Taylor diagram for python/matplotlib [ 10.5281/zenodo.5548061 ]

taylorDiagram.py

#!/usr/bin/env python
# Copyright: This document has been placed in the public domain.

"""
Taylor diagram (Taylor, 2001) implementation.

Note: If you have found these software useful for your research, I would
appreciate an acknowledgment.
"""

__version__ = "Time-stamp: <2018-12-06 11:43:41 ycopin>"
__author__ = "Yannick Copin <yannick.copin@laposte.net>"

import numpy as NP
import matplotlib.pyplot as PLT


class TaylorDiagram(object):
    """
    Taylor diagram.

    Plot model standard deviation and correlation to reference (data)
    sample in a single-quadrant polar plot, with r=stddev and
    theta=arccos(correlation).
    """

    def __init__(self, refstd,
                 fig=None, rect=111, label='_', srange=(0, 1.5), extend=False):
        """
        Set up Taylor diagram axes, i.e. single quadrant polar
        plot, using `mpl_toolkits.axisartist.floating_axes`.

        Parameters:

        * refstd: reference standard deviation to be compared to
        * fig: input Figure or None
        * rect: subplot definition
        * label: reference label
        * srange: stddev axis extension, in units of *refstd*
        * extend: extend diagram to negative correlations
        """

        from matplotlib.projections import PolarAxes
        import mpl_toolkits.axisartist.floating_axes as FA
        import mpl_toolkits.axisartist.grid_finder as GF

        self.refstd = refstd            # Reference standard deviation

        tr = PolarAxes.PolarTransform()

        # Correlation labels
        rlocs = NP.array([0, 0.2, 0.4, 0.6, 0.7, 0.8, 0.9, 0.95, 0.99, 1])
        if extend:
            # Diagram extended to negative correlations
            self.tmax = NP.pi
            rlocs = NP.concatenate((-rlocs[:0:-1], rlocs))
        else:
            # Diagram limited to positive correlations
            self.tmax = NP.pi/2
        tlocs = NP.arccos(rlocs)        # Conversion to polar angles
        gl1 = GF.FixedLocator(tlocs)    # Positions
        tf1 = GF.DictFormatter(dict(zip(tlocs, map(str, rlocs))))

        # Standard deviation axis extent (in units of reference stddev)
        self.smin = srange[0] * self.refstd
        self.smax = srange[1] * self.refstd

        ghelper = FA.GridHelperCurveLinear(
            tr,
            extremes=(0, self.tmax, self.smin, self.smax),
            grid_locator1=gl1, tick_formatter1=tf1)

        if fig is None:
            fig = PLT.figure()

        ax = FA.FloatingSubplot(fig, rect, grid_helper=ghelper)
        fig.add_subplot(ax)

        # Adjust axes
        ax.axis["top"].set_axis_direction("bottom")   # "Angle axis"
        ax.axis["top"].toggle(ticklabels=True, label=True)
        ax.axis["top"].major_ticklabels.set_axis_direction("top")
        ax.axis["top"].label.set_axis_direction("top")
        ax.axis["top"].label.set_text("Correlation")

        ax.axis["left"].set_axis_direction("bottom")  # "X axis"
        ax.axis["left"].label.set_text("Standard deviation")

        ax.axis["right"].set_axis_direction("top")    # "Y-axis"
        ax.axis["right"].toggle(ticklabels=True)
        ax.axis["right"].major_ticklabels.set_axis_direction(
            "bottom" if extend else "left")

        if self.smin:
            ax.axis["bottom"].toggle(ticklabels=False, label=False)
        else:
            ax.axis["bottom"].set_visible(False)          # Unused

        self._ax = ax                   # Graphical axes
        self.ax = ax.get_aux_axes(tr)   # Polar coordinates

        # Add reference point and stddev contour
        l, = self.ax.plot([0], self.refstd, 'k*',
                          ls='', ms=10, label=label)
        t = NP.linspace(0, self.tmax)
        r = NP.zeros_like(t) + self.refstd
        self.ax.plot(t, r, 'k--', label='_')

        # Collect sample points for latter use (e.g. legend)
        self.samplePoints = [l]

    def add_sample(self, stddev, corrcoef, *args, **kwargs):
        """
        Add sample (*stddev*, *corrcoeff*) to the Taylor
        diagram. *args* and *kwargs* are directly propagated to the
        `Figure.plot` command.
        """

        l, = self.ax.plot(NP.arccos(corrcoef), stddev,
                          *args, **kwargs)  # (theta, radius)
        self.samplePoints.append(l)

        return l

    def add_grid(self, *args, **kwargs):
        """Add a grid."""

        self._ax.grid(*args, **kwargs)

    def add_contours(self, levels=5, **kwargs):
        """
        Add constant centered RMS difference contours, defined by *levels*.
        """

        rs, ts = NP.meshgrid(NP.linspace(self.smin, self.smax),
                             NP.linspace(0, self.tmax))
        # Compute centered RMS difference
        rms = NP.sqrt(self.refstd**2 + rs**2 - 2*self.refstd*rs*NP.cos(ts))

        contours = self.ax.contour(ts, rs, rms, levels, **kwargs)

        return contours


def test1():
    """Display a Taylor diagram in a separate axis."""

