=period.Color,
bottom=period.End,
width=1,
edgecolor="k",
)
ax.set_xticks(range(len(ts.levels)))
ax.set_xticklabels(ts.levels, rotation=60)
ax.xaxis.set_ticks_position("top")
ax.set_ylabel("Age (Ma)")
ax.invert_yaxis()
This doesn’t quite look like the geological timescale you may be used to. We can improve
on the output somewhat with a bit of customisation for the positioning. Notably, this is
less readable, but produces something closer to what we’re after. Some of this may soon
be integrated as a Timescale method, if there’s interest.
import numpy as np
from matplotlib.patches import Rectangle
# first let's set up some x-limits for the different timescale levels
xlims = {
"Eon": (0, 1),
"Era": (1, 2),
"Period": (2, 3),
"Superepoch": (3, 4),
"Epoch": (3, 5),
"Age": (5, 7),
}
fig, ax = plt.subplots(1, figsize=(4, 10))
for ix, level in enumerate(ts.levels[::-1]):
ldf = ts.data.loc[ts.data.Level == level, :]
for pix, period in ldf.iterrows():
left, right = xlims[level]
if ix != len(ts.levels) - 1:
time = np.mean(ts.text2age(period.Name))
general = None
_ix = ix
while general is None:
try:
general = ts.named_age(time, level=ts.levels[::-1][_ix + 1])
except:
pass
_ix += 1
_l, _r = xlims[ts.levels[::-1][_ix]]
if _r > left:
left = _r
rect = Rectangle(
(left, period.End),
right - left,
period.Start - period.End,
facecolor=period.Color,
edgecolor="k",
)
ax.add_artist(rect)
ax.set_xticks([np.mean(xlims[lvl]) for lvl in ts.levels])
ax.set_xticklabels(ts.levels, rotation=60)
ax.xaxis.set_ticks_position("top")
ax.set_xlim(0, 7)
ax.set_ylabel("Age (Ma)")
ax.set_ylim(500, 0)
(500.0, 0.0)
Total running time of the script: (0 minutes 2.035 seconds)
Tutorials
This page is home to longer examples which incorporate multiple components of
pyrolite or provide examples of how to integrate these into your own workflows.
Note
This page is a work in progress. Feel free to request tutorials or examples with a feature request.
Formatting and Cleaning Up Plots
Note
This tutorial is a work in progress and will be gradually updated.
In this tutorial we will illustrate some straightfoward formatting for your plots which
will allow for greater customisation as needed. As pyrolite heavily uses
and exposes the API of matplotlib for the visualisation components
(and also mpltern for ternary diagrams), you should also check out their
documentation pages for more in-depth guides, examples and API documentation.
First let’s pull in a simple dataset to use throughout these examples:
from pyrolite.util.synthetic import normal_frame
df = normal_frame(columns=["SiO2", "CaO", "MgO", "Al2O3", "TiO2", "27Al", "d11B"])
Basic Figure and Axes Settings
matplotlib makes it relatively straightfoward to customise most settings for
your figures and axes. These settings can be defined at creation (e.g. in a call to
subplots()), or they can be defined after you’ve created an
axis (with the methods ax.set_<parameter>()). For example:
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1)
ax.set_xlabel("My X Axis Label")
ax.set_title("My Axis Title", fontsize=12)
ax.set_yscale("log")
ax.set_xlim((0.5, 10))
fig.suptitle("My Figure Title", fontsize=15)
plt.show()
You can use a single method to set most of these things:
set(). For example:
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1)
ax.set(yscale="log", xlim=(0, 1), ylabel="YAxis", xlabel="XAxis")
plt.show()
Labels and Text
matplotlib enables you to use \(\TeX\) within all text elements, including
labels and annotations. This can be leveraged for more complex formatting,
incorporating math and symbols into your plots. Check out the mod:matplotlib
tutorial, and
for more on working with text generally in matplotlib, check out the
relevant tutorials gallery.
The ability to use TeX syntax in matplotlib text objects can also be used
for typsetting, like for subscripts and superscripts. This is particularly relevant
for geochemical oxides labels (e.g. Al2O3, which would ideally be rendered as
\(Al_2O_3\)) and isotopes (e.g. d11B, which should be \(\delta^{11}B\)).
At the moment, pyrolite won’t do this for you, so you may want to adjust the labelling
after you’ve made them. For example:
import pyrolite.plot
import matplotlib.pyplot as plt
fig, ax = plt.subplots(2, 1)
df[["Al2O3", "TiO2"]].pyroplot.scatter(ax=ax[0])
ax[0].set_xlabel("Al$_2$O$_3$")
ax[0].set_ylabel("TiO$_2$")
df[["27Al", "d11B"]].pyroplot.scatter(ax=ax[1])
ax[1].set_xlabel("$^{27}$Al")
ax[1].set_ylabel("$\delta^{11}$B")
plt.tight_layout() # rearrange the plots to fit nicely together
plt.show()
Sharing Axes
If you’re building figures which have variables which are re-used, you’ll typically
want to ‘share’ them between your axes. The matplotlib.pyplot API makes
this easy for when you want to share among all the axes as your create them:
import matplotlib.pyplot as plt
fig, ax = plt.subplots(2, 2, sharex=True, sharey=True)
plt.show()
However, if you want to share axes in a way which is less standard, it can be
difficult to set up using this function. pyrolite has a utility function
which can be used to share axes after they’re created in slightly more arbitrary
ways. For example, imagine we wanted to share the first and third x-axes, and the
first three y-axes, you could use:
import matplotlib.pyplot as plt
from pyrolite.util.plot.axes import share_axes
fig, ax = plt.subplots(2, 2)
ax = ax.flat # turn the (2,2) array of axes into one flat axes with shape (4,)
share_axes([ax[0], ax[2]], which="x") # share x-axes for 0, 2
share_axes(ax[0:3], which="y") # share y-axes for 0, 1, 2
ax[0].set_xlim((0, 10))
ax[1].set_ylim((-5, 5))
plt.show()
Legends
While it’s simple to set up basic legends in maplotlib (see the docs for
matplotlib.axes.Axes.legend()), often you’ll want to customise
your legends to fit nicely within your figures. Here we’ll create a few
synthetic datasets, add them to a figure and create the default legend:
import pyrolite.plot
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1)
for i in range(3):
sample_data = normal_frame(columns=["CaO", "MgO", "FeO"]) # a new random sample
sample_data[["CaO", "MgO"]].pyroplot.scatter(ax=ax, label="Sample {:d}".format(i))
ax.legend()
plt.show()
On many of the pyrolite examples, you’ll find legends formatted along the
lines of the following to clean them up a little (these are the default styles):
ax.legend(
facecolor=None, # have a transparent legend background
frameon=False, # remove the legend frame
bbox_to_anchor=(1, 1), # anchor legend's corner to the axes' top-right
loc="upper left", # use the upper left corner for the anchor
)
plt.show()
Check out the matplotlib
legend guide
for more.
Ternary Plots
The ternary plots in pyrolite are generated using mpltern, and while
the syntax is very similar to the matplotlib API, as we have three axes
to deal with sometimes things are little different. Here we demonstrate how to
complete some common tasks, but you should check out the mpltern documentation
if you want to dig deeper into customising your ternary diagrams (e.g. see the
example gallery),
which these examples were developed from.
One of the key things to note in mpltern is that you have top, left and
right axes.
Ternary Plot Axes Labels
Labelling ternary axes is done similarly to in matplotlib, but using the
axes prefixes t, l and r for top, left and right axes, respectively:
import pyrolite.plot
import matplotlib.pyplot as plt
ax = df[["CaO", "MgO", "Al2O3"]].pyroplot.scatter()
ax.set_tlabel("Top")
ax.set_llabel("Left")
ax.set_rlabel("Right")
plt.show()
Ternary Plot Grids
To add a simple grid to your ternary plot, you can use
grid():
import pyrolite.plot
import matplotlib.pyplot as plt
ax = df[["CaO", "MgO", "Al2O3"]].pyroplot.scatter()
ax.grid()
plt.show()
With this method, you can also specify an axis, which tickmarks you want to use for the grid (‘major’, ‘minor’ or ‘both’) and a linestyle:
import pyrolite.plot
import matplotlib.pyplot as plt
ax = df[["CaO", "MgO", "Al2O3"]].pyroplot.scatter()
ax.grid(axis="r", which="both", linestyle="--")
plt.show()
Ternary Plot Limits
To focus on a specific area, you can reset the limits of your ternary axes with
set_ternary_lim().
Also check out the mpltern
inset axes example
if you’re after ways to focus on specific regions.
import pyrolite.plot
import matplotlib.pyplot as plt
ax = df[["CaO", "MgO", "Al2O3"]].pyroplot.scatter()
ax.set_ternary_lim(
0.1, 0.5, 0.2, 0.6, 0.3, 0.7 # tmin # tmax # lmin # lmax # rmin # rmax
)
plt.show()
Total running time of the script: (0 minutes 16.165 seconds)
Making the Logo
Having some funky ellipses in a simplex inspired some interest when I put the logo together for pyrolite, so I put together a cleaned-up example of how you can create these kinds of plots for your own data. These examples illustrate different methods to show distribution of (homogeneous, or near so) compositional data for exploratory analysis.
import matplotlib
import matplotlib.cm
import matplotlib.colors
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import pyrolite.plot
from pyrolite.comp.codata import *
from pyrolite.util.plot.helpers import plot_pca_vectors, plot_stdev_ellipses
from pyrolite.util.skl.transform import ALRTransform, ILRTransform
from pyrolite.util.synthetic import random_composition
np.random.seed(82)
# ignore sphinx_gallery warnings
import warnings
warnings.filterwarnings("ignore", "Matplotlib is currently using agg")
First we choose some colors, create some log-distributed synthetic data. Here I’ve
generated a synthetic dataset with four samples having means equidistant from the
log-space centre and with varying covariance. This should illustrate the spatial
warping of the simplex nicely. Additionally, I chose a log-transform here to go
from and to compositional space (ILRTransform, which uses
the isometric log-ratio function ilr()). Choosing
another transform will change the distortion observed in the simplex slightly.
This synthetic dataset is added into a DataFrame for convenient access
to plotting functions via the pandas API defined in pyrolite.plot.pyroplot.
t10b3 = [ # tableau 10 colorblind safe colors, a selection of 4
(0, 107, 164),
(171, 171, 171),
(89, 89, 89),
(95, 158, 209),
]
t10b3 = [(r / 255.0, g / 255.0, b / 255.0) for r, g, b in t10b3]
d = 1.0 # distance from centre
sig = 0.1 # scale for variance
# means for logspace (D=2)
means = np.array(np.meshgrid([-1, 1], [-1, 1])).T.reshape(-1, 2) * d
# means = np.array([(-d, -d), (d, -d), (-d, d), (d, d)])
covs = ( # covariance for logspace (D=2)
np.array(
[
[[1, 0], [0, 1]],
[[0.5, 0.15], [0.15, 0.5]],
[[1.5, -1], [-1, 1.5]],
[[1.2, -0.6], [-0.6, 1.2]],
]
)
* sig
)
means = ILRTransform().inverse_transform(means) # compositional means (D=3)
size = 2000 # logo @ 10000
pts = [random_composition(mean=M, cov=C, size=size) for M, C in zip(means, covs)]
T = ILRTransform()
to_log = T.transform
from_log = T.inverse_transform
df = pd.DataFrame(np.vstack(pts))
df.columns = ["SiO2", "MgO", "FeO"]
df["Sample"] = np.repeat(np.arange(df.columns.size + 1), size).flatten()
chem = ["MgO", "SiO2", "FeO"]
fig, ax = plt.subplots(
2, 2, figsize=(10, 10 * np.sqrt(3) / 2), subplot_kw=dict(projection="ternary")
)
ax = ax.flat
_ = [[x.set_ticks([]) for x in [a.taxis, a.laxis, a.raxis]] for a in ax]
First, let’s look at the synthetic data itself in the ternary space:
kwargs = dict(alpha=0.2, s=3, no_ticks=True, axlabels=False)
for ix, sample in enumerate(df.Sample.unique()):
comp = df.query("Sample == {}".format(sample))
comp.loc[:, chem].pyroplot.scatter(ax=ax[0], c=t10b3[ix], **kwargs)
plt.show()
We can take the mean and covariance in log-space to create covariance ellipses and vectors using principal component analysis:
kwargs = dict(ax=ax[1], transform=from_log, nstds=3)
ax[1].set_title("Covariance Ellipses and PCA Vectors")
for ix, sample in enumerate(df.Sample.unique()):
comp = df.query("Sample == {}".format(sample))
tcomp = to_log(comp.loc[:, chem])
plot_stdev_ellipses(tcomp.values, color=t10b3[ix], resolution=1000, **kwargs)
plot_pca_vectors(tcomp.values, ls="-", lw=0.5, color="k", **kwargs)
plt.show()
We can also look at data density (here using kernel density estimation) in logratio-space:
kwargs = dict(ax=ax[-2], bins=100, axlabels=False)
ax[-2].set_title("Individual Density, with Contours")
for ix, sample in enumerate(df.Sample.unique()):
comp = df.query("Sample == {}".format(sample))
comp.loc[:, chem].pyroplot.density(cmap="Blues", vmin=0.05, **kwargs)
comp.loc[:, chem].pyroplot.density(
contours=[0.68, 0.95],
cmap="Blues_r",
contour_labels={0.68: "σ", 0.95: "2σ"},
**kwargs,
)
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/comp/codata.py:177: RuntimeWarning: invalid value encountered in log
Y = np.log(X) # Log operation
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/comp/codata.py:177: RuntimeWarning: invalid value encountered in log
Y = np.log(X) # Log operation
We can also do this for individual samples, and estimate percentile contours:
kwargs = dict(ax=ax[-1], axlabels=False)
ax[-1].set_title("Overall Density")
df.loc[:, chem].pyroplot.density(bins=100, cmap="Greys", **kwargs)
plt.show()
for a in ax:
a.set_aspect("equal")
a.patch.set_visible(False)
plt.show()
Total running time of the script: (0 minutes 11.266 seconds)
One Way to Do Ternary Heatmaps
There are multiple ways you can acheive ternary heatmaps, but those based on the cartesian axes (e.g. a regularly spaced rectangular grid, or even a regularly spaced triangular grid) can result in difficulties and data misrepresentation.
Here we illustrate how the ternary heatmaps for pyrolite are constructed using an irregualr triangulated grid and log transforms, and how this avoids some of the potential issues of the methods mentioned above.
Let’s first get some data to deal with. mpltern has a conventient dataset
which we can use here:
import numpy as np
import pandas as pd
from mpltern.ternary.datasets import get_scatter_points
np.random.seed(43)
df = pd.DataFrame(np.array([*get_scatter_points(n=80)]).T, columns=["A", "B", "C"])
df = df.loc[(df > 0.1).all(axis=1), :]
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/envs/main/lib/python3.10/site-packages/mpltern/ternary/datasets.py:9: UserWarning: `mpltern.ternary.datasets.py` has been moved to `mpltern.datasets.py` and will be removed from the present directory in mpltern 0.6.0.
warnings.warn(msg)
From this dataset we’ll generate a
ternary_heatmap(), which is the basis
for ternary density diagrams via density():
from pyrolite.comp.codata import ILR, inverse_ILR
from pyrolite.plot.density.ternary import ternary_heatmap
coords, H, data = ternary_heatmap(
df.values,
bins=10,
mode="density",
remove_background=True,
transform=ILR,
inverse_transform=inverse_ILR,
grid_border_frac=0.2,
)
This function returns more than just the coordinates and histogram/density estimate, which will come in handy for exploring how it came together. The data variable here is a dictonary with contains the grids and coordiantes used to construct the histogram/density diagram. We can use these to show how the ternary log-grid is constructed, and then transformed back to ternary space before being triangulated and interpoalted for the ternary heatmap:
import matplotlib.pyplot as plt
import pyrolite.plot
from pyrolite.util.math import flattengrid
from pyrolite.util.plot.axes import axes_to_ternary, share_axes
fig, ax = plt.subplots(3, 2, figsize=(6, 9))
ax = ax.flat
share_axes([ax[1], ax[2], ax[3]])
ax = axes_to_ternary([ax[0], ax[4], ax[5]])
ax[0].set_title("data", y=1.2)
df.pyroplot.scatter(ax=ax[0], c="k", alpha=0.1)
ax[0].scatter(*data["tern_bound_points"].T, c="k")
ax[1].set_title("transformed data", y=1.2)
ax[1].scatter(*data["tfm_tern_bound_points"].T, c="k")
ax[1].scatter(*data["grid_transform"](df.values).T, c="k", alpha=0.1)
ax[2].set_title("log grid", y=1.2)
ax[2].scatter(*flattengrid(data["tfm_centres"]).T, c="k", marker=".", s=5)
ax[2].scatter(*flattengrid(data["tfm_edges"]).T, c="k", marker=".", s=2)
ax[2].scatter(*data["tfm_tern_bound_points"].T, c="k")
ax[3].set_title("log-grid heatmap", y=1.2)
ax[3].pcolormesh(*data["tfm_edges"], H)
ax[3].scatter(*data["grid_transform"](df.values).T, c="white", alpha=0.8, s=1)
ax[4].set_title("ternary log-grid", y=1.2)
ax[4].scatter(*data["tern_centres"].T, c="k", marker=".", s=5)
ax[4].scatter(*data["tern_edges"].T, c="k", marker=".", s=2)
ax[4].scatter(*data["tern_bound_points"].T, c="k")
ax[5].set_title("ternary heatmap", y=1.2)
ax[5].tripcolor(*coords.T, H.flatten())
ax[5].scatter(*data["tern_bound_points"].T, c="k")
plt.tight_layout()
plt.close("all") # let's save some memory..
We can see how this works almost exactly the same for the histograms:
coords, H, data = ternary_heatmap(
df.values,
bins=10,
mode="histogram",
remove_background=True,
transform=ILR,
inverse_transform=inverse_ILR,
grid_border_frac=0.2,
)
fig, ax = plt.subplots(3, 2, figsize=(6, 9))
ax = ax.flat
share_axes([ax[1], ax[2], ax[3]])
ax = axes_to_ternary([ax[0], ax[4], ax[5]])
ax[0].set_title("data", y=1.2)
df.pyroplot.scatter(ax=ax[0], c="k", alpha=0.1)
ax[0].scatter(*data["tern_bound_points"].T, c="k")
ax[1].set_title("transformed data", y=1.2)
ax[1].scatter(*data["tfm_tern_bound_points"].T, c="k")
ax[1].scatter(*data["grid_transform"](df.values).T, c="k", alpha=0.1)
ax[2].set_title("log grid", y=1.2)
ax[2].scatter(*flattengrid(data["tfm_centres"]).T, c="k", marker=".", s=5)
ax[2].scatter(*flattengrid(data["tfm_edges"]).T, c="k", marker=".", s=2)
ax[2].scatter(*data["tfm_tern_bound_points"].T, c="k")
ax[3].set_title("log-grid heatmap", y=1.2)
ax[3].pcolormesh(*data["tfm_edges"], H)
ax[3].scatter(*data["grid_transform"](df.values).T, c="white", alpha=0.8, s=1)
ax[4].set_title("ternary log-grid", y=1.2)
ax[4].scatter(*data["tern_centres"].T, c="k", marker=".", s=5)
ax[4].scatter(*data["tern_edges"].T, c="k", marker=".", s=2)
ax[4].scatter(*data["tern_bound_points"].T, c="k")
ax[5].set_title("ternary heatmap", y=1.2)
ax[5].tripcolor(*coords.T, H.flatten())
ax[5].scatter(*data["tern_bound_points"].T, c="k")
plt.tight_layout()
Total running time of the script: (0 minutes 6.755 seconds)
Citation
Note
pyrolite began as a personal project, but as the project develops
there are likely to be other contributors. Check the
Contributors list and add major contributors as
authors.
If you use pyrolite extensively for your research, citation of the software
would be particularly appreciated. It helps quantify the impact of the project
(assisting those contributing through paid and volunteer work), and is one way to get
the message out and help build the pyrolite community.
pyrolite has been published in the Journal of Open Source Software (JOSS),
and generally this paper is what you should cite. This paper was published in reference
to pyrolite v0.2.7; if you’re using a different version please note that in the
citation.
While the exact format of your citation will vary with wherever you’re publishing, it should take the general form:
Williams et al., (2020). pyrolite: Python for geochemistry. Journal of Open Source Software, 5(50), 2314, doi: 10.21105/joss.02314
Or, if you wish to cite a specific version of the archive:
Williams et al. (2024). pyrolite v 0.3.5, Zenodo, doi:10.5281/zenodo.2545106
If you’re after a BibTeX citation for pyrolite, I’ve added one below.
@article{Williams2020,
title = {pyrolite: Python for geochemistry},
author = {Morgan J. Williams and
Louise Schoneveld and
Yajing Mao and
Jens Klump and
Justin Gosses and
Hayden Dalton and
Adam Bath and
Steve Barnes},
year = {2020},
journal = {Journal of Open Source Software}
doi = {10.21105/joss.02314},
url = {https://doi.org/10.21105/joss.02314},
publisher = {The Open Journal},
volume = {5},
number = {50},
pages = {2314},
}
If you’re using pyrolite’s implementation of lambdas, please consider
citing a more recent publication directly related to this:
Anenburg, M., & Williams, M. J. (2021). Quantifying the Tetrad Effect, Shape Components, and Ce–Eu–Gd Anomalies in Rare Earth Element Patterns. Mathematical Geosciences. doi: 10.1007/s11004-021-09959-5
Or, if you’re using BibTeX:
@article{Anenburg_Williams_2021,
title={Quantifying the Tetrad Effect, Shape Components,
and Ce–Eu–Gd Anomalies in Rare Earth Element Patterns},
author={Anenburg, Michael and Williams, Morgan J.},
year={2021},
journal={Mathematical Geosciences},
doi={10.1007/s11004-021-09959-5},
url={https://doi.org/10.1007/s11004-021-09959-5},
ISSN={1874-8953},
month={Jul}
}
Development
Contributing
Development Installation
To access and use the development version, you can either clone the repository or install via pip directly from GitHub:
pip install --user git+https://github.com/morganjwilliams/pyrolite.git@develop#egg=pyrolite
Tests
If you clone the source repository, unit tests can be run using pytest from the root
directory after installation with development dependencies
(pip install -e .[dev]):
python setup.py test
If instead you only want to test a subset, you can call pytest directly from
within the pyrolite repository:
pytest ./test/<path to test or test folder>
Changelog
All notable changes to this project will be documented here.
Development
Note
Changes noted in this subsection are to be released in the next version. If you’re keen to check something out before its released, you can use a development install .
0.3.5
New Contributor: Malte Mues
New Contributor: Bob Myhill
Bugfix: Fixed a bug with the index structure for the documentation example galleries.
Expanded test suite for a text coverage bump.
Started testing against and supporting Python 3.12.
pyrolite.geochem
PR Merged: Malte Mues contributed a PR to allow series and dataframes with Pm data to be used with the pyrolite.pyrochem REE accessors (i.e., the column will not be dropped if it exists; #100). This PR aslo included an update for the pyrolite.util.lambdas functions to be more flexible in terms of access, including as indvidual series (allowing performant usage with pandarallel).
Updates to pyrolite.pyrochem accessors to be more flexible, generally allowing usage with both DataFrame and Series objects (e.g. df.pyrochem.REE, ser.pyrochem.REE).
pyrolite.plot
PR Merged: Bob Myhill contributed a series of pull requests to fix formatting of TAS diagram labels (#91), update the TAS field names in the JSON template (#92), improve the formatting and scaling of TAS diagrams. (#93), add an option to add field labels in the visual centre of polygons (rather than the ‘centroid’; #94), update some usage of
matplotlib(#96), and allow selective plotting of indiviudal fields when adding a classification diagram to axes (#98).
pyrolite.mineral
Suppressed
pandasperformance warnings related to sequential construction ofpandas.DataFrame`s in :func:`pyrolite.mineral.normative.CIPW_norm.
0.3.4
Bugfix: Tom Buckle contributed a PR with some minor bugfixes for the CIPW Norm (#87).
Various maintenance updates, including migrating the package to use pyproject.toml.
0.3.3
New Contributor: Sarah Shi
New Contributor: Ondrej Lexa
Bugfix: Updated docs builds to be compatible with recent versions of sphinx-gallery.
Bugfix: Updated some
pandasassignment, aggregation and similar operations to be compatible with more recent versions of Pandas.Added explicit Python 3.10 and 3.11 support.
Removed Python 3.7 support (now end of life).
pyrolite.mineral
PR Merged: Added an option to get expanded outputs for the CIPW Norm (from Tom Buckle; #80).
Bugfix: Fixes and updated tests for CIPW Norm outputs.
pyrolite.plot
PR Merged: Sarah Shi contributed a PR to add variations on the TAS diagram from Le Maitre ( #79). These can be accessed by providing a
which_modelkeyword argument to theTASconstructor (or plot template).PR Merged: Ondrej Lexa contributed a PR to add sandstone bulk geochemistry discrimination diagrams (
Pettijohn,Herron; #82).Bugfix: Fixed issue with handling vmin and vmax for colormapping in
pyrolite.plot.color.Suppressed warnings for ‘division by zero’/’invalid value encountered in divide’ in ternary diagram scatter plots.
Added explicit support for colormapping categorical data in
pyrolite.plot.color, such that ordering is preserved/consistent in e.g. legends.
pyrolite.util
Feature: Added new version of ICS International Chronostratigraphic Chart (2022-10;
pyrolite.util.time.Timescale).Bugfix: Corrected TAS diagram references, and fixed an issue where only the ID names were able to we added to diagrams.
Updated axes-sharing utility function
share_axes()to reflect more recent versions ofmatplotlib.Fixed issue in path interpolation for contours (
pyrolite.util.plot.interpolation.get_contour_paths) for recentmatplotlibversions.Updated figure export utility function to use
pathlibsyntax for suffixes, which should avoid potential for double suffixes (e.g. figure_name.png.png).
0.3.2
New Contributor: Angela Rodrigues
Bugfix: Edited docstrings and added ignore-warning for
numpydocwarnings.Bugfix: Updated installation instructions and Binder configuration to use secure protocols when installing via git (i.e. https://)
Bugfix: Update CI builds so that tests can be run on MacOS.
pyrolite.mineral
Feature: Added a TAS-based iron correction following Middlemost (1989).
Bugfix: Fixed some errors in mineral formulae and handling leading to inaccurate outputs from CIPW Norm.
Split out volcanic from intrusive samples in the CIPW Norm volcanic rock comparison.
Added SINCLAS abbreviations to the mineral dictionary associated with the CIPW Norm, so alternate mineral naming systems can be compared.
pyrolite.util
PR Merged: Louise Schoneveld submitted a pull request to add bivariate and ternary classifier models for spinel compositions (
SpinelFeBivariate,SpinelTrivalentTernary).PR Merged: Angela Rodrigues submitted a pull request to add the Jensen ternary cation classifier model for subalkalic volcanic rocks (
JensenPlot).Updated
pyrolite.util.skl.vis.plot_confusion_matrix()to be able to plot on existing axes, use an explicit class order and use rotation for e.g. long x-axis class label names.Updated references to
scipy.stats.gaussian_kde()after namespace deprecation.
0.3.1
New Contributor: Martin Bentley
New Contributor: Chetan Nathwani
New Contributor: Tom Buckle
New Contributor: Nicolas Piette-Lauziere
Removed a redundant
pathlibdependency (which is standard library as of Python 3.4). This will fix an issue blocking setting up a conda-forge recipe (#51).Updated instances of redundant
numpytypes throughout to silence deprecation warnings (using base typesfloat,intexcept where specificnumpytypes are required).Added a minimum
sympyversion requirement (v1.7) to avoid potential import errors.Updated minimum versions for
matplotlibandmplternto address potential version conflicts.A user installation is now recommended by default. This solves some potential issues on *-nix and MacOS systems.
Fixed broken links to documentation in the README (thanks to Alessandro Gentilini).
Fixed a bad documentation link the PyPI package information.
Updated supported Python versions (Python 3.7-3.9).
Bugfix: Updated use of
tinydbdatabases to default to read-only access except where write access is explicitly needed. This should solve issues with permissions during installation and use of pyrolite on some systems ( #61). Thanks to Antoine Ouellet for bringing this to attention, and both Sam Bradley and Alex Hunt for following up with the idea for the current solution.
pyrolite.geochem
Feature: Nicolas Piette-Lauziere contributed two new functions for
pyrolite.geochem.alteration: The chlorite-carbonate-pyrite index of Large et al. (2001;CCPI()) and the Alteration index of Ishikawa (1976;IshikawaAltIndex()).Bugfix: Fixed a bug where incomplete results where being returned for calls to
lambda_lnREE()using the O’Neill algorithm. In this instance only the rows with the least missing data (typically those with no missing data) would return lambda values, other rows would contain null values. Thanks to Mark Pearce for identifying this one! In the meantime, usingdf.pyrochem.lambda_lnREE(algorithm='opt')will allow you to avoid the issue.Bugfix: Modified a few of the
pyrolite.geochem.pyrochemmethods to a avoid a bug due to assignment of the dataframe (to_molecular(),to_weight(),recalculate_Fe()). This bug seems to be contained to the dataframe accessor, the individual functions frompyrolite.geochem.transformappear to work as expected outside of this context. Thanks to Chetan Nathwani for highlighting this one!Renamed (private) package variables
__common_oxides__and__common_elements__to_common_oxidesand_common_elements
pyrolite.mineral
Feature: CIPW function added to
pyrolite.mineral.normative, largely from contributions by both Chetan Nathwani and Tom Buckle ( #53). Note that the implementation still has a bug or two to be ironed out; it will currently raise a warning when used to make sure you’re aware of this. An example has been added demonstrating the intended functionality and demonstrating how coherent this is with existing implementations of CIPW (e.g. SINCLAS).
pyrolite.comp
Updated
pyrolite.comp.codata.close()to better deal with zeros (avoiding unnecessary warnings).Added spherical coordinate transformation to
pyrolite.comp.pyrocompandpyrolite.comp.codata(seepyrolite.comp.pyrocomp.sphere()).
pyrolite.plot
Feature: Added ternary classification plot templates
USDASoilTexture,FeldsparTernaryandQAP( #49; idea and implementation of the latter thanks to Martin Bentley !). The idea for implementing the ternary diagram came from a discussion with Jordan Lubbers and Penny Wieser (of the Thermobar team, who are working in similar spaces); they’ve now implemented a version usingpython-ternary(rather thanmpltern, which pyrolite is currently using).Updated examples and documentation for density and contour plots.
Added autoscaling for standard
spider()and related plots to address (#55)process_color()has been updated to better deal with data explicitly declared to be of a ‘category’ data type (as apandas.Series), and also to better handle variation in mapping notations. Ordering of categorical variables will now be preserved during color-mapping.Added the option to have a ‘bad’ color to be used in categorical color-mapping where a category cannot be found.
Inconsistent color specifications (e.g. a list or array of multiple types) will now result in an error when passed to
process_color().parallel()has been updated to align with other plotting functions (taking an optional components keyword argument).
pyrolite.util
Feature: Added ternary classification models for
USDASoilTexture,FeldsparTernaryandQAP( #49; idea and implementation of the latter thanks to Martin Bentley).Added some functionality to
pyrolite.util.classificationto allow classifier fields to be precisely specified by ratios (useful in ternary systems), for multiple ‘modes’ of diagrams to be contained a single configuration file, and fixed some issues with labelling (arguments add_labels and which_labels can now be used to selectively add either field IDs/abbreviations or field names to classification diagrams).Limits are no longer explicitly required for bivariate templates (xlim, ylim) in
pyrolite.util.classification.Update default parameterisation to
"full"for lambdas, using all REE to generate orthogonal polynomial functions.Expanded
pyrolite.util.text.int_to_alpha()to handle integers which are greater than 25 by adding multiple alphabetical characters (e.g. 26 > aa), and to use the built-in string.ascii_lowercase.save_figure()will now create the directory it’s given if it doesn’t exist.Citation information for
lambdasupdated to include recent publications.Updated
plot_pca_vectors()to accept line colors and linestyles arguments.Updated
init_spherical_octant()to accept a fontsize argument.Added example for coloring ternary diagrams and ternary scatter points based on a ternary color system.
Added helper for generating PCA component labels from a scikit-learn PCA object (
get_PCA_component_labels())Updated confusion matrix visualisation helper
plot_confusion_matrix()to remove grid and provide more useful default colormap normalization options.Moved the manifold visualisation example to utility examples from plotting examples.
Added a fmt_string argument to
LogTransformfor use in automated naming of transformed columns; this may be expanded to other transformers soon.Fixed some string issues for
pyrolite.util.text.
0.3.0
New Contributor: Lucy Mathieson
Continuous Integration has been migrated from Travis to GitHub Actions.
Added an
environment.ymlfile for development environment consistency.Removed some tests dependent on
xlrddue to external issues with reading.xlsand.xlsxfiles with some OS-Python version combinations.Fixed some broken documentation links.
