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taylorDiagram.py

-# Copyright: This document has been placed in the public domain.
-
-"""
-Taylor diagram (Taylor, 2001) implementation.
-"""
-
-__version__ = "Time-stamp: <2017-11-24 18:01:03 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, 1.0)):
-        """
-        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*
-        """
-
-        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.concatenate((np.arange(10)/10., [0.95, 0.99]))
-        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, np.pi/2,  # 1st quadrant
-                                                     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("left")
-
-        ax.axis["bottom"].set_visible(False)         # Useless
-
-        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, np.pi/2)
-        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, np.pi/2))
-        # 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=0)           # 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")
-
-    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 fig
-
-
-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')
-    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')
-
-    # 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 fig
-
-
-if __name__ == '__main__':
-
-    test2()
-
-    plt.show()