    # Reference dataset
    x = NP.linspace(0, 4*NP.pi, 100)
    data = NP.sin(x)
    refstd = data.std(ddof=1)           # Reference standard deviation

    # Generate models
    m1 = data + 0.2*NP.random.randn(len(x))     # Model 1
    m2 = 0.8*data + .1*NP.random.randn(len(x))  # Model 2
    m3 = NP.sin(x-NP.pi/10)                     # Model 3

    # Compute stddev and correlation coefficient of models
    samples = NP.array([ [m.std(ddof=1), NP.corrcoef(data, m)[0, 1]]
                         for m in (m1, m2, m3)])

    fig = PLT.figure(figsize=(10, 4))

    ax1 = fig.add_subplot(1, 2, 1, xlabel='X', ylabel='Y')
    # Taylor diagram
    dia = TaylorDiagram(refstd, fig=fig, rect=122, label="Reference",
                        srange=(0.5, 1.5))

    colors = PLT.matplotlib.cm.jet(NP.linspace(0, 1, len(samples)))

    ax1.plot(x, data, 'ko', label='Data')
    for i, m in enumerate([m1, m2, m3]):
        ax1.plot(x, m, c=colors[i], label='Model %d' % (i+1))
    ax1.legend(numpoints=1, prop=dict(size='small'), loc='best')

    # Add the models to Taylor diagram
    for i, (stddev, corrcoef) in enumerate(samples):
        dia.add_sample(stddev, corrcoef,
                       marker='$%d$' % (i+1), ms=10, ls='',
                       mfc=colors[i], mec=colors[i],
                       label="Model %d" % (i+1))

    # Add grid
    dia.add_grid()

    # Add RMS contours, and label them
    contours = dia.add_contours(colors='0.5')
    PLT.clabel(contours, inline=1, fontsize=10, fmt='%.2f')

    # Add a figure legend
    fig.legend(dia.samplePoints,
               [ p.get_label() for p in dia.samplePoints ],
               numpoints=1, prop=dict(size='small'), loc='upper right')

    return dia


def test2():
    """
    Climatology-oriented example (after iteration w/ Michael A. Rawlins).
    """

    # Reference std
    stdref = 48.491

    # Samples std,rho,name
    samples = [[25.939, 0.385, "Model A"],
               [29.593, 0.509, "Model B"],
               [33.125, 0.585, "Model C"],
               [29.593, 0.509, "Model D"],
               [71.215, 0.473, "Model E"],
               [27.062, 0.360, "Model F"],
               [38.449, 0.342, "Model G"],
               [35.807, 0.609, "Model H"],
               [17.831, 0.360, "Model I"]]

    fig = PLT.figure()

    dia = TaylorDiagram(stdref, fig=fig, label='Reference', extend=True)
    dia.samplePoints[0].set_color('r')  # Mark reference point as a red star

    # Add models to Taylor diagram
    for i, (stddev, corrcoef, name) in enumerate(samples):
        dia.add_sample(stddev, corrcoef,
                       marker='$%d$' % (i+1), ms=10, ls='',
                       mfc='k', mec='k',
                       label=name)

    # Add RMS contours, and label them
    contours = dia.add_contours(levels=5, colors='0.5')  # 5 levels in grey
    PLT.clabel(contours, inline=1, fontsize=10, fmt='%.0f')

    dia.add_grid()                                  # Add grid
    dia._ax.axis[:].major_ticks.set_tick_out(True)  # Put ticks outward

    # Add a figure legend and title
    fig.legend(dia.samplePoints,
               [ p.get_label() for p in dia.samplePoints ],
               numpoints=1, prop=dict(size='small'), loc='upper right')
    fig.suptitle("Taylor diagram", size='x-large')  # Figure title

    return dia


if __name__ == '__main__':

    dia = test1()
    dia = test2()

    PLT.show()

test_taylor_4panel.py

#!/usr/bin/env python

__version__ = "Time-stamp: <2018-12-06 11:55:22 ycopin>"
__author__ = "Yannick Copin <yannick.copin@laposte.net>"

"""
Example of use of TaylorDiagram. Illustration dataset courtesy of Michael
Rawlins.