Added
psutilto requirements.
pyrolite.plot
Bugfix: Fixed a bug where there scatter and line arguments would conflict for
spider()(#46). To address this,spider()and related functions will now accept the keyword argumentsline_kwandscatter_kwto explicitly configure the scatter and line aspects of the spider plot - enabling finer customization. An extra example has been added to the docs to illustrate the use of these parameters. Thanks go to Lucy Mathieson for raising this one!Added the
set_tickskeyword argument tospider()and associated functions, allowing ticks to be optionally set (set_ticks=Falseif you don’t want to set the x-ticks).Updated
pyrolite.plot.color.process_color()to better handle colour mapping and added examples illustrating this. You can also now use RGBA colours when using thecolor_mappingskeyword argument.Updated automated pyrolite
matplotlibstyle export to be more reliable.Changed the default shading for
density()to suppress error about upcomingmatplotlibdeprecation.Ordering for contours, contour names and contour styles is now preserved for
density()and related functions.Updated
pyrolite.plot.templates.pearceto use ratios from Sun & McDonough (1989), as in the Pearce (2008) paper.
pyrolite.geochem
Bugfix: Fixed a bug where Eu was unnecessarily excluded from the
lambda_lnREE()fit in all cases.Bugfix: Fixed a bug where ratio-based normalisation was not implemented for
get_ratio()and related functions (#34)Added a local variable to
pyrolite.geochem.indto allow referencing of indexing functions (e.g.by_incompatibility()) by name, allowing easier integration withspider().Added
by_number()for indexing a set of elements by atomic number.
pyrolite.comp
Updated the docstring for
pyrolite.comp.impute.EMCOMP().Minor updates for
pyrolite.comp.codatalabelling, and reflected changes inpyrolite.util.skl.transform. Issues were identified where the column name ‘S’ appears, and a workaround has been put in place for now.
pyrolite.util
Expanded
pyrolite.util.lambdasto allow fitting of tetrad functions, anomalies and estimation of parameter uncertainties for all three algorithms.Added
pyrolite.util.resamplingfor weighted spatiotemporal bootstrap resampling and estimation, together with added a number of updates topyrolite.util.spatialto provide required spatial-similarity functionality.Updated the geological timescale in
pyrolite.util.timeto use the 2020/03 version of the International Chronostratigraphic Chart (#45).Added
alphalabel_subplots()for automatic alphabetic labelling of subplots (e.g. for a manuscript figure).Fixed an low-precision integer rollover issue in a combinatorial calculation for
pyrolite.util.missingby increasing precision to 64-bit integers.Added
example_patterns_from_parameters()to work withpyrolite.util.lambdasand generate synthetic REE patterns based on lambda and/or tetrad-parameterised curves.Moved
get_centroid()frompyrolite.util.classificationtopyrolite.util.plot.helpersMade a small change to
densityto allow passing contour labels as a list.mappable_from_values()will not accept anormkeyword argument, allowing use of colormap normalisers likematplotlib.colors.Normalize. This function was also updated to better handleSeriesobjects.Fixed a small bug for
TASinstantiation which didn’t allow passing the variables to be used from apandas.DataFrame. If you have different variable names, you can now pass them as a list with theaxeskeyword argument (e.g.TAS(axes=['sio2', 'alkali'])).Homogenised logging throughout the package - now all managed through
pyrolite.util.log. The debugging and logging streaming functionstream_log()can now also be accessed here (pyrolite.util.log.stream_log()).
0.2.8
Updated citation information.
Added specific testing for OSX for Travis, and updated the install method to better pick up issues with pip installations.
Feature: Added a gallery of pages for each of the datasets included with
pyrolite. This will soon be expanded, especially for the reference compositions (to address #38).
pyrolite.geochem
PR Merged: Kaarel Mand submitted a pull request to add a number of shale and crustal compositions to the reference database.
Bugfix: Fixed a bug where lambdas would only be calculated for rows without missing data. Where missing data was present, this would result in an assertion error and hence no returned values.
Bugfix: Fixed a bug where missing data wasn’t handled correctly for calculating lambdas. The functions now correctly ignore the potential contribution of elements which are missing when parameterising REE patterns. Thanks to Steve Barnes for the tip off which led to identifying this issue!
Feature: Added
pyrolite.geochem.ind.REY(),list_REY(), andREY()to address (#35). This issue was also opened by Kaarel Mand!As a lead-in to a potential change in default parameterisation, you can now provide additional specifications for the calculation of lambdas to
lambda_lnREE()andcalc_lambdas()to determine the basis over which the individual orthogonal polynomials are defined (i.e. which REE are included to define the orthonormality of these functions). For the keyword argumentparams, (as before) you can pass a list of tuples defining the constants representing the polynomials, but you can now alternatively pass the string"ONeill2016"to explicitly specify the original parameterisation, or"full"to use all REE (including Eu) to define the orthonormality of the component functions (i.e. usingparams="full"). To determine which elements are used to perform the fit, you can either filter the columns passed to these functions or specifically exclude columns using the exclude keyword argument (e.g. the default remainsexclude=["Eu"]which excludes Eu from the fitting process). Note that the default for fitting will remain, but going forward the default for the definition of the polynomial functions will change to use all the REE by default (i.e. change toparams="full").Significant performance upgrades for
lambda_lnREE()and associated functions (up to 3000x for larger datasets).Added a minimum number of elements, configurable for
lambda_lnREE(). This is currently set to seven elements (about half of the REE), and probably lower than it should be ideally. If for some reason you want to test what lambdas (maybe just one or two) look like with less elements, you can use the min_elements keyword argument.Added
list_isotope_ratios()and corresponding selectorisotope_ratios()to subset isotope ratios.Added
parse_chem()to translate geochemical columns to a standardised (and pyrolite-recognised) column name format.
pyrolite.plot
Bugfix: Fixed a bug where arguments processing by
pyrolite.plot.colorwould consume the ‘alpha’ parameter if no colour was specified (and as such it would have no effect on the default colors used bypyplot)Bugfix:
pyrolite.plot.colornow better handles colour and value arrays.Bugfix: Keyword arguments passed to
pyrolite.plot.densitywill now correctly be forwarded to respective functions for histogram and hexbin methods.Customised
matplotlibstyling has been added forpyroliteplotting functions, including legends. This is currently relatively minimal, but could be expanded slightly in the future.The bw_method argument for
scipy.stats.kde.gaussian_kde()can now be parsed bypyrolitedensity-plot functions (e.g.density(),heatscatter()). This means you can modify the default bandwidth of the gaussian kernel density plots. Future updates may allow non-Gaussian kernels to also be used for these purposes - keep an eye out!You can now specify the y-extent for conditional spider plots to restrict the range over which the plot is generated (and focus the plot to where your data actually is). For this, feed in a
(min, max)tuple for the yextent keyword argument.The ybins argument for
spider()and related functions has been updated to bins to be in line with other functions.Conditional density
REE()plots now work as expected, after some fixes for generating reverse-ordered indexes and binsAdded a filter for ternary density plots to ignore true zeroes.
Some updates for
pyrolite.plot.colorfor alpha handling and colour arrays .
pyrolite.comp
Updated transform naming to be consistent between functions and class methods. From this version use capitalised versions for the transform name acronyms (e.g.
ILRinstead ofilr).Added for transform metadata storage within DataFrames for
pyrocomp, and functions to access transforms by name.Added labelling functions for use with
pyrolite.comp.pyrocompandcodatato illustrate the precise relationships depicted by the logratio metrics (specified using the label_mode parameter supplied to each of the resepectivepyrocomplogratio transforms).
pyrolite.util
Revamped
pyrolite.util.classificationto remove cross-compatibility bugs with OSX/other systems. This is now much simpler and uses JSON for serialization.Small fix for
mappable_from_values()to deal with NaN values.Added
pyrolite.util.logfor more streamlined logging (frompyrolite-meltsutil)Added
pyrolite.util.spatial.levenshtein_distance()for comparing sequence differences/distances between 1D iterables (e.g. strings, lists).
0.2.6
New Contributors: Kaarel Mand and Laura Miller
PR Merged: Louise Schoneveld submitted a pull request to fill out the newly-added Formatting and Cleaning Up Plots tutorial. This tutorial aims to provide some basic guidance for common figure and axis formatting tasks as relevant to
pyrolite.Added codacy for code quality checking, and implemented numerous clean-ups and a few new tests across the package.
Performance upgrades, largely for the documentation page. The docs page should build and load faster, and have less memory hang-ups - due to smaller default image sizes/DPI.
Removed dependency on
fancyimpute, instead using functions fromscikit-learn
pyrolite.geochem
Bugfix: pyrolite lambdas differ slightly from [ONeill2016] (#39). Differences between the lambda coefficients of the original and pyrolite implementations of the lambdas calculation were identified (thanks to Laura Miller for this one). With further investigation, it’s likely the cost function passed to
scipy.optimize.least_squares()contained an error. This has been remedied, and the relevant pyrolite functions now by default should give values comparable to [ONeill2016]. As part of this, the reference composition ChondriteREE_ON was added to the reference database with the REE abundances presented in [ONeill2016].Bugfix: Upgrades for
convert_chemistry()to improve performance (#29). This bug appears to have resulted from caching the function calls topyrolite.geochem.ind.simple_oxides(), which is addressed with 18fede0.Feature: Added the [WhittakerMuntus1970] ionic radii for use in silicate geochemistry ( #41), which can optionally be used with
pyrolite.geochem.ind.get_ionic_radii()using the source keyword argument (source='Whittaker'). Thanks to Charles Le Losq for the suggestion!Bugfix: Removed an erroneous zero from the GLOSS reference composition (GLOSS_P2014 value for Pr).
Updated
REE()to default todropPm=TrueMoved
pyrolite.mineral.ionstopyrolite.geochem.ions
- ONeill2016(1,2,3)
O’Neill, H.S.C., 2016. The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57, 1463–1508. doi: 10.1093/petrology/egw047.
- WhittakerMuntus1970
Whittaker, E.J.W., Muntus, R., 1970. Ionic radii for use in geochemistry. Geochimica et Cosmochimica Acta 34, 945–956. doi: 10.1016/0016-7037(70)90077-3.
pyrolite.mineral
Bugfix: Added the mineral database to MANIFEST.in to allow this to be installed with
pyrolite(fixing a bug where this isn’t present, identified by Kaarel Mand).
pyrolite.plot
Bugfix: Updated
pyrolite.plotto usepandas.DataFrame.reindex()overpandas.DataFrame.loc()where indexes could include missing values to deal with #31.Updated
spider()to acceptlogykeyword argument, defaulting toTrue
pyrolite.util
Broke down
pyrolite.util.plotinto submodules, and updated relevant imports. This will result in minimal changes to API usage where functions are imported explicitly.Split out
pyrolite.util.lambdasfrompyrolite.util.mathAdded a minimum figure dimension to
init_axes()to avoid having null-dimensions during automatic figure generation from empty datasets.Added
example_spider_data()to generate an example dataset for demonstrating spider diagrams and associated functions. This allowed detailed synthetic data generation forspider()andpyrolite.plot.pyroplot.REE()plotting examples to be cut down significantly.Removed unused submodule
pyrolite.util.wfs
0.2.5
PR Merged: @lavender22 updated the spider diagram example to add a link to the normalisation example (which lists different reservoirs you can normalise to).
Added an ‘Importing Data’ section to the docs Getting Started page.
Disabled automatic extension loading (e.g. for
pyrolite_meltsutil) to avoid bugs during version mismatches.
pyrolite.comp
Updated the
pyrolite.comp.pyrocompdataframe accessor API to include reference to compositional data log transform functions withinpyrolite.comp.codata
pyrolite.plot
Added support for spider plot index ordering added with the keyword
index_order(#30)Added support for color indexing in
colorusingpandas.Series, and also for list-like arrays of categoriesAdded a workaround for referring to axes positions where the projection is changed to a ternary projection (displacing the original axis), but the reference to the original axes object (now booted from
fig.axes/fig.orderedaxes) is subsequently used.Updated
process_color()processing of auxillary color keyword arguments (fixing a bug for color arguments instem())Added support for a
color_mappingskeyword argument for mapping categorical variables to specific colors.Updated the effect of
relimkeyword argument ofdensity()to remove the scaling (it will no longer log-scale the axes, just the grid/histogram bins).Updated
Gridto accept an x-y tuple to specify numbers of bins in each direction within a grid (e.g.bins=(20, 40))Updated the grids used in some of the
density()methods to be edges, lining up the arrays such that shading parameters will work as expected (e.g.shading='gouraud')
pyrolite.geochem
Added sorting function
~pyrolite.geochem.ind.by_incompatibilityfor incompatible element sorting (based on BCC/PM relative abundances).
pyrolite.mineral
Minor bugfix for
update_database()
pyrolite.util
Moved
check_perl()out ofpyroliteintopyrolite_meltsutil
0.2.4
Removed Python 3.5 support, added Python 3.8 support.
Updated ternary plots to use
mpltern(#28)Added a ternary heatmap tutorial
pyrolite.plot
Added
pyrolite.plot.pyroplot.plot()methodRemoved
pyrolite.plot.pyroplot.ternary()method (ternary plots now served through the same interface as bivariate plots usingpyrolite.plot.pyroplot.scatter(),pyrolite.plot.pyroplot.plot(), andpyrolite.plot.pyroplot.plot())Added
pyrolite.plot.colorfor processing color arguments.Moved
pyrolite.plot.densityto its own sub-submodule, includingpyrolite.plot.density.ternaryandpyrolite.plot.density.grid
pyrolite.util
Updated
timeto include official colors.Added
pyrolite.util.timeexampleUpdated
stream_log()to deal with logger duplication issues.Various updates to
pyrolite.util.plot, noted below:Added universal axes initiation for bivariate/ternary diagrams using
init_axes()and axes labelling withlabel_axes(),Added keyword argument processing functions
scatterkwargs(),linekwargs(), andpatchkwargs()Added functions for replacing non-projected axes with ternary axes, including
replace_with_ternary_axis(),axes_to_ternary()(andget_axes_index()to maintain ordering of new axes)Added
get_axis_density_methods()to access the relevant histogram/density methods for bivariate and ternary axesRenamed private attributes for default colormaps to
DEFAULT_DISC_COLORMAPandDEFAULT_CONT_COLORMAPUpdated
add_colorbar()to better handle colorbars for ternary diagrams
0.2.3
Added Getting Started page
pyrolite.mineral
Updated database for
pyrolite.mineral.mindbto include epidotes, garnets, micas
pyrolite.plot
Minor updates for
pyrolite.plot.templates, added functionality topyrolite.plot.templates.TAS()stub.Fixed a bug for
vmininpyrolite.plot.spiderdensity modes
pyrolite.geochem
pyrolite.geochem.parsenow also includes functions which were previously included inpyrolite.geochem.validateFixed some typos in reference compositions from Gale et al. (2013)
pyrolite.util
Added
pyrolite.util.plot.set_ternary_labels()for setting and positioning ternary plot labels
0.2.2
pyrolite.geochem
Added
SCSS()for modelling sulfur content at sulfate/sulfide saturation.
pyrolite.mineral
Added mineral database and and mineral endmember decomposition examples
0.2.1
Updated and refactored documentation
Added Development, Debugging section, Extensions
Added
sphinx_gallerywith binder links for examplesRemoved duplicated examples
Amended citation guidelines
Removed extensions from pyrolite (
pyrolite.ext.datarepo,pyrolite.ext.alphamelts). These will soon be available as separate extension packages. This enabled faster build and test times, and removed extraneous dependencies for the corepyrolitepackage.Added
stats_requireas optional requirements insetup.py
pyrolite.geochem
Added
pyrolite.geochem.pyrochem.compositional()selector
pyrolite.plot
parallel()now better handlespyplotfigure and subplot argumentsternary()and related functions now handle label offsets and label fontsizesMinor bugfixes for
densityAdded
unity_lineargument tospider()to be consistent withREE_v_radii()
pyrolite.mineral
Added a simple
pyrolite.mineral.mindbdatabaseAdded
pyrolite.mineral.transformto house mineral transformation functionsExpanded
pyrolite.mineral.normativeto includeunmix()andpyrolite.mineral.normative.endmember_decompose()for composition-based mineral endmember decomposition
pyrolite.util
Added
pyrolite.util.plot.mappable_from_values()to enable generatingScalarMappableobjects from an array of values, for use in generating colorbars
0.2.0
Added alt-text to documentation example images
Updated contributing guidelines
Added Python 3.8-dev to Travis config (not yet available)
Removed
pandas-flavordecorators frompyrolite.geochemandpyrolite.comp, eliminating the dependency onpandas-flavor
pyrolite.geochem
Expanded
pyrolite.geochem.pyrochemDataFrame accessor and constituent methodsUpdates and bugfixes for
pyrolite.geochem.transformandpyrolite.geochem.normUpdated the normalization example
pyrolite.comp
Added
pyrolite.comp.pyrocompDataFrame accessor with thepyrolite.comp.codata.renormalise()method.Removed unused imputation and aggregation functions.
pyrolite.plot
Added
heatscatter()and example.Updates and bugfixes for
pyrolite.plot.spider.REE_v_radii(), including updating spacing to reflect relative ionic radii
pyrolite.util
Added
pyrolite.util.plot.get_twins()
0.1.21
pyrolite.plot
Added parallel coordinate plots:
pyrolite.plot.pyroplot.parallel()Updated
scatter()andternary()to better deal with colormaps
pyrolite.ext.alphamelts
Updated
pyrolite.ext.alphameltsinterface:Docs
Updated to default to tables with percentages (Wt%, Vol%)
Updated
plottemplatesy-labelsFixed
automationgrid bug
0.1.20
pyrolite.geochem
Stub for
pyrolite.geochem.pyrochemaccessor (yet to be fully developed)Convert reference compositions within of
pyrolite.geochem.normto use a JSON database
pyrolite.util.skl
Added
pyrolite.util.skl.vis.plot_mapping()for manifold dimensional reductionAdded
pyrolite.util.skl.vis.alphas_from_multiclass_prob()for visualising multi-class classification probabilities in scatter plots
pyrolite.plot
Added
pyrolite.plot.biplotto API docsUpdated default y-aspect for ternary plots and axes patches
pyrolite.ext.alphamelts
Updated
pyrolite.ext.alphamelts.automation,pyrolite.ext.alphamelts.meltsfile,pyrolite.ext.alphamelts.tablesUpdated docs to use
pyrolite.ext.alphamelts.automation.MeltsBatchwith a parameter grid
0.1.19
Added this changelog
Require
pandas>= v0.23 for DataFrame accessors
pyrolite.geochem
Moved normalization into
pyrolite.geochemImproved support for molecular-based calculations in
pyrolite.geochemAdded
pyrolite.geochemsection to API docsAdded the
convert_chemistry()docs example
pyrolite.ext.alphamelts
Improvements for
pyrolite.ext.alphamelts.downloadCompleted
pyrolite.ext.alphamelts.automation.MeltsBatchAdded the
pyrolite.ext.alphamelts.webdocs exampleAdded
pyrolite.ext.alphamelts.plottemplatesto API docsAdded
pyrolite.ext.alphamelts.tables.write_summary_phaselist()Added
pyrolite.ext.alphamelts.automation.exp_name()for automated alphaMELTS experiment within batches
pyrolite.util
Added
pyrolite.util.meta.ToLoggeroutput stream for loggingAdded
pyrolite.util.multip.combine_choices()for generating parameter combination grids
0.1.18
Require
scipy>= 1.2
pyrolite.plot
Automatic import of dataframe accessor df.pyroplot removed; import
pyrolite.plotto usepyrolite.plot.pyroplotdataframe accessorUpdated label locations for
pyrolite.plot.biplotDefault location of the y-axis updated for
pyrolite.plot.stem.stem()
pyrolite.geochem
Added stub for
pyroilte.geochem.qualilty
pyrolite.util
Moved pyrolite.classification to
pyrolite.util.classificationAdded
pyrolite.util.plot.marker_cycle()
0.1.17
Update status to Beta
pyrolite.geochem
Added database for geochemical components (geochemdb.json) for faster import via
common_elements()andcommon_oxides()Added stub for
pyrolite.geochem.isotopeUpdate to using
pyrolite.util.transform.aggregate_element()rather than aggregate_cation
pyrolite.plot
Expanded use of
pyrolite.plot.pyroplotdataframe accessorAdded
pyrolite.plot.pyrochem.cooccurence()Added
pyrolite.plot.biplotAdded support for conditional density spiderplots within
spider()andREE_v_radii()Updated keyword argument parsing for
spider()
pyrolite.mineral
Removed automatic import of mineral structures to reduce delay
Added stub for
pyrolite.mineral.normative()Updated
pyrolite.mineral.sites.Site
pyrolite.util
Added functions for interpolating paths and patches (e.g. contours) and exporting these:
interpolate_path(),interpolated_patch_path(),get_contour_paths(),path_to_csv()Added
util.plot._mpl_sp_kw_split()Added
util.text.remove_suffix()Added
util.text.int_to_alpha()
pyrolite.ext
Updated alphaMELTS interface location to external package interface rather than utility (from
pyrolite.utiltopyrolite.ext)Added
pyrolite.ext.datarepostub
0.1.16
pyrolite.mineral
Added
pyrolite.mineral.latticeexampleAdded
pyrolite.mineral.lattice.youngs_modulus_approximation()
pyrolite.ext.alphamelts
Added
pyrolite.ext.alphameltsMonte Carlo uncertainty estimation exampleAdded
pyrolite.ext.alphamelts.automation.MeltsExperiment.callstring()to facilitate manual reproducibility of pyrolite calls to alphaMELTS.Improved alphaMELTS interface termination
Added
pyrolite.ext.alphamelts.plottemplates.phase_linestyle()to for auto-differentiated linestyles in plots generated from alphaMELTS output tablesAdded
pyrolite.ext.alphamelts.plottemplates.table_by_phase()to generate axes per phase from a specific output table
pyrolite.geochem
Added MORB compositions from Gale et al. (2013) to Reference Compositions
Updated pyrolite.geochem.ind.get_radii to
pyrolite.geochem.ind.get_ionic_radii()dropPmparameter added topyrolite.geochem.ind.REE()
pyrolite.plot
Updated pyrolite.plot.spider.REE_radii_plot to
pyrolite.plot.spider.REE_v_radii()Updated
pyrolite.util.meta.steam_log()to take into account active logging handlers
pyrolite.util
Added
pyrolite.util.pd.read_table()for simple.csvand.xlsx/.xlsimportsAdded
pyrolite.util.plot.rect_from_centre()Added
pyrolite.util.text.slugify()for removing spaces and non-alphanumeric characters
0.1.15
pyrolite.ext.alphamelts
Bugfixes for
automationanddownloadAdd a
permissionskeyword argument topyrolite.util.general.copy_file()
0.1.14
Added Contributor Covenant Code of Conduct
pyrolite.plot
Added
pyrolite.plot.stem.stem()exampleAdded
pyrolite.plot.stemAdded
pyrolite.plot.stemto API docsAdded
pyrolite.plot.stemexample
pyrolite.mineral
Added
pyrolite.mineral.latticefor lattice strain calculationsAdded
pyrolite.mineralto API docs
pyrolite.ext.alphamelts
Improved
pyrolite.ext.alphamelts.automationworkflows, process tracking and terminationIncorporated
MeltsProcessintoMeltsExperimentAdded
MeltsBatchstubAdded
read_meltsfile()andread_envfile()Added
pyrolite.ext.alphamelts.plottemplatesAdded
pyrolite.ext.alphamelts.tables.get_experiments_summary()for aggregating alphaMELTS experiment results across folders
pyrolite.util
Added manifold uncertainty example with
pyrolite.util.skl.vis.plot_mapping()Updated
pyrolite.util.ditributions.norm_to_lognormAdded
pyrolite.util.general.get_process_tree()to extract related processes
0.1.13
pyrolite.ext.alphamelts
Updated
pyrolite.ext.alphamelts.automation.MeltsProcessworkflowUpdated
pyrolite.ext.alphamelts.downloadlocal installationAdded
pyrolite.ext.alphamelts.installexampleAdded
pyrolite.ext.alphamelts.tablesexampleAdded
pyrolite.ext.alphamelts.automationexampleAdded
pyrolite.ext.alphamelts.envexample
0.1.12
pyrolite.util.pd
Bugfix for
pyrolite.util.pd.to_frame()
0.1.11
Added citation page to docs
Added contributors page to docs
Updated docs future page
Updated docs config and logo
pyrolite.geochem
Added stub for
pyrolite.geochem.isotope,pyrolite.geochem.isotope.count
pyrolite.comp
Added compositional data example
Added
pyrolite.data.Aitchisonand assocaited data files
pyroilite.ext.alphamelts
Added
pyrolite.ext.alphameltsto API docsAdded
pyrolite.ext.alphamelts.automation
pyrolite.util
Expanded
pyrolite.utilAPI docsMoved pyrolite_datafolder from
pyrolite.util.generaltopyrolite.util.meta.pyrolite_datafolder()Added
share_axes(),ternary_patch(),subaxes()Added
pyrolite.util.units, moved pyrolite.geochem.norm.scale_multiplier topyrolite.util.units.scale()Updated
pyrolite.util.synthetic.random_cov_matrix()to optionally take asigmaskeyword argument
0.1.10
Updated installation docs
pyrolite.util
Added
pyrolite.util.typesAdded
pyrolite.util.webAdded manifold uncertainty example with
pyrolite.util.skl.vis.plot_mapping()Moved stream log to
pyrolite.util.meta.stream_log()Updated
pyrolite.util.skl.vis
pyrolite.ext.datarepo
Updated
pyrolite.ext.datarepo.georoc(then pyrolite.util.repositories.georoc)
0.1.9
pyrolite.plot
Added
pyrolite.plot.templates, and related API docsAdded Pearce templates under
pyrolite.plot.templates.pearceUpdate default color schemes in scatter plots within
pyrolite.plotto fall-back tomatplotlib.pyplotcycling
pyrolite.util
Added conditional import for
PCAandstatsmodelswithinpyrolite.util.plotRefactored
sklearnutilities to submodulepyrolite.util.sklUpdated
pyrolite.util.meta.inargs()Updated
pyrolite.util.meta.stream_log()(then pyrolite.util.general.stream_log)Added conditional import for
imblearnunderpyrolite.util.skl.pipeline
pyrolite.ext.alphamelts
Added
pyrolite.ext.alphamelts(then pyrolite.util.alphamelts)Bugfix for Python 3.5 style strings in
pyrolite.ext.alphamelts.parse
0.1.8
Bugfixes for
pyrolite.plot.spiderandpyrolite.util.plot.conditional_prob_density
0.1.7
pyrolite.plot
Added
cooccurence()method topyrolite.plot.pyroplotDataFrame accessor
pyrolite.util
Moved pyrolite.util.skl.plot_cooccurence to
pyrolite.util.plot.plot_cooccurence()Updated
pyrolite.util.plot.conditional_prob_density(),pyrolite.util.plot.bin_edges_to_centres()andpyrolite.util.plot.bin_centres_to_edges()
0.1.6
pyrolite.plot
Update
spider()to usecontourskeyword argument, and pass these topyrolite.util.plot.plot_Z_percentiles()
pyrolite.util
Bugfixes for invalid steps in
pyrolite.util.math.linspc_(),pyrolite.util.math.logspc_()
0.1.5
Updated docs future page
pyrolite.geochem
Bugfix for iron redox recalcuation in
pyrolite.geochem.transform.convert_chemistry()
pyrolite.plot
Added
modekeyword argument topyrolite.plot.spider.spider()to enable density-based visualisation of spider plots.Update
pyrolite.plot.pyroplot.spider()to acceptmodekeyword argumentUpdate
pyrolite.plot.pyroplot.REE()to use aindexkeyword arguument in the place of the previousmode;modeis now used to switch between line and density base methods of visualising spider plots consistent withspider()Added
spider()examples for conditional density plots usingconditional_prob_density()Bugfix for
set_underindensity()Updated logo example
pyrolite.util
Updated
pyrolite.util.metaAdded
pyrolite.util.plot.conditional_prob_density(); added conditionalstatsmodelsimport withinpyrolite.util.plotto accessKDEMultivariateConditionalAdded keyword argument
logytopyrolite.util.math.interpolate_line()Added
pyrolite.util.math.grid_from_ranges()andpyrolite.util.math.flattengrid()Added support for differential x-y padding in
pyrolite.util.plot.get_full_extent()andpyrolite.util.plot.save_axes()Added
pyrolite.util.skl.pipeline.fit_save_classifier()(then pyrolite.util.skl.fit_save_classifier)
0.1.4
pyrolite.plot
Updated relevant docs and references for
pyrolite.plotand thepyrolite.plot.pyroplotDataFrame accessor
pyrolite.comp
Expanded
pyrolite.comp.imputeand improvedpyrolite.comp.impute.EMCOMP()Added EMCOMP example (later removed in 0.2.5, pending validation and improvements for EMCOMP).
pyrolite.util
Updated
pyrolite.util.metawith docstring utilitiesnumpydoc_str_param_list()andget_additional_params()
0.1.2
Fixed logo naming issue in docs
pyrolite.plot
Bugfixes for
pyrolite.plot.density.density()(then pyrolite.plot.density) andpyrolite.plot.util.ternary_heatmap()
0.1.1
pyrolite.plot
Added logo example
Refactored
pyrolite.plotto use thepyrolite.plot.pyroplotDataFrame accessor:Renamed pyrolite.plot.spiderplot to
pyrolite.plot.spider.spider()Renamed pyrolite.plot.spider.REE_radii_plot to
pyrolite.plot.spider.REE_v_radii()Renamed pyrolite.plot.ternaryplot to
pyrolite.plot.tern.ternary()Renamed pyrolite.plot.densityplot to
pyrolite.plot.density.density()
Updated
pyrolite.plot.density.density()andpyrolite.plot.tern.ternary()
pyrolite.comp
Bugfixes and improvements for
pyrolite.comp.impute
pyrolite.geochem
Updated
oxide_conversion()andconvert_chemistry()
pyrolite.util
Added
plot_stdev_ellipses()andplot_pca_vectors()Updated
pyrolite.util.plot.plot_Z_percentiles()Updated
pyrolite.util.plot.ternary_heatmap()Updated
pyrolite.util.plot.vector_to_line()
0.1.0
pyrolite.plot
Updates to
pyrolite.plot.density.density()to better deal with linear/log spaced and a ternary heatmap
pyrolite.comp
Added
EMCOMP()topyrolite.comp.imputeRenamed inv_alr, inv_clr, inv_ilr and inv_boxcox to
inverse_alr(),inverse_clr(),inverse_ilr()andinverse_boxcox()
pyrolite.util
Added
pyrolite.util.syntheticMoved pyrolite.util.pd.normal_frame and pyrolite.util.pd.normal_series to
pyrolite.util.synthetic.normal_frame()andpyrolite.util.synthetic.normal_series()Added
pyrolite.util.missingandpyrolite.util.missing.md_pattern()Added
pyrolite.util.math.eigsorted(),pyrolite.util.math.augmented_covariance_matrix(),pyrolite.util.math.interpolate_line()
Note
Releases before 0.1.0 are available via
GitHub for reference,
but were alpha versions which were never considered stable.
Future
This page details some of the under-development and planned features for
pyrolite. Note that while no schedules are attached, features under development
are likely to be completed with weeks to months, while those ‘On The Horizon’ may be
significantly further away (or in some cases may not make it to release).
Under Development
These features are either under development or planned to be implemented and should be released in the near future.
Interactive Plotting Backend Options:
pyrolitevisualisation is currently based entirely on static plot generation viamatplotlib. While this works well for publication-style figures, it may be possible to leveragepandas-based frameworks to provide options for alternative backends, some of which are more interactive and amendable to data exploration (e.g.hvplot,plotly). See thepandasextension docs for one option for implementing this (plotting-backends).Units and Uncertainty Aware Geochemistry DataFrames: Work has started on a prototype implementation to bring in native data types related to units, and incorporate uncertainties which can be propogated through calculations. This is principally based around
pint,pint_pandasanduncertainties.
On the Horizon, Potential Future Updates
These are a number of features which are in various stages of development, which are planned be integrated over the longer term.
There are a few components which will make better use of mineral chemistry data, and facilitate better comparison of whole-rock and mineral data (Issue #5):
Normative mineral calculations
Mineral formulae recalculation, site partitioning, endmember calculations
Stable isotope calculations
Simple radiogenic isotope system calculations and plots
Expansion of compositional data imputation algorithms beyond EMCOMP (Issue #6).
Utilities for simple melting and fractionation models.
pyrolite.geochem.quality
- Utilities for:
assessing data quality
identifying potential analytical artefacts
assessing uncertainties
Governance and Documentation
Depending on how the community grows, and whether
pyrolitebrings with it a series of related tools, the project and related tools may be migrated to an umbrella organization on GitHub (e.g. pyrolite/pyrolite`) so they can be collectively managed by a community.Internationalization: While the pyrolite source is documented in English, it would be good to be able to provide translated versions of the documentation to minimise hurdles to getting started.
Teaching Resources:
pyroliteis well placed to provide solutions and resources for use in under/post-graduate education. While we have documentation sections dedicated to examples and tutorials, perhaps we could develop explicit sections for educational resources and exercises.
Code of Conduct
Our Pledge
In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, sex characteristics, gender identity and expression, level of experience, education, socio-economic status, nationality, personal appearance, race, religion, or sexual identity and orientation.
Our Standards
Examples of behaviour that contributes to creating a positive environment include:
Using welcoming and inclusive language
Being respectful of differing viewpoints and experiences
Gracefully accepting constructive criticism
Focusing on what is best for the community
Showing empathy towards other community members
Examples of unacceptable behaviour by participants include:
The use of sexualized language or imagery and unwelcome sexual attention or advances
Trolling, insulting/derogatory comments, and personal or political attacks
Public or private harassment
Publishing others’ private information, such as a physical or electronic address, without explicit permission
Other conduct which could reasonably be considered inappropriate in a professional setting
Our Responsibilities
Project maintainers are responsible for clarifying the standards of acceptable behaviour and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behaviour.
Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviours that they deem inappropriate, threatening, offensive, or harmful.
Scope
This Code of Conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Examples of representing a project or community include using an official project e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers.
Enforcement
Instances of abusive, harassing, or otherwise unacceptable behaviour may be reported by contacting the project admins. All complaints will be reviewed and investigated and will result in a response that is deemed necessary and appropriate to the circumstances. The project team is obligated to maintain confidentiality with regard to the reporter of an incident. Further details of specific enforcement policies may be posted separately.
Project maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project’s leadership.
Attribution
This Code of Conduct is adapted from the Contributor Covenant Version 1.4, available at https://www.contributor-covenant.org/version/1/4/code-of-conduct.html. The Contributor Covenant is released under the Creative Commons Attribution 4.0 License.
For answers to common questions about this code of conduct, see https://www.contributor-covenant.org/faq.
Contributing
The long-term aim of this project is to be designed, built and supported by (and for) the geochemistry community. In the present, the majority of the work involves incorporating geological knowledge and frameworks into a practically useful core set of tools which can be later be expanded. As such, requests for features and bug reports are particularly valuable contributions, in addition to code and expanding the documentation. All individuals contributing to the project are expected to follow the Code of Conduct, which outlines community expectations and responsibilities.
Also, be sure to add your name or GitHub username to the contributors list.
Note
This project is currently in beta, and as such there’s much work to be done.
Feature Requests
If you’re new to Python, and want to implement a specific process, plot or framework
as part of pyrolite, you can submit a
Feature Request.
Perhaps also check the
Issues Board first to see if
someone else has suggested something similar (or if something is in development),
and comment there.
Bug Reports
If you’ve tried to do something with pyrolite, but it didn’t work, and googling
error messages didn’t help (or, if the error messages are full of
pyrolite.XX.xx), you can submit a
Bug Report .
