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#!/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() |
#!/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() |
@ilgatto88 As mentioned in the code (lines 78-79), this is because dia.ax
points to the polar plot (the one to be used to add points/lines/etc.), while the true graphical axes (the one which can be moved around) is referred to by dia._ax
:
dia._ax.set_position([left, bottom, width, height])
should work! This is not a bug, but an undocumented feature ;-)
Hi, thanks for sharing your code. i want to know how to change the font properties of the left and right axis. I have used "dia._ax.axis[:].label.set_font_properties(fontName)" and "dia._ax.axis[:].major_ticklabels.set_font_properties(fontName)
" , but it doesn't work well for left and right axis. Thanks very much.
@ycopin thanks for sharing your code!
Hi Yannick Copin, thanks for share.
I tested test_taylor_4panel.py, and it works very well.
But, there is an issue at the lines 95 and 96, where you may need to change to "dia._ax.plot(...)".
Thanks again.
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?
@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 thanax
(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?
Note that two Python packages have recently been made available within the past year for producing Taylor diagrams: SkillMetrics and verif. They can be found on PyPI and can be easily installed using pip. A Matlab version of the SkillMetrics package is also available as the Skill Metrics Toolbox. Hope this proves helpful to anyone looking to produce Taylor diagrams.