def plot_taylor_diag(std, corr, ref_std, normalized=True):
import mpl_toolkits.axisartist.grid_finder as gf
import mpl_toolkits.axisartist.floating_axes as fa
# define polar axes transform
tr = PolarAxes.PolarTransform()
# define correlation labels
rlocs = np.concatenate((np.arange(10) / 10., [0.95, 0.99]))
tlocs = np.arccos(rlocs)
gl1 = gf.FixedLocator(tlocs)
tf1 = gf.DictFormatter(dict(zip(tlocs, map(str, rlocs))))
smin = 0
smax = max(2.0, 1.1 * std.max())
# add the curvilinear grid
fig = plt.figure()
ghelper = fa.GridHelperCurveLinear(tr,
extremes=(0, np.pi / 2, smin, smax),
grid_locator1=gl1,
tick_formatter1=tf1)
ax = fa.FloatingSubplot(fig, 111, grid_helper=ghelper)
fig.add_subplot(ax)
# adjust axes
ax.axis["top"].set_axis_direction("bottom")
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")
if normalize:
ax.axis["left"].label.set_text("Normalized standard deviation")
else:
ax.axis["left"].label.set_text("Standard deviation")
ax.axis["right"].set_axis_direction("top")
ax.axis["right"].toggle(ticklabels=True)
ax.axis["right"].major_ticklabels.set_axis_direction("left")
ax.axis["bottom"].set_visible(False)
ax.grid(True)
def __init__(self, fig=None, label='expected', max_normed_std=2.5, std_ratios=None, \
bias_vmin=None, bias_vmax=None, normalized=True, \
cmap=plt.cm.jet, s=80, title_expected=r'expected'):
"""
Set up Taylor diagram axes.
"""
self.normalized = normalized
self.title_polar = r'Correlation'
if self.normalized:
self.title_xy = r'Normalized Standard Deviation'
else:
self.title_xy = r'Standard Deviation'
self.max_normed_std = max_normed_std
self.s_min = 0
self.std_ratios = std_ratios
self.bias_vmin = bias_vmin
self.bias_vmax = bias_vmax
self.cmap = cmap
self.s = s # marker size
self.title_expected = title_expected
# Correlation labels
corln_r = np.concatenate((np.arange(10) / 10., [0.95, 0.99]))
corln_ang = np.arccos(corln_r) # Conversion to polar angles
grid_loc1 = gf.FixedLocator(corln_ang) # Positions
tick_fmttr1 = gf.DictFormatter(dict(zip(corln_ang, map(str, corln_r))))
# Normalized standard deviation axis
tr = PolarAxes.PolarTransform()
grid_helper = fa.GridHelperCurveLinear(
tr,
extremes=(
0,
np.pi / 2, # 1st quadrant
self.s_min,
self.max_normed_std),
grid_locator1=grid_loc1,
tick_formatter1=tick_fmttr1)
self.fig = fig
if self.fig is None:
self.fig = plt.figure()
# setup axes
ax = fa.FloatingSubplot(self.fig, 111, grid_helper=grid_helper)
# make the axis (polar ax child used for plotting)
self.ax = self.fig.add_subplot(ax)
# hide base-axis labels etc
self.ax.axis['bottom'].set_visible(False)
self._setup_axes()
# attach the polar axes and plot the correlation lines
self.polar_ax = self.ax.get_aux_axes(tr)
self.polar_ax.plot([np.pi / 2.135, np.pi / 2.135],
[self.s_min, self.max_normed_std],
color='grey')
self.polar_ax.plot([np.pi / 2.484, np.pi / 2.484],
[self.s_min, self.max_normed_std],
color='grey')
self.polar_ax.plot([np.pi / 3, np.pi / 3],
[self.s_min, self.max_normed_std],
color='grey')
self.polar_ax.plot([np.pi / 3.95, np.pi / 3.95],
[self.s_min, self.max_normed_std],
color='grey')
self.polar_ax.plot([np.pi / 6.95, np.pi / 6.95],
[self.s_min, self.max_normed_std],
color='grey')
# Add norm stddev ratio contours
if self.normalized:
self._plot_req_cont()
self.points = []
def Taylor_diag(series, smax=1.5):
""" Taylor Diagram : obs is reference data sample
in a full diagram (0 --> npi)
--------------------------------------------------------------------------
Input: series - dict with all time series (lists) to analyze
series[0] - is the observation, the reference by default.
