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 <[email protected]>"

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 <[email protected]>"

"""
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()

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?