Rawlins, M. A., R. S. Bradley, H. F. Diaz, 2012. Assessment of regional climate
model simulation estimates over the Northeast United States, Journal of
Geophysical Research (2012JGRD..11723112R).
"""

from taylorDiagram import TaylorDiagram
import numpy as NP
import matplotlib.pyplot as PLT

# Reference std
stdrefs = dict(winter=48.491,
               spring=44.927,
               summer=37.664,
               autumn=41.589)

# Sample std,rho: Be sure to check order and that correct numbers are placed!
samples = dict(winter=[[17.831, 0.360, "CCSM CRCM"],
                       [27.062, 0.360, "CCSM MM5"],
                       [33.125, 0.585, "CCSM WRFG"],
                       [25.939, 0.385, "CGCM3 CRCM"],
                       [29.593, 0.509, "CGCM3 RCM3"],
                       [35.807, 0.609, "CGCM3 WRFG"],
                       [38.449, 0.342, "GFDL ECP2"],
                       [29.593, 0.509, "GFDL RCM3"],
                       [71.215, 0.473, "HADCM3 HRM3"]],
               spring=[[32.174, -0.262, "CCSM CRCM"],
                       [24.042, -0.055, "CCSM MM5"],
                       [29.647, -0.040, "CCSM WRFG"],
                       [22.820, 0.222, "CGCM3 CRCM"],
                       [20.505, 0.445, "CGCM3 RCM3"],
                       [26.917, 0.332, "CGCM3 WRFG"],
                       [25.776, 0.366, "GFDL ECP2"],
                       [18.018, 0.452, "GFDL RCM3"],
                       [79.875, 0.447, "HADCM3 HRM3"]],
               summer=[[35.863, 0.096, "CCSM CRCM"],
                       [43.771, 0.367, "CCSM MM5"],
                       [35.890, 0.267, "CCSM WRFG"],
                       [49.658, 0.134, "CGCM3 CRCM"],
                       [28.972, 0.027, "CGCM3 RCM3"],
                       [60.396, 0.191, "CGCM3 WRFG"],
                       [46.529, 0.258, "GFDL ECP2"],
                       [35.230, -0.014, "GFDL RCM3"],
                       [87.562, 0.503, "HADCM3 HRM3"]],
               autumn=[[27.374, 0.150, "CCSM CRCM"],
                       [20.270, 0.451, "CCSM MM5"],
                       [21.070, 0.505, "CCSM WRFG"],
                       [25.666, 0.517, "CGCM3 CRCM"],
                       [35.073, 0.205, "CGCM3 RCM3"],
                       [25.666, 0.517, "CGCM3 WRFG"],
                       [23.409, 0.353, "GFDL ECP2"],
                       [29.367, 0.235, "GFDL RCM3"],
                       [70.065, 0.444, "HADCM3 HRM3"]])

# Colormap (see http://www.scipy.org/Cookbook/Matplotlib/Show_colormaps)
colors = PLT.matplotlib.cm.Set1(NP.linspace(0,1,len(samples['winter'])))

# Here set placement of the points marking 95th and 99th significance
# levels. For more than 102 samples (degrees freedom > 100), critical
# correlation levels are 0.195 and 0.254 for 95th and 99th
# significance levels respectively. Set these by eyeball using the
# standard deviation x and y axis.

#x95 = [0.01, 0.68] # For Tair, this is for 95th level (r = 0.195)
#y95 = [0.0, 3.45]
#x99 = [0.01, 0.95] # For Tair, this is for 99th level (r = 0.254)
#y99 = [0.0, 3.45]

x95 = [0.05, 13.9] # For Prcp, this is for 95th level (r = 0.195)
y95 = [0.0, 71.0]
x99 = [0.05, 19.0] # For Prcp, this is for 99th level (r = 0.254)
y99 = [0.0, 70.0]

rects = dict(winter=221,
             spring=222,
             summer=223,
             autumn=224)

fig = PLT.figure(figsize=(11,8))
fig.suptitle("Precipitations", size='x-large')

for season in ['winter','spring','summer','autumn']:

    dia = TaylorDiagram(stdrefs[season], fig=fig, rect=rects[season],
                        label='Reference')

    dia.ax.plot(x95,y95,color='k')
    dia.ax.plot(x99,y99,color='k')