"""
corr,std ={},{}
for i in series.keys():
corr[i] = ma.corrcoef(series[0],series[i])[1,0]
std[i] = ma.std(series[i])/ma.std(series[0])
ref = 1# ma.std(series[0])
# radial grid
# rlocs = np.concatenate((np.arange(0,1,0.2),[0.95,0.99])) # correlation coefficient tick marks
rlocs = [0, .3, .6, .8, .95, .99]
str_rlocs = np.concatenate((np.arange(0,1,0.2),[0.95,0.99],np.arange(0,10,0.2),[0.95,0.99]))
tlocs = np.arccos(rlocs) # Conversion to polar angles
gl1 = GF.FixedLocator(tlocs) # Positions
tf1 = GF.DictFormatter(dict(zip(tlocs, map("{:.2f}".format, rlocs))))
# circumferencial grid
str_locs2 = tlocs2 = np.arange(0, 2, 0.2)
g22 = GF.FixedLocator(tlocs2)
tf2 = GF.DictFormatter(dict(zip(tlocs2, map("{:.1f}".format, str_locs2))))
tr = PolarAxes.PolarTransform()
smin = 0
ghelper = FA.GridHelperCurveLinear(tr,
extremes=(0, np.pi/2, # 1st quadrant
smin,smax),
grid_locator1=gl1,
tick_formatter1=tf1,
tick_formatter2=tf2,
)
fig = plt.figure(figsize=(7, 5), dpi=100)
ax = FA.FloatingSubplot(fig, 111, grid_helper=ghelper)
fig.add_subplot(ax)
ax.axis["top"].set_axis_direction("bottom")
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 Coefficient")
ax.axis["left"].set_axis_direction("bottom")
ax.axis["left"].label.set_text("Standard Deviation")
ax.axis["right"].set_axis_direction("top")
ax.axis["right"].toggle(ticklabels=True, label=True)
ax.axis["right"].set_visible(True)
ax.axis["right"].major_ticklabels.set_axis_direction("bottom")
#ax.axis["right"].label.set_text("Standard Deviation")
ax.axis["bottom"].set_visible(False)
ax.grid(True)
ax = ax.get_aux_axes(tr)
# radial RMS error lines from observed.
t = np.linspace(0, np.pi)
r = np.zeros_like(t) + ref
ax.plot(t, r, 'k--', label='_')
rs,ts = np.meshgrid(np.linspace(smin,smax),
np.linspace(0,np.pi))
rms = np.sqrt(ref**2 + rs**2 - 2*ref*rs*np.cos(ts))
# CS = ax.contour(ts, rs, rms, colors='k', alpha=0.6, linewidths=1)
# plt.clabel(CS, inline=1, fontsize=10)
# plot observed point
ax.plot(np.arccos(0.9999),ref,'k',marker='*',ls='', ms=10, label='Observed')
# plot modelled points
aux = [k for k in series.keys() if k != 0]
for i in aux:
ax.scatter(np.arccos(corr[i]), std[i], marker='o', label=i, zorder=5, s=50)
# ax.text(np.arccos(corr[i]), std[i], i)
plt.legend(bbox_to_anchor=(1.7, 1),prop=dict(size='large'),loc='best', fontsize=8)
return fig, ax
def __init__(self, refstd, fig=None, rect=None, 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
"""
self.refstd = refstd # Reference standard deviation
tr = PolarAxes.PolarTransform()
# Correlation labels
rlocs = numpy.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 = numpy.pi
rlocs = numpy.concatenate((-rlocs[:0:-1], rlocs))
else:
# Diagram limited to positive correlations
self.tmax = numpy.pi / 2
tlocs = numpy.arccos(rlocs) # Conversion to polar angles
gl1 = grid_finder.FixedLocator(tlocs) # Positions
tf1 = grid_finder.DictFormatter(dict(zip(tlocs, map(str, rlocs))))
# set s locator
gl2 = grid_finder.MaxNLocator(7) # Max 7 ticks
# Standard deviation axis extent (in units of reference stddev)
self.smin = srange[0] * self.refstd
self.smax = srange[1] * self.refstd
ghelper = floating_axes.GridHelperCurveLinear(
tr,
extremes=(0, self.tmax, self.smin, self.smax),
grid_locator1=gl1, tick_formatter1=tf1,
grid_locator2=gl2)
self.fig = plt.figure() if fig is None else fig
if rect is None:
rect = 111
ax = floating_axes.FloatingSubplot(self.fig, rect, grid_helper=ghelper)
self.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 = numpy.linspace(0, self.tmax)
r = numpy.zeros_like(t) + self.refstd
self.ax.plot(t, r, 'k--', label='_', zorder=1)
# Collect sample points for latter use (e.g. legend)
self.sample_points = [l]
# set color and marker styles
self.ax.set_prop_cycle(get_point_style_cycler())
def TaylorDiagram(stddev,corrcoef,refstd,fig,colors,normalize=True):
"""Plot a Taylor diagram.