Perhaps also check the
Issues Board first to see if
someone else is having the same issue, and comment there.
Contributing to Documentation
The documentation and examples for pyrolite
are gradually being developed, and any contributions or corrections would be greatly
appreciated. Currently the examples are patchy, and any ‘getting started’ guides would
be a helpful addition.
- These pages serve multiple purposes:
A human-readable reference of the source code (compiled from docstrings).
A set of simple examples to demonstrate use and utility.
A place for developing extended examples 1
Contributing Code
Code contributions are always welcome, whether it be small modifications or entire
features. As the project gains momentum, check the
Issues Board for outstanding
issues, features under development. If you’d like to contribute, but you’re not so
experienced with Python, look for good first issue tags or email the maintainer
for suggestions.
To contribute code, the place to start will be forking the source for pyrolite
from GitHub. Once forked,
clone a local copy and from the repository directory you can install a development
(editable) copy via python setup.py develop. To incorporate suggested
changes back to into the project, push your changes to your
remote fork, and then submit a pull request onto
pyrolite/develop
or a relevant feature branch.
Note
See Development for directions for installing extra dependencies for development and for information on development environments and tests.
pyrolitedevelopment roughly follows a gitflow workflow.pyrolite/mainis only used for releases, and large separable features should be build onfeaturebranches offdevelop.Contributions introducing new functions, classes or entire features should also include appropriate tests where possible (see Writing Tests, below).
pyroliteuses Black for code formatting, and submissions which have passed throughBlackare appreciated, although not critical.
Writing Tests
There is currently a broad unit test suite for pyrolite, which guards
against breaking changes and assures baseline functionality. pyrolite uses
continuous integration via
GitHub Actions,
where the full suite of tests are run for each commit and pull request, and test
coverage output to Coveralls.
Adding or expanding tests is a helpful way to ensure pyrolite does what is meant to,
and does it reproducibly. The unit test suite one critical component of the package,
and necessary to enable sufficient trust to use pyrolite for scientific purposes.
- 1
Such examples could easily be distributed as educational resources showcasing the utility of programmatic approaches to geochemistry
Contributors
This list includes people who have contributed to the project in the form of code, comments, testing, bug reports, or feature requests.
Hayden Dalton
Adam Bath
Yajing Mao
Steve Barnes
Lucy Mathieson
API
pyrolite.plot
Submodule with various plotting and visualisation functions.
pyrolite.plot.pyroplot (Pandas Interface)
- class pyrolite.plot.pyroplot(obj)[source]
- cooccurence(ax=None, normalize=True, log=False, colorbar=False, **kwargs)[source]
Plot the co-occurence frequency matrix for a given input.
- Parameters
ax (
matplotlib.axes.Axes,None) – The subplot to draw on.normalize (
bool) – Whether to normalize the cooccurence to compare disparate variables.log (
bool) – Whether to take the log of the cooccurence.colorbar (
bool) – Whether to append a colorbar.- Returns
Axes on which the cooccurence plot is added.
- Return type
- density(components: Optional[list] = None, ax=None, axlabels=True, **kwargs)[source]
Method for plotting histograms (mode=’hist2d’|’hexbin’) or kernel density esitimates from point data. Convenience access function to
density()(see Other Parameters, below), where further parameters for relevant matplotlib functions are also listed.
- Parameters
components (
list,None) – Elements or compositional components to plot.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.axlabels (
bool, True) – Whether to add x-y axis labels.Note
The following additional parameters are from
pyrolite.plot.density.density().
- Other Parameters
arr (
numpy.ndarray) – Dataframe from which to draw data.logx (
bool, False) – Whether to use a logspaced grid on the x axis. Values strictly >0 required.logy (
bool, False) – Whether to use a logspaced grid on the y axis. Values strictly >0 required.bins (
int, 20) – Number of bins used in the gridded functions (histograms, KDE evaluation grid).mode (
str, ‘density’) – Different modes used here: [‘density’, ‘hexbin’, ‘hist2d’]extent (
list) – Predetermined extent of the grid for which to from the histogram/KDE. In the general form (xmin, xmax, ymin, ymax).contours (
list) – Contours to add to the plot, wheremode='density'is used.percentiles (
bool, True) – Whether contours specified are to be converted to percentiles.relim (
bool,True) – Whether to relimit the plot based on xmin, xmax values.cmap (
matplotlib.colors.Colormap) – Colormap for mapping surfaces.vmin (
float, 0.) – Minimum value for colormap.shading (
str, ‘auto’) – Shading to apply to pcolormesh.colorbar (
bool, False) – Whether to append a linked colorbar to the generated mappable image.- Returns
Axes on which the density diagram is plotted.
- Return type
- heatscatter(components: Optional[list] = None, ax=None, axlabels=True, logx=False, logy=False, **kwargs)[source]
Heatmapped scatter plots using the pyroplot API. See further parameters for matplotlib.pyplot.scatter function below.
- Parameters
components (
list,None) – Elements or compositional components to plot.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.axlabels (
bool,True) – Whether to add x-y axis labels.logx (
bool, False) – Whether to log-transform x values before the KDE for bivariate plots.logy (
bool, False) – Whether to log-transform y values before the KDE for bivariate plots.- Returns
Axes on which the heatmapped scatterplot is added.
- Return type
- parallel(components=None, rescale=False, legend=False, ax=None, **kwargs)[source]
Create a
pyrolite.plot.parallel.parallel(). coordinate plot from the columns of theDataFrame.
- Parameters
components (
list,None) – Components to use as axes for the plot.rescale (
bool) – Whether to rescale values to [-1, 1].legend (
bool,False) – Whether to include or suppress the legend.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.Note
The following additional parameters are from
pyrolite.plot.parallel.parallel().
- Other Parameters
df (
pandas.DataFrame) – Dataframe to create a plot from.- Returns
Axes on which the parallel coordinates plot is added.
- Return type
Todo
Adapt figure size based on number of columns.
- plot(components: Optional[list] = None, ax=None, axlabels=True, **kwargs)[source]
Convenience method for line plots using the pyroplot API. See further parameters for matplotlib.pyplot.scatter function below.
- Parameters
components (
list,None) – Elements or compositional components to plot.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.axlabels (
bool,True) – Whether to add x-y axis labels.Note
The following additional parameters are from
matplotlib.pyplot.plot().
- Other Parameters
x, y (array-like or scalar) – The horizontal / vertical coordinates of the data points. x values are optional and default to
range(len(y)).Commonly, these parameters are 1D arrays.
They can also be scalars, or two-dimensional (in that case, the columns represent separate data sets).
These arguments cannot be passed as keywords.
fmt (str, optional) – A format string, e.g. ‘ro’ for red circles. See the Notes section for a full description of the format strings.
Format strings are just an abbreviation for quickly setting basic line properties. All of these and more can also be controlled by keyword arguments.
This argument cannot be passed as keyword.
data (indexable object, optional) – An object with labelled data. If given, provide the label names to plot in x and y.
Note
Technically there’s a slight ambiguity in calls where the second label is a valid fmt.
plot('n', 'o', data=obj)could beplt(x, y)orplt(y, fmt). In such cases, the former interpretation is chosen, but a warning is issued. You may suppress the warning by adding an empty format stringplot('n', 'o', '', data=obj).- Returns
Axes on which the plot is added.
- Return type
- REE(index='elements', ax=None, mode='plot', dropPm=True, scatter_kw={}, line_kw={}, **kwargs)[source]
Pass the pandas object to
pyrolite.plot.spider.REE_v_radii().
- Parameters
ax (
matplotlib.axes.Axes,None) – The subplot to draw on.index (
str) – Whether to plot radii (‘radii’) on the principal x-axis, or elements (‘elements’).mode (
str, :code`[“plot”, “fill”, “binkde”, “ckde”, “kde”, “hist”]`) – Mode for plot. Plot will produce a line-scatter diagram. Fill will return a filled range. Density will return a conditional density diagram.dropPm (
bool) – Whether to exclude the (almost) non-existent element Promethium from the REE list.scatter_kw (
dict) – Keyword parameters to be passed to the scatter plotting function.line_kw (
dict) – Keyword parameters to be passed to the line plotting function.Note
The following additional parameters are from
pyrolite.plot.spider.REE_v_radii().
- Other Parameters
arr (
numpy.ndarray) – Data array.ree (
list) – List of REE to use as an index.logy (
bool) – Whether to use a log y-axis.tl_rotation (
float) – Rotation of the numerical index labels in degrees.unity_line (
bool) – Add a line at y=1 for reference.set_labels (
bool) – Whether to set the x-axis ticklabels for the REE.set_ticks (
bool) – Whether to set the x-axis ticks according to the specified index.- Returns
Axes on which the REE plot is added.
- Return type
- scatter(components: Optional[list] = None, ax=None, axlabels=True, **kwargs)[source]
Convenience method for scatter plots using the pyroplot API. See further parameters for matplotlib.pyplot.scatter function below.
- Parameters
components (
list,None) – Elements or compositional components to plot.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.axlabels (
bool,True) – Whether to add x-y axis labels.Note
The following additional parameters are from
matplotlib.pyplot.scatter().
- Other Parameters
x, y (float or array-like, shape (n, )) – The data positions.
s (float or array-like, shape (n, ), optional) – The marker size in points**2 (typographic points are 1/72 in.). Default is
rcParams['lines.markersize'] ** 2.The linewidth and edgecolor can visually interact with the marker size, and can lead to artifacts if the marker size is smaller than the linewidth.
If the linewidth is greater than 0 and the edgecolor is anything but ‘none’, then the effective size of the marker will be increased by half the linewidth because the stroke will be centered on the edge of the shape.
To eliminate the marker edge either set linewidth=0 or edgecolor=’none’.
c (array-like or list of colors or color, optional) – The marker colors. Possible values:
A scalar or sequence of n numbers to be mapped to colors using cmap and norm.
A 2D array in which the rows are RGB or RGBA.
A sequence of colors of length n.
A single color format string.
Note that c should not be a single numeric RGB or RGBA sequence because that is indistinguishable from an array of values to be colormapped. If you want to specify the same RGB or RGBA value for all points, use a 2D array with a single row. Otherwise, value-matching will have precedence in case of a size matching with x and y.
If you wish to specify a single color for all points prefer the color keyword argument.
Defaults to None. In that case the marker color is determined by the value of color, facecolor or facecolors. In case those are not specified or None, the marker color is determined by the next color of the
Axes’ current “shape and fill” color cycle. This cycle defaults torcParams["axes.prop_cycle"].marker (~.markers.MarkerStyle, default:
rcParams["scatter.marker"]) – The marker style. marker can be either an instance of the class or the text shorthand for a particular marker. Seematplotlib.markersfor more information about marker styles.cmap (str or ~matplotlib.colors.Colormap, default:
rcParams["image.cmap"]) – The Colormap instance or registered colormap name used to map scalar data to colors.This parameter is ignored if c is RGB(A).
norm (str or ~matplotlib.colors.Normalize, optional) – The normalization method used to scale scalar data to the [0, 1] range before mapping to colors using cmap. By default, a linear scaling is used, mapping the lowest value to 0 and the highest to 1.
If given, this can be one of the following:
An instance of .Normalize or one of its subclasses (see Colormap normalization).
A scale name, i.e. one of “linear”, “log”, “symlog”, “logit”, etc. For a list of available scales, call matplotlib.scale.get_scale_names(). In that case, a suitable .Normalize subclass is dynamically generated and instantiated.
This parameter is ignored if c is RGB(A).
vmin, vmax (float, optional) – When using scalar data and no explicit norm, vmin and vmax define the data range that the colormap covers. By default, the colormap covers the complete value range of the supplied data. It is an error to use vmin/vmax when a norm instance is given (but using a str norm name together with vmin/vmax is acceptable).
This parameter is ignored if c is RGB(A).
alpha (float, default: None) – The alpha blending value, between 0 (transparent) and 1 (opaque).
linewidths (float or array-like, default:
rcParams["lines.linewidth"]) – The linewidth of the marker edges. Note: The default edgecolors is ‘face’. You may want to change this as well.edgecolors ({‘face’, ‘none’, None} or color or sequence of color, default:
rcParams["scatter.edgecolors"]) – The edge color of the marker. Possible values:
‘face’: The edge color will always be the same as the face color.
‘none’: No patch boundary will be drawn.
A color or sequence of colors.
For non-filled markers, edgecolors is ignored. Instead, the color is determined like with ‘face’, i.e. from c, colors, or facecolors.
plotnonfinite (bool, default: False) – Whether to plot points with nonfinite c (i.e.
inf,-infornan). IfTruethe points are drawn with the bad colormap color (see .Colormap.set_bad).- Returns
Axes on which the scatterplot is added.
- Return type
- spider(components: Optional[list] = None, indexes: Optional[list] = None, ax=None, mode='plot', index_order=None, autoscale=True, scatter_kw={}, line_kw={}, **kwargs)[source]
Method for spider plots. Convenience access function to
spider()(see Other Parameters, below), where further parameters for relevant matplotlib functions are also listed.
- Parameters
components (
list, None) – Elements or compositional components to plot.indexes (
list, None) – Elements or compositional components to plot.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.index_order – Function to order spider plot indexes (e.g. by incompatibility).
autoscale (
bool) – Whether to autoscale the y-axis limits for standard spider plots.mode (
str, :code`[“plot”, “fill”, “binkde”, “ckde”, “kde”, “hist”]`) – Mode for plot. Plot will produce a line-scatter diagram. Fill will return a filled range. Density will return a conditional density diagram.scatter_kw (
dict) – Keyword parameters to be passed to the scatter plotting function.line_kw (
dict) – Keyword parameters to be passed to the line plotting function.Note
The following additional parameters are from
pyrolite.plot.spider.spider().
- Other Parameters
arr (
numpy.ndarray) – Data array.label (
str,None) – Label for the individual series.logy (
bool) – Whether to use a log y-axis.yextent (
tuple) – Extent in the y direction for conditional probability plots, to limit the gridspace over which the kernel density estimates are evaluated.unity_line (
bool) – Add a line at y=1 for reference.set_ticks (
bool) – Whether to set the x-axis ticks according to the specified index.- Returns
Axes on which the spider diagram is plotted.
- Return type
Todo
Add ‘compositional data’ filter for default components if None is given
- stem(components: Optional[list] = None, ax=None, orientation='horizontal', axlabels=True, **kwargs)[source]
Method for creating stem plots. Convenience access function to
stem()(see Other Parameters, below), where further parameters for relevant matplotlib functions are also listed.
- Parameters
components (
list,None) – Elements or compositional components to plot.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.orientation (
str) – Orientation of the plot (horizontal or vertical).axlabels (
bool, True) – Whether to add x-y axis labels.Note
The following additional parameters are from
pyrolite.plot.stem.stem().
- Other Parameters
x, y (
numpy.ndarray) – 1D arrays for independent and dependent axes.- Returns
Axes on which the stem diagram is plotted.
- Return type
pyrolite.plot.spider
- pyrolite.plot.spider.spider(arr, indexes=None, ax=None, label=None, logy=True, yextent=None, mode='plot', unity_line=False, scatter_kw={}, line_kw={}, set_ticks=True, autoscale=True, **kwargs)[source]
Plots spidergrams for trace elements data. Additional arguments are typically forwarded to respective
matplotlibfunctionsplot()andscatter()(see Other Parameters, below).
- Parameters
arr (
numpy.ndarray) – Data array.indexes (:
numpy.ndarray) – Numerical indexes of x-axis positions.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.label (
str,None) – Label for the individual series.logy (
bool) – Whether to use a log y-axis.yextent (
tuple) – Extent in the y direction for conditional probability plots, to limit the gridspace over which the kernel density estimates are evaluated.mode (
str,["plot", "fill", "binkde", "ckde", "kde", "hist"]) – Mode for plot. Plot will produce a line-scatter diagram. Fill will return a filled range. Density will return a conditional density diagram.unity_line (
bool) – Add a line at y=1 for reference.scatter_kw (
dict) – Keyword parameters to be passed to the scatter plotting function.line_kw (
dict) – Keyword parameters to be passed to the line plotting function.set_ticks (
bool) – Whether to set the x-axis ticks according to the specified index.autoscale (
bool) – Whether to autoscale the y-axis limits for standard spider plots.Note
The following additional parameters are from
matplotlib.pyplot.scatter().
- Other Parameters
x, y (float or array-like, shape (n, )) – The data positions.
s (float or array-like, shape (n, ), optional) – The marker size in points**2 (typographic points are 1/72 in.). Default is
rcParams['lines.markersize'] ** 2.The linewidth and edgecolor can visually interact with the marker size, and can lead to artifacts if the marker size is smaller than the linewidth.
If the linewidth is greater than 0 and the edgecolor is anything but ‘none’, then the effective size of the marker will be increased by half the linewidth because the stroke will be centered on the edge of the shape.
To eliminate the marker edge either set linewidth=0 or edgecolor=’none’.
c (array-like or list of colors or color, optional) – The marker colors. Possible values:
A scalar or sequence of n numbers to be mapped to colors using cmap and norm.
A 2D array in which the rows are RGB or RGBA.
A sequence of colors of length n.
A single color format string.
Note that c should not be a single numeric RGB or RGBA sequence because that is indistinguishable from an array of values to be colormapped. If you want to specify the same RGB or RGBA value for all points, use a 2D array with a single row. Otherwise, value-matching will have precedence in case of a size matching with x and y.
If you wish to specify a single color for all points prefer the color keyword argument.
Defaults to None. In that case the marker color is determined by the value of color, facecolor or facecolors. In case those are not specified or None, the marker color is determined by the next color of the
Axes’ current “shape and fill” color cycle. This cycle defaults torcParams["axes.prop_cycle"].marker (~.markers.MarkerStyle, default:
rcParams["scatter.marker"]) – The marker style. marker can be either an instance of the class or the text shorthand for a particular marker. Seematplotlib.markersfor more information about marker styles.cmap (str or ~matplotlib.colors.Colormap, default:
rcParams["image.cmap"]) – The Colormap instance or registered colormap name used to map scalar data to colors.This parameter is ignored if c is RGB(A).
norm (str or ~matplotlib.colors.Normalize, optional) – The normalization method used to scale scalar data to the [0, 1] range before mapping to colors using cmap. By default, a linear scaling is used, mapping the lowest value to 0 and the highest to 1.
If given, this can be one of the following:
An instance of .Normalize or one of its subclasses (see Colormap normalization).
A scale name, i.e. one of “linear”, “log”, “symlog”, “logit”, etc. For a list of available scales, call matplotlib.scale.get_scale_names(). In that case, a suitable .Normalize subclass is dynamically generated and instantiated.
This parameter is ignored if c is RGB(A).
vmin, vmax (float, optional) – When using scalar data and no explicit norm, vmin and vmax define the data range that the colormap covers. By default, the colormap covers the complete value range of the supplied data. It is an error to use vmin/vmax when a norm instance is given (but using a str norm name together with vmin/vmax is acceptable).
This parameter is ignored if c is RGB(A).
alpha (float, default: None) – The alpha blending value, between 0 (transparent) and 1 (opaque).
linewidths (float or array-like, default:
rcParams["lines.linewidth"]) – The linewidth of the marker edges. Note: The default edgecolors is ‘face’. You may want to change this as well.edgecolors ({‘face’, ‘none’, None} or color or sequence of color, default:
rcParams["scatter.edgecolors"]) – The edge color of the marker. Possible values:
‘face’: The edge color will always be the same as the face color.
‘none’: No patch boundary will be drawn.
A color or sequence of colors.
For non-filled markers, edgecolors is ignored. Instead, the color is determined like with ‘face’, i.e. from c, colors, or facecolors.
plotnonfinite (bool, default: False) – Whether to plot points with nonfinite c (i.e.
inf,-infornan). IfTruethe points are drawn with the bad colormap color (see .Colormap.set_bad).Note
The following additional parameters are from
matplotlib.pyplot.plot().
- Other Parameters
x, y (array-like or scalar) – The horizontal / vertical coordinates of the data points. x values are optional and default to
range(len(y)).Commonly, these parameters are 1D arrays.
They can also be scalars, or two-dimensional (in that case, the columns represent separate data sets).
These arguments cannot be passed as keywords.
fmt (str, optional) – A format string, e.g. ‘ro’ for red circles. See the Notes section for a full description of the format strings.
Format strings are just an abbreviation for quickly setting basic line properties. All of these and more can also be controlled by keyword arguments.
This argument cannot be passed as keyword.
data (indexable object, optional) – An object with labelled data. If given, provide the label names to plot in x and y.
Note
Technically there’s a slight ambiguity in calls where the second label is a valid fmt.
plot('n', 'o', data=obj)could beplt(x, y)orplt(y, fmt). In such cases, the former interpretation is chosen, but a warning is issued. You may suppress the warning by adding an empty format stringplot('n', 'o', '', data=obj).- Returns
Axes on which the spiderplot is plotted.
- Return type
Notes
By using separate lines and scatterplots, values between two missing items are still presented.
Todo
Might be able to speed up lines with ~matplotlib.collections.LineCollection.
Legend entries
- pyrolite.plot.spider.REE_v_radii(arr=None, ax=None, ree=['La', 'Ce', 'Pr', 'Nd', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Ho', 'Er', 'Tm', 'Yb', 'Lu'], index='elements', mode='plot', logy=True, tl_rotation=60, unity_line=False, scatter_kw={}, line_kw={}, set_labels=True, set_ticks=True, **kwargs)[source]
Creates an axis for a REE diagram with ionic radii along the x axis.
- Parameters
arr (
numpy.ndarray) – Data array.ax (
matplotlib.axes.Axes,None) – Optional designation of axes to reconfigure.ree (
list) – List of REE to use as an index.index (
str) – Whether to plot using radii on the x-axis (‘radii’), or elements (‘elements’).mode (
str,["plot", "fill", "binkde", "ckde", "kde", "hist"]) – Mode for plot. Plot will produce a line-scatter diagram. Fill will return a filled range. Density will return a conditional density diagram.logy (
bool) – Whether to use a log y-axis.tl_rotation (
float) – Rotation of the numerical index labels in degrees.unity_line (
bool) – Add a line at y=1 for reference.scatter_kw (
dict) – Keyword parameters to be passed to the scatter plotting function.line_kw (
dict) – Keyword parameters to be passed to the line plotting function.set_labels (
bool) – Whether to set the x-axis ticklabels for the REE.set_ticks (
bool) – Whether to set the x-axis ticks according to the specified index.Note
The following additional parameters are from
pyrolite.plot.spider.spider().
- Other Parameters
indexes (:
numpy.ndarray) – Numerical indexes of x-axis positions.label (
str,None) – Label for the individual series.yextent (
tuple) – Extent in the y direction for conditional probability plots, to limit the gridspace over which the kernel density estimates are evaluated.autoscale (
bool) – Whether to autoscale the y-axis limits for standard spider plots.- Returns
Axes on which the REE_v_radii plot is added.
- Return type
Todo
Turn this into a plot template within pyrolite.plot.templates submodule
pyrolite.plot.density
Kernel desnity estimation plots for geochemical data.
- pyrolite.plot.density.density(arr, ax=None, logx=False, logy=False, bins=25, mode='density', extent=None, contours=[], percentiles=True, relim=True, cmap=<matplotlib.colors.ListedColormap object>, shading='auto', vmin=0.0, colorbar=False, **kwargs)[source]
Creates diagramatic representation of data density and/or frequency for either binary diagrams (X-Y) or ternary plots. Additional arguments are typically forwarded to respective
matplotlibfunctionspcolormesh(),hist2d(),hexbin(),contour(), andcontourf()(see Other Parameters, below).
- Parameters
arr (
numpy.ndarray) – Dataframe from which to draw data.ax (
matplotlib.axes.Axes, None) – The subplot to draw on.logx (
bool, False) – Whether to use a logspaced grid on the x axis. Values strictly >0 required.logy (
bool, False) – Whether to use a logspaced grid on the y axis. Values strictly >0 required.bins (
int, 20) – Number of bins used in the gridded functions (histograms, KDE evaluation grid).mode (
str, ‘density’) – Different modes used here: [‘density’, ‘hexbin’, ‘hist2d’]extent (
list) – Predetermined extent of the grid for which to from the histogram/KDE. In the general form (xmin, xmax, ymin, ymax).contours (
list) – Contours to add to the plot, wheremode='density'is used.percentiles (
bool, True) – Whether contours specified are to be converted to percentiles.relim (
bool,True) – Whether to relimit the plot based on xmin, xmax values.cmap (
matplotlib.colors.Colormap) – Colormap for mapping surfaces.vmin (
float, 0.) – Minimum value for colormap.shading (
str, ‘auto’) – Shading to apply to pcolormesh.colorbar (
bool, False) – Whether to append a linked colorbar to the generated mappable image.Note
The following additional parameters are from
matplotlib.pyplot.pcolormesh().
- Other Parameters
C (array-like) – The mesh data. Supported array shapes are:
(M, N) or M*N: a mesh with scalar data. The values are mapped to colors using normalization and a colormap. See parameters norm, cmap, vmin, vmax.
(M, N, 3): an image with RGB values (0-1 float or 0-255 int).
(M, N, 4): an image with RGBA values (0-1 float or 0-255 int), i.e. including transparency.
The first two dimensions (M, N) define the rows and columns of the mesh data.
X, Y (array-like, optional) –
The coordinates of the corners of quadrilaterals of a pcolormesh:
(X[i+1, j], Y[i+1, j]) (X[i+1, j+1], Y[i+1, j+1]) ●╶───╴● │ │ ●╶───╴● (X[i, j], Y[i, j]) (X[i, j+1], Y[i, j+1])Note that the column index corresponds to the x-coordinate, and the row index corresponds to y. For details, see the Notes section below.
If
shading='flat'the dimensions of X and Y should be one greater than those of C, and the quadrilateral is colored due to the value atC[i, j]. If X, Y and C have equal dimensions, a warning will be raised and the last row and column of C will be ignored.If
shading='nearest'or'gouraud', the dimensions of X and Y should be the same as those of C (if not, a ValueError will be raised). For'nearest'the colorC[i, j]is centered on(X[i, j], Y[i, j]). For'gouraud', a smooth interpolation is caried out between the quadrilateral corners.If X and/or Y are 1-D arrays or column vectors they will be expanded as needed into the appropriate 2D arrays, making a rectangular grid.
norm (str or ~matplotlib.colors.Normalize, optional) – The normalization method used to scale scalar data to the [0, 1] range before mapping to colors using cmap. By default, a linear scaling is used, mapping the lowest value to 0 and the highest to 1.
If given, this can be one of the following:
An instance of .Normalize or one of its subclasses (see Colormap normalization).
A scale name, i.e. one of “linear”, “log”, “symlog”, “logit”, etc. For a list of available scales, call matplotlib.scale.get_scale_names(). In that case, a suitable .Normalize subclass is dynamically generated and instantiated.
vmin, vmax (float, optional) – When using scalar data and no explicit norm, vmin and vmax define the data range that the colormap covers. By default, the colormap covers the complete value range of the supplied data. It is an error to use vmin/vmax when a norm instance is given (but using a str norm name together with vmin/vmax is acceptable).
edgecolors ({‘none’, None, ‘face’, color, color sequence}, optional) – The color of the edges. Defaults to ‘none’. Possible values:
‘none’ or ‘’: No edge.
None:
rcParams["patch.edgecolor"]will be used. Note that currentlyrcParams["patch.force_edgecolor"]has to be True for this to work.‘face’: Use the adjacent face color.
A color or sequence of colors will set the edge color.
The singular form edgecolor works as an alias.
alpha (float, default: None) – The alpha blending value, between 0 (transparent) and 1 (opaque).
snap (bool, default: False) – Whether to snap the mesh to pixel boundaries.
rasterized (bool, optional) – Rasterize the pcolormesh when drawing vector graphics. This can speed up rendering and produce smaller files for large data sets. See also /gallery/misc/rasterization_demo.
Note
The following additional parameters are from
matplotlib.pyplot.hist2d().
- Other Parameters
x, y (array-like, shape (n, )) – Input values
range (array-like shape(2, 2), optional) – The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the bins parameters):
[[xmin, xmax], [ymin, ymax]]. All values outside of this range will be considered outliers and not tallied in the histogram.density (bool, default: False) – Normalize histogram. See the documentation for the density parameter of ~.Axes.hist for more details.
weights (array-like, shape (n, ), optional) – An array of values w_i weighing each sample (x_i, y_i).
cmin, cmax (float, default: None) – All bins that has count less than cmin or more than cmax will not be displayed (set to NaN before passing to ~.Axes.pcolormesh) and these count values in the return value count histogram will also be set to nan upon return.
Note
The following additional parameters are from
matplotlib.pyplot.hexbin().
- Other Parameters
x, y (array-like) – The data positions. x and y must be of the same length.
C (array-like, optional) – If given, these values are accumulated in the bins. Otherwise, every point has a value of 1. Must be of the same length as x and y.
gridsize (int or (int, int), default: 100) – If a single int, the number of hexagons in the x-direction. The number of hexagons in the y-direction is chosen such that the hexagons are approximately regular.
Alternatively, if a tuple (nx, ny), the number of hexagons in the x-direction and the y-direction. In the y-direction, counting is done along vertically aligned hexagons, not along the zig-zag chains of hexagons; see the following illustration.
To get approximately regular hexagons, choose \(n_x = \sqrt{3}\,n_y\).
xscale ({‘linear’, ‘log’}, default: ‘linear’) – Use a linear or log10 scale on the horizontal axis.
yscale ({‘linear’, ‘log’}, default: ‘linear’) – Use a linear or log10 scale on the vertical axis.
mincnt (int >= 0, default: *None*) – If not None, only display cells with at least mincnt number of points in the cell.
marginals (bool, default: *False*) – If marginals is True, plot the marginal density as colormapped rectangles along the bottom of the x-axis and left of the y-axis.
Note
The following additional parameters are from
matplotlib.pyplot.contour().
- Other Parameters
X, Y (array-like, optional) – The coordinates of the values in Z.
X and Y must both be 2D with the same shape as Z (e.g. created via numpy.meshgrid), or they must both be 1-D such that
len(X) == Nis the number of columns in Z andlen(Y) == Mis the number of rows in Z.X and Y must both be ordered monotonically.
If not given, they are assumed to be integer indices, i.e.
X = range(N),Y = range(M).Z ((M, N) array-like) – The height values over which the contour is drawn. Color-mapping is controlled by cmap, norm, vmin, and vmax.
levels (int or array-like, optional) – Determines the number and positions of the contour lines / regions.
If an int n, use ~matplotlib.ticker.MaxNLocator, which tries to automatically choose no more than n+1 “nice” contour levels between minimum and maximum numeric values of Z.
If array-like, draw contour lines at the specified levels. The values must be in increasing order.
Note
The following additional parameters are from
matplotlib.pyplot.contourf().
- Other Parameters
X, Y (array-like, optional) – The coordinates of the values in Z.
X and Y must both be 2D with the same shape as Z (e.g. created via numpy.meshgrid), or they must both be 1-D such that
len(X) == Nis the number of columns in Z andlen(Y) == Mis the number of rows in Z.X and Y must both be ordered monotonically.
If not given, they are assumed to be integer indices, i.e.
X = range(N),Y = range(M).Z ((M, N) array-like) – The height values over which the contour is drawn. Color-mapping is controlled by cmap, norm, vmin, and vmax.
levels (int or array-like, optional) – Determines the number and positions of the contour lines / regions.
If an int n, use ~matplotlib.ticker.MaxNLocator, which tries to automatically choose no more than n+1 “nice” contour levels between minimum and maximum numeric values of Z.
If array-like, draw contour lines at the specified levels. The values must be in increasing order.
- Returns
matplotlib.axes.Axes– Axes on which the densityplot is plotted... seealso:: –
Functions:
Notes
The default density estimates and derived contours are generated based on kernel density estimates. Assumptions around e.g. 95% of points lying within a 95% contour won’t necessarily be valid for non-normally distributed data (instead, this represents the approximate 95% percentile on the kernel density estimate). Note that contours are currently only generated; for mode=”density”; future updates may allow the use of a histogram basis, which would give results closer to 95% data percentiles.
Todo
- Allow generation of contours from histogram data, rather than just
the kernel density estimate.
- Implement an option and filter to ‘scatter’ points below the minimum threshold
or maximum percentile contours.
pyrolite.plot.density.grid
pyrolite.plot.density.ternary
- pyrolite.plot.density.ternary.ternary_heatmap(data, bins=20, mode='density', transform=<function ILR>, inverse_transform=<function inverse_ILR>, ternary_min_value=0.0001, grid_border_frac=0.1, grid=None, **kwargs)[source]
Heatmap for ternary diagrams. This invokes a 3D to 2D transform such as a log transform prior to creating a grid.
- Parameters
data (
numpy.ndarray) – Ternary data to obtain heatmap coords from.bins (
int) – Number of bins for the grid.mode (
str,{'histogram', 'density'}) – Which mode to render the histogram/KDE in.transform (
callable|sklearn.base.TransformerMixin) – Callable function or Transformer class.inverse_transform (
callable) – Inverse function for transform, necessary if transformer class not specified.ternary_min_value (
float) – Optional specification of minimum values within a ternary diagram to draw the transformed grid.grid_border_frac (
float) – Size of border around the grid, expressed as a fraction of the total grid range.grid (
numpy.ndarray) – Grid coordinates to sample at, if already calculated. For the density mode, this is a (nsamples, 2) array. For histograms, this is a two-member list of bin edges.- Returns
t, l, r (
tupleofnumpy.ndarray) – Ternary coordinates for the heatmap.H (
numpy.ndarray) – Histogram/density estimates for the coordinates.data (
dict) – Data dictonary with grid arrays and relevant information.Notes
Zeros will not render in this heatmap, consider replacing zeros with small values or imputing them if they must be incorporated.
pyrolite.plot.parallel
- pyrolite.plot.parallel.parallel(df, components=None, classes=None, rescale=True, legend=False, ax=None, label_rotate=60, **kwargs)[source]
Create a parallel coordinate plot across dataframe columns, with individual lines for each row.
- Parameters
df (
pandas.DataFrame) – Dataframe to create a plot from.components (
list) – Subset of dataframe columns to use as indexes along the x-axis.rescale (
bool) – Whether to rescale values to [-1, 1].legend (
bool,False) – Whether to include or suppress the legend.ax (
matplotlib.axes.Axes) – Axis to plot on (optional).Todo
A multi-axis version would be more compatible with independent rescaling and zoom
Enable passing a list of colors
Rather than just a list of numbers to be converted to colors.
pyrolite.plot.stem
- pyrolite.plot.stem.stem(x, y, ax=None, orientation='horizontal', **kwargs)[source]
Create a stem (or ‘lollipop’) plot, with optional orientation.