    # Add samples to Taylor diagram
    for i,(stddev,corrcoef,name) in enumerate(samples[season]):
        dia.add_sample(stddev, corrcoef,
                       marker='$%d$' % (i+1), ms=10, ls='',
                       #mfc='k', mec='k', # B&W
                       mfc=colors[i], mec=colors[i], # Colors
                       label=name)

    # Add RMS contours, and label them
    contours = dia.add_contours(levels=5, colors='0.5') # 5 levels
    dia.ax.clabel(contours, inline=1, fontsize=10, fmt='%.1f')
    # Tricky: ax is the polar ax (used for plots), _ax is the
    # container (used for layout)
    dia._ax.set_title(season.capitalize())

# Add a figure legend and title. For loc option, place x,y tuple inside [ ].
# Can also use special options here:
# http://matplotlib.sourceforge.net/users/legend_guide.html

fig.legend(dia.samplePoints,
           [ p.get_label() for p in dia.samplePoints ],
           numpoints=1, prop=dict(size='small'), loc='center')

fig.tight_layout()

PLT.savefig('test_taylor_4panel.png')
PLT.show()

Hi, thanks very much for sharing this useful code. I am new to Python and creating Taylor diagrams so I am sorry if this is an obvious question.
I see in test_taylor_4panel.py the "samples" consists of std and rho. Is rho referring to Spearman's rank correlation coefficient and can the script be used with Pearson's correlation coefficient instead?

I see in test_taylor_4panel.py the "samples" consists of std and rho. Is rho referring to Spearman's rank correlation coefficient and can the script be used with Pearson's correlation coefficient instead?

You input whatever correlation coeff you want!

Hi @ycopin, I used your code in a recent paper and the editors are actually asking for a DOI (not just the link). Do you have one for this gist? I'll see so far if there are ok with just the link, but it would be nice to have a DOI for each version of your code in the future. You can use Zenodo for example for this! Thanks in advance for your answer and a big thanks for this piece of code that is very valuable!

Hi @ycopin, I used your code in a recent paper and the editors are actually asking for a DOI (not just the link). Do you have one for this gist? I'll see so far if there are ok with just the link, but it would be nice to have a DOI for each version of your code in the future. You can use Zenodo for example for this! Thanks in advance for your answer and a big thanks for this piece of code that is very valuable!

The latest version (2018-12-06) has been tagged in zenodo: 10.5281/zenodo.5548061

Hi @ycopin, thanks for sharing this code!! I made a plot and my points are accumulated in a small area, most of them overllaping, not a graph very easy to read. I was wondering how to re-scale the correlation coefficient contours. For example in the very top of y-axis the correlation coefficient is 0, I would like it to start from 0.8, so the limits of Cor. coeff. would be from 0.8 to 1.0 and thus my points would spread across the whole graph.

Hi @ycopin, thanks for sharing this code!! I made a plot and my points are accumulated in a small area, most of them overllaping, not a graph very easy to read. I was wondering how to re-scale the correlation coefficient contours. For example in the very top of y-axis the correlation coefficient is 0, I would like it to start from 0.8, so the limits of Cor. coeff. would be from 0.8 to 1.0 and thus my points would spread across the whole graph.

That would not follow anymore the Taylor diagram theory, see https://en.wikipedia.org/wiki/Taylor_diagram#Theoretical_basis

Hi @ycopin,
Could do help me to modify the axis of the plot?. LIke the size of the ticks, ticklabels etc., the rotation of the ticklabels

Hi @ycopin, Could do help me to modify the axis of the plot?. LIke the size of the ticks, ticklabels etc., the rotation of the ticklabels

The editable axes is self._ax (see L99 and e.g. L80-92).

Thanks for the code @ycopin.

How would you go about changing the color of the X or Y grid lines only?

I've tried
dia.add_grid()
a=dia._ax.get_ygridlines()
a[4].set_color('red')

But to no avail.

Could you point me to the right direction please?

Hi Yannick Is there a way to pull the actual RMSE values displayed in the Taylor Diagram? Jess

@jess253 What do you mean? You're basically inputing everything to the Taylor plot, and nothing is really computed in there...

@jess253, @ycopin's code takes standard deviations of model and reference, and correlation coefficient for input, and plotting them on a polar plot by converting them to radius (standard deviation) and angle (correlation). Centered RMSD can be derived from standard deviations of model and reference, and correlation coefficient. I think you can do something like below, which I followed the Taylor 2001 paper.

crmsd = math.sqrt(stddev**2 + refstd**2 - 2 * stddev * refstd * corrcoef)  # centered rms difference

Hi @ycopin,

Thanks for sharing your code.
How can I make the size of the markers uniform? Which part of your code controls it? Can you please help?

The size of the markers is supposed to be uniform (I use plot, not scatter), so I'm not sure what is your problem...

