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perso.py
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perso.py
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# -*- coding: utf-8 -*-
## ===========================================================================
##
## This software is governed by the CeCILL license under French law and
## abiding by the rules of distribution of free software. You can use,
## modify and/ or redistribute the software under the terms of the CeCILL
## license as circulated by CEA, CNRS and INRIA at the following URL
## "http://www.cecill.info".
##
## Warning, to install, configure, run, use any of Olivier Marti's
## software or to read the associated documentation you'll need at least
## one (1) brain in a reasonably working order. Lack of this implement
## will void any warranties (either express or implied).
## O. Marti assumes no responsability for errors, omissions,
## data loss, or any other consequences caused directly or indirectly by
## the usage of his software by incorrectly or partially configured
## personal.
##
## ===========================================================================
'''
Utilitaires
'''
def aire_maille ( bounds_lat, bounds_lon, vertex=None ) :
'''
Aire of a grid box on the sphere
'''
if not vertex : vertex = bounds_lat.dims[-1]
S1 = aire_triangle ( bounds_lat[{vertex:0}], bounds_lon[{vertex:0}],
bounds_lat[{vertex:1}], bounds_lon[{vertex:1}],
bounds_lat[{vertex:2}], bounds_lon[{vertex:2}] )
S2 = aire_triangle ( bounds_lat[{vertex:2}], bounds_lon[{vertex:2}],
bounds_lat[{vertex:3}], bounds_lon[{vertex:3}],
bounds_lat[{vertex:0}], bounds_lon[{vertex:0}] )
return S1 + S2
def cmap_long ( cmap, ncolors ) :
'''
Cycle sur une palette de couleur pour en créer une plus longue par répétition
'''
import numpy as np, matplotlib as mpl
# Longueur de la colormap (nombre de couleurs disponibles)
nc = len (cmap.colors)
# Création d'une liste de couleurs bidon (juste pour avoir le bon type d'objet)
colors = cmap.resampled (ncolors) (np.linspace (0, 1, ncolors))
# Remplacement des couleurs
for nn in range (ncolors) : colors[nn,:]= cmap (nn%nc)
# Creation d'un objet colormap
cmap_long = mpl.colors.ListedColormap (colors)
return cmap_long
def rgb2hex (r,g,b) :
'''Converti du RGB décimal (valeurs dans [0,255]) vers HEXA [#00,#FF]'''
return "#{:02x}{:02x}{:02x}".format(r,g,b)
def hex2rgb (hexcode) :
'''Converti RGB HEXA [#00,#FF] vers RGB décimal [0-255]'''
return tuple (map(ord,hexcode[1:].decode('hex')))
def color2hex ( r, g, b ) :
'''Converti du RGB fraactionaire (valeurs dans [0,1]) vers HEXA'''
return "#{:02X}{:02X}{:02X}".format( int(r*255), int(g*255), int(b*255) )
class TaylorDiagram (object) :
"""
Taylor diagram (Taylor, 2001) test implementation.
Plot model standard deviation and correlation to reference (data)
sample in a single-quadrant polar plot, with r=stddev and
theta=arccos(correlation).
Based on Copin's implementation in Python.
Co-authors :
- "Yannick Copin <yannick.copin@laposte.net>"
- "Pritthijit Nath <pritthijit.nath@icloud.com>"
Useful links :
- https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000JD900719
- http://www-pcmdi.llnl.gov/about/staff/Taylor/CV/Taylor_diagram_primer.htm
- https://gist.github.com/ycopin/3342888
- https://zenodo.org/record/5548061
- https://gist.github.com/nathzi1505/1d9e879881605a91e05f9afc1089e53f
"""
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
"""
import numpy as np
import matplotlib.pyplot as plt
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.
"""
import numpy as np
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."""
import numpy as np
self._ax.grid (*args, **kwargs)
def add_contours (self, levels=5, **kwargs) :
"""
Add constant centered RMS difference contours, defined by *levels*.
"""
import numpy as np
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."""
import numpy as np
import matplotlib.pyplot as plt
# 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=f'Model {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=f"Model {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).
"""
import numpy as np
import matplotlib.pyplot as plt
# 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