- Parameters
x, y (
numpy.ndarray) – 1D arrays for independent and dependent axes.ax (
matplotlib.axes.Axes,None) – The subplot to draw on.orientation (
str) – Orientation of the plot (horizontal or vertical).- Returns
Axes on which the stem diagram is plotted.
- Return type
pyrolite.plot.biplot
- pyrolite.plot.biplot.compositional_SVD(X: ndarray)[source]
Breakdown a set of compositions to vertexes and cases for adding to a compositional biplot.
- Parameters
X (
numpy.ndarray) – Compositional array.- Returns
vertexes, cases
- Return type
- pyrolite.plot.biplot.plot_origin_to_points(xs, ys, labels=None, ax=None, origin=(0, 0), color='k', marker='o', pad=0.05, **kwargs)[source]
Plot lines radiating from a specific origin. Fornulated for creation of biplots (
covariance_biplot(),compositional_biplot()).
- Parameters
xs, ys (
numpy.ndarray) – Coordinates for points to add.labels (
list) – Labels for verticies.ax (
matplotlib.axes.Axes) – Axes to plot on.origin (
tuple) – Origin to plot from.color (
str) – Line color to use.marker (
str) – Marker to use for ends of vectors and origin.pad (
float) – Fraction of vector to pad text label.- Returns
Axes on which radial plot is added.
- Return type
- pyrolite.plot.biplot.compositional_biplot(data, labels=None, ax=None, **kwargs)[source]
Create a compositional biplot.
- Parameters
data (
numpy.ndarray) – Coordinates for points to add.labels (
list) – Labels for verticies.ax (
matplotlib.axes.Axes) – Axes to plot on.- Returns
Axes on which biplot is added.
- Return type
pyrolite.plot.templates
A utility submodule for standardised plot templates to be added to matplotlib axes.
Todo
Make use of new ax.axline features (https://matplotlib.org/3.3.1/users/whats_new.html#new-axes-axline-method)
- pyrolite.plot.templates.pearceThNbYb(ax=None, relim=True, color='k', **kwargs)[source]
Adds the Th-Nb-Yb delimiter lines from Pearce (2008) 1 to an axes.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the template onto.relim (
bool) – Whether to relimit axes to fit the built in ranges for this diagram.color (
str) – Line color for the diagram.References
- 1
Pearce J. A. (2008) Geochemical fingerprinting of oceanic basalts with applications to ophiolite classification and the search for Archean oceanic crust. Lithos 100, 14–48. doi: 10.1016/j.lithos.2007.06.016
- Returns
ax
- Return type
- pyrolite.plot.templates.pearceTiNbYb(ax=None, relim=True, color='k', annotate=True, **kwargs)[source]
Adds the Ti-Nb-Yb delimiter lines from Pearce (2008) 2 to an axes.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the template onto.relim (
bool) – Whether to relimit axes to fit the built in ranges for this diagram.color (
str) – Line color for the diagram.References
- 2
Pearce J. A. (2008) Geochemical fingerprinting of oceanic basalts with applications to ophiolite classification and the search for Archean oceanic crust. Lithos 100, 14–48. doi: {pearce2008}
- Returns
ax
- Return type
- pyrolite.plot.templates.JensenPlot(ax=None, add_labels=False, color='k', **kwargs)[source]
Jensen Plot for classification of sub-alkaline volcanic rocks 3.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the template on to.add_labels (
bool) – Whether to include the labels for the diagram.color (
str) – Line color for the diagram.- Returns
ax
- Return type
References
- 3
Jensen, L. S. (1976). A new cation plot for classifying sub-alkaline volcanic rocks. Ontario Division of Mines. Miscellaneous Paper No. 66.
Notes
Diagram used for the classification classification of subalkalic volcanic rocks. The diagram is constructed for molar cation percentages of Al, Fe+Ti and Mg, on account of these elements’ stability upon metamorphism. This particular version uses updated labels relative to Jensen (1976), in which the fields have been extended to the full range of the ternary plot.
- pyrolite.plot.templates.TAS(ax=None, add_labels=False, which_labels='ID', relim=True, color='k', which_model=None, **kwargs)[source]
Adds the TAS diagram to an axes. Diagram from Middlemost (1994) 4, a closed-polygon variant after Le Bas et al (1992) 5.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the template on to.add_labels (
bool) – Whether to add labels at polygon centroids.which_labels (
str) – Which labels to add to the polygons (e.g. for TAS, ‘volcanic’, ‘intrusive’ or the field ‘ID’).relim (
bool) – Whether to relimit axes to fit the built in ranges for this diagram.color (
str) – Line color for the diagram.which_model (
str) – The name of the model variant to use, if not Middlemost.- Returns
ax
- Return type
References
- 4
Middlemost, E. A. K. (1994). Naming materials in the magma/igneous rock system. Earth-Science Reviews, 37(3), 215–224. doi: 10.1016/0012-8252(94)90029-9
- 5
Le Bas, M.J., Le Maitre, R.W., Woolley, A.R. (1992). The construction of the Total Alkali-Silica chemical classification of volcanic rocks. Mineralogy and Petrology 46, 1–22. doi: 10.1007/BF01160698
- pyrolite.plot.templates.USDASoilTexture(ax=None, add_labels=False, color='k', **kwargs)[source]
United States Department of Agriculture Soil Texture classification model 6 7.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the template on to.add_labels (
bool) – Whether to include the labels for the diagram.color (
str) – Line color for the diagram.- Returns
ax
- Return type
References
- 6
Soil Science Division Staff (2017). Soil Survey Manual. C. Ditzler, K. Scheffe, and H.C. Monger (eds.). USDA Handbook 18. Government Printing Office, Washington, D.C.
- 7
Thien, Steve J. (1979). A Flow Diagram for Teaching Texture-by-Feel Analysis. Journal of Agronomic Education 8:54–55. doi: 10.2134/jae.1979.0054
- pyrolite.plot.templates.QAP(ax=None, add_labels=False, which_labels='ID', color='k', **kwargs)[source]
IUGS QAP ternary classification diagram 8 9.
- Parameters
ax (
matplotlib.axes.Axes) – Ternary axes to add the diagram to.add_labels (
bool) – Whether to add labels at polygon centroids.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.color (
str) – Color for the polygon edges in the diagram.References
- 8
Streckeisen, A. Classification and nomenclature of plutonic rocks recommendations of the IUGS subcommission on the systematics of Igneous Rocks. Geol Rundsch 63, 773–786 (1974). doi: 10.1007/BF01820841
- 9
Le Maitre,R.W. 2002. Igneous Rocks: A Classification and Glossary of Terms : Recommendations of International Union of Geological Sciences Subcommission on the Systematics of Igneous Rocks. Cambridge University Press, 236pp
- pyrolite.plot.templates.FeldsparTernary(ax=None, add_labels=False, which_labels='ID', mode='miscibility-gap', color='k', **kwargs)[source]
Simplified feldspar classifcation diagram, based on a version printed in the second edition of ‘An Introduction to the Rock Forming Minerals’ (Deer, Howie and Zussman). [#pyrolite.plot.templates.feldspar.FeldsparTernary_1]
- Parameters
ax (
matplotlib.axes.Axes) – Ternary axes to add the diagram to.add_labels (
bool) – Whether to add labels at polygon centroids.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.mode (
str) – Which mode of the diagram to use; the two implemented for the feldspar ternary diagram are ‘default’ and ‘miscibility-gap’, the second of which provides a simplified approximation of the miscibility gap between k-feldspar and plagioclase.color (
str) – Color for the polygon edges in the diagram.References
- 10
Deer, W. A., Howie, R. A., & Zussman, J. (2013). An introduction to the rock-forming minerals (3rd ed.). Mineralogical Society of Great Britain and Ireland.
- pyrolite.plot.templates.SpinelFeBivariate(ax=None, add_labels=False, which_labels='ID', color='k', **kwargs)[source]
Fe-Spinel classification, designed for data in atoms per formula unit.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the diagram to.add_labels (
bool) – Whether to add labels at polygon centroids.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.color (
str) – Color for the polygon edges in the diagram.
- pyrolite.plot.templates.SpinelTrivalentTernary(ax=None, add_labels=False, which_labels='ID', color='k', **kwargs)[source]
Spinel Trivalent Ternary classification - designed for data in atoms per formula unit.
- Parameters
ax (
matplotlib.axes.Axes) – Ternary axes to add the diagram to.add_labels (
bool) – Whether to add labels at polygon centroids.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.color (
str) – Color for the polygon edges in the diagram.
- pyrolite.plot.templates.Pettijohn(ax=None, add_labels=False, which_labels='ID', relim=True, color='k', **kwargs)[source]
Adds the Pettijohn (1973) [#pyrolite.plot.templates.sandstones.Pettijohn_1] sandstones classification diagram.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the template on to.add_labels (
bool) – Whether to add labels at polygon centroids.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.relim (
bool) – Whether to relimit axes to fit the built in ranges for this diagram.color (
str) – Line color for the diagram.- Returns
ax
- Return type
References
- 11
Pettijohn, F. J., Potter, P. E. and Siever, R. (1973). Sand and Sandstone. New York, Springer-Verlag. 618p. doi: 10.1007/978-1-4615-9974-6
- pyrolite.plot.templates.Herron(ax=None, add_labels=False, which_labels='ID', relim=True, color='k', **kwargs)[source]
Adds the Herron (1988) [#pyrolite.plot.templates.sandstones.Herron_1] sandstones classification diagram.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to add the template on to.add_labels (
bool) – Whether to add labels at polygon centroids.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.relim (
bool) – Whether to relimit axes to fit the built in ranges for this diagram.color (
str) – Line color for the diagram.- Returns
ax
- Return type
References
- 12
Herron, M.M. (1988). Geochemical classification of terrigenous sands and shales from core or log data. Journal of Sedimentary Research, 58(5), pp.820-829. doi: 10.1306/212F8E77-2B24-11D7-8648000102C1865D
pyrolite.plot.color
- pyrolite.plot.color.get_cmode(c=None)[source]
Find which mode a color is supplied as, such that it can be processed.
- Parameters
c (
str|list|tuple|numpy.ndarray) – Color arguments as typically passed tomatplotlib.pyplot.scatter()ormatplotlib.pyplot.plot().
- pyrolite.plot.color.process_color(c=None, color=None, cmap=None, alpha=None, norm=None, bad='0.5', cmap_under=(1, 1, 1, 0.0), color_converter=<function to_rgba>, color_mappings={}, size=None, **otherkwargs)[source]
Color argument processing for pyrolite plots, returning a standardised output.
- Parameters
c (
str|list|tuple|numpy.ndarray) – Color arguments as typically passed tomatplotlib.pyplot.scatter().color (
str|list|tuple|numpy.ndarray) – Color arguments as typically passed tomatplotlib.pyplot.plot()cmap (
str|ScalarMappable) – Colormap for mapping unknown color values.alpha (
float) – Alpha to modulate color opacity.norm (
Normalize) – Normalization for the colormap.cmap_under (
str|tuple) – Color for values below the lower threshold for the cmap.color_converter – Function to use to convert colors (from strings, hex, tuples etc).
color_mappings (
dict) – Dictionary containing category-color mappings for individual color variables, with the default color mapping having the key ‘color’. For use where categorical values are specified for a color variable.size (
int) – Size of the data array along the first axis.- Returns
C – Color returned in standardised RGBA format.
- Return type
Notes
As formulated here, the addition of unused styling parameters may cause some properties (associated with ‘c’) to be set to None - and hence revert to defaults. This might be mitigated if the context could be checked - e.g. via checking keyword argument membership of
scatterkwargs()etc.
pyrolite.geochem
Submodule for working with geochemical data.
pyrolite.geochem.pyrochem (Pandas Interface)
- class pyrolite.geochem.pyrochem(obj)[source]
- property list_elements
Get the subset of columns which are element names.
- Return type
Notes
The list will have the same ordering as the source DataFrame.
- property list_isotope_ratios
Get the subset of columns which are isotope ratios.
- Return type
Notes
The list will have the same ordering as the source DataFrame.
- property list_REE
Get the subset of columns which are Rare Earth Element names.
- Return type
Notes
The returned list will reorder REE based on atomic number.
- property list_REY
Get the subset of columns which are Rare Earth Element names.
- Return type
Notes
The returned list will reorder REE based on atomic number.
- property list_oxides
Get the subset of columns which are oxide names.
- Return type
Notes
The list will have the same ordering as the source DataFrame.
- property list_compositional
- property elements
Get an elemental subset of a DataFrame.
- Return type
pandas.Dataframe
- property REE
Get a Rare Earth Element subset of a DataFrame.
- Return type
pandas.Dataframe
- property REY
Get a Rare Earth Element + Yttrium subset of a DataFrame.
- Return type
pandas.Dataframe
- property oxides
Get an oxide subset of a DataFrame.
- Return type
pandas.Dataframe
- property isotope_ratios
Get an isotope ratio subset of a DataFrame.
- Return type
pandas.Dataframe
- property compositional
Get an oxide & elemental subset of a DataFrame.
- Return type
pandas.DataframeNotes
This wil not include isotope ratios.
- parse_chem(abbrv=['ID', 'IGSN'], split_on='[\\s_]+')[source]
Convert column names to pyrolite-recognised elemental, oxide and isotope ratio column names where valid names are found.
- check_multiple_cation_inclusion(exclude=['LOI', 'FeOT', 'Fe2O3T'])[source]
Returns cations which are present in both oxide and elemental form.
- to_molecular(renorm=True)[source]
Converts mass quantities to molar quantities.
- Parameters
renorm (
bool,True) – Whether to renormalise the dataframe after converting to relative moles.Notes
Does not convert units (i.e. mass% –> mol%; mass-ppm –> mol-ppm).
- Returns
Transformed dataframe.
- Return type
- to_weight(renorm=True)[source]
Converts molar quantities to mass quantities.
- Parameters
renorm (
bool,True) – Whether to renormalise the dataframe after converting to relative moles.Notes
Does not convert units (i.e. mol% –> mass%; mol-ppm –> mass-ppm).
- Returns
Transformed dataframe.
- Return type
- devolatilise(exclude=['H2O', 'H2O_PLUS', 'H2O_MINUS', 'CO2', 'LOI'], renorm=True)[source]
Recalculates components after exclusion of volatile phases (e.g. H2O, CO2).
- Parameters
- Returns
Transformed dataframe.
- Return type
- elemental_sum(component=None, to=None, total_suffix='T', logdata=False, molecular=False)[source]
Sums abundance for a cation to a single series, starting from a dataframe containing multiple componnents with a single set of units.
- Parameters
- Returns
Series with cation aggregated.
- Return type
- aggregate_element(to, total_suffix='T', logdata=False, renorm=False, molecular=False)[source]
Aggregates cation information from oxide and elemental components to either a single species or a designated mixture of species.
- Parameters
to (
str|Element|Formula|dict) – Component(s) to convert to. If one component is specified, the element will be converted to the target species.If more than one component is specified with proportions in a dictionary (e.g.
{'FeO': 0.9, 'Fe2O3': 0.1}), the components will be split as a fraction of the elemental sum.renorm (
bool,True) – Whether to renormalise the dataframe after recalculation.total_suffix (
str, ‘T’) – Suffix of ‘total’ variables. E.g. ‘T’ for FeOT, Fe2O3T.logdata (
bool,False) – Whether the data has been log transformed.molecular (
bool,False) – Whether to perform a sum of molecular data.Notes
This won’t convert units, so need to start from single set of units.
- Returns
Series with cation aggregated.
- Return type
- recalculate_Fe(to='FeOT', renorm=False, total_suffix='T', logdata=False, molecular=False)[source]
Recalculates abundances of iron, and normalises a dataframe to contain either a single species, or multiple species in certain proportions.
- Parameters
to (
str|Element|Formula|dict) – Component(s) to convert to.If one component is specified, all iron will be converted to the target species.
If more than one component is specified with proportions in a dictionary (e.g.
{'FeO': 0.9, 'Fe2O3': 0.1}), the components will be split as a fraction of Fe.renorm (
bool,False) – Whether to renormalise the dataframe after recalculation.total_suffix (
str, ‘T’) – Suffix of ‘total’ variables. E.g. ‘T’ for FeOT, Fe2O3T.logdata (
bool,False) – Whether the data has been log transformed.molecular (
bool,False) – Flag that data is in molecular units, rather than weight units.- Returns
Transformed dataframe.
- Return type
- get_ratio(ratio: str, alias: Optional[str] = None, norm_to=None, molecular=False)[source]
Add a ratio of components A and B, given in the form of string ‘A/B’. Returned series be assigned an alias name.
- Parameters
ratio (
str) – String decription of ratio in the form A/B[_n].alias (
str) – Alternate name for ratio to be used as column name.norm_to (
str|pyrolite.geochem.norm.Composition, None) – Reference composition to normalise to.molecular (
bool,False) – Flag that data is in molecular units, rather than weight units.- Returns
Dataframe with ratio appended.
- Return type
See also
- add_ratio(ratio: str, alias: Optional[str] = None, norm_to=None, molecular=False)[source]
Add a ratio of components A and B, given in the form of string ‘A/B’. Returned series be assigned an alias name.
- Parameters
ratio (
str) – String decription of ratio in the form A/B[_n].alias (
str) – Alternate name for ratio to be used as column name.norm_to (
str|pyrolite.geochem.norm.Composition, None) – Reference composition to normalise to.molecular (
bool,False) – Flag that data is in molecular units, rather than weight units.- Returns
Dataframe with ratio appended.
- Return type
See also
- add_MgNo(molecular=False, use_total_approx=False, approx_Fe203_frac=0.1, name='Mg#')[source]
Append the magnesium number to a dataframe.
- Parameters
molecular (
bool,False) – Whether the input data is molecular.use_total_approx (
bool,False) – Whether to use an approximate calculation using total iron rather than just FeO.approx_Fe203_frac (
float) – Fraction of iron which is oxidised, used in approximation mentioned above.name (
str) – Name to use for the Mg Number column.- Returns
Dataframe with ratio appended.
- Return type
See also
add_ratio()
- lambda_lnREE(norm_to='ChondriteREE_ON', exclude=['Pm', 'Eu'], params=None, degree=4, scale='ppm', sigmas=None, **kwargs)[source]
Calculates orthogonal polynomial coefficients (lambdas) for a given set of REE data, normalised to a specific composition 1. Lambda factors are given for the radii vs. ln(REE/NORM) polynomial combination.
- Parameters
norm_to (
str|Composition|numpy.ndarray) – Which reservoir to normalise REE data to (defaults to"ChondriteREE_ON").exclude (
list,["Pm", "Eu"]) – Which REE elements to exclude from the fit. May wish to include Ce for minerals in which Ce anomalies are common.params (
list|str,None) – Pre-computed parameters for the orthogonal polynomials (a list of tuples). Optionally specified, otherwise defaults the parameterisation as in O’Neill (2016). If a string is supplied,"O'Neill (2016)"or similar will give the original defaults, while"full"will use all of the REE (including Eu) as a basis for the orthogonal polynomials.degree (
int, 4) – Maximum degree polynomial fit component to include.scale (
str) – Current units for the REE data, used to scale the reference dataset.sigmas (
float|numpy.ndarray|pandas.Series) – Value or 1D array of fractional REE uncertaintes (i.e. \(\sigma_{REE}/REE\)).References
- 1
O’Neill HSC (2016) The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57:1463–1508. doi: 10.1093/petrology/egw047
See also
get_ionic_radii(),calc_lambdas(),orthogonal_polynomial_constants(),REE_radii_plot()
- convert_chemistry(to=[], logdata=False, renorm=False, molecular=False)[source]
Attempts to convert a dataframe with one set of components to another.
- Parameters
to (
list) – Set of columns to try to extract from the dataframe.Can also include a dictionary for iron speciation. See
pyrolite.geochem.recalculate_Fe().logdata (
bool,False) – Whether chemical data has been log transformed. Necessary for aggregation functions.renorm (
bool,False) – Whether to renormalise the data after transformation.molecular (
bool,False) – Flag that data is in molecular units, rather than weight units.- Returns
Dataframe with converted chemistry.
- Return type
Todo
Check for conflicts between oxides and elements
Aggregator for ratios
Implement generalised redox transformation.
Add check for dicitonary components (e.g. Fe) in tests
- normalize_to(reference=None, units=None, convert_first=False)[source]
Normalise a dataframe to a given reference composition.
- Parameters
reference (
str|Composition|numpy.ndarray) – Reference composition to normalise to.units (
str) – Units of the input dataframe, to convert the reference composition.convert_first (
bool) – Whether to first convert the referenece compostion before normalisation. This is useful where elements are presented as different components (e.g. Ti, TiO2).- Returns
Dataframe with normalised chemistry.
- Return type
Notes
This assumes that dataframes have a single set of units.
- denormalize_from(reference=None, units=None)[source]
De-normalise a dataframe from a given reference composition.
- Parameters
reference (
str|Composition|numpy.ndarray) – Reference composition which the composition is normalised to.units (
str) – Units of the input dataframe, to convert the reference composition.- Returns
Dataframe with normalised chemistry.
- Return type
Notes
This assumes that dataframes have a single set of units.
pyrolite.geochem.ind
Collections and indexes of elements and oxides, and functions for obtaining these and relevant properties (e.g. radii).
Todo
Incompatibility indexes for spider plot ordering.
- pyrolite.geochem.ind.common_elements(cutoff=92, output='string', order=None, as_set=False)[source]
Provides a list of elements up to a particular cutoff (by default including U).
- Parameters
cutoff (
int) – Upper cutoff on atomic number for the output list. Defaults to stopping at uranium (92).output (
str) – Whether to return output list as formulae (‘formula’) or strings (anthing else).order (
callable) – Sorting function for elements.as_set (
bool,False) – Whether to return aset(True) orlist(False).- Returns
List of elements.
- Return type
Notes
Formulae cannot be used as members of a set, and hence sets returned will instead consist only of strings.
Todo
Implement ordering for e.g. incompatibility.
- pyrolite.geochem.ind.REE(output='string', dropPm=True)[source]
Provides a list of Rare Earth Elements.
- pyrolite.geochem.ind.REY(output='string', dropPm=True)[source]
Provides a list of Rare Earth Elements, with the addition of Yttrium.
- Parameters
output (
str) – Whether to return output list as formulae (‘formula’) or strings (anthing else).- Returns
List of REE+Y.
- Return type
Notes
This currently modifies the hardcoded list of
REE(), but could be adapated for different element ordering.
- pyrolite.geochem.ind.common_oxides(elements: list = [], output='string', addition: list = ['FeOT', 'Fe2O3T', 'LOI'], exclude=['O', 'He', 'Ne', 'Ar', 'Kr', 'Xe'], as_set=False)[source]
Creates a list of oxides based on a list of elements.
- Parameters
elements (
list, []) – List of elements to obtain oxide forms for.output (
str) – Whether to return output list as formulae (‘formula’) or strings (anthing else).addition (
list, []) – Additional components to append to the list.exclude (
list) – Elements to not produce oxide forms for (e.g. oxygen, noble gases).as_set (
bool) – Whether to return aset(True) orlist(False).- Returns
List of oxides.
- Return type
Notes
Formulae cannot be used as members of a set, and hence sets returned will instead consist only of strings.
Todo
Element verification
Conditional additional components on the presence of others (e.g. Fe - FeOT)
- pyrolite.geochem.ind.simple_oxides(cation, output='string')[source]
Creates a list of oxides for a cationic element (oxide of ions with c=1+ and above).
- Parameters
cation (
str|periodictable.core.Element) – Cation to obtain oxide forms for.output (
str) – Whether to return output list as formulae (‘formula’) or strings (anthing else).- Returns
List of oxides.
- Return type
- pyrolite.geochem.ind.get_cations(component: str, exclude=[], total_suffix='T')[source]
Returns the principal cations in an oxide component.
- Parameters
component (
str|periodictable.formulas.Formula) – Component to obtain cations for.exclude (
list) – Components to exclude, i.e. anions (e.g. O, Cl, F).- Returns
List of cations.
- Return type
Todo
Consider implementing
periodictable.core.Elementreturn.
- pyrolite.geochem.ind.by_incompatibility(els, reverse=False)[source]
Order a list of elements by their relative ‘incompatibility’ given by a proxy of the relative abundances in Bulk Continental Crust over a Primitive Mantle Composition.
- Parameters
- Returns
Reordered list of elements.
- Return type
Notes
Some elements are missing from this list, as as such will be omitted.
- pyrolite.geochem.ind.by_number(els, reverse=False)[source]
Order a list of elements by their atomic number.
- pyrolite.geochem.ind.get_ionic_radii(element, charge=None, coordination=None, variant=[], source='shannon', pauling=True, **kwargs)[source]
Function to obtain ionic radii for a given ion and coordination 1 2.
- Parameters
element (
str|list) – Element to obtain a radii for. If a list is passed, the function will be applied over each of the items.charge (
int) – Charge of the ion to obtain a radii for. If unspecified will use the default charge frompyrolite.mineral.ions.coordination (
int) – Coordination of the ion to obtain a radii for.variant (
list) – List of strings specifying particular variants (here ‘squareplanar’ or ‘pyramidal’, ‘highspin’ or ‘lowspin’).source (
str) – Name of the data source for ionic radii (‘shannon’ 1 or ‘whittaker’ 2).pauling (
bool) – Whether to use the radii consistent with Pauling (1960) 3 from the Shannon (1976) radii dataset 1.- Returns
Series with viable ion charge and coordination, with associated radii in angstroms. If the ion charge and coordiation are completely specified and found in the table, a single value will be returned instead.
- Return type
Notes
Shannon published two sets of radii. The first (‘Crystal Radii’) were using Shannon’s value for \(r(O^{2-}_{VI})\) of 1.26 Å, while the second (‘Ionic Radii’) is consistent with the Pauling (1960) value of \(r(O^{2-}_{VI})\) of 1.40 Å 3.
References
- 1(1,2,3)
Shannon RD (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A 32:751–767. doi: 10.1107/S0567739476001551
- 2(1,2)
Whittaker, E.J.W., Muntus, R., 1970. Ionic radii for use in geochemistry. Geochimica et Cosmochimica Acta 34, 945–956. doi: 10.1016/0016-7037(70)90077-3
- 3(1,2)
Pauling, L., 1960. The Nature of the Chemical Bond. Cornell University Press, Ithaca, NY.
Todo
Implement interpolation for coordination +/- charge.
pyrolite.geochem.transform
Functions for converting, transforming and parameterizing geochemical data.
- pyrolite.geochem.transform.to_molecular(df: DataFrame, renorm=True)[source]
Converts mass quantities to molar quantities of the same order.
- Parameters
df (
pandas.DataFrame) – Dataframe to transform.renorm (
bool,True) – Whether to renormalise the dataframe after converting to relative moles.- Returns
Transformed dataframe.
- Return type
Notes
Does not convert units (i.e. mass% –> mol%; mass-ppm –> mol-ppm).
- pyrolite.geochem.transform.to_weight(df: DataFrame, renorm=True)[source]
Converts molar quantities to mass quantities of the same order.
- Parameters
df (
pandas.DataFrame) – Dataframe to transform.renorm (
bool,True) – Whether to renormalise the dataframe after converting to relative moles.- Returns
Transformed dataframe.
- Return type
Notes
Does not convert units (i.e. mol% –> mass%; mol-ppm –> mass-ppm).
- pyrolite.geochem.transform.devolatilise(df: DataFrame, exclude=['H2O', 'H2O_PLUS', 'H2O_MINUS', 'CO2', 'LOI'], renorm=True)[source]
Recalculates components after exclusion of volatile phases (e.g. H2O, CO2).
- Parameters
df (
pandas.DataFrame) – Dataframe to devolatilise.exclude (
list) – Components to exclude from the dataset.renorm (
bool,True) – Whether to renormalise the dataframe after devolatilisation.- Returns
Transformed dataframe.
- Return type
- pyrolite.geochem.transform.oxide_conversion(oxin, oxout, molecular=False)[source]
Factory function to generate a function to convert oxide components between two elemental oxides, for use in redox recalculations.
- pyrolite.geochem.transform.elemental_sum(df: DataFrame, component=None, to=None, total_suffix='T', logdata=False, molecular=False)[source]
Sums abundance for a cation to a single series, starting from a dataframe containing multiple componnents with a single set of units.
- Parameters
df (
pandas.DataFrame) – DataFrame for which to aggregate cation data.component (
str) – Component indicating which element to aggregate.to (
str) – Component to cast the output as.logdata (
bool,False) – Whether data has been log transformed.molecular (
bool,False) – Whether to perform a sum of molecular data.- Returns
Series with cation aggregated.
- Return type
- pyrolite.geochem.transform.aggregate_element(df: DataFrame, to, total_suffix='T', logdata=False, renorm=False, molecular=False)[source]
Aggregates cation information from oxide and elemental components to either a single species or a designated mixture of species.
- Parameters
df (
pandas.DataFrame) – DataFrame for which to aggregate cation data.to (
str|Element|Formula|dict) – Component(s) to convert to. If one component is specified, the element will be converted to the target species.If more than one component is specified with proportions in a dictionary (e.g.
{'FeO': 0.9, 'Fe2O3': 0.1}), the components will be split as a fraction of the elemental sum.renorm (
bool,True) – Whether to renormalise the dataframe after recalculation.total_suffix (
str, ‘T’) – Suffix of ‘total’ variables. E.g. ‘T’ for FeOT, Fe2O3T.logdata (
bool,False) – Whether the data has been log transformed.molecular (
bool,False) – Whether to perform a sum of molecular data.Notes
This won’t convert units, so need to start from single set of units.
- Returns
Dataframe with cation aggregated to the desired species.
- Return type
- pyrolite.geochem.transform.get_ratio(df: DataFrame, ratio: str, alias: Optional[str] = None, norm_to=None, molecular=False)[source]
Get a ratio of components A and B, given in the form of string ‘A/B’. Returned series be assigned an alias name.
- Parameters
df (
pandas.DataFrame) – Dataframe to append ratio to.ratio (
str) – String decription of ratio in the form A/B[_n].alias (
str) – Alternate name for ratio to be used as column name.norm_to (
str|pyrolite.geochem.norm.Composition, None) – Reference composition to normalise to.molecular (
bool,False) – Flag that data is in molecular units, rather than weight units.- Returns
Dataframe with ratio appended.
- Return type
Todo
Use elemental sum from reference compositions
Use sympy-like functionality to accept arbitrary input for calculation
e.g.
"MgNo = Mg / (Mg + Fe)"See also
- pyrolite.geochem.transform.add_MgNo(df: DataFrame, molecular=False, use_total_approx=False, approx_Fe203_frac=0.1, name='Mg#')[source]
Append the magnesium number to a dataframe.
- Parameters
df (
pandas.DataFrame) – Input dataframe.molecular (
bool,False) – Whether the input data is molecular.use_total_approx (
bool,False) – Whether to use an approximate calculation using total iron rather than just FeO.approx_Fe203_frac (
float) – Fraction of iron which is oxidised, used in approximation mentioned above.name (
str) – Name to use for the Mg Number column.- Returns
Dataframe with ratio appended.
- Return type
See also
- pyrolite.geochem.transform.lambda_lnREE(df, norm_to='ChondriteREE_ON', exclude=['Pm', 'Eu'], params=None, degree=4, scale='ppm', allow_missing=True, min_elements=7, algorithm='ONeill', sigmas=None, **kwargs)[source]
Calculates orthogonal polynomial coefficients (lambdas) for a given set of REE data, normalised to a specific composition 1. Lambda coefficeints are given for the polynomial regression of ln(REE/NORM) vs radii.
- Parameters
df (
pandas.DataFrame) – Dataframe to calculate lambda coefficients for.norm_to (
str|Composition|numpy.ndarray) – Which reservoir to normalise REE data to (defaults to"ChondriteREE_ON").exclude (
list,["Pm", "Eu"]) – Which REE elements to exclude from the fit. May wish to include Ce for minerals in which Ce anomalies are common.params (
list|str,None) – Pre-computed parameters for the orthogonal polynomials (a list of tuples). Optionally specified, otherwise defaults the parameterisation as in O’Neill (2016). If a string is supplied,"O'Neill (2016)"or similar will give the original defaults, while"full"will use all of the REE (including Eu) as a basis for the orthogonal polynomials.degree (
int, 4) – Maximum degree polynomial fit component to include.scale (
str) – Current units for the REE data, used to scale the reference dataset.allow_missing (
True) – Whether to calculate lambdas for rows which might be missing values.min_elements (
int) – Minimum columns present to return lambda values.algorithm (
str) – Algorithm to use for fitting the orthogonal polynomials.sigmas (
float|numpy.ndarray|pandas.Series) – Value or 1D array of fractional REE uncertaintes (i.e. \(\sigma_{REE}/REE\)).Todo
Operate only on valid rows.
Add residuals, Eu, Ce anomalies as options.
References
- 1
O’Neill HSC (2016) The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57:1463–1508. doi: 10.1093/petrology/egw047
See also
get_ionic_radii(),calc_lambdas(),orthogonal_polynomial_constants(),REE_radii_plot()
- pyrolite.geochem.transform.convert_chemistry(input_df, to=[], total_suffix='T', renorm=False, molecular=False, logdata=False, **kwargs)[source]
Attempts to convert a dataframe with one set of components to another.
- Parameters
input_df (
pandas.DataFrame) – Dataframe to convert.to (
list) – Set of columns to try to extract from the dataframe.Can also include a dictionary for iron speciation. See
aggregate_element().total_suffix (
str, ‘T’) – Suffix of ‘total’ variables. E.g. ‘T’ for FeOT, Fe2O3T.renorm (
bool,False) – Whether to renormalise the data after transformation.molecular (
bool,False) – Flag that data is in molecular units, rather than weight units.logdata (
bool,False) – Whether chemical data has been log transformed. Necessary for aggregation functions.- Returns
Dataframe with converted chemistry.
- Return type
Todo
Check for conflicts between oxides and elements
Aggregator for ratios
Implement generalised redox transformation.
Add check for dicitonary components (e.g. Fe) in tests
pyrolite.geochem.norm
Reference compostitions and compositional normalisation.
- pyrolite.geochem.norm.all_reference_compositions(path=None)[source]
Get a dictionary of all reference compositions indexed by name.