@Bluedot96 I believe ms parameter in the dia.add_sample controls the marker size, in case you want to change.

I am new to python, I have six model outputs all in netCDF format which I what to use in the Taylor diagram. At what stage would I declare or import the variable in this code?

When I try this code, the Taylor diagram looks fine when I do plt.show(), but when I save it as a PNG or PDF file, it gets slightly squished, in the sense that the vertical standard deviation axis becomes shorter (by maybe 20%) than the horizontal standard deviation axis. Has anyone else experienced this problem? Anyone knows what might cause it and what the solution is?

when I save it as a PNG or PDF file, it gets slightly squished, in the sense that the vertical standard deviation axis becomes shorter (by maybe 20%) than the horizontal standard deviation axis.

I don't know, maybe you can force the axes aspect to equal?

Usingax.axis("equal") seems to fix the aspect ratio issue. However, while saving the figure generated by test2 as the code is now (or doing ax.set_aspect('equal', adjustable='box') and then saving) yields this image (where the aspect ratio is clearly off) and adding either ax.axis("equal") or ax.set_aspect('equal', adjustable='datalim') yields this image, which seems to have correct aspect ratio, the sides are now have now been cut off. The corresponding thing, but less extreme, happens to the Taylor diagram when I try to save the figure generated by test1.

I'm not knowledgeable enough about Matplotlib to know how to prevent the sides from being cut off. Do you have any idea of how to solve that?

Sorry I cannot really help. Did you try to set aspect of _ax rather than ax (there are 2 axes system, but I don't remember the difference... Maybe check the code). Which matplotlib version are you using? It might also be worth/needed to update this old code to latest mpl versions...

With some more experimentation, I was able to prevent the edges from being cut off by using the code

ax.set_xlim([self.smax * -((1 if extend else 0) + margin), self.smax * (1 + margin)])
ax.set_ylim([self.smax * -margin, self.smax * (1 + margin)])

where I have margin set to 0.25 (anything smaller seems to cause a cut-off).

An interesting thing is that the numbers that annotate the axes don't seem to be cut off by the same mechanism, but if the part of the axis that they are supposed to annotate is cut off, the numbers don't show up.

I'm also experimenting a bit with using plt.tight_layout() and with using the bbox_inches='tight' option in plt.savefig (they seem to have different effects), and I think the combination with both activated seems to produce the best results (so far).

Feel free to provide a Change Request! :-)

Sorry I cannot really help. Did you try to set aspect of _ax rather than ax (there are 2 axes system, but I don't remember the difference... Maybe check the code).

I only tried it on

self._ax = ax                   # Graphical axes

and not on

self.ax = ax.get_aux_axes(tr)   # Polar coordinates

Which matplotlib version are you using? It might also be worth/needed to update this old code to latest mpl versions...

pip list yields 3.6.1 for matplotlib so I guess that's the version of Matplotlib I use.

I have noticed that when I plot curves using self._ax instead of self.ax, I get different a different line width, making the figure seem inconsistent. Do you have any idea why using self._ax instead results in a different line width?

I pushed the modified version to my repository MLDown; you can see it here.

I updated the header of the file to include the modifications that I made. Currently, I placed those changes under the MIT license, but I can perhaps (with my organizations permission) place them in the public domain instead (like the rest of the file) if you think that would simplify the file header and the copyright status?

I pushed the modified version to my repository MLDown; you can see it here.

Thanks for the heads up. It's nice to see that this old benign piece of code is still useful!

I ended up placing the entire file including my changes in the public domain (as written in the repository's LICENSE.txt file).

Btw, the paper in which I used the code is now published and is available here. In the diagrams (Figures 11 and 12), you can see an extra arc (the dashed grey arc), which I added to indicate where ML models trained with MSE loss tend to put their predictions, and the reason they tend to put them there is the following: For predictions that don't correlate perfectly with the ground truth (which they basically never do), there is going to be a prediction error. That error can be reduced by scaling the predictions (which the ML model can do easily)—which is akin to how you can apply a linear filter to reduce the amount of noise in a signal in signal processing—and the optimal scaling factor for a given correlation (i.e. the scaling factor that minimizes the MSE loss) is also the scaling factor that puts the data on the dashed grey arc in the Taylor diagram (although we chose to omit this explanation from the paper). This is especially clear in Figure 12.

It's nice to see that this old benign piece of code is still useful!

It is nice that you chose to make it freely available so that other people can use it! :)

Do you want me to create a change request, btw?

Do you want me to create a change request, btw?

Yes, please, so we can make this code better! (I'm not using it on a regular basis)