- Parameters
path (
str|pathlib.Path)- Return type
- pyrolite.geochem.norm.get_reference_composition(name)[source]
Retrieve a particular composition from the reference database.
- Parameters
name (
str) – Name of the reference composition model.- Return type
- pyrolite.geochem.norm.get_reference_files(directory=None, formats=['csv'])[source]
Get a list of the reference composition files.
pyrolite.geochem.parse
Functions for parsing, formatting and validating chemical names and formulae.
- pyrolite.geochem.parse.is_isotoperatio(s)[source]
Check if text is plausibly an isotope ratio.
Todo
Validate the isotope masses vs natural isotopes
- pyrolite.geochem.parse.repr_isotope_ratio(isotope_ratio)[source]
Format an isotope ratio pair as a string.
Todo
Consider returning additional text outside of the match (e.g. 87Sr/86Sri should include the ‘i’).
- pyrolite.geochem.parse.ischem(s)[source]
Checks if a string corresponds to chemical component (compositional). Here simply checking whether it is a common element or oxide.
Todo
Implement checking for other compounds, e.g. carbonates.
- pyrolite.geochem.parse.tochem(strings: list, abbrv=['ID', 'IGSN'], split_on='[\\s_]+')[source]
Converts a list of strings containing come chemical compounds to appropriate case.
- pyrolite.geochem.parse.check_multiple_cation_inclusion(df, exclude=['LOI', 'FeOT', 'Fe2O3T'])[source]
Returns cations which are present in both oxide and elemental form.
- Parameters
df (
pandas.DataFrame) – Dataframe to check duplication within.exclude (
list,["LOI", "FeOT", "Fe2O3T"]) – List of components to exclude from the duplication check.- Returns
Set of elements for which multiple components exist in the dataframe.
- Return type
Todo
Options for output (string/formula).
pyrolite.geochem.magma
Submodule for calculating and modelling melt chemistry. Includes common functions for predicting and accounting for melt evolution.
- pyrolite.geochem.magma.FeAt8MgO(FeOT: float, MgO: float) float[source]
To account for differences in the slopes and curvature of liquid lines of descent as a function of parental magma composition 1 2 (after 3).
References
- 1
Castillo PR, Klein E, Bender J, et al (2000). Petrology and Sr, Nd, and Pb isotope geochemistry of mid-ocean ridge basalt glasses from the 11°45’N to 15°00’N segment of the East Pacific Rise. Geochemistry, Geophysics, Geosystems 1:1. doi: 10.1029/1999GC000024
- 2
Klein EM, Langmuir CH (1987). Global correlations of ocean ridge basalt chemistry with axial depth and crustal thickness. Journal of Geophysical Research: Solid Earth 92:8089–8115. doi: 10.1029/JB092iB08p08089
- 3
Langmuir CH, Bender JF (1984). The geochemistry of oceanic basalts in the vicinity of transform faults: Observations and implications. Earth and Planetary Science Letters 69:107–127. doi: 10.1016/0012-821X(84)90077-3
- pyrolite.geochem.magma.NaAt8MgO(Na2O: float, MgO: float) float[source]
To account for differences in the slopes and curvature of liquid lines of descent as a function of parental magma composition 4 5 (after 6).
References
- 4
Castillo PR, Klein E, Bender J, et al (2000). Petrology and Sr, Nd, and Pb isotope geochemistry of mid-ocean ridge basalt glasses from the 11°45’N to 15°00’N segment of the East Pacific Rise. Geochemistry, Geophysics, Geosystems 1:1. doi: 10.1029/1999GC000024
- 5
Klein EM, Langmuir CH (1987). Global correlations of ocean ridge basalt chemistry with axial depth and crustal thickness. Journal of Geophysical Research: Solid Earth 92:8089–8115. doi: 10.1029/JB092iB08p08089
- 6
Langmuir CH, Bender JF (1984). The geochemistry of oceanic basalts in the vicinity of transform faults: Observations and implications. Earth and Planetary Science Letters 69:107–127. doi: 10.1016/0012-821X(84)90077-3
- pyrolite.geochem.magma.SCSS(df, T, P, kelvin=False, grid=None, outunit='wt%')[source]
Obtain the sulfur content at sulfate and sulfide saturation 7 8.
- Parameters
df (
pandas.DataFrame) – Dataframe of compositions.T (
float|numpy.ndarray) – TemperatureP (
float|numpy.ndarray) – Pressure (kbar)kelvin (
bool) – Whether temperature values are in kelvin (True) or celsuis (False)grid (
None,'geotherm','grid') – Whether to consider temperature and pressure as a geotherm (geotherm), or independently (as a grid,grid).- Returns
sulfate, sulfide – Arrays of mass fraction sulfate and sulfide abundances at saturation.
- Return type
Notes
For anhydrite-saturated systems, the sulfur content at sulfate saturation is given by the following:
\[\begin{split}\begin{align} ln(X_S) = &10.07 - 1.151 \cdot (10^4 / T_K) + 0.104 \cdot P_{kbar}\\ &- 7.1 \cdot X_{SiO_2} - 14.02 \cdot X_{MgO} - 14.164 \cdot X_{Al_2O_3}\\ \end{align}\end{split}\]For sulfide-liquid saturated systems, the sulfur content at sulfide saturation is given by the following:
\[\begin{split}\begin{align} ln(X_S) = &{-1.76} - 0.474 \cdot (10^4 / T_K) + 0.021 \cdot P_{kbar}\\ &+ 5.559 \cdot X_{FeO} + 2.565 \cdot X_{TiO_2} + 2.709 \cdot X_{CaO}\\ &- 3.192 \cdot X_{SiO_2} - 3.049 \cdot X_{H_2O}\\ \end{align}\end{split}\]References
- 7
Li, C., and Ripley, E.M. (2009). Sulfur Contents at Sulfide-Liquid or Anhydrite Saturation in Silicate Melts: Empirical Equations and Example Applications. Economic Geology 104, 405–412. doi: gsecongeo.104.3.405
- 8
Smythe, D.J., Wood, B.J., and Kiseeva, E.S. (2017). The S content of silicate melts at sulfide saturation: New experiments and a model incorporating the effects of sulfide composition. American Mineralogist 102, 795–803. doi: 10.2138/am-2017-5800CCBY
Todo
Produce an updated version based on log-regressions?
Add updates from Smythe et al. (2017)?
pyrolite.geochem.alteration
Functions for calcuating indexes of chemical alteration.
- pyrolite.geochem.alteration.CIA(df: DataFrame)[source]
Chemical Index of Alteration (molecular) 1
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
References
- 1
Nesbitt HW, Young GM (1984). Prediction of some weathering trends of plutonic and volcanic rocks based on thermodynamic and kinetic considerations. Geochimica et Cosmochimica Acta 48:1523–1534. doi: 10.1016/0016-7037(84)90408-3
- pyrolite.geochem.alteration.CIW(df: DataFrame)[source]
Chemical Index of Weathering (molecular) 2
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
References
- 2
Harnois L (1988). The CIW index: A new chemical index of weathering. Sedimentary Geology 55:319–322. doi: 10.1016/0037-0738(88)90137-6
- pyrolite.geochem.alteration.PIA(df: DataFrame)[source]
Plagioclase Index of Alteration (molecular) 3
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
References
- 3
Fedo CM, Nesbitt HW, Young GM (1995). Unraveling the effects of potassium metasomatism in sedimentary rocks and paleosols, with implications for paleoweathering conditions and provenance. Geology 23:921–924. doi: `10.1130/0091-7613(1995)023<0921:UTEOPM>2.3.CO;2 <https://dx.doi.org/10.1130/0091-7613(1995)023<0921:UTEOPM>2.3.CO;2>`__
- pyrolite.geochem.alteration.SAR(df: DataFrame)[source]
Silica-Alumina Ratio (molecular)
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
- pyrolite.geochem.alteration.SiTiIndex(df: DataFrame)[source]
Silica-Titania Index (molecular) 4
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
References
- 4
Jayawardena U de S, Izawa E (1994). A new chemical index of weathering for metamorphic silicate rocks in tropical regions: A study from Sri Lanka. Engineering Geology 36:303–310. doi: 10.1016/0013-7952(94)90011-6
- pyrolite.geochem.alteration.WIP(df: DataFrame)[source]
Weathering Index of Parker (molecular) 5
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
References
- 5
Parker A (1970). An Index of Weathering for Silicate Rocks. Geological Magazine 107:501–504. doi: 10.1017/S0016756800058581
- pyrolite.geochem.alteration.IshikawaAltIndex(df: DataFrame)[source]
Alteration Index of Ishikawa (wt%) 6
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
References
- 6
Ishikawa Y, Sawaguchi T, Iwaya S, Horiuchi M (1976). Delineation of prospecting targets for Kuroko deposits based on modes of volcanism of underlying dacite and alteration halos. Mining Geology 27:106-117.
- pyrolite.geochem.alteration.CCPI(df: DataFrame)[source]
Chlorite-carbonate-pyrite index of Large et al. (wt%) 7.
- Parameters
df (
pandas.DataFrame) – DataFrame to calculate index from.- Returns
Alteration index series.
- Return type
Notes
Here FeO is taken as total iron (FeO+Fe2O3).
References
- 7
Large RR, Gemmell, JB, Paulick, H (2001). The alteration box plot: A simple approach to understanding the relationship between alteration mineralogy and lithogeochemistry associated with volcanic-hosted massive sulfide deposits. Economic Geology 96:957-971. doi:10.2113/gsecongeo.96.5.957
pyrolite.geochem.ions
pyrolite.geochem.isotope
Submodule for calculation and transformation of mass spectrometry data (particularly for ion-counting and isotope ratio data). Currently in the early stages of development.
Todo
Dodson ratios 1
Add noise-corrected quasi-unbiased ratios of Coath et al. (2012) 2
Synthetic data, file format parsing
Capability for dealing with pyrolite.geochem.isotopeerence materials
This would be handy for
pyrolite.geochemin general, and could be implemented in a similar way to howpyrolite.geochem.normhandles pyrolite.geochem.isotopeerence compositions.Stable isotope calculations
Simple radiogenic isotope system calculations and plots
U-Pb, U-series data reduction and uncertainty propagation
References
- 1
Dodson M. H. (1978) A linear method for second-degree interpolation in cyclical data collection. Journal of Physics E: Scientific Instruments 11, 296. doi: 10.1088/0022-3735/11/4/004
- 2
Coath C. D., Steele R. C. J. and Lunnon W. F. (2012). Statistical bias in isotope ratios. J. Anal. At. Spectrom. 28, 52–58. doi: 10.1039/C2JA10205F
- 3
Tyler B. J. (2014). The accuracy and precision of the advanced Poisson dead-time correction and its importance for multivariate analysis of high mass resolution ToF-SIMS data. Surface and Interface Analysis 46, 581–590. doi: 10.1002/sia.5543
- 4
Takano A., Takenaka H., Ichimaru S. and Nonaka H. (2012). Comparison of a new dead-time correction method and conventional models for SIMS analysis. Surface and Interface Analysis 44, 1287–1293. doi: 10.1002/sia.5004
- 5
Müller J. W. (1991). Generalized dead times. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 301, 543–551. doi: 10.1016/0168-9002(91)90021-H
pyrolite.comp
Submodule for working with compositional data.
pyrolite.comp.pyrocomp (Pandas Interface)
- class pyrolite.comp.pyrocomp(obj)[source]
- renormalise(components: list = [], scale=100.0)[source]
Renormalises compositional data to ensure closure.
- Parameters
- Returns
Renormalized dataframe.
- Return type
Notes
This won’t modify the dataframe in place, you’ll need to assign it to something. If you specify components, those components will be summed to 100%, and others remain unchanged.
- ALR(components=[], ind=-1, null_col=False, label_mode='simple')[source]
Additive Log Ratio transformation.
- Parameters
- Returns
ALR-transformed array, of shape
(N, D-1).- Return type
- inverse_ALR(ind=None, null_col=False)[source]
Inverse Additive Log Ratio transformation.
- Parameters
- Returns
Inverse-ALR transformed array, of shape
(N, D).- Return type
- CLR(label_mode='simple')[source]
Centred Log Ratio transformation.
- Parameters
label_mode (
str) – Labelling mode for the output dataframe (numeric,simple,LaTeX). If you plan to use the outputs for automated visualisation and want to know which components contribute, usesimpleorLaTeX.- Returns
CLR-transformed array, of shape
(N, D).- Return type
- inverse_CLR()[source]
Inverse Centred Log Ratio transformation.
- Returns
Inverse-CLR transformed array, of shape
(N, D).- Return type
- ILR(label_mode='simple')[source]
Isometric Log Ratio transformation.
- Parameters
label_mode (
str) – Labelling mode for the output dataframe (numeric,simple,LaTeX). If you plan to use the outputs for automated visualisation and want to know which components contribute, usesimpleorLaTeX.- Returns
ILR-transformed array, of shape
(N, D-1).- Return type
- inverse_ILR(X=None)[source]
Inverse Isometric Log Ratio transformation.
- Parameters
X (
numpy.ndarray,None) – Optional specification for an array from which to derive the orthonormal basis, with shape(N, D).- Returns
Inverse-ILR transformed array, of shape
(N, D).- Return type
- boxcox(lmbda=None, lmbda_search_space=(-1, 5), search_steps=100, return_lmbda=False)[source]
Box-Cox transformation.
- Parameters
lmbda (
numpy.number,None) – Lambda value used to forward-transform values. If none, it will be calculated using the meanlmbda_search_space (
tuple) – Range tuple (min, max).search_steps (
int) – Steps for lambda search range.- Returns
Box-Cox transformed array.
- Return type
- inverse_boxcox(lmbda=None)[source]
Inverse Box-Cox transformation.
- Parameters
lmbda (
float) – Lambda value used to forward-transform values.- Returns
Inverse Box-Cox transformed array.
- Return type
- sphere()[source]
Spherical coordinate transformation for compositional data.
- Returns
θ – Array of angles in radians (\((0, \pi / 2]\))
- Return type
- inverse_sphere(variables=None)[source]
Inverse spherical coordinate transformation to revert back to compositional data in the simplex.
pyrolite.comp.codata
- pyrolite.comp.codata.close(X: ~numpy.ndarray, sumf=<function sum>)[source]
Closure operator for compositional data.
- Parameters
X (
numpy.ndarray) – Array to close.sumf (
callable,numpy.sum()) – Sum function to use for closure.- Returns
Closed array.
- Return type
Notes
Does not check for non-positive entries.
- pyrolite.comp.codata.renormalise(df: DataFrame, components: list = [], scale=100.0)[source]
Renormalises compositional data to ensure closure.
- Parameters
df (
pandas.DataFrame) – Dataframe to renomalise.components (
list) – Option subcompositon to renormalise to 100. Useful for the use case where compostional data and non-compositional data are stored in the same dataframe.scale (
float,100.) – Closure parameter. Typically either 100 or 1.- Returns
Renormalized dataframe.
- Return type
- pyrolite.comp.codata.ALR(X: ndarray, ind: int = -1, null_col=False)[source]
Additive Log Ratio transformation.
- Parameters
X (
numpy.ndarray) – Array on which to perform the transformation, of shape(N, D).ind (
int) – Index of column used as denominator.null_col (
bool) – Whether to keep the redundant column.- Returns
ALR-transformed array, of shape
(N, D-1).- Return type
- pyrolite.comp.codata.inverse_ALR(Y: ndarray, ind=-1, null_col=False)[source]
Inverse Centred Log Ratio transformation.
- Parameters
Y (
numpy.ndarray) – Array on which to perform the inverse transformation, of shape(N, D-1).ind (
int) – Index of column used as denominator.null_col (
bool,False) – Whether the array contains an extra redundant column (i.e. shape is(N, D)).- Returns
Inverse-ALR transformed array, of shape
(N, D).- Return type
- pyrolite.comp.codata.CLR(X: ndarray)[source]
Centred Log Ratio transformation.
- Parameters
X (
numpy.ndarray) – 2D array on which to perform the transformation, of shape(N, D).- Returns
CLR-transformed array, of shape
(N, D).- Return type
- pyrolite.comp.codata.inverse_CLR(Y: ndarray)[source]
Inverse Centred Log Ratio transformation.
- Parameters
Y (
numpy.ndarray) – Array on which to perform the inverse transformation, of shape(N, D).- Returns
Inverse-CLR transformed array, of shape
(N, D).- Return type
- pyrolite.comp.codata.ILR(X: ndarray, psi=None, **kwargs)[source]
Isometric Log Ratio transformation.
- Parameters
X (
numpy.ndarray) – Array on which to perform the transformation, of shape(N, D).psi (
numpy.ndarray) – Array or matrix representing the ILR basis; optionally specified.- Returns
ILR-transformed array, of shape
(N, D-1).- Return type
- pyrolite.comp.codata.inverse_ILR(Y: ndarray, X: Optional[ndarray] = None, psi=None, **kwargs)[source]
Inverse Isometric Log Ratio transformation.
- Parameters
Y (
numpy.ndarray) – Array on which to perform the inverse transformation, of shape(N, D-1).X (
numpy.ndarray,None) – Optional specification for an array from which to derive the orthonormal basis, with shape(N, D).psi (
numpy.ndarray) – Array or matrix representing the ILR basis; optionally specified.- Returns
Inverse-ILR transformed array, of shape
(N, D).- Return type
- pyrolite.comp.codata.logratiomean(df, transform=<function CLR>)[source]
Take a mean of log-ratios along the index of a dataframe.
- Parameters
df (
pandas.DataFrame) – Dataframe from which to compute a mean along the index.transform (
callable) – Log transform to use.inverse_transform (
callable) – Inverse of log transform.- Returns
Mean values as a pandas series.
- Return type
- pyrolite.comp.codata.get_ALR_labels(df, mode='simple', ind=-1, **kwargs)[source]
Get symbolic labels for ALR coordinates based on dataframe columns.
- Parameters
df (
pandas.DataFrame) – Dataframe to generate ALR labels for.mode (
str) – Mode of label to return (LaTeX,simple).- Returns
List of ALR coordinates corresponding to dataframe columns.
- Return type
Notes
Some variable names are protected in
sympyand if used can result in errors. If one of these column names is found, it will be replaced with a title-cased duplicated version of itself (e.g. ‘S’ will be replaced by ‘Ss’).
- pyrolite.comp.codata.get_CLR_labels(df, mode='simple', **kwargs)[source]
Get symbolic labels for CLR coordinates based on dataframe columns.
- Parameters
df (
pandas.DataFrame) – Dataframe to generate CLR labels for.mode (
str) – Mode of label to return (LaTeX,simple).- Returns
List of CLR coordinates corresponding to dataframe columns.
- Return type
Notes
Some variable names are protected in
sympyand if used can result in errors. If one of these column names is found, it will be replaced with a title-cased duplicated version of itself (e.g. ‘S’ will be replaced by ‘Ss’).
- pyrolite.comp.codata.get_ILR_labels(df, mode='latex', **kwargs)[source]
Get symbolic labels for ILR coordinates based on dataframe columns.
- Parameters
df (
pandas.DataFrame) – Dataframe to generate ILR labels for.mode (
str) – Mode of label to return (LaTeX,simple).- Returns
List of ILR coordinates corresponding to dataframe columns.
- Return type
Notes
Some variable names are protected in
sympyand if used can result in errors. If one of these column names is found, it will be replaced with a title-cased duplicated version of itself (e.g. ‘S’ will be replaced by ‘Ss’).
- pyrolite.comp.codata.boxcox(X: ndarray, lmbda=None, lmbda_search_space=(-1, 5), search_steps=100, return_lmbda=False)[source]
Box-Cox transformation.
- Parameters
X (
numpy.ndarray) – Array on which to perform the transformation.lmbda (
numpy.number,None) – Lambda value used to forward-transform values. If none, it will be calculated using the meanlmbda_search_space (
tuple) – Range tuple (min, max).search_steps (
int) – Steps for lambda search range.return_lmbda (
bool) – Whether to also return the lambda value.- Returns
Box-Cox transformed array. If return_lmbda is true, tuple contains data and lambda value.
- Return type
numpy.ndarray|numpy.ndarray`(:class:`float)
- pyrolite.comp.codata.inverse_boxcox(Y: ndarray, lmbda)[source]
Inverse Box-Cox transformation.
- Parameters
Y (
numpy.ndarray) – Array on which to perform the transformation.lmbda (
float) – Lambda value used to forward-transform values.- Returns
Inverse Box-Cox transformed array.
- Return type
- pyrolite.comp.codata.sphere(ys)[source]
Spherical coordinate transformation for compositional data.
- Parameters
ys (
numpy.ndarray) – Compositional data to transform (shape (n, D)).- Returns
θ – Array of angles in radians (\((0, \pi / 2]\))
- Return type
Notes
numpy.arccos()will return angles in the range \((0, \pi)\). This shouldn’t be an issue for this function given that the input values are all positive.
- pyrolite.comp.codata.inverse_sphere(θ)[source]
Inverse spherical coordinate transformation to revert back to compositional data in the simplex.
- Parameters
θ (
numpy.ndarray) – Angular coordinates to revert.- Returns
ys – Compositional (simplex) coordinates, normalised to 1.
- Return type
- pyrolite.comp.codata.compositional_cosine_distances(arr)[source]
Calculate a distance matrix corresponding to the angles between a number of compositional vectors.
- Parameters
arr (
numpy.ndarray) – Array of n-dimensional compositions of shape (n_samples, n).- Returns
Array of angular distances of shape (n_samples, n_samples).
- Return type
pyrolite.comp.aggregate
- pyrolite.comp.aggregate.get_full_column(X: ndarray)[source]
Returns the index of the first array column which contains only finite numbers (i.e. no missing data, nan, inf).
- Parameters
X (
numpy.ndarray) – Array for which to find the first full column within.- Returns
Index of the first full column.
- Return type
- pyrolite.comp.aggregate.weights_from_array(X: ndarray)[source]
Returns a set of equal weights with size equal to that of the first axis of an array.
- Parameters
X (
numpy.ndarray) – Array of compositions to produce weights for.- Returns
Array of weights.
- Return type
- pyrolite.comp.aggregate.nan_weighted_mean(X: ndarray, weights=None)[source]
Returns a weighted mean of compositions, where weights are renormalised to account for missing data.
- Parameters
X (
numpy.ndarray) – Array of compositions to take a weighted mean of.weights (
numpy.ndarray) – Array of weights.- Returns
Array mean.
- Return type
- pyrolite.comp.aggregate.compositional_mean(df, weights=[], **kwargs)[source]
Implements an aggregation using a compositional weighted mean.
- Parameters
df (
pandas.DataFrame) – Dataframe of compositions to aggregate.weights (
numpy.ndarray) – Array of weights.- Returns
Mean values along index of dataframe.
- Return type
- pyrolite.comp.aggregate.nan_weighted_compositional_mean(X: ndarray, weights=None, ind=None, renorm=True, **kwargs)[source]
Implements an aggregation using a weighted mean, but accounts for nans. Requires at least one non-nan column for ALR mean.
When used for internal standardisation, there should be only a single common element - this would be used by default as the divisor here. When used for multiple-standardisation, the [specified] or first common element will be used.
- Parameters
X (
numpy.ndarray) – Array of compositions to aggregate.weights (
numpy.ndarray) – Array of weights.ind (
int) – Index of the column to use as the ALR divisor.renorm (
bool,True) – Whether to renormalise the output compositional mean to unity.- Returns
An array with the mean composition.
- Return type
- pyrolite.comp.aggregate.cross_ratios(df: DataFrame)[source]
Takes ratios of values across a dataframe, such that columns are denominators and the row indexes the numerators, to create a square array. Returns one array per record.
- Parameters
df (
pandas.DataFrame) – Dataframe of compositions to create ratios of.- Returns
A 3D array of ratios.
- Return type
- pyrolite.comp.aggregate.np_cross_ratios(X: ndarray, debug=False)[source]
Takes ratios of values across an array, such that columns are denominators and the row indexes the numerators, to create a square array. Returns one array per record.
- Parameters
X (
numpy.ndarray) – Array of compositions to create ratios of.- Returns
A 3D array of ratios.
- Return type
- pyrolite.comp.aggregate.standardise_aggregate(df: DataFrame, int_std=None, fixed_record_idx=0, renorm=True, **kwargs)[source]
Performs internal standardisation and aggregates dissimilar geochemical records. Note: this changes the closure parameter, and is generally intended to integrate major and trace element records.
- Parameters
df (
pandas.DataFrame) – Dataframe of compositions to aggregate of.int_std (
str) – Name of the internal standard column.fixed_record_idx (
int) – Numeric index of a specific record’s for which to retain the internal standard value (e.g for standardising trace element data).renorm (
bool,True) – Whether to renormalise to unity.- Returns
A series representing the internally standardised record.
- Return type
pyrolite.comp.impute
- pyrolite.comp.impute.EMCOMP(X, threshold=None, tol=0.0001, convergence_metric=<function <lambda>>, max_iter=30)[source]
EMCOMP replaces rounded zeros in a compositional data set based on a set of thresholds. After Palarea-Albaladejo and Martín-Fernández (2008) 1.
- Parameters
X (
numpy.ndarray) – Dataset with rounded zerosthreshold (
numpy.ndarray) – Array of threshold values for each component as a proprotion.tol (
float) – Tolerance to check for convergence.convergence_metric (
callable) – Callable function to check for convergence. Here we use a compositional distance rather than a maximum absolute difference, with very similar performance. Function needs to accept twonumpy.ndarrayarguments and third tolerance argument.max_iter (
int) – Maximum number of iterations before an error is thrown.- Returns
X_est (
numpy.ndarray) – Dataset with rounded zeros replaced.prop_zeros (
float) – Proportion of zeros in the original data set.n_iters (
int) – Number of iterations needed for convergence.Notes
At least one component without missing values is needed for the divisor. Rounded zeros/missing values are replaced by values below their respective detection limits.
This routine is not completely numerically stable as written.
Todo
Implement methods to deal with variable decection limits (i.e thresholds are array shape
(N, D))Conisder non-normal models for data distributions.
Improve numerical stability to reduce the chance of
np.infappearing.References
- 1
Palarea-Albaladejo J. and Martín-Fernández J. A. (2008) A modified EM ALR-algorithm for replacing rounded zeros in compositional data sets. Computers & Geosciences 34, 902–917. doi: 10.1016/j.cageo.2007.09.015
pyrolite.mineral
A submodule for working with mineral data.
Note
This module is a work in progress and will be gradually updated.
pyrolite.mineral.template
- class pyrolite.mineral.template.MineralTemplate(name, *components)[source]
- class pyrolite.mineral.template.Mineral(name=None, template=None, composition=None, endmembers=None)[source]
- set_composition(composition=None)[source]
Parse and assign a composition to the mineral.
- Parameters
composition – Composition to assign to the mineral. Can be provided in any form which is digestable by parse_composition.
- recalculate_cations(composition=None, ideal_cations=None, ideal_oxygens=None, Fe_species=['FeO', 'Fe', 'Fe2O3'], oxygen_constrained=False)[source]
Recalculate a composition to give an elemental ionic breakdown.
- Parameters
composition – Composition to recalculate. If not provided, will try to use the mineral composition as set.
ideal_cations (int) – Ideal number of cations to use for formulae calcuations. Will only be used if oxygen is constrained (i.e. multiple Fe species present or oxygen_constrained=True).
ideal_oxygens (int) – Ideal number of oxygens to use for formulae calcuations. Will only be used if oxygen is not constrained (i.e. single Fe species present and oxygen_constrained=False).
Fe_species (list) – List of iron species for identifying redox-defined compositions.
oxygen_constrained (bool, False) – Whether the oxygen is a closed or open system for the specific composition.
- endmember_decompose(det_lim=0.01)[source]
Decompose a mineral composition into endmember components.
- Parameters
det_lim (float) – Detection limit for individual
Notes
Currently implmented using optimization based on mass fractions.
Todo
Implement site-based endmember decomposition, which will enable more checks and balances.
- calculate_occupancy(composition=None, error=1e-05, balances=[['Fe{2+}', 'Mg{2+}']])[source]
Calculate the estimated site occupancy for a given composition. Ions will be assigned to sites according to affinities. Sites with equal affinities should recieve equal assignment.
- Parameters
composition – Composition to calculate site occupancy for.
error (float) – Absolute error for floating point occupancy calculations.
balances (list) – List of iterables containing ions to balance across multiple sites. Note that the partitioning will occur after non-balanced cations are assigned, and that ions are only balanced between sites which have defined affinities for all of the particular ions defined in the ‘balance’.
pyrolite.mineral.normative
- pyrolite.mineral.normative.unmix(comp, parts, order=1, det_lim=0.0001)[source]
From a composition and endmember components, find a set of weights which best approximate the composition as a weighted sum of components.
- Parameters
comp (
numpy.ndarray) – Array of compositions (shape \(n_S, n_C\)).parts (
numpy.ndarray) – Array of endmembers (shape \(n_E, n_C\)).order (
int) – Order of regularization, defaults to L1 for sparsity.det_lim (
float) – Detection limit, below which minor components will be omitted for sparsity.- Returns
Array of endmember modal abundances (shape \(n_S, n_E\))
- Return type
- pyrolite.mineral.normative.endmember_decompose(composition, endmembers=[], drop_zeros=True, molecular=True, order=1, det_lim=0.0001)[source]
Decompose a given mineral composition to given endmembers.
- Parameters
composition (
DataFrame|Series|Formula|str) – Composition to decompose into endmember components.endmembers (
str|list|dict) – List of endmembers to use for the decomposition.drop_zeros (
bool,True) – Whether to omit components with zero estimated abundance.molecular (
bool,True) – Whether to convert the chemistry to molecular before calculating the decomposition.order (
int) – Order of regularization passed tounmix(), defaults to L1 for sparsity.det_lim (
float) – Detection limit, below which minor components will be omitted for sparsity.- Return type
- pyrolite.mineral.normative.MiddlemostOxRatio(df)[source]
Apply a TAS classification to a dataframe, and get estimated Fe2O3/FeO ratios from Middlemost (1989).
- Parameters
df (
pandas.DataFrame) – Dataframe to get Fe2O3/FeO ratios for, containing the required oxides to calculate TAS diagrams from (i.e. SiO2, Na2O, K2O).- Returns
ratios – Series of estimated Fe2O3/FeO ratios, based on TAS classification.
- Return type
References
Middlemost, Eric A. K. (1989). Iron Oxidation Ratios, Norms and the Classification of Volcanic Rocks. Chemical Geology 77, 1: 19–26. https://doi.org/10.1016/0009-2541(89)90011-9.
- pyrolite.mineral.normative.LeMaitreOxRatio(df, mode=None)[source]
- Parameters
df (
pandas.DataFrame) – Dataframe containing compositions to calibrate against.mode (
str) – Mode for the correction - ‘volcanic’ or ‘plutonic’.- Returns
Series with oxidation ratios.
- Return type
Notes
This is a \(\mathrm{FeO / (FeO + Fe_2O_3)}\) mass ratio, not a standard molar ratio \(\mathrm{Fe^{2+}/(Fe^{2+} + Fe^{3+})}\) which is more straightfowardly used; data presented should be in mass units. For the calculation, SiO2, Na2O and K2O are expected to be present.
References
Le Maitre, R. W (1976). Some Problems of the Projection of Chemical Data into Mineralogical Classifications. Contributions to Mineralogy and Petrology 56, no. 2 (1 January 1976): 181–89. https://doi.org/10.1007/BF00399603.
- pyrolite.mineral.normative.Middlemost_Fe_correction(df)[source]
- Parameters
df (
pandas.DataFrame) – Dataframe containing compositions to calibrate against.- Returns
Series with two corrected iron components (\(\mathrm{FeO, Fe_2O_3}\)).
- Return type
References
Middlemost, Eric A. K. (1989). Iron Oxidation Ratios, Norms and the Classification of Volcanic Rocks. Chemical Geology 77, 1: 19–26. https://doi.org/10.1016/0009-2541(89)90011-9.
- pyrolite.mineral.normative.LeMaitre_Fe_correction(df, mode='volcanic')[source]
- Parameters
df (
pandas.DataFrame) – Dataframe containing compositions to correct iron for.mode (
str) – Mode for the correction - ‘volcanic’ or ‘plutonic’.- Returns
Series with two corrected iron components (\(\mathrm{FeO, Fe_2O_3}\)).
- Return type
References
Le Maitre, R. W (1976). Some Problems of the Projection of Chemical Data into Mineralogical Classifications. Contributions to Mineralogy and Petrology 56, no. 2 (1 January 1976): 181–89. https://doi.org/10.1007/BF00399603.
Middlemost, Eric A. K. (1989). Iron Oxidation Ratios, Norms and the Classification of Volcanic Rocks. Chemical Geology 77, 1: 19–26. https://doi.org/10.1016/0009-2541(89)90011-9.
- pyrolite.mineral.normative.CIPW_norm(df, Fe_correction=None, Fe_correction_mode=None, adjust_all_Fe=False, return_adjusted_input=False, return_free_components=False, rounding=3)[source]
Standardised calcuation of estimated mineralogy from bulk rock chemistry. Takes a dataframe of chemistry & creates a dataframe of estimated mineralogy. This is the CIPW norm of Verma et al. (2003). This version only uses major elements.
- Parameters
df (
pandas.DataFrame) – Dataframe containing compositions to transform.Fe_correction (
str) – Iron correction to apply, if any. Will default to ‘LeMaitre’.Fe_correction_mode (
str) – Mode for the iron correction, where applicable.adjust_all_Fe (
bool) – Where correcting iron compositions, whether to adjust all iron compositions, or only those where singular components are specified.return_adjusted_input (
bool) – Whether to return the adjusted input chemistry with the output.return_free_components (
bool) – Whether to return the free components in the output.rounding (
int) – Rounding to be applied to input and output data.- Return type
References
Verma, Surendra P., Ignacio S. Torres-Alvarado, and Fernando Velasco-Tapia (2003). A Revised CIPW Norm. Swiss Bulletin of Mineralogy and Petrology 83, 2: 197–216. Verma, S. P., & Rivera-Gomez, M. A. (2013). Computer Programs for the Classification and Nomenclature of Igneous Rocks. Episodes, 36(2), 115–124.
Todo
Note whether data needs to be normalised to 1 or 100?
Notes
The function expect oxide components to be in wt% and elemental data to be in ppm.
pyrolite.mineral.transform
- pyrolite.mineral.transform.formula_to_elemental(formula, weight=True)[source]
Convert a periodictable.formulas.Formula to elemental composition.
pyrolite.mineral.sites
- class pyrolite.mineral.sites.MX(name='M', coordination=8, *args, **kwargs)[source]
Octahedrally coordinated M site.
- class pyrolite.mineral.sites.TX(name='T', coordination=4, affinities={'Al{3+}': 1, 'Fe{3+}': 2, 'Si{4+}': 0}, *args, mode='cation', **kwargs)[source]
Tetrahedrally coordinated T site.
- class pyrolite.mineral.sites.IX(name='I', coordination=12, *args, **kwargs)[source]
Dodecahedrally coordinated I site.
pyrolite.mineral.lattice
Submodule for calcuating relative ion paritioning based on the lattice strain model 1 2 3.
References
- 1
Brice, J.C., 1975. Some thermodynamic aspects of the growth of strained crystals. Journal of Crystal Growth 28, 249–253. doi: 10.1016/0022-0248(75)90241-9
- 2
Blundy, J., Wood, B., 1994. Prediction of crystal–melt partition coefficients from elastic moduli. Nature 372, 452. doi: 10.1038/372452a0
- 3(1,2)
Wood, B.J., Blundy, J.D., 2014. Trace Element Partitioning: The Influences of Ionic Radius, Cation Charge, Pressure, and Temperature. Treatise on Geochemistry (Second Edition) 3, 421–448. doi: 10.1016/B978-0-08-095975-7.00209-6
- 4
Anderson, D.L., Anderson, O.L., 1970. Brief report: The bulk modulus-volume relationship for oxides. Journal of Geophysical Research (1896-1977) 75, 3494–3500. doi: 10.1029/JB075i017p03494
- 5
Hazen, R.M., Finger, L.W., 1979. Bulk modulus—volume relationship for cation-anion polyhedra. Journal of Geophysical Research: Solid Earth 84, 6723–6728. doi: 10.1029/JB084iB12p06723
- pyrolite.mineral.lattice.strain_coefficient(ri, rx, r0=None, E=None, T=298.15, z=None, **kwargs)[source]
Calculate the lattice strain associated with an ionic substitution 6 7.
- Parameters
ri (
float) – Ionic radius to calculate strain relative to, in angstroms (Å).rj (
float) – Ionic radius to calculate strain for, in angstroms (Å).r0 (
float,None) – Fictive ideal ionic radii for the site. The value forriwill be used in its place if none is given, and a warning issued.E (
float,None) – Young’s modulus (stiffness) for the site, in pascals (Pa). Will be estimated usingyoungs_modulus_approximation()if none is given.T (
float) – Temperature, in Kelvin (K).z (
int) – Optional specification of cationic valence, for calcuation of approximate Young’s modulus usingyoungs_modulus_approximation(), where the modulus is not specified.- Returns
The strain coefficent \(e^{\frac{-\Delta G_{strain}}{RT}}\).
- Return type
Notes
The lattice strain model relates changes in paritioning to differences in ionic radii for ions of a given cationic charge, and for a for a specific site (with Young’s modulus \(E\)). This is calcuated using the work done to expand a spherical shell centred on the lattice site, which alters the \(\Delta G\) for the formation of the mineral. This can be related to changes in partition coefficients using the following 7:
\[D_{j^{n+}} = D_{A^{n+}} \cdot e^{\frac{-4\pi E N \Big(\frac{r_{0}}{2}(r_j - r_0)^2 + \frac{1}{3}(r_j - r_0)^3\Big)}{RT}}\]Where \(D_{A^{n+}}\) is the partition coefficient for the ideal ion A, and N is Avagadro’s number (6.023e23 atoms/mol). This can also be calcuated relative to an ‘ideal’ fictive ion which has a maximum \(D\) where this data are available. This relationship arises via i) the integration to calcuate the strain energy mentioned above (\(4\pi E (\frac{r_{0}}{2}(r_j - r_0)^2 + \frac{1}{3}(r_j - r_0)^3)\)), and ii) the assumption that the changes in \(\Delta G\) occur only to size differences, and the difference is additive. The ‘segregation coefficient’ \(K_j\) can be expressed relative to the non-doped equilibirum constant \(K_0\) 6:
\[\begin{split}\begin{align} K_j &= e^{\frac{-\Delta G_0 -\Delta G_{strain}}{RT}}\\ &= e^{\frac{-\Delta G_0}{RT}} \cdot e^{\frac{-\Delta G_{strain}}{RT}}\\ &= K_0 \cdot e^{\frac{-\Delta G_{strain}}{RT}}\\ \end{align}\end{split}\]The model assumes that the crystal is elastically isotropic.
References
- 6(1,2)
Brice, J.C., 1975. Some thermodynamic aspects of the growth of strained crystals. Journal of Crystal Growth 28, 249–253. doi: 10.1016/0022-0248(75)90241-9
- 7(1,2)
Blundy, J., Wood, B., 1994. Prediction of crystal–melt partition coefficients from elastic moduli. Nature 372, 452. doi: 10.1038/372452a0
- pyrolite.mineral.lattice.youngs_modulus_approximation(z, r)[source]
Young’s modulus approximation for cationic sites in silicates and oxides 8 9 10.
- Parameters
z (
integer) – Cationic valence.r (
float) – Ionic radius of the cation (Å).- Returns
E – Young’s modulus for the cationic site, in Pascals (Pa)
- Return type
Notes
The bulk modulus \(K\) for an an ionic crystal is esimated using 8:
\[K = \frac{A Z_a Z_c e^2 (n-1)}{9 d_0 V_0}\]Where \(A\) is the Madelung constant, \(Z_c\) and \(Z_a\) are the anion and cation valences, \(e\) is the charge on the electron, \(n\) is the Born power law coefficent, and \(d_0\) is the cation-anion distance 8. Using the Shannon ionic radius for oxygen (1.38 Å), this is approximated for cations coordinated by oxygen in silicates and oxides using the following relationship 9:
\[K = 750 Z_c d^{-3}\]Where \(d\) is the cation-anion distance (Å), \(Z_c\) is the cationic valence (and \(K\) is in GPa). The Young’s modulus \(E\) is then calculated through the relationship 10:
\[E = 3 K (1 - 2 \sigma)\]Where \(\sigma\) is Poisson’s ratio, which in the case of minerals can be approimxated by 0.25 10, and hence:
\[\begin{split}\begin{align} E &\approx 1.5 K\\ E &\approx 1025 Z_c d^{-3} \end{align}\end{split}\]Todo
Add links to docstring
References
- 8(1,2,3)
Anderson, D.L., Anderson, O.L., 1970. Brief report: The bulk modulus-volume relationship for oxides. Journal of Geophysical Research (1896-1977) 75, 3494–3500. doi: 10.1029/JB075i017p03494
- 9(1,2)
Hazen, R.M., Finger, L.W., 1979. Bulk modulus—volume relationship for cation-anion polyhedra. Journal of Geophysical Research: Solid Earth 84, 6723–6728. doi: 10.1029/JB084iB12p06723
- 10(1,2,3)
Wood, B.J., Blundy, J.D., 2014. Trace Element Partitioning: The Influences of Ionic Radius, Cation Charge, Pressure, and Temperature. Treatise on Geochemistry (Second Edition) 3, 421–448. doi: 10.1016/B978-0-08-095975-7.00209-6
pyrolite.mineral.mindb
Submodule for accessing the rock forming mineral database.
Notes
Accessing and modifying the database across multiple with multiple threads/processes could result in database corruption (e.g. through repeated truncation etc).
- pyrolite.mineral.mindb.list_groups()[source]
List the mineral groups present in the mineral database.
- Return type
- pyrolite.mineral.mindb.list_minerals()[source]
List the minerals present in the mineral database.
- Return type
- pyrolite.mineral.mindb.list_formulae()[source]
List the mineral formulae present in the mineral database.
- Return type
- pyrolite.mineral.mindb.get_mineral(name='', dbpath=None)[source]
Get a specific mineral from the database.
- Parameters
name (
str) – Name of the desired mineral.dbpath (
pathlib.Path,str) – Optional overriding of the default database path.- Return type
pd.Series
- pyrolite.mineral.mindb.parse_composition(composition, drop_zeros=True)[source]
Parse a composition reference to provide an ionic elemental version in the form of a
Series. Currently acceptspandas.Series,periodictable.formulas.Formulaand structures which will directly convert topandas.Series(list of tuples, dict).
- Parameters
composition (
str|periodictable.formulas.Formula|pandas.Series) – Name of a mineral, a formula or composition as a seriesdrop_zeros (
bool) – Whether to drop compositional zeros.- Returns
mineral – Composition formatted as a series.
- Return type
- pyrolite.mineral.mindb.get_mineral_group(group='')[source]
Extract a mineral group from the database.
- Parameters
group (
str) – Group to extract from the mineral database.- Returns
Dataframe of group members and compositions.
- Return type
- pyrolite.mineral.mindb.update_database(path=None, **kwargs)[source]
Update the mineral composition database.
- Parameters
path (
str|pathlib.Path) – The desired filepath for the JSON database.Notes
This will take the ‘mins.csv’ file from the mineral pyrolite data folder and construct a document-based JSON database.
pyrolite.util
Various utilities used by other submodules.
pyrolite.util.general
- pyrolite.util.general.flatten_dict(d, climb=False, safemode=False)[source]
Flattens a nested dictionary containing only string keys.
This will work for dictionaries which don’t have two equivalent keys at the same level. If you’re worried about this, use safemode=True.
Partially taken from https://stackoverflow.com/a/6043835.
- pyrolite.util.general.swap_item(startlist: list, pull: object, push: object)[source]
Swap a specified item in a list for another.
- pyrolite.util.general.copy_file(src, dst, ext=None, permissions=None)[source]
Copy a file from one place to another. Uses the full filepath including name.
- Parameters
src (
str|pathlib.Path) – Source filepath.dst (
str|pathlib.Path) – Destination filepath or directory.ext (
str,None) – Optional file extension specification.pyrolite.util.pd
- pyrolite.util.pd.drop_where_all_empty(df)[source]
Drop rows and columns which are completely empty.
- Parameters
df (
pandas.DataFrame|pandas.Series) – Pandas object to ensure is in the form of a series.
- pyrolite.util.pd.read_table(filepath, index_col=0, **kwargs)[source]
Read tabluar data from an excel or csv text-based file.
- Parameters
filepath (
str|pathlib.Path) – Path to file.- Return type
- pyrolite.util.pd.column_ordered_append(df1, df2, **kwargs)[source]
Appends one dataframe to another, preserving the column order of the first and adding new columns on the right. Also accepts and passes on standard keyword arguments for pd.DataFrame.append.
- Parameters
df1 (
pandas.DataFrame) – The dataframe for which columns order is preserved in the output.df2 (
pandas.DataFrame) – The dataframe for which new columns are appended to the output.- Return type
- pyrolite.util.pd.accumulate(dfs, ignore_index=False, trace_source=False, names=[])[source]
Accumulate an iterable containing multiple
pandas.DataFrameto a single frame.
- Parameters
- Returns
Accumulated dataframe.
- Return type
- pyrolite.util.pd.to_frame(ser)[source]
Simple utility for converting to
pandas.DataFrame.
- Parameters
ser (
pandas.Series|pandas.DataFrame) – Pandas object to ensure is in the form of a dataframe.- Return type
- pyrolite.util.pd.to_ser(df)[source]
Simple utility for converting single column
pandas.DataFrametopandas.Series.
- Parameters
df (
pandas.DataFrame|pandas.Series) – Pandas object to ensure is in the form of a series.- Return type
- pyrolite.util.pd.to_numeric(df, errors: str = 'coerce', exclude=['float', 'int'])[source]
Converts non-numeric columns to numeric type where possible.
Notes
Avoid using .loc or .iloc on the LHS to make sure that data dtypes are propagated.
- pyrolite.util.pd.zero_to_nan(df, rtol=1e-05, atol=1e-08)[source]
Replace floats close, less or equal to zero with np.nan in a dataframe.
- Parameters
df (
pandas.DataFrame) – DataFrame to censor.rtol (
float) – The relative tolerance parameter.atol (
float) – The absolute tolerance parameter.- Returns
Censored DataFrame.
- Return type
- pyrolite.util.pd.outliers(df, cols=[], detect=<function <lambda>>, quantile_select=(0.02, 0.98), logquantile=False, exclude=False)[source]
- pyrolite.util.pd.concat_columns(df, columns=None, astype=<class 'str'>, **kwargs)[source]
Concatenate strings across columns.
- Parameters
df (
pandas.DataFrame) – Dataframe to concatenate.columns (
list) – List of columns to concatenate.astype (
type) – Type to convert final concatenation to.- Return type
- pyrolite.util.pd.uniques_from_concat(df, columns=None, hashit=True)[source]
Creates ideally unique keys from multiple columns. Optionally hashes string to standardise length of identifier.
- Parameters
df (
pandas.DataFrame) – DataFrame to create indexes for.columns (
list) – Columns to use in the string concatenatation.hashit (
bool,True) – Whether to use a hashing algorithm to create the key from a typically longer string.- Return type
- pyrolite.util.pd.df_from_csvs(csvs, dropna=True, ignore_index=False, **kwargs)[source]
Takes a list of .csv filenames and converts to a single DataFrame. Combines columns across dataframes, preserving order of the first entered.
E.g. SiO2, Al2O3, MgO, MnO, CaO SiO2, MgO, FeO, CaO SiO2, Na2O, Al2O3, FeO, CaO => SiO2, Na2O, Al2O3, MgO, FeO, MnO, CaO - Existing neighbours take priority (i.e. FeO won’t be inserted bf Al2O3) - Earlier inputs take priority (where ordering is ambiguous, place the earlier first)
Todo
Attempt to preserve column ordering across column sets, assuming they are generally in the same order but preserving only some of the information.
pyrolite.util.plot
Utility functions for working with matplotlib.
- Parameters
DEFAULT_CONT_COLORMAP (
matplotlib.colors.ScalarMappable) – Default continuous colormap.DEFAULT_DICS_COLORMAP (
matplotlib.colors.ScalarMappable) – Default discrete colormap.USE_PCOLOR (
bool) – Option to use thematplotlib.pyplot.pcolor()function in place ofmatplotlib.pyplot.pcolormesh().pyrolite.util.plot.axes
Functions for creating, ordering and modifying
Axes.
- pyrolite.util.plot.axes.get_ordered_axes(fig)[source]
Get the axes from a figure, which may or may not have been modified by pyrolite functions. This ensures that ordering is preserved.
- pyrolite.util.plot.axes.get_axes_index(ax)[source]
Get the three-digit integer index of a subplot in a regular grid.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to to get the gridspec index for.- Returns
Rows, columns and axis index for the gridspec.
- Return type
- pyrolite.util.plot.axes.replace_with_ternary_axis(ax)[source]
Replace a specified axis with a ternary equivalent.
- Parameters
ax (
Axes)- Returns
tax
- Return type
- pyrolite.util.plot.axes.label_axes(ax, labels=[], **kwargs)[source]
Convenience function for labelling rectilinear and ternary axes.
- pyrolite.util.plot.axes.axes_to_ternary(ax)[source]
Set axes to ternary projection after axis creation. As currently implemented, note that this will replace and reorder axes as acecessed from the figure (the ternary axis will then be at the end), and as such this returns a list of axes in the correct order.
- pyrolite.util.plot.axes.check_default_axes(ax)[source]
Simple test to check whether an axis is empty of artists and hasn’t been rescaled from the default extent.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to check for artists and scaling.- Return type
- pyrolite.util.plot.axes.check_empty(ax)[source]
Simple test to check whether an axis is empty of artists.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to check for artists.- Return type
- pyrolite.util.plot.axes.init_axes(ax=None, projection=None, minsize=1.0, **kwargs)[source]
Get or create an Axes from an optionally-specified starting Axes.
Link the x, y or both axes across a group of
Axes.
- pyrolite.util.plot.axes.get_twins(ax, which='y')[source]
Get twin axes of a specified axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to get twins for.which (
str) – Which twins to get (shared'x', shared'y'or the concatenatation of both,'xy').- Return type
Notes
This function was designed to assist in avoiding creating a series of duplicate axes when replotting on an existing axis using a function which would typically create a twin axis.
- pyrolite.util.plot.axes.subaxes(ax, side='bottom', width=0.2, moveticks=True)[source]
Append a sub-axes to one side of an axes.
- Parameters
ax (
matplotlib.axes.Axes) – Axes to append a sub-axes to.side (
str) – Which side to append the axes on.width (
float) – Fraction of width to give to the subaxes.moveticks (
bool) – Whether to move ticks to the outer axes.- Returns
Subaxes instance.
- Return type
- pyrolite.util.plot.axes.add_colorbar(mappable, **kwargs)[source]
Adds a colorbar to a given mappable object.
Source: http://joseph-long.com/writing/colorbars/
- Parameters
mappable – The Image, ContourSet, etc. to which the colorbar applies.
- Return type
Todo
Where no mappable specificed, get most recent axes, and check for collections etc
pyrolite.util.plot.density
Functions for dealing with kernel density estimation.
- ivar USE_PCOLOR
Option to use the
matplotlib.pyplot.pcolor()function in place ofmatplotlib.pyplot.pcolormesh().- vartype USE_PCOLOR
- pyrolite.util.plot.density.get_axis_density_methods(ax)[source]
Get the relevant density and contouring methods for a given axis.
- Parameters
ax (
matplotlib.axes.Axes|mpltern.ternary.TernaryAxes) – Axis to check.- Returns
Relevant functions for this axis.
- Return type
pcolor, contour, contourf
- pyrolite.util.plot.density.percentile_contour_values_from_meshz(z, percentiles=[0.95, 0.66, 0.33], resolution=1000)[source]
Integrate a probability density distribution Z(X,Y) to obtain contours in Z which correspond to specified percentile contours. Contour values will be returned with the same order as the inputs.
- Parameters
z (
numpy.ndarray) – Probability density function over x, y.percentiles (
numpy.ndarray) – Percentile values for which to create contours.resolution (
int) – Number of bins for thresholds between 0. and max(Z)- Returns
Todo
This may error for a list of percentiles where one or more requested values are below the miniumum threshold. The exception handling should be updated to cater for arrays - where some of the values may be above the minimum.
- pyrolite.util.plot.density.plot_Z_percentiles(*coords, zi=None, percentiles=[0.95, 0.66, 0.33], ax=None, extent=None, fontsize=8, cmap=None, colors=None, linewidths=None, linestyles=None, contour_labels=None, label_contours=True, **kwargs)[source]
Plot percentile contours onto a 2D (scaled or unscaled) probability density distribution Z over X,Y.
- Parameters
coords (
numpy.ndarray) – Arrays of (x, y) or (a, b, c) coordinates.z (
numpy.ndarray) – Probability density function over x, y.percentiles (
list) – Percentile values for which to create contours.ax (
matplotlib.axes.Axes,None) – Axes on which to plot. If none given, will create a new Axes instance.extent (
list,None) – List or np.ndarray in the form [-x, +x, -y, +y] over which the image extends.fontsize (
float) – Fontsize for the contour labels.cmap (
matplotlib.colors.ListedColormap) – Color map for the contours and contour labels.colors (
str|list) – Colors for the contours, can optionally be specified in place of cmap.contour_labels (
dict|list) – Labels to assign to contours, organised by level.label_contours :class:`bool` – Whether to add text labels to individual contours.
- Returns
Plotted and formatted contour set.
- Return type
Notes
When the contours are percentile based, high percentile contours tend to get washed our with colormapping - consider adding different controls on coloring, especially where there are only one or two contours specified. One way to do this would be via the string based keyword argument colors for plt.contour, with an adaption for non-string colours which post-hoc modifies the contour lines based on the specified colours?
- pyrolite.util.plot.density.conditional_prob_density(y, x=None, logy=False, resolution=5, bins=50, yextent=None, rescale=True, mode='binkde', ret_centres=False, **kwargs)[source]
Estimate the conditional probability density of one dependent variable.
- Parameters
y (
numpy.ndarray) – Dependent variable for which to calculate conditional probability P(y | X=x)x (
numpy.ndarray,None) – Optionally-specified independent index.logy (
bool) – Whether to use a logarithmic bin spacing on the y axis.resolution (
int) – Points added per segment via interpolation along the x axis.bins (
int) – Bins for histograms and grids along the independent axis.yextent (
tuple) – Extent in the y direction.rescale (
bool) – Whether to rescale bins to give the same max Z across x.mode (
str) –Mode of computation.
If mode is
"ckde", usestatsmodels.nonparametric.KDEMultivariateConditional()to compute a conditional kernel density estimate. If mode is"kde", use a normal gaussian kernel density estimate. If mode is"binkde", use a gaussian kernel density estimate over y for each bin. If mode is"hist", compute a histogram.ret_centres (
bool) – Whether to return bin centres in addtion to histogram edges, e.g. for later contouring.- Returns
xbin edgesxe,ybin edgesye, histogram/density estimatesZ. Ifret_centresisTrue, the last two return values will contain the bin centresxi,yi.- Return type
pyrolite.util.plot.export
Functions for export of figures and figure elements from matplolib.
- pyrolite.util.plot.export.save_figure(figure, name='fig', save_at='', save_fmts=['png'], **kwargs)[source]
Save a figure at a specified location in a number of formats.
- pyrolite.util.plot.export.save_axes(ax, name='fig', save_at='', save_fmts=['png'], pad=0.0, **kwargs)[source]
Save either a single or multiple axes (from a single figure) based on their extent. Uses the save_figure procedure to save at a specific location using a number of formats.
Todo
Add legend to items
- pyrolite.util.plot.export.get_full_extent(ax, pad=0.0)[source]
Get the full extent of an axes, including axes labels, tick labels, and titles. Text objects are first drawn to define the extents.
- Parameters
ax (
matplotlib.axes.Axes) – Axes of which to check items to get full extent.pad (
float|tuple) – Amount of padding to add to the full extent prior to returning. If a tuple is passed, the padding will be as above, but for x and y directions, respectively.- Returns
Bbox of the axes with optional additional padding.
- Return type
pyrolite.util.plot.grid
Gridding and binning functions.
- pyrolite.util.plot.grid.bin_centres_to_edges(centres, sort=True)[source]
Translates point estimates at the centres of bins to equivalent edges, for the case of evenly spaced bins.
Todo
This can be updated to unevenly spaced bins, just need to calculate outer bins.
- pyrolite.util.plot.grid.bin_edges_to_centres(edges)[source]
Translates edges of histogram bins to bin centres.
- pyrolite.util.plot.grid.ternary_grid(data=None, nbins=10, margin=0.001, force_margin=False, yscale=1.0, tfm=<function <lambda>>)[source]
Construct a graphical linearly-spaced grid within a ternary space.
- Parameters
data (
numpy.ndarray) – Data to construct the grid around ((samples, 3)).nbins (
int) – Number of bins for grid.margin (
float) – Proportional value for the position of the outer boundary of the grid.forge_margin (
bool) – Whether to enforce the grid margin.yscale (
float) – Y scale for the specific ternary diagram.tfm – Log transform to use for the grid creation.
- Returns
bins (
numpy.ndarray) – Bin centres along each of the ternary axes ((samples, 3))binedges (
numpy.ndarray) – Position of bin edges.centregrid (
listofnumpy.ndarray) – Meshgrid of bin centres.edgegrid (
listofnumpy.ndarray) – Meshgrid of bin edges.pyrolite.util.plot.helpers
matplotlib helper functions for commong drawing tasks.
- pyrolite.util.plot.helpers.alphalabel_subplots(ax, fmt='{}', xy=(0.03, 0.95), ha='left', va='top', **kwargs)[source]
Add alphabetical labels to a successive series of subplots with a specified format.
- Parameters
ax (
list|numpy.ndarray|numpy.flatiter) – Axes to label, in desired order.fmt (
str) – Format string to use. To add e.g. parentheses, you could specify"({})".xy (
tuple) – Position of the labels in axes coordinates.ha (
str) – Horizontal alignment of the labels ({"left", "right"}).va (
str) – Vertical alignment of the labels ({"top", "bottom"}).
- pyrolite.util.plot.helpers.get_centroid(poly)[source]
Centroid of a closed polygon using the Shoelace formula.
- Parameters
poly (
matplotlib.patches.Polygon) – Polygon to obtain the centroid of.- Returns
cx, cy – Centroid coordinates.
- Return type
- pyrolite.util.plot.helpers.get_visual_center(poly, vertical_exaggeration=1)[source]
Visual center of a closed polygon.
- Parameters
poly (
matplotlib.patches.Polygon) – Polygon for which to obtain the visual center.vertical_exaggeration (
float) – Apparent vertical exaggeration of the plot (pixels per unit in y direction divided by pixels per unit in the x direction).- Returns
cx, cy – Centroid coordinates.
- Return type
- pyrolite.util.plot.helpers.rect_from_centre(x, y, dx=0, dy=0, **kwargs)[source]
Takes an xy point, and creates a rectangular patch centred about it.
- pyrolite.util.plot.helpers.draw_vector(v0, v1, ax=None, **kwargs)[source]
Plots an arrow represnting the direction and magnitue of a principal component on a biaxial plot.
Modified after Jake VanderPlas’ Python Data Science Handbook https://jakevdp.github.io/PythonDataScienceHandbook/ 05.09-principal-component-analysis.html
Todo
Update for ternary plots.
- pyrolite.util.plot.helpers.vector_to_line(mu: array, vector: array, variance: float, spans: int = 4, expand: int = 10)[source]
Creates an array of points representing a line along a vector - typically for principal component analysis. Modified after Jake VanderPlas’ Python Data Science Handbook https://jakevdp.github.io/PythonDataScienceHandbook/ 05.09-principal-component-analysis.html
- pyrolite.util.plot.helpers.plot_stdev_ellipses(comp, nstds=4, scale=100, resolution=1000, transform=None, ax=None, **kwargs)[source]
Plot covariance ellipses at a number of standard deviations from the mean.
- Parameters
comp (
numpy.ndarray) – Composition to use.nstds (
int) – Number of standard deviations from the mean for which to plot the ellipses.scale (
float) – Scale applying to all x-y data points. For intergration with python-ternary.transform (
callable) – Function for transformation of data prior to plotting (to either 2D or 3D).ax (
matplotlib.axes.Axes) – Axes to plot on.- Returns
ax
- Return type
- pyrolite.util.plot.helpers.plot_pca_vectors(comp, nstds=2, scale=100.0, transform=None, ax=None, colors=None, linestyles=None, **kwargs)[source]
Plot vectors corresponding to principal components and their magnitudes.
- Parameters
comp (
numpy.ndarray) – Composition to use.nstds (
int) – Multiplier for magnitude of individual principal component vectors.scale (
float) – Scale applying to all x-y data points. For intergration with python-ternary.transform (
callable) – Function for transformation of data prior to plotting (to either 2D or 3D).ax (
matplotlib.axes.Axes) – Axes to plot on.- Returns
ax
- Return type
Todo
Minor reimplementation of the sklearn PCA to avoid dependency.
- pyrolite.util.plot.helpers.plot_2dhull(data, ax=None, splines=False, s=0, **plotkwargs)[source]
Plots a 2D convex hull around an array of xy data points.
- pyrolite.util.plot.helpers.plot_cooccurence(arr, ax=None, normalize=True, log=False, colorbar=False, **kwargs)[source]
Plot the co-occurence frequency matrix for a given input.
- Parameters
ax (
matplotlib.axes.Axes,None) – The subplot to draw on.normalize (
bool) – Whether to normalize the cooccurence to compare disparate variables.log (
bool) – Whether to take the log of the cooccurence.colorbar (
bool) – Whether to append a colorbar.- Returns
Axes on which the cooccurence plot is added.
- Return type
- pyrolite.util.plot.helpers.nan_scatter(xdata, ydata, ax=None, axes_width=0.2, **kwargs)[source]
Scatter plot with additional marginal axes to plot data for which data is partially missing. Additional keyword arguments are passed to matplotlib.
- Parameters
xdata (
numpy.ndarray) – X dataydata (class:numpy.ndarray | pd.Series) – Y data
ax (
matplotlib.axes.Axes) – Axes on which to plot.axes_width (
float) – Width of the marginal axes.- Returns
Axes on which the nan_scatter is plotted.
- Return type
- pyrolite.util.plot.helpers.init_spherical_octant(angle_indicated=30, labels=None, view_init=(25, 55), fontsize=10, **kwargs)[source]
Initalize a figure with a 3D octant of a unit sphere, appropriately labeled with regard to angles corresponding to the handling of the respective compositional data transformation function (
sphere()).
- Parameters
- Returns
ax – Initialized 3D axis.
- Return type
matplotlib.axes.Axes3Dpyrolite.util.plot.interpolation
Line interpolation for matplotlib lines and paths.
- pyrolite.util.plot.interpolation.interpolate_path(path, resolution=100, periodic=False, aspath=True, closefirst=False, **kwargs)[source]
Obtain the interpolation of an existing path at a given resolution. Keyword arguments are forwarded to
scipy.interpolate.splprep().
- Parameters
path (
matplotlib.path.Path) – Path to interpolate.resolution :class:`int` – Resolution at which to obtain the new path. The verticies of the new path will have shape (resolution, 2).
periodic (
bool) – Whether to use a periodic spline.periodic (
bool) – Whether to return amatplotlib.path.Path, or simply a tuple of x-y arrays.closefirst (
bool) – Whether to first close the path by appending the first point again.- Returns
Interpolated
Pathobject, if aspath isTrue, else a tuple of x-y arrays.- Return type
- pyrolite.util.plot.interpolation.interpolated_patch_path(patch, resolution=100, **kwargs)[source]
Obtain the periodic interpolation of the existing path of a patch at a given resolution.
- Parameters
patch (
matplotlib.patches.Patch) – Patch to obtain the original path from.resolution :class:`int` – Resolution at which to obtain the new path. The verticies of the new path will have shape (resolution, 2).
- Returns
Interpolated
Pathobject.- Return type
- pyrolite.util.plot.interpolation.get_contour_paths(src, resolution=100, minsize=3)[source]
Extract the paths of contours from a contour plot.
- Parameters
ax (
matplotlib.axes.Axes|) – Axes to extract contours from.resolution (
int) – Resolution of interpolated splines to return.- Returns
contourspaths (
list(list)) – List of lists, each represnting one line collection (a single contour). In the case where this contour is multimodal, there will be multiple paths for each contour.contournames (
list) – List of names for contours, where they have been labelled, and there are no other text artists on the figure.contourstyles (
list) – List of styles for contours.Notes
This method assumes that contours are the only
matplotlib.collections.LineCollectionobjects within an axes; and when this is not the case, additional non-contour objects will be returned.pyrolite.util.plot.legend
Functions for creating and modifying legend entries for matplotlib.
Todo
Functions for working with and modifying legend entries.
ax.lines + ax.patches + ax.collections + ax.containers, handle ax.parasites
- pyrolite.util.plot.legend.proxy_rect(**kwargs)[source]
Generates a legend proxy for a filled region.
- Return type
- pyrolite.util.plot.legend.proxy_line(**kwargs)[source]
Generates a legend proxy for a line region.
- Return type
- pyrolite.util.plot.legend.modify_legend_handles(ax, **kwargs)[source]
Modify the handles of a legend based for a single axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis for which to obtain modifed legend handles.- Returns
pyrolite.util.plot.style
Functions for automated plot styling and argument handling.
- ivar DEFAULT_CONT_COLORMAP
Default continuous colormap.
- vartype DEFAULT_CONT_COLORMAP
matplotlib.colors.ScalarMappable- ivar DEFAULT_DISC_COLORMAP
Default discrete colormap.
- vartype DEFAULT_DISC_COLORMAP
matplotlib.colors.ScalarMappable
- pyrolite.util.plot.style.linekwargs(kwargs)[source]
Get a subset of keyword arguments to pass to a matplotlib line-plot call.
- pyrolite.util.plot.style.scatterkwargs(kwargs)[source]
Get a subset of keyword arguments to pass to a matplotlib scatter call.
- pyrolite.util.plot.style.marker_cycle(markers=['D', 's', 'o', '+', '*'])[source]
Cycle through a set of markers.
- Parameters
markers (
list) – List of markers to provide to matplotlib.
- pyrolite.util.plot.style.mappable_from_values(values, cmap=<matplotlib.colors.ListedColormap object>, norm=None, **kwargs)[source]
Create a scalar mappable object from an array of values.
- Return type
- pyrolite.util.plot.style.ternary_color(tlr, alpha=1.0, colors=([1, 0, 0], [0, 1, 0], [0, 0, 1]), coefficients=(1, 1, 1))[source]
Color a set of points by their ternary combinations of three specified colors.
- Parameters
tlr (
numpy.ndarray)alpha (
float) – Alpha coefficient for the colors; to be applied multiplicatively with any existing alpha value (for RGBA colors specified).colors (
tuple) – Set of colours corresponding to the top, left and right verticies, respectively.coefficients (
tuple) – Coefficients for the ternary data to adjust the centre.- Returns
Color array for the ternary points.
- Return type
- pyrolite.util.plot.style.color_ternary_polygons_by_centroid(ax=None, patches=None, alpha=1.0, colors=([1, 0, 0], [0, 1, 0], [0, 0, 1]), coefficients=(1, 1, 1))[source]
Color a set of polygons within a ternary diagram by their centroid colors.
- Parameters
ax (
matplotlib.axes.Axes) – Ternary axes to check for patches, if patches is not supplied.patches (
list) – List of ternary-hosted patches to apply color to.alpha (
float) – Alpha coefficient for the colors; to be applied multiplicatively with any existing alpha value (for RGBA colors specified).colors (
tuple) – Set of colours corresponding to the top, left and right verticies, respectively.coefficients (
tuple) – Coefficients for the ternary data to adjust the centre.- Returns
patches – List of patches, with updated facecolors.
- Return type
pyrolite.util.plot.transform
Transformation utilites for matplotlib.
- pyrolite.util.plot.transform.affine_transform(mtx=array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]))[source]
Construct a function which will perform a 2D affine transform based on a 3x3 affine matrix.
- Parameters
mtx (
numpy.ndarray)
- pyrolite.util.plot.transform.tlr_to_xy(tlr)[source]
Transform a ternary coordinate system (top-left-right) to an xy-cartesian coordinate system.
- Parameters
tlr (
numpy.ndarray) – Array of shape (n, 3) in the t-l-r coordinate system.- Returns
xy – Array of shape (n, 2) in the x-y coordinate system.
- Return type
- pyrolite.util.plot.transform.xy_to_tlr(xy)[source]
- Parameters
xy (
numpy.ndarray) – Array of shape (n, 2) in the x-y coordinate system.- Returns
tlr – Array of shape (n, 3) in the t-l-r coordinate system.
- Return type
- pyrolite.util.plot.transform.ABC_to_xy(ABC, xscale=1.0, yscale=1.0)[source]
Convert ternary compositional coordiantes to x-y coordinates for visualisation within a triangle.
- Parameters
ABC (
numpy.ndarray) – Ternary array (samples, 3).xscale (
float) – Scale for x-axis.yscale (
float) – Scale for y-axis.- Returns
Array of x-y coordinates (
samples, 2)- Return type
- pyrolite.util.plot.transform.xy_to_ABC(xy, xscale=1.0, yscale=1.0)[source]
Convert x-y coordinates within a triangle to compositional ternary coordinates.
- Parameters
xy (
numpy.ndarray) – XY array (samples, 2).xscale (
float) – Scale for x-axis.yscale (
float) – Scale for y-axis.- Returns
Array of ternary coordinates (
samples, 3)- Return type
pyrolite.util.text
- pyrolite.util.text.to_width(multiline_string, width=79, **kwargs)[source]
Uses builtin textwapr for text wrapping to a specific width.
- pyrolite.util.text.normalise_whitespace(strg)[source]
Substitutes extra tabs, newlines etc. for a single space.
- pyrolite.util.text.remove_prefix(z, prefix)[source]
Remove a specific prefix from the start of a string.
- pyrolite.util.text.remove_suffix(x, suffix=' ')[source]
Remove a specific suffix from the end of a string.
- pyrolite.util.text.titlecase(s, exceptions=['and', 'in', 'a'], abbrv=['ID', 'IGSN', 'CIA', 'CIW', 'PIA', 'SAR', 'SiTiIndex', 'WIP'], capitalize_first=True, split_on='[\\.\\s_-]+', delim='')[source]
Formats strings in CamelCase, with exceptions for simple articles and omitted abbreviations which retain their capitalization.
Todo
Option for retaining original CamelCase.
- pyrolite.util.text.string_variations(names, preprocess=['lower', 'strip'], swaps=[(' ', '_'), (' ', '_'), ('-', ' '), ('_', ' '), ('-', ''), ('_', '')])[source]
Returns equilvaent string variations based on an input set of strings.
- Parameters
names ({list, str}) – String or list of strings to generate name variations of.
preprocess (list) – List of preprocessing string functions to apply before generating variations.
swaps (list) – List of tuples for str.replace(out, in).
- Returns
Set (or SortedSet, if sortedcontainers installed) of unique string variations.
- Return type
- pyrolite.util.text.parse_entry(entry, regex='(\\s)*?(?P<value>[\\.\\w]+)(\\s)*?', delimiter=',', values_only=True, first_only=True, errors=None, replace_nan='None')[source]
Parses an arbitrary string data entry to return values based on a regular expression containing named fields including ‘value’ (and any others). If the entry is of non-string type, this will return the value (e.g. int, float, NaN, None).
- Parameters
entry (
str) – String entry which to search for the regex pattern.regex (
str) – Regular expression to compile and use to search the entry for a value.delimiter (
str, :',') – Optional delimiter to split the string in case of multiple inclusion.values_only (
bool,True) – Option to return only values (single or list), or to instead return the dictionary corresponding to the matches.first_only (
bool,True) – Option to return only the first match, or else all matcheserrors – Error value to denote ‘no match’. Not yet implemented.
- pyrolite.util.text.split_records(data, delimiter='\\r\\n')[source]
Splits records in a csv where quotation marks are used. Splits on a delimiter followed by an even number of quotation marks.
pyrolite.util.web
pyrolite.util.time
- pyrolite.util.time.listify(df, axis=1)[source]
Consdense text information across columns into a single list.
- Parameters
df (
pandas.DataFrame) – Dataframe (or slice of dataframe) to condense along axis.axis (
int) – Axis to condense along.
- pyrolite.util.time.age_name(agenamelist, prefixes=['Lower', 'Middle', 'Upper'], suffixes=['Stage', 'Series'])[source]
Condenses an agename list to a specific agename, given a subset of ambiguous_names.
- Parameters
agenamelist (
list) – List of name components (i.e.[Eon, Era, Period, Epoch])prefixes (
list) – Name components which occur prior to the higher order classification (e.g."Upper Triassic").suffixes (
list) – Name components which occur after the higher order classification (e.g."Cambrian Series 2").
- pyrolite.util.time.import_colors(filename=PosixPath('/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/data/timescale/timecolors.csv'), delim='/')[source]
Import a list of timescale names with associated colors.
- pyrolite.util.time.timescale_reference_frame(filename=PosixPath('/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/data/timescale/geotimescale_202210.csv'), info_cols=['Start', 'End', 'Aliases'], color_info=None)[source]
Rearrange the text-based timescale dataframe. Utility function for timescale class.
- Parameters
filename (
str|pathlib.Path) – File from which to generate the timescale information.info_cols (
list) – List of columns beyond hierarchial group labels (e.g. Eon, Era..).- Returns
Dataframe containing timescale information.
- Return type
- class pyrolite.util.time.Timescale(filename=None)[source]
- text2age(entry, nulls=[None, 'None', 'none', nan, 'NaN'])[source]
Converts a text-based age to the corresponding age range (in Ma).
String-based entries return (max_age, min_age). Collection-based entries return a list of tuples.
pyrolite.util.math
- pyrolite.util.math.eigsorted(cov)[source]
Returns arrays of eigenvalues and eigenvectors sorted by magnitude.
- Parameters
cov (
numpy.ndarray) – Covariance matrix to extract eigenvalues and eigenvectors from.- Returns
vals (
numpy.ndarray) – Sorted eigenvalues.vecs (
numpy.ndarray) – Sorted eigenvectors.
- pyrolite.util.math.augmented_covariance_matrix(M, C)[source]
Constructs an augmented covariance matrix from means M and covariance matrix C.
- Parameters
M (
numpy.ndarray) – Array of means.C (
numpy.ndarray) – Covariance matrix.- Returns
Augmented covariance matrix A.
- Return type
Notes
Augmented covariance matrix constructed from mean of shape (D, ) and covariance matrix of shape (D, D) as follows:
\[\begin{split}\begin{array}{c|c} -1 & M.T \\ \hline M & C \end{array}\end{split}\]
- pyrolite.util.math.interpolate_line(x, y, n=0, logy=False)[source]
Add intermediate evenly spaced points interpolated between given x-y coordinates, assuming the x points are the same.
- Parameters
x (
numpy.ndarray) – 1D array of x values.y (
numpy.ndarray) – ND array of y values.
- pyrolite.util.math.grid_from_ranges(X, bins=100, **kwargs)[source]
Create a meshgrid based on the ranges along columns of array X.
- Parameters
X (
numpy.ndarray) – Array of shape(samples, dimensions)to create a meshgrid from.bins (
int|tuple) – Shape of the meshgrid. If an integer, provides a square mesh. If a tuple, values for each column are required.- Return type
Notes
Can pass keyword arg indexing = {‘xy’, ‘ij’}
- pyrolite.util.math.flattengrid(grid)[source]
Convert a collection of arrays to a concatenated array of flattened components. Useful for passing meshgrid values to a function which accepts argumnets of shape
(samples, dimensions).
- Parameters
grid (
list) – Collection of arrays (e.g. a meshgrid) to flatten and concatenate.- Return type
- pyrolite.util.math.linspc_(_min, _max, step=0.0, bins=20)[source]
Linear spaced array, with optional step for grid margins.
- Parameters
- Returns
Linearly-spaced array.
- Return type
- pyrolite.util.math.logspc_(_min, _max, step=1.0, bins=20)[source]
Log spaced array, with optional step for grid margins.
- Parameters
- Returns
Log-spaced array.
- Return type
- pyrolite.util.math.isclose(a, b)[source]
Implementation of np.isclose with equal nan.
- Parameters
a,b (
float|numpy.ndarray) – Numbers or arrays to compare.- Return type
- pyrolite.util.math.is_numeric(obj)[source]
Check for numerical behaviour.
- Parameters
obj – Object to check.
- Return type
- pyrolite.util.math.significant_figures(n, unc=None, max_sf=20, rtol=1e-20)[source]
Iterative method to determine the number of significant digits for a given float, optionally providing an uncertainty.
- Parameters
n (
float) – Number from which to ascertain the significance level.unc (
float,None) – Uncertainty, which if provided is used to derive the number of significant digits.max_sf (
int) – An upper limit to the number of significant digits suggested.rtol (
float) – Relative tolerance to determine similarity of numbers, used in calculations.- Returns
Number of significant digits.
- Return type
- pyrolite.util.math.signify_digit(n, unc=None, leeway=0, low_filter=True)[source]
Reformats numbers to contain only significant_digits. Uncertainty can be provided to digits with relevant precision.
- Parameters
n (
float) – Number to reformatunc (
float,None) – Absolute uncertainty on the number, optional.leeway (
int, 0) – Manual override for significant figures. Positive values will force extra significant figures; negative values will remove significant figures.low_filter (
bool,True) – Whether to returnnp.nanin place of values which are within precision equal to zero.- Returns
Reformatted number.
- Return type
Notes
Will not pad 0s at the end or before floats.
- pyrolite.util.math.most_precise(arr)[source]
Get the most precise element from an array.
- Parameters
arr (
numpy.ndarray) – Array to obtain the most precise element/subarray from.- Returns
Returns the most precise array element (for ndim=1), or most precise subarray (for ndim > 1).
- Return type
- pyrolite.util.math.equal_within_significance(arr, equal_nan=False, rtol=1e-15)[source]
Test whether elements of an array are equal within the precision of the least precise.
- Parameters
arr (
numpy.ndarray) – Array to test.equal_nan (
bool,False) – Whether to considernp.nanelements equal to one another.rtol (
float) – Relative tolerance for comparison.- Return type
bool|numpy.ndarray`(:class:`bool)
- pyrolite.util.math.helmert_basis(D: int, full=False, **kwargs)[source]
Generate a set of orthogonal basis vectors in the form of a helmert matrix.
- Parameters
D (
int) – Dimension of compositional vectors.- Returns
(D-1, D) helmert matrix corresponding to default orthogonal basis.
- Return type
- pyrolite.util.math.symbolic_helmert_basis(D, full=False)[source]
Get a symbolic representation of a Helmert Matrix.
- Parameters
D (
int) – Order of the matrix. Equivalent to dimensionality for compositional data analysis.full (
bool) – Whether to return the full matrix, or alternatively exclude the first row. Analogous to the option forscipy.linalg.helmert().- Return type
- pyrolite.util.math.on_finite(X, f)[source]
Calls a function on an array ignoring np.nan and +/- np.inf. Note that the shape of the output may be different to that of the input.
- Parameters
X (
numpy.ndarray) – Array on which to perform the function.f (
Callable) – Function to call on the array.- Return type
- pyrolite.util.math.nancov(X)[source]
Generates a covariance matrix excluding nan-components.
- Parameters
X (
numpy.ndarray) – Input array for which to derive a covariance matrix.- Return type
pyrolite.util.lambdas
- pyrolite.util.lambdas.calc_lambdas(df, params=None, degree=4, exclude=[], algorithm='ONeill', anomalies=[], fit_tetrads=False, sigmas=None, add_uncertainties=False, add_X2=False, **kwargs)[source]
Parameterises values based on linear combination of orthogonal polynomials over a given set of values for independent variable x 1 . This function expects to recieve data already normalised and log-transformed.
- Parameters
df (
pd.DataFrame) – Dataframe containing REE Data.params (
list|str) – Pre-computed parameters for the orthogonal polynomials (a list of tuples). Optionally specified, otherwise defaults the parameterisation as in O’Neill (2016). 1 If a string is supplied,"O'Neill (2016)"or similar will give the original defaults, while"full"will use all of the REE (including Eu) as a basis for the orthogonal polynomials.degree (
int) – Degree of orthogonal polynomial fit.exclude (
list) – REE to exclude from the fit.algorithm (
str) – Algorithm to use for fitting the orthogonal polynomials.anomalies (
list) – List of relative anomalies to append to the dataframe.fit_tetrads (
bool) – Whether to fit tetrad functions in addition to orthogonal polynomial functions. This will force the use of the optimization algorithm.sigmas (
float|numpy.ndarray) – Single value or 1D array of observed value uncertainties.add_uncertainties (
bool) – Whether to append estimated parameter uncertainties to the dataframe.add_X2 (
bool) – Whether to append the chi-squared values (χ2) to the dataframe.- Return type
pd.DataFrameReferences
- 1(1,2)
O’Neill HSC (2016) The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57:1463–1508. doi: 10.1093/petrology/egw047
pyrolite.util.lambdas.params
Functions to generate parameters for the construction of orthogonal polynomials which are used to fit REE patterns.
- pyrolite.util.lambdas.params.orthogonal_polynomial_constants(xs, degree=3, rounding=None, tol=1e-14)[source]
Finds the parameters \((\beta_0), (\gamma_0, \gamma_1), (\delta_0, \delta_1, \delta_2)\) etc. for constructing orthogonal polynomial functions f(x) over a fixed set of values of independent variable x. Used for obtaining lambda values for dimensional reduction of REE data 2.
- Parameters
xs (
numpy.ndarray) – Indexes over which to generate the orthogonal polynomials.degree (
int) – Maximum polynomial degree. E.g. 2 will generate constant, linear, and quadratic polynomial components.tol (
float) – Convergence tolerance for solver.rounding (
int) – Precision for the orthogonal polynomial coefficents.- Returns
List of tuples corresponding to coefficients for each of the polynomial components. I.e the first tuple will be empty, the second will contain a single coefficient etc.
- Return type
Notes
Parameters are used to construct orthogonal polymomials of the general form:
\[\begin{split}f(x) &= a_0 \\ &+ a_1 * (x - \beta) \\ &+ a_2 * (x - \gamma_0) * (x - \gamma_1) \\ &+ a_3 * (x - \delta_0) * (x - \delta_1) * (x - \delta_2) \\\end{split}\]See also
References
- 2
O’Neill HSC (2016) The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57:1463–1508. doi: 10.1093/petrology/egw047
- pyrolite.util.lambdas.params.parse_sigmas(size, sigmas=None)[source]
Disambigaute a value or set of sigmas for a dataset for use in lambda-fitting algorithms.
- Parameters
sigmas (
float|numpy.ndarray) – 2D array of REE uncertainties. Values as fractional uncertaintes (i.e. \(\sigma_{REE} / REE\)).- Returns
sigmas – 1D array of sigmas (\(\sigma_{REE} / REE\)).
- Return type
Notes
Note that the y-array is passed here only to infer the shape which should be assumed by the uncertainty array. Through propagation of uncertainties, the uncertainty on the natural logarithm of the normalised REE values are equivalent to \(\sigma_{REE} / REE\) where the uncertainty in the reference composition is assumed to be zero. Thus, standard deviations of 1% in REE will result in \(\sigma=0.01\) for the log-transformed REE. If no sigmas are provided, 1% uncertainty will be assumed and an array of 0.01 will be returned.
pyrolite.util.lambdas.eval
Generation and evalutation of orthogonal polynomial and tetrad functions from sets of parameters (the sequence of polymomial roots and tetrad centres and widths).
- pyrolite.util.lambdas.eval.lambda_poly(x, ps)[source]
Evaluate polynomial lambda_n(x) given a tuple of parameters ps with length equal to the polynomial degree.
- Parameters
x (
numpy.ndarray) – X values to calculate the function at.ps (
tuple) – Parameter set tuple. E.g. parameters (a, b) from \(f(x) = (x-a)(x-b)\).- Return type
- pyrolite.util.lambdas.eval.tetrad(x, centre, width)[source]
Evaluate \(f(z)\) describing a tetrad with specified centre and width.
- pyrolite.util.lambdas.eval.get_lambda_poly_function(lambdas: ndarray, params=None, radii=None, degree=5)[source]
Expansion of lambda parameters back to the original space. Returns a function which evaluates the sum of the orthogonal polynomials at given x values.
- Parameters
lambdas (
numpy.ndarray) – Lambda values to weight combination of polynomials.params (
list(tuple)) – Parameters for the orthogonal polynomial decomposition.radii (
numpy.ndarray) – Radii values used to construct the lambda values. 3degree (
int) – Degree of the orthogonal polynomial decomposition. 3Notes
pyrolite.util.lambdas.oneill
Linear algebra methods for fitting a series of orthogonal polynomial functions to REE patterns.
- pyrolite.util.lambdas.oneill.get_polynomial_matrix(radii, params=None)[source]
Create the matrix A with polynomial components across the columns, and increasing order down the rows.
- Parameters
radii (
list,numpy.ndarray) – Radii at which to evaluate the orthogonal polynomial.params (
tuple) – Tuple of constants for the orthogonal polynomial.- Return type
See also
- pyrolite.util.lambdas.oneill.lambdas_ONeill2016(df, radii, params=None, sigmas=None, add_X2=False, add_uncertainties=False, **kwargs)[source]
Implementation of the original algorithm. 4
- Parameters
df (
pandas.DataFrame|pandas.Series) – Dataframe of REE data, with sample analyses organised by row.radii (
list,numpy.ndarray) – Radii at which to evaluate the orthogonal polynomial.params (
tuple) – Tuple of constants for the orthogonal polynomial.sigmas (
float|numpy.ndarray) – Single value or 1D array of normalised observed value uncertainties (\(\sigma_{REE} / REE\)).add_X2 (
bool) – Whether to append the chi-squared values (χ2) to the dataframe/series.add_uncertainties (
bool) – Append parameter standard errors to the dataframe/series.- Return type
References
- 4
O’Neill HSC (2016) The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57:1463–1508. doi: 10.1093/petrology/egw047
pyrolite.util.lambdas.opt
Functions for optimization-based REE profile fitting and parameter uncertainty estimation.
- pyrolite.util.lambdas.opt.pcov_from_jac(jac)[source]
Extract a covariance matrix from a Jacobian matrix returned from
scipy.optimizefunctions.
- Parameters
jac (
numpy.ndarray) – Jacobian array.- Returns
pcov – Square covariance array; this hasn’t yet been scaled by residuals.
- Return type
- pyrolite.util.lambdas.opt.linear_fit_components(y, x0, func_components, sigmas=None)[source]
Fit a weighted sum of function components using linear algebra.
- Parameters
y (
numpy.ndarray) – Array of target values to fit.x0 (
numpy.ndarray) – Starting guess for the function weights.func_components (
list(numpy.ndarray)) – List of arrays representing static/evaluated function components.sigmas (
float|numpy.ndarray) – Single value or 1D array of normalised observed value uncertainties (\(\sigma_{REE} / REE\)).- Returns
B, s, χ2 – Arrays for the optimized parameter values (B; (n, d)), parameter uncertaintes (s, 1σ; (n, d)) and chi-chi_squared (χ2; (n, 1)).
- Return type
- pyrolite.util.lambdas.opt.optimize_fit_components(y, x0, func_components, residuals_function=<function _residuals_func>, sigmas=None)[source]
Fit a weighted sum of function components using
scipy.optimize.least_squares().
- Parameters
y (
numpy.ndarray) – Array of target values to fit.x0 (
numpy.ndarray) – Starting guess for the function weights.func_components (
list(numpy.ndarray)) – List of arrays representing static/evaluated function components.redsiduals_function (callable) – Callable funciton to compute residuals which accepts ordered arguments for weights, target values and function components.
sigmas (
float|numpy.ndarray) – Single value or 1D array of normalised observed value uncertainties (\(\sigma_{REE} / REE\)).- Returns
B, s, χ2 – Arrays for the optimized parameter values (B; (n, d)), parameter uncertaintes (s, 1σ; (n, d)) and chi-chi_squared (χ2; (n, 1)).
- Return type
- pyrolite.util.lambdas.opt.lambdas_optimize(df, radii, params=None, fit_tetrads=False, tetrad_params=None, fit_method='opt', sigmas=None, add_uncertainties=False, add_X2=False, **kwargs)[source]
Parameterises values based on linear combination of orthogonal polynomials over a given set of values for independent variable x. 5
- Parameters
df (
pandas.DataFrame| :class:`pandas.Series) – Target data to fit. For geochemical data, this is typically normalised so we can fit a smooth function.radii (
list,numpy.ndarray) – Radii at which to evaluate the orthogonal polynomial.params (
list,None) – Orthogonal polynomial coefficients (seeorthogonal_polynomial_constants()).fit_tetrads (
bool) – Whether to also fit the patterns for tetrads.tetrad_params (
list) – List of parameter sets for tetrad functions.fit_method (
str) – Which fit method to use:"optimization"or"linear".sigmas (
float|numpy.ndarray) – Single value or 1D array of observed value uncertainties.add_uncertainties (
bool) – Whether to append estimated parameter uncertainties to the dataframe/series.add_X2 (
bool) – Whether to append the chi-squared values (χ2) to the dataframe/series.- Returns
Optimial results for weights of orthogonal polymomial regression (lambdas).
- Return type
References
- 5
O’Neill HSC (2016) The Smoothness and Shapes of Chondrite-normalized Rare Earth Element Patterns in Basalts. J Petrology 57:1463–1508. doi: 10.1093/petrology/egw047
pyrolite.util.lambdas.plot
Functions for the visualisation of reconstructed and deconstructed parameterised REE profiles based on parameterisations using ‘lambdas’ (and tetrad-equivalent weights ‘taus’).
- pyrolite.util.lambdas.plot.plot_lambdas_components(lambdas, params=None, ax=None, **kwargs)[source]
Plot a decomposed orthogonal polynomial from a single set of lambda coefficients.
- Parameters
lambdas – 1D array of lambdas.
params (
list) – List of orthongonal polynomial parameters, if defaults are not used.ax (
matplotlib.axes.Axes) – Optionally specified axes to plot on.index (
str) – Index to use for the plot (one of"index", "radii", "z").- Return type
- pyrolite.util.lambdas.plot.plot_tetrads_components(taus, tetrad_params=None, ax=None, index='radii', logy=True, drop0=True, **kwargs)[source]
Individually plot the four tetrad components for one set of $ au$s.
- Parameters
taus (
numpy.ndarray) – 1D array of $ au$ tetrad function coefficients.tetrad_params (
list) – List of tetrad parameters, if defaults are not used.ax (
matplotlib.axes.Axes) – Optionally specified axes to plot on.index (
str) – Index to use for the plot (one of"index", "radii", "z").logy (
bool) – Whether to log-scale the y-axis.drop0 (
bool) – Whether to remove zeroes from the outputs such that individual tetrad functions are shown only within their respective bounds (and not across the entire REE, where their effective values are zero).
- pyrolite.util.lambdas.plot.plot_profiles(coefficients, tetrads=False, params=None, tetrad_params=None, ax=None, index='radii', logy=False, **kwargs)[source]
Plot the reconstructed REE profiles of a 2D dataset of coefficients ($lambda$s, and optionally $tau$s).
- Parameters
coefficients (
numpy.ndarray) – 2D array of $lambda$ orthogonal polynomial coefficients, and optionally including $tau$ tetrad function coefficients in the last four columns (wheretetrads=True).tetrads (
bool) – Whether the coefficient array contains tetrad coefficients ($tau$s).params (
list) – List of orthongonal polynomial parameters, if defaults are not used.tetrad_params (
list) – List of tetrad parameters, if defaults are not used.ax (
matplotlib.axes.Axes) – Optionally specified axes to plot on.index (
str) – Index to use for the plot (one of"index", "radii", "z").logy (
bool) – Whether to log-scale the y-axis.- Return type
pyrolite.util.lambdas.transform
Functions for transforming ionic radii to and from atomic number for the visualisation of REE patterns.
- pyrolite.util.lambdas.transform.REE_z_to_radii(z, fit=None, degree=7, **kwargs)[source]
Estimate the ionic radii which would be approximated by a given atomic number based on a provided (or calcuated) fit for the Rare Earth Elements.
- Parameters
z (
float|list|numpy.ndarray) – Atomic nubmers to be converted.fit (callable) – Callable function optionally specified; if not specified it will be calculated from Shannon Radii.
degree (
int) – Degree of the polynomial fit between atomic number and radii.- Returns
r – Approximate atomic nubmers for given radii.
- Return type
- pyrolite.util.lambdas.transform.REE_radii_to_z(r, fit=None, degree=7, **kwargs)[source]
Estimate the atomic number which would be approximated by a given ionic radii based on a provided (or calcuated) fit for the Rare Earth Elements.
- Parameters
r (
float|list|numpy.ndarray) – Radii to be converted.fit (callable) – Callable function optionally specified; if not specified it will be calculated from Shannon Radii.
degree (
int) – Degree of the polynomial fit between radii and atomic number.- Returns
z – Approximate atomic numbers for given radii.
- Return type
pyrolite.util.distributions
- pyrolite.util.distributions.get_scaler(*fs)[source]
Generate a function which will transform columns of an array based on input functions (e.g.
np.logwill log-transform the x values,None, np.logwill log-transform the y values but not the x).
- Parameters
fs – A series of functions to apply to subsequent axes of an array.
- pyrolite.util.distributions.sample_kde(data, samples, renorm=False, transform=<function <lambda>>, bw_method=None)[source]
Sample a Kernel Density Estimate at points or a grid defined.
- Parameters
data (
numpy.ndarray) – Source data to estimate the kernel density estimate; observations should be in rows (npoints, ndim).samples (
numpy.ndarray) – Coordinates to sample the KDE estimate at (npoints, ndim).transform – Transformation used prior to kernel density estimate.
bw_method (
str,float, callable) – Method used to calculate the estimator bandwidth. Seescipy.stats.gaussian_kde().- Return type
- pyrolite.util.distributions.sample_ternary_kde(data, samples, transform=<function ILR>)[source]
Sample a Kernel Density Estimate in ternary space points or a grid defined by samples.
- Parameters
data (
numpy.ndarray) – Source data to estimate the kernel density estimate (npoints, ndim).samples (
numpy.ndarray) – Coordinates to sample the KDE estimate at (npoints, ndim)..transform – Log-transformation used prior to kernel density estimate.
- Return type
- pyrolite.util.distributions.lognorm_to_norm(mu, s)[source]
Calculate mean and variance for a normal random variable from the lognormal parameters
muands.
- pyrolite.util.distributions.norm_to_lognorm(mean, sigma, exp=True)[source]
Calculate
muandsigmaparameters for a lognormal random variable with a given mean and variance. Lognormal with parametersmeanandsigma.
- Parameters
mean (
float) – Mean of the normal distribution.sigma (
float) –sigmaof the normal distribution.exp (
bool) – If using thescipy.statsparameterisation; this usesscale = np.exp(mu).- Returns
pyrolite.util.synthetic
Utility functions for creating synthetic (geochemical) data.
- pyrolite.util.synthetic.random_cov_matrix(dim, sigmas=None, validate=False, seed=None)[source]
Generate a random covariance matrix which is symmetric positive-semidefinite.
- Parameters
dim (
int) – Dimensionality of the covariance matrix.sigmas (
numpy.ndarray) – Optionally specified sigmas for the variables.validate (
bool) – Whether to validate output.- Returns
Covariance matrix of shape
(dim, dim).- Return type
Todo
Implement a characteristic scale for the covariance matrix.
- pyrolite.util.synthetic.random_composition(size=1000, D=4, mean=None, cov=None, propnan=0.1, missing_columns=None, missing=None, seed=None)[source]
Generate a simulated random unimodal compositional dataset, optionally with missing data.
- Parameters
size (
int) – Size of the dataset.D (
int) – Dimensionality of the dataset.mean (
numpy.ndarray,None) – Optional specification of mean composition.cov (
numpy.ndarray,None) – Optional specification of covariance matrix (in log space).propnan (
float, [0, 1)) – Proportion of missing values in the output dataset.missing_columns (
int|tuple) – Specification of columns to be missing. If an integer is specified, interpreted to be the number of columns containin missing data (at a proportion defined by propnan). If a tuple or list, the specific columns to contain missing data.missing (
str,None) – Missingness pattern. If notNone, one of"MCAR", "MAR", "MNAR".
If
missing = "MCAR", data will be missing at random.If
missing = "MAR", data will be missing with some relationship to other parameters.If
missing = "MNAR", data will be thresholded at some lower bound.seed (
int,None) – Random seed to use, optionally specified.- Returns
Simulated dataset with missing values.
- Return type
Todo
Add feature to translate rough covariance in D to logcovariance in D-1
Update the :code:`missing = “MAR”` example to be more realistic/variable.
- pyrolite.util.synthetic.normal_frame(columns=['SiO2', 'CaO', 'MgO', 'FeO', 'TiO2'], size=10, mean=None, **kwargs)[source]
Creates a
pandas.DataFramewith samples from a single multivariate-normal distributed composition.
- Parameters
columns (
list) – List of columns to use for the dataframe. These won’t have any direct impact on the data returned, and are only for labelling.size (
int) – Index length for the dataframe.mean (
numpy.ndarray,None) – Optional specification of mean composition.- Return type
- pyrolite.util.synthetic.normal_series(index=['SiO2', 'CaO', 'MgO', 'FeO', 'TiO2'], mean=None, **kwargs)[source]
Creates a
pandas.Serieswith a single sample from a single multivariate-normal distributed composition.
- Parameters
index (
list) – List of indexes for the series. These won’t have any direct impact on the data returned, and are only for labelling.mean (
numpy.ndarray,None) – Optional specification of mean composition.- Return type
- pyrolite.util.synthetic.example_spider_data(start='EMORB_SM89', norm_to='PM_PON', size=120, noise_level=0.5, offsets=None, units='ppm')[source]
Generate some random data for demonstrating spider plots.
By default, this generates a composition based around EMORB, normalised to Primitive Mantle.
- Parameters
start (
str) – Composition to start with.norm_to (
str) – Composition to normalise to. Can optionally specifyNone.size (
int) – Number of observations to include (index length).noise_level (
float) – Log-units of noise (1sigma).offsets (
dict) – Dictionary of offsets in log-units (in log units).units (
str) – Units to use before conversion. Should have no effect other than reducing calculation times if norm_to isNone.- Returns
df – Dataframe of example synthetic data.
- Return type
pyrolite.util.spatial
Baisc spatial utility functions.
- pyrolite.util.spatial.great_circle_distance(a, b=None, absolute=False, degrees=True, r=6371.0088, method=None, dtype='float32', max_memory_fraction=0.25)[source]
Calculate the great circle distance between two lat, long points.
- Parameters
a, b (
float|numpy.ndarray) – Lat-Long points or arrays to calculate distance between. If only one array is specified, a full distance matrix (i.e. calculate a point-to-point distance for every combination of points) will be returned.absolute (
bool,False) – Whether to return estimates of on-sphere distances [True], or simply return the central angle between the points.degrees (
bool,True) – Whether lat-long coordinates are in degrees [True] or radians [False].r (
float) – Earth radii for estimating absolute distances.method (
str,{'vicenty', 'cosines', 'haversine'}) – Which method to use for great circle distance calculation. Defaults to the Vicenty formula.dtype (
numpy.dtype) – Data type for distance arrays, to constrain memory management.max_memory_fraction (
float) – Constraint to switch to calculating mean distances wherematrix=Trueand the distance matrix requires greater than a specified fraction of total avaialbe physical memory.
- pyrolite.util.spatial.piecewise(segment_ranges: list, segments=2, output_fmt=<class 'numpy.float64'>)[source]
Generator to provide values of quantizable paramaters which define a grid, here used to split up queries from databases to reduce load.
- pyrolite.util.spatial.spatiotemporal_split(segments=4, nan_lims=[nan, nan], **kwargs)[source]
Creates spatiotemporal grid using piecewise function and arbitrary ranges for individial kw-parameters (e.g. age=(0., 450.)), and sequentially returns individial grid cell attributes.
pyrolite.util.resampling
Utilities for (weighted) bootstrap resampling applied to geoscientific point-data.
- pyrolite.util.resampling.univariate_distance_matrix(a, b=None, distance_metric=None)[source]
Get a distance matrix for a single column or array of values (here used for ages).
- Parameters
a, b (
numpy.ndarray) – Points or arrays to calculate distance between. If only one array is specified, a full distance matrix (i.e. calculate a point-to-point distance for every combination of points) will be returned.distance_metric – Callable function f(a, b) from which to derive a distance metric.
- Returns
2D distance matrix.
- Return type
- pyrolite.util.resampling.get_spatiotemporal_resampling_weights(df, spatial_norm=1.8, temporal_norm=38, latlong_names=['Latitude', 'Longitude'], age_name='Age', max_memory_fraction=0.25, normalized_weights=True, **kwargs)[source]
Takes a dataframe with lat, long and age and returns a sampling weight for each sample which is essentailly the inverse of the mean distance to other samples.
- Parameters
df (
pandas.DataFrame) – Dataframe to calculate weights for.spatial_norm (
float) – Normalising constant for spatial measures (1.8 arc degrees).temporal_norm (
float) – Normalising constant for temporal measures (38 Mya).latlong_names (
list) – List of column names referring to latitude and longitude.age_name (
str) – Column name corresponding to geological age or time.max_memory_fraction (
float) – Constraint to switch to calculating mean distances wherematrix=Trueand the distance matrix requires greater than a specified fraction of total avaialbe physical memory. This is passed on togreat_circle_distance().normalized_weights (
bool) – Whether to renormalise weights to unity.- Returns
weights – Sampling weights.
- Return type
Notes
This function is equivalent to Eq(1) from Keller and Schone:
\[W_i \propto 1 \Big / \sum_{j=1}^{n} \Big ( \frac{1}{((z_i - z_j)/a)^2 + 1} + \frac{1}{((t_i - t_j)/b)^2 + 1} \Big )\]
- pyrolite.util.resampling.add_age_noise(df, min_sigma=50, noise_level=1.0, age_name='Age', age_uncertainty_name='AgeUncertainty', min_age_name='MinAge', max_age_name='MaxAge')[source]
Add gaussian noise to a series of geological ages based on specified uncertainties or age ranges.
- Parameters
df (
pandas.DataFrame) – Dataframe with age data within which to look up the age name and add noise.min_sigma (
float) – Minimum uncertainty to be considered for adding age noise.noise_level (
float) – Scaling of the noise added to the ages. By default the uncertaines are unscaled, but where age uncertaines are specified and are the one standard deviation level this can be used to expand the range of noise added (e.g. to 2SD).age_name (
str) – Column name for absolute ages.age_uncertainty_name (
str) – Name of the column specifiying absolute age uncertainties.min_age_name (
str) – Name of the column specifying minimum absolute ages (used where uncertainties are otherwise unspecified).max_age_name (
str) – Name of the column specifying maximum absolute ages (used where uncertainties are otherwise unspecified).- Returns
df – Dataframe with noise-modified ages.
- Return type
Notes
This modifies the dataframe which is input - be aware of this if using outside of the bootstrap resampling for which this was designed.
- pyrolite.util.resampling.spatiotemporal_bootstrap_resample(df, columns=None, uncert=None, weights=None, niter=100, categories=None, transform=None, bootstrap_method='smooth', add_gaussian_age_noise=True, metrics=['mean', 'var'], default_uncertainty=0.02, relative_uncertainties=True, noise_level=1, age_name='Age', latlong_names=['Latitude', 'Longitude'], **kwargs)[source]
Resample and aggregate metrics from a dataframe, optionally aggregating by a given set of categories. Formulated specifically for dealing with resampling to address uneven sampling density in space and particularly geological time.
- Parameters
df (
pandas.DataFrame) – Dataframe to resample.columns (
list) – Columns to provide bootstrap resampled estimates for.uncert (
float|numpy.ndarray|pandas.Series|pandas.DataFrame) – Fractional uncertainties for the dataset.weights (
numpy.ndarray|pandas.Series) – Array of weights for resampling, if precomputed.niter (
int) – Number of resampling iterations. This will be the minimum index size of the output metric dataframes.categories (
list|numpy.ndarray|pandas.Series) – List of sample categories to group the ouputs by, which has the same size as the dataframe index.transform – Callable function to transform input data prior to aggregation functions. Note that the outputs will need to be inverse-transformed.
bootstrap_method (
str) – Which method to use to add gaussian noise to the input dataset parameters.add_gaussian_age_noise (
bool) – Whether to add gassian noise to the input dataset ages, where present.metrics (
list) – List of metrics to use for dataframe aggregation.default_uncertainty (
float) – Default (fractional) uncertainty where uncertainties are not given.relative_uncertainties (
bool) – Whether uncertainties are relative (True, i.e. fractional proportions of parameter values), or absolute (False)noise_level (
float) – Multiplier for the random gaussian noise added to the dataset and ages.age_name (
str) – Column name for geological age.latlong_names (
list) – Column names for latitude and longitude, or equvalent orthogonal spherical spatial measures.- Returns
Dictionary of aggregated Dataframe(s) indexed by statistical metrics. If categories are specified, the dataframe(s) will have a hierarchical index of
categories, iteration.- Return type
pyrolite.util.missing
- pyrolite.util.missing.md_pattern(Y)[source]
Get the missing data patterns from an array.
- Parameters
Y (
numpy.ndarray|pandas.DataFrame) – Input dataset.- Returns
pattern_ids (
numpy.ndarray) – Pattern ID array.pattern_dict (
dict) – Dictionary of patterns indexed by pattern IDs. Contains a pattern and count for each pattern ID.
- pyrolite.util.missing.cooccurence_pattern(Y, normalize=False, log=False)[source]
Get the co-occurence patterns from an array.
- Parameters
Y (
numpy.ndarray|pandas.DataFrame) – Input dataset.normalize (
bool) – Whether to normalize the cooccurence to compare disparate variables.log (
bool) – Whether to take the log of the cooccurence.- Returns
co_occur – Cooccurence frequency array.
- Return type
pyrolite.util.units
pyrolite.util.types
pyrolite.util.meta
- pyrolite.util.meta.get_module_datafolder(module='pyrolite', subfolder=None)[source]
Returns the path of a module data folder.
- Parameters
subfolder (
str) – Subfolder within the module data folder.- Return type
- pyrolite.util.meta.pyrolite_datafolder(subfolder=None)[source]
Returns the path of the pyrolite data folder.
- Parameters
subfolder (
str) – Subfolder within the pyrolite data folder.- Return type
- pyrolite.util.meta.sphinx_doi_link(doi)[source]
Generate a string with a restructured text link to a given DOI.
- pyrolite.util.meta.subkwargs(kwargs, *f)[source]
Get a subset of keyword arguments which are accepted by a function.
- pyrolite.util.meta.inargs(name, *funcs)[source]
Check if an argument is a possible input for a specific function.
- pyrolite.util.meta.numpydoc_str_param_list(iterable, indent=4)[source]
Format a list of numpydoc parameters.
- pyrolite.util.meta.get_additional_params(*fs, t='Parameters', header='', indent=4, subsections=False, subsection_delim='Note')[source]
Checks the base Parameters section of docstrings to get ‘Other Parameters’ for a specific function. Designed to incorporate information on inherited or forwarded parameters.
- Parameters
fs (
list) – List of functions.t (
str) – Target block of docstrings.header (
str) – Optional seciton header.indent (
int|str) – Indent as number of spaces, or a string of a given length.subsections (
bool, False) – Whether to include headers specific for each function, creating subsections.subsection_delim (
str) – Subsection delimiter.- Return type
Todo
Add delimiters between functions to show where arguments should be passed.
- pyrolite.util.meta.update_docstring_references(obj, ref='ref')[source]
Updates docstring reference names to strings including the function name. Decorator will return the same function with a modified docstring. Sphinx likes unique names - specifically for citations, not so much for footnotes.
- Parameters
obj (
func|class) – Class or function for which to update documentation references.ref (
str) – String to replace with the object name.- Returns
Object with modified docstring.
- Return type
func|classpyrolite.util.skl
Utilities for use with
sklearn.pyrolite.util.skl.vis
- pyrolite.util.skl.vis.plot_confusion_matrix(*args, ax=None, classes=[], class_order=None, normalize=False, title='Confusion Matrix', cmap=<matplotlib.colors.LinearSegmentedColormap object>, norm=None, xlabelrotation=None)[source]
This function prints and plots the confusion matrix. Normalization can be applied by setting normalize=True.
- Parameters
args (
tuple) –Data to evaluate and visualise a confusion matrix:
A single confusion matrix (n x n)
A tuple of (y_test, y_predict)
A tuple of (classifier_model, X_test, y_test)
ax (
matplotlib.axes.Axes) – Axis to plot on, if one exists.classes (
list) – List of class names to use as labels, and for ordering (see below). This should match the order contained within the model. Where a classifier model is passed, the classes will be directly extracted.class_order (
list) – List of classes in the desired order along the axes. Should match the supplied classes where classes are given, or integer indicies for where no named classes are given.normalize (
bool) – Whether to normalize the counts for the confusion matrix to the sum of all cases (i.e. be between 0 and 1).title (
str) – Title for the axes.cmap (
str|matplotlib.color.Colormap) – Colormap for the visualisation of the confusion matrix.norm (
bool) – Normalization for the colormap visualisation across the confusion matrix.xlabelrotation (
float) – Rotation in degrees for the xaxis labels.- Returns
ax
- Return type
- pyrolite.util.skl.vis.plot_gs_results(gs, xvar=None, yvar=None)[source]
Plots the results from a GridSearch showing location of optimum in 2D.
- pyrolite.util.skl.vis.alphas_from_multiclass_prob(probs, method='entropy', alpha=1.0)[source]
Take an array of multiclass probabilities and map to an alpha variable.
- Parameters
probs (
numpy.ndarray) – Multiclass probabilities with shape (nsamples, nclasses).method (
str,entropy|kl_div) – Method for mapping probabilities to alphas.alpha (
float) – Optional specification of overall maximum alpha value.- Returns
a – Alpha values for each sample with shape (nsamples, 1).
- Return type
- pyrolite.util.skl.vis.plot_mapping(X, Y, mapping=None, ax=None, cmap=None, alpha=1.0, s=10, alpha_method='entropy', **kwargs)[source]
- Parameters
X (
numpy.ndarray) – Coordinates in multidimensional space.Y (
numpy.ndarray|sklearn.base.BaseEstimator) – An array of targets, or a method to obtain such an array of targets viaY.predict(). Transformers with probabilistic output (viaY.predict_proba()) will have these probability estimates accounted for via the alpha channel.mapping (
numpy.ndarray|TransformerMixin) – Mapped points or transformer to create mapped points.ax (
matplotlib.axes.Axes) – Axes to plot on.cmap (
matplotlib.cm.ListedColormap) – Colormap to use for the classification visualisation (ideally this should be a discrete colormap unless the classes are organised ).alpha (
float) – Coefficient for alpha.alpha_method (
'entropy' or 'kl_div') – Method to map class probabilities to alpha.'entropy'uses a measure of entropy relative to null-scenario of equal distribution across classes, while'kl_div'calculates the information gain relative to the same null-scenario.- Returns
ax (
Axes) – Axes on which the mapping is plotted.tfm (
BaseEstimator) – Fitted mapping transform.Todo
Option to generate colors for individual classes
This could be based on the distances between their centres in multidimensional space (or low dimensional mapping of this space), enabling a continuous (n-dimensional) colormap to be used to show similar classes, in addition to classification confidence.
pyrolite.util.skl.pipeline
- pyrolite.util.skl.pipeline.fit_save_classifier(clf, X_train, y_train, directory='.', name='clf', extension='.joblib')[source]
Fit and save a classifier model. Also save relevant metadata where possible.
- Parameters
clf (
sklearn.base.BaseEstimator) – Classifier or gridsearch.X_train (
numpy.ndarray|pandas.DataFrame) – Training data.y_train (
numpy.ndarray|pandas.Series) – Training true classes.directory (
str|pathlib.Path) – Path to the save directory.name (
str) – Name of the classifier.extension (
str) – Extension to give the saved classifier pickled witih joblib.- Returns
clf – Fitted classifier.
- Return type
- pyrolite.util.skl.pipeline.classifier_performance_report(clf, X_test, y_test, classes=[], directory='.', name='clf')[source]
Output a performance report for a classifier. Currently outputs the overall classification score, a confusion matrix and where relevant an indication of variation seen across the gridsearch (currently only possible for 2D searches).
- Parameters
clf (
sklearn.base.BaseEstimator| sklearn.model_selection.GridSearchCV) – Classifer or gridsearch.X_test (
numpy.ndarray|pandas.DataFrame) – Input data for testing.y_test (
numpy.ndarray|pandas.Series) – Labelled/target data for testing.classes (list) – Names of classes. directory :
str|pathlib.PathPath to the save directory.
name (
str) – Name of the classifier.- Returns
clf – Fitted classifier.
- Return type
- pyrolite.util.skl.pipeline.SVC_pipeline(sampler=None, balance=True, transform=None, scaler=None, kernel='rbf', decision_function_shape='ovo', probability=False, cv=StratifiedKFold(n_splits=10, random_state=None, shuffle=True), param_grid={}, n_jobs=4, verbose=10, cache_size=500, **kwargs)[source]
A convenience function for constructing a Support Vector Classifier pipeline.
- Parameters
sampler (
sklearn.base.TransformerMixin) – Resampling transformer.balance (
bool) – Whether to balance the class weights for the classifier.transform (
sklearn.base.TransformerMixin) – Preprocessing transformer.scaler (
sklearn.base.TransformerMixin) – Scale transformer.kernel (
str|callable) – Name of kernel to use for the support vector classifier ('linear'|'rbf'|'poly'|'sigmoid'). Optionally, a custom kernel function can be supplied (seesklearndocs for more info).decision_function_shape (
str,'ovo' or 'ovr') – Shape of the decision function surface.'ovo'one-vs-one classifier of libsvm (returning classification of shape(samples, classes*(classes-1)/2)), or the default'ovr' one-vs-rest classifier which will return classification estimation shape of :code:`(samples, classes).probability (
bool) – Whether to implement Platt-scaling to enable probability estimates. This must be enabled prior to calling fit, and will slow down that method.cv (
int|sklearn.model_selection.BaseSearchCV) – Cross validation search. If an integerkis provided, results in defaultk-fold cross validation. Optionally, if asklearn.model_selection.BaseSearchCVinstance is provided, it will be used directly (enabling finer control, e.g. over sorting/shuffling etc).param_grid (
dict) – Dictionary reprenting a parameter grid for the support vector classifier. Typically contains 1D arrays of grid indicies forSVC()parameters each prefixed withsvc__(e.g.dict(svc__gamma=np.logspace(-1, 3, 5), svc__C=np.logspace(-0.5, 2, 5)).n_jobs (
int) – Number of processors to use for the SVC construction. Note that providingn_jobs = -1will use all available processors.verbose (
int) – Level of verbosity for the pipeline logging output.cache_size (
float) – Specify the size of the kernel cache (in MB).Note
The following additional parameters are from
sklearn.svm._classes.SVC().
- Other Parameters
C (float, default=1.0) – Regularization parameter. The strength of the regularization is inversely proportional to C. Must be strictly positive. The penalty is a squared l2 penalty.
degree (int, default=3) – Degree of the polynomial kernel function (‘poly’). Must be non-negative. Ignored by all other kernels.
gamma ({‘scale’, ‘auto’} or float, default=’scale’) – Kernel coefficient for ‘rbf’, ‘poly’ and ‘sigmoid’.
if
gamma='scale'(default) is passed then it uses 1 / (n_features * X.var()) as value of gamma,if ‘auto’, uses 1 / n_features
if float, must be non-negative.
Changed in version 0.22: The default value of
gammachanged from ‘auto’ to ‘scale’.coef0 (float, default=0.0) – Independent term in kernel function. It is only significant in ‘poly’ and ‘sigmoid’.
shrinking (bool, default=True) – Whether to use the shrinking heuristic. See the User Guide.
tol (float, default=1e-3) – Tolerance for stopping criterion.
cache_size (float, default=200) – Specify the size of the kernel cache (in MB).
class_weight (dict or ‘balanced’, default=None) – Set the parameter C of class i to class_weight[i]*C for SVC. If not given, all classes are supposed to have weight one. The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as
n_samples / (n_classes * np.bincount(y)).max_iter (int, default=-1) – Hard limit on iterations within solver, or -1 for no limit.
break_ties (bool, default=False) – If true,
decision_function_shape='ovr', and number of classes > 2, predict will break ties according to the confidence values of decision_function; otherwise the first class among the tied classes is returned. Please note that breaking ties comes at a relatively high computational cost compared to a simple predict.New in version 0.22.
random_state (int, RandomState instance or None, default=None) – Controls the pseudo random number generation for shuffling the data for probability estimates. Ignored when probability is False. Pass an int for reproducible output across multiple function calls. See Glossary.
- Returns
gs – Gridsearch object containing the results of the SVC training across the parameter grid. Access the best estimator with
gs.best_estimator_and its parameters withgs.best_params_.- Return type
pyrolite.util.skl.select
pyrolite.util.skl.transform
- class pyrolite.util.skl.transform.Devolatilizer(exclude=['H2O', 'H2O_PLUS', 'H2O_MINUS', 'CO2', 'LOI'], renorm=True)[source]
pyrolite.util.skl.impute
- class pyrolite.util.skl.impute.MultipleImputer(multiple=5, max_iter=10, groupby=None, *args, **kwargs)[source]
- fit(X, y=None)[source]
Fit the imputers.
- Parameters
X (
pandas.DataFrame) – Data to use to fit the imputations.y (
pandas.Series) – Target class; optionally specified, and used similarly to groupby.pyrolite.util.classification
Utilities for rock chemistry and mineral abundance classification.
Todo
Petrological classifiers: QAPF (aphanitic/phaneritic), gabbroic Pyroxene-Olivine-Plagioclase, ultramafic Olivine-Orthopyroxene-Clinopyroxene
- class pyrolite.util.classification.PolygonClassifier(name=None, axes=None, fields=None, scale=1.0, transform=None, mode=None, **kwargs)[source]
A classifier model built form a series of polygons defining specific classes.
- Parameters
name (
str) – A name for the classifier model.axes (
dict) – Mapping from plot axes to variables to be used for labels.fields (
dict) – Dictionary describing indiviudal polygons, with identifiers as keys and dictionaries containing ‘name’ and ‘fields’ items.scale (
float) – Default maximum scale for the axes. Typically 100 (wt%) or 1 (fractional).xlim (
tuple) – Default x-limits for this classifier for plotting.ylim (
tuple) – Default y-limits for this classifier for plotting.
- predict(X, data_scale=None)[source]
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)[source]
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- class pyrolite.util.classification.TAS(which_model=None, **kwargs)[source]
Total-alkali Silica Diagram classifier from Middlemost (1994) 1, a closed-polygon variant after Le Bas et al. (1992) 2.
- Parameters
name (
str) – A name for the classifier model.axes (
list|tuple) – Names of the axes corresponding to the polygon coordinates.fields (
dict) – Dictionary describing indiviudal polygons, with identifiers as keys and dictionaries containing ‘name’ and ‘fields’ items.scale (
float) – Default maximum scale for the axes. Typically 100 (wt%) or 1 (fractional).xlim (
tuple) – Default x-limits for this classifier for plotting.ylim (
tuple) – Default y-limits for this classifier for plotting.which_model (
str) – The name of the model variant to use, if not Middlemost.References
- 1
Middlemost, E. A. K. (1994). Naming materials in the magma/igneous rock system. Earth-Science Reviews, 37(3), 215–224. doi: 10.1016/0012-8252(94)90029-9
- 2
Le Bas, M.J., Le Maitre, R.W., Woolley, A.R. (1992). The construction of the Total Alkali-Silica chemical classification of volcanic rocks. Mineralogy and Petrology 46, 1–22. doi: 10.1007/BF01160698
- 3
Le Maitre, R.W. (2002). Igneous Rocks: A Classification and Glossary of Terms : Recommendations of International Union of Geological Sciences Subcommission on the Systematics of Igneous Rocks. Cambridge University Press, 236pp. doi: 10.1017/CBO9780511535581
- add_to_axes(ax=None, fill=False, axes_scale=100.0, add_labels=False, which_labels='ID', which_ids=[], label_at_centroid=True, **kwargs)[source]
Add the TAS fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which labels to add to the polygons (e.g. for TAS, ‘volcanic’, ‘intrusive’ or the field ‘ID’).which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.label_at_centroid (
bool) – Whether to label the fields at the centroid (True) or at the visual center of the field (False).- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.USDASoilTexture(**kwargs)[source]
United States Department of Agriculture Soil Texture classification model 4 5.
- Parameters
References
- 4
Soil Science Division Staff (2017). Soil Survey Manual. C. Ditzler, K. Scheffe, and H.C. Monger (eds.). USDA Handbook 18. Government Printing Office, Washington, D.C.
- 5
Thien, Steve J. (1979). A Flow Diagram for Teaching Texture-by-Feel Analysis. Journal of Agronomic Education 8:54–55. doi: 10.2134/jae.1979.0054
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.QAP(**kwargs)[source]
IUGS QAP ternary classification 6 7.
- Parameters
References
- 6
Streckeisen, A. (1974). Classification and nomenclature of plutonic rocks: recommendations of the IUGS subcommission on the systematics of Igneous Rocks. Geol Rundsch 63, 773–786. doi: 10.1007/BF01820841
- 7
Le Maitre,R.W. (2002). Igneous Rocks: A Classification and Glossary of Terms : Recommendations of International Union of Geological Sciences Subcommission on the Systematics of Igneous Rocks. Cambridge University Press, 236pp doi: 10.1017/CBO9780511535581
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.FeldsparTernary(**kwargs)[source]
Simplified feldspar diagram classifier, based on a version printed in the second edition of ‘An Introduction to the Rock Forming Minerals’ (Deer, Howie and Zussman).
- Parameters
name (
str) – A name for the classifier model.axes (
list|tuple) – Names of the axes corresponding to the polygon coordinates.fields (
dict) – Dictionary describing indiviudal polygons, with identifiers as keys and dictionaries containing ‘name’ and ‘fields’ items.mode (
str) – Mode of the diagram to use; two are currently available - ‘default’, which fills the entire ternary space, and ‘miscibility-gap’ which gives a simplified approximation of the miscibility gap.References
- 8
Deer, W. A., Howie, R. A., & Zussman, J. (2013). An introduction to the rock-forming minerals (3rd ed.). Mineralogical Society of Great Britain and Ireland.
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.JensenPlot(**kwargs)[source]
Jensen Plot for classification of subalkaline volcanic rocks 9.
- Parameters
References
- 9
Jensen, L. S. (1976). A new cation plot for classifying sub-alkaline volcanic rocks. Ontario Division of Mines. Miscellaneous Paper No. 66.
Notes
Diagram used for the classification classification of subalkalic volcanic rocks. The diagram is constructed for molar cation percentages of Al, Fe+Ti and Mg, on account of these elements’ stability upon metamorphism. This particular version uses updated labels relative to Jensen (1976), in which the fields have been extended to the full range of the ternary plot.
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.SpinelTrivalentTernary(**kwargs)[source]
Spinel Trivalent Ternary classification - designed for data in atoms per formula unit
- Parameters
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.SpinelFeBivariate(**kwargs)[source]
Fe-Spinel classification, designed for data in atoms per formula unit.
- Parameters
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.Pettijohn(**kwargs)[source]
Pettijohn (1973) sandstones classification 10.
- Parameters
References
- 10
Pettijohn, F. J., Potter, P. E. and Siever, R. (1973). Sand and Sandstone. New York, Springer-Verlag. 618p. doi: 10.1007/978-1-4615-9974-6
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
- class pyrolite.util.classification.Herron(**kwargs)[source]
Herron (1988) sandstones classification 11.
- Parameters
References
- 11
Herron, M.M. (1988). Geochemical classification of terrigenous sands and shales from core or log data. Journal of Sedimentary Research, 58(5), pp.820-829. doi: 10.1306/212F8E77-2B24-11D7-8648000102C1865D
- add_to_axes(ax=None, fill=False, axes_scale=1.0, add_labels=False, which_labels='ID', which_ids=[], **kwargs)
Add the fields from the classifier to an axis.
- Parameters
ax (
matplotlib.axes.Axes) – Axis to add the polygons to.fill (
bool) – Whether to fill the polygons.axes_scale (
float) – Maximum scale for the axes. Typically 100 (for wt%) or 1 (fractional).add_labels (
bool) – Whether to add labels for the polygons.which_labels (
str) – Which data to use for field labels - field ‘name’ or ‘ID’.which_ids (
list) – List of field IDs corresponding to the polygons to add to the axes object. (e.g. for TAS, [‘F’, ‘T1’] to plot the Foidite and Trachyte fields). An empty list corresponds to plotting all the polygons.- Returns
ax
- Return type
- property axis_components
Get the axis components used by the classifier.
- Returns
Ordered names for axes used by the classifier.
- Return type
- predict(X, data_scale=None)
Predict the classification of samples using the polygon-based classifier.
- Parameters
X (
numpy.ndarray|pandas.DataFrame) – Data to classify.data_scale (
float) – Maximum scale for the data. Typically 100 (wt%) or 1 (fractional).- Returns
Series containing classifer predictions. If a dataframe was input, it inherit the index.
- Return type
pyrolite.util.log
- pyrolite.util.log.Handle(logger, handler_class=<class 'logging.StreamHandler'>, formatter='%(asctime)s %(name)s - %(levelname)s: %(message)s', level=None)[source]
Handle a logger with a standardised formatting.
- Parameters
logger (
logging.Logger|str) – Logger or module name to source a logger from.handler_class (
logging.Handler) – Handler class for the logging messages.formatter (
str|logging.Formatter) – Formatter for the logging handler. Strings will be passed to thelogging.Formatterconstructor.level (
str) – Logging level for the handler.- Returns
Configured logger.
- Return type
- class pyrolite.util.log.ToLogger(logger, level=None)[source]
Output stream which will output to logger module instead of stdout.
- buf = ''
- logger = None
- level = None
- pyrolite.util.log.stream_log(logger=None, level='INFO')[source]
Stream the log from a specific package or subpackage.
- Parameters
logger (
str|logging.Logger) – Name of the logger or module to monitor logging from.level (
str,'INFO') – Logging level at which to set the handler output.- Returns
Logger for the specified package with stream handler added.
- Return type
See also
Data
This gallery describes the datasets used by pyrolite, how to access them, and their sources.
Mineral Database
pyrolite includes a limited mineral database which is useful for for looking up endmember compositions. This part of the package is being actively developed, so expect expansions and improvements soon.
See also
- Examples:
Total running time of the script: (0 minutes 0.000 seconds)
Geological Timescale
pyrolite includes a simple geological timescale, based on a recent verion
of the International Chronostratigraphic Chart 1. The
Timescale class can be used to look up names for
specific geological ages, to look up times for known geological age names
and to access a reference table for all of these.
from pyrolite.util.time import Timescale, age_name
ts = Timescale()
eg = ts.data.iloc[:, :5] # the first five columns of this data table
eg
References
- 1
Cohen, K.M., Finney, S.C., Gibbard, P.L., Fan, J.-X., 2013. The ICS International Chronostratigraphic Chart. Episodes 36, 199–204.
See also
- Examples:
- Modules, Classes and Functions:
Total running time of the script: (0 minutes 0.061 seconds)
Ionic Radii
pyrolite incldues a few sets of reference tables for ionic radii in aangstroms
(Å) from [Shannon1976] and [WhittakerMuntus1970], each with tables indexed
by element, ionic charge and coordination. The easiset way to access these is via
the get_ionic_radii() function. The function can be used
to get radii for individual elements, using a source keyword argument to swap
between the datasets:
import matplotlib.pyplot as plt
import pandas as pd
from pyrolite.geochem.ind import REE, get_ionic_radii
REE_radii = pd.Series(
get_ionic_radii(REE(), coordination=8, charge=3, source="Whittaker"), index=REE()
)
REE_radii
La 1.26
Ce 1.22
Pr 1.22
Nd 1.20
Sm 1.17
Eu 1.15
Gd 1.14
Tb 1.12
Dy 1.11
Ho 1.10
Er 1.08
Tm 1.07
Yb 1.06
Lu 1.05
dtype: float64
REE_radii.pyroplot.spider(color="k", logy=False)
plt.show()
References
- Shannon1976
Shannon RD (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallographica Section A 32:751–767. doi: 10.1107/S0567739476001551.
- WhittakerMuntus1970
Whittaker, E.J.W., Muntus, R., 1970. Ionic radii for use in geochemistry. Geochimica et Cosmochimica Acta 34, 945–956. doi: 10.1016/0016-7037(70)90077-3.
- Pauling1960
Pauling, L., 1960. The Nature of the Chemical Bond. Cornell University Press, Ithaca, NY.
See also
Total running time of the script: (0 minutes 0.233 seconds)
Aitchison Examples
pyrolite includes four synthetic datasets which are used in [Aitchison1984]
which can be accessed using each of the respective functions
load_boxite(),
load_coxite(),
load_hongite() and
load_kongite()
(all returning a DataFrame).
from pyrolite.data.Aitchison import load_boxite, load_coxite, load_hongite, load_kongite
df = load_boxite()
df.head()
import matplotlib.pyplot as plt
import pyrolite.plot
fig, ax = plt.subplots(1)
for loader in [load_boxite, load_coxite, load_hongite, load_kongite]:
df = loader()
ax = df[["A", "B", "C"]].pyroplot.scatter(ax=ax, label=df.attrs["name"])
ax.legend()
plt.show()
References
- Aitchison1984
Aitchison, J., 1984. The statistical analysis of geochemical compositions. Journal of the International Association for Mathematical Geology 16, 531–564. doi: 10.1007/BF01029316
See also
- Examples:
Log Ratio Means, Log Transforms, Compositional Data, Ternary Plots
- Tutorials:
- Modules and Functions:
Total running time of the script: (0 minutes 3.308 seconds)
Reference Compositions
This page presents the range of compositions within the reference compositon database
accessible within pyrolite. It’s currently a work in progress, but will soon
contain extended descriptions and notes for some of the compositions and associated
references.
import matplotlib.pyplot as plt
from pyrolite.geochem.norm import all_reference_compositions, get_reference_composition
refcomps = all_reference_compositions()
norm = "Chondrite_PON" # a constant composition to normalise to
Chondrites
fltr = lambda c: c.reservoir == "Chondrite"
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
Mantle
Primitive Mantle & Pyrolite
fltr = lambda c: c.reservoir in ["PrimitiveMantle", "BSE"]
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Depleted Mantle
fltr = lambda c: ("Depleted" in c.reservoir) & ("Mantle" in c.reservoir)
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Mid-Ocean Ridge Basalts (MORB)
Average MORB, NMORB
fltr = lambda c: c.reservoir in ["MORB", "NMORB"]
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Enriched MORB
fltr = lambda c: "EMORB" in c.reservoir
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Ocean Island Basalts
fltr = lambda c: "OIB" in c.reservoir
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Continental Crust
Bulk Continental Crust
fltr = lambda c: c.reservoir == "BulkContinentalCrust"
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Upper Continental Crust
fltr = lambda c: c.reservoir == "UpperContinentalCrust"
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Mid-Continental Crust
fltr = lambda c: c.reservoir == "MidContinentalCrust"
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Lower Continental Crust
fltr = lambda c: c.reservoir == "LowerContinentalCrust"
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Shales
fltr = lambda c: "Shale" in c.reservoir
compositions = [x for (name, x) in refcomps.items() if fltr(x)]
fig, ax = plt.subplots(1)
for composition in compositions:
composition.set_units("ppm")
df = composition.comp.pyrochem.normalize_to(norm, units="ppm")
df.pyroplot.REE(unity_line=True, ax=ax, label=composition.name)
ax.legend()
plt.show()
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
/home/docs/checkouts/readthedocs.org/user_builds/pyrolite/checkouts/main/pyrolite/plot/spider.py:276: UserWarning: Attempt to set non-positive ylim on a log-scaled axis will be ignored.
ax.set_ylim(_ymin, _ymax)
Composition List
- LCC_McLennan2001
- LCC_McLennan2001 Model of LowerContinentalCrust from McLennan (2001).
- LCC_RG2003
- LCC_RG2003 Model of LowerContinentalCrust from Rudnick & Gao (2003).
- LCC_RG2014
- LCC_RG2014 Model of LowerContinentalCrust from Rudnick & Gao (2014).
- PRS_Condie1993
- PRS_Condie1993 Model of ProterozoicCratonicShale from Condie (1993).
- Chondrite_MS95
- Chondrite_MS95 Model of Chondrite from McDonough & Sun (1995).
- Chondrite_PON
- Chondrite_PON Model of Chondrite from Palme and O'Neill (2014).
- ChondriteREE_ON
- ChondriteREE_ON Model of Chondrite from O'Neill (2016).
- Chondrite_SM89
- Chondrite_SM89 Model of Chondrite from Sun & McDonough (1989).
- BCC_McLennan2001
- BCC_McLennan2001 Model of BulkContinentalCrust from McLennan (2001).
- BCC_RG2003
- BCC_RG2003 Model of BulkContinentalCrust from Rudnick & Gao (2003).
- BCC_RG2014
- BCC_RG2014 Model of BulkContinentalCrust from Rudnick & Gao (2014).
- NMORB_Gale2013
- NMORB_Gale2013 Model of NMORB from Gale et al. (2013).
- NMORB_SM89
- NMORB_SM89 Model of NMORB from Sun & McDonough (1989).
- MCC_RG2014
- MCC_RG2014 Model of MidContinentalCrust from Rudnick & Gao (2014).
- MORB_Gale2013
- MORB_Gale2013 Model of MORB from Gale et al. (2013).
- DMORB_Gale2013
- DMORB_Gale2013 Model of DMORB from Gale et al. (2013).
- NASC_Gromet1984
- NASC_Gromet1984 Model of NorthAmericanShaleComposite from Gromet et al. (1984); Taylor and McLennan (1985); Condie (1993); McLennan (2001).
- Pyrolite_MS95
- Pyrolite_MS95 Model of BSE from McDonough & Sun (1995).
- PM_PON
- PM_PON Model of PrimitiveMantle from Palme and O'Neill (2014).
- PM_SM89
- PM_SM89 Model of PrimitiveMantle from Sun & McDonough (1989).
- MUQ_Kamber2005
- MUQ_Kamber2005 Model of MudFromQueensland from Kamber et al. (2005).
- DMM_WH2005
- DMM_WH2005 Model of DepletedMORBMantle from Workman & Hart (2005).
- D-DMM_WH2005
- D-DMM_WH2005 Model of DepletedDepletedMORBMantle from Workman & Hart (2005).
- PHS_Condie1993
- PHS_Condie1993 Model of PhanerozoicCratonicShale from Condie (1993).
- ARS_Condie1993
- ARS_Condie1993 Model of ArcheanCratonicShale from Condie (1993).
- DM_SS2004
- DM_SS2004 Model of DepletedMantle from Salters & Strake (2004).
- OIB_SM89
- OIB_SM89 Model of OIB from Sun & McDonough (1989).
- EUS_Bau2018
- EUS_Bau2018 Model of EuropeanShale from Bau et al. (2018).
- GLOSS2_P2014
- GLOSS2_P2014 Model of GLOSS from Plank (2014).
- GLOSS_P2014
- GLOSS_P2014 Model of GLOSS from Plank (2014).
- EMORB_Gale2013
- EMORB_Gale2013 Model of EMORB from Gale et al. (2013).
- EMORB_SM89
- EMORB_SM89 Model of EMORB from Sun & McDonough (1989).
- E-DMM_WH2005
- E-DMM_WH2005 Model of EnrichedDepletedMORBMantle from Workman & Hart (2005).
- PAAS_Pourmand2012
- PAAS_Pourmand2012 Model of PostArcheanAustralianShale from Pourmand et al. (2012).
- PAAS_TM1985
- PAAS_TM1985 Model of PostArcheanAustralianShale from Taylor & McLennan (1985); McLennan (2001).
- UCC_McLennan2001
- UCC_McLennan2001 Model of UpperContinentalCrust from McLennan (2001).
- UCC_RG2003
- UCC_RG2003 Model of UpperContinentalCrust from Rudnick & Gao (2003).
- UCC_RG2014
- UCC_RG2014 Model of UpperContinentalCrust from Rudnick & Gao (2014).
See also
- Examples:
Total running time of the script: (0 minutes 12.379 seconds)
Extensions
This page will list packages which have been developed as extensions to pyrolite.
Note
This page is a work in progress and will updated soon as submodules from
pyrolite.ext are migrated out of pyrolite to reduce installation overheads
and unnecessary dependencies.
pyrolite-meltsutil
pyroliteextension which wraps thealphaMELTSexecutableFunctions for working with
alphaMELTStablesEventually, this will likely instead link to under-development python-MELTS.
Note
There are some great things happening on the MELTS-for-scripting front; these utilities will be intended to link your data to these tools.