This is adapted from the code by Yannick Copin found here:
https://gist.github.com/ycopin/3342888
Parameters
----------
stddev : numpy.ndarray
an array of standard deviations
corrcoeff : numpy.ndarray
an array of correlation coefficients
refstd : float
the reference standard deviation
fig : matplotlib figure
the matplotlib figure
colors : array
an array of colors for each element of the input arrays
normalize : bool, optional
disable to skip normalization of the standard deviation
"""
from matplotlib.projections import PolarAxes
import mpl_toolkits.axisartist.floating_axes as FA
import mpl_toolkits.axisartist.grid_finder as GF
# define transform
tr = PolarAxes.PolarTransform()
# correlation labels
rlocs = np.concatenate((np.arange(10)/10.,[0.95,0.99]))
tlocs = np.arccos(rlocs)
gl1 = GF.FixedLocator(tlocs)
tf1 = GF.DictFormatter(dict(zip(tlocs,map(str,rlocs))))
# standard deviation axis extent
if normalize:
stddev = stddev/refstd
refstd = 1.
smin = 0
smax = max(2.0,1.1*stddev.max())
# add the curvilinear grid
ghelper = FA.GridHelperCurveLinear(tr,
extremes=(0,np.pi/2,smin,smax),
grid_locator1=gl1,
tick_formatter1=tf1)
ax = FA.FloatingSubplot(fig, 111, grid_helper=ghelper)
fig.add_subplot(ax)
# adjust axes
ax.axis["top"].set_axis_direction("bottom")
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")
if normalize:
ax.axis["left"].label.set_text("Normalized standard deviation")
else:
ax.axis["left"].label.set_text("Standard deviation")
ax.axis["right"].set_axis_direction("top")
ax.axis["right"].toggle(ticklabels=True)
ax.axis["right"].major_ticklabels.set_axis_direction("left")
ax.axis["bottom"].set_visible(False)
ax.grid(True)
ax = ax.get_aux_axes(tr)
# Plot data
corrcoef = corrcoef.clip(-1,1)
for i in range(len(corrcoef)):
ax.plot(np.arccos(corrcoef[i]),stddev[i],'o',color=colors[i],mew=0,ms=8)
# Add reference point and stddev contour
l, = ax.plot([0],refstd,'k*',ms=12,mew=0)
t = np.linspace(0, np.pi/2)
r = np.zeros_like(t) + refstd
ax.plot(t,r, 'k--')
# centralized rms contours
rs,ts = np.meshgrid(np.linspace(smin,smax),
np.linspace(0,np.pi/2))
rms = np.sqrt(refstd**2 + rs**2 - 2*refstd*rs*np.cos(ts))
contours = ax.contour(ts,rs,rms,5,colors='k',alpha=0.4)
ax.clabel(contours,fmt='%1.1f')
return ax
def __init__(
self,
ref_point: float,
fig: Optional[plt.figure] = None,
subplot: Optional[int] = 111,
extend_angle: bool = False,
corr_labels: Optional[np.ndarray] = None,
ref_range: Tuple[float, float] = (0, 10),
ref_label: str = "Reference Point",
angle_label: str = "Correlation",
var_label: str = "Standard Deviation",
) -> None:
self.angle_label = angle_label
self.ref_label = ref_label
self.var_label = var_label
self.extend_angle = extend_angle
# correlation labels
if corr_labels is None:
corr_labels = np.array(
[0, 0.2, 0.4, 0.6, 0.7, 0.8, 0.9, 0.95, 0.99, 1.0])
# extend
if extend_angle:
# Extend to negative correlations
self.tmax = np.pi
corr_labels = np.concatenate((-corr_labels[:0:-1], corr_labels))
else:
# limit to only positive correlations
self.tmax = np.pi / 2.0
# init figure
if fig is None:
fig = plt.figure(figsize=(8, 8))
# extend or not
self.smin = ref_range[0] * ref_point
self.smax = (ref_range[1] / 100) * ref_point + ref_point
corr_ticks = np.arccos(corr_labels)
gl1 = grid_finder.FixedLocator(corr_ticks)
tf1 = grid_finder.DictFormatter(
dict(zip(corr_ticks, map(str, corr_labels))))
# Grid Helper
ghelper = floating_axes.GridHelperCurveLinear(
aux_trans=PolarAxes.PolarTransform(),
extremes=(0, self.tmax, self.smin, self.smax),
grid_locator1=gl1,
tick_formatter1=tf1,
)
# create graphical axes
ax = floating_axes.FloatingSubplot(fig, subplot, grid_helper=ghelper)
fig.add_subplot(ax)
self.graph_axes = ax
self.polar_axes = ax.get_aux_axes(PolarAxes.PolarTransform())
self.sample_points = []
# Setup Axes
self.reset_axes()
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"].major_ticklabels.set_fontsize(15)
ax.axis["top"].label.set_axis_direction("top")
ax.axis["top"].label.set_text("Standardized gauge density")
ax.axis["top"].label.set_fontsize(15)
ax.axis["left"].set_axis_direction("bottom") # "X axis"
ax.axis["left"].label.set_text("RMSD (mm/h)")
ax.axis["left"].label.set_fontsize(15)
ax.axis["left"].major_ticklabels.set_fontsize(15)
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")
ax.axis["right"].major_ticklabels.set_fontsize(15)
ax.axis["right"].label.set_text("RMSD (mm/h)")
ax.axis["right"].label.set_fontsize(15)
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, '.', 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 __init__(self, refstd, fig=None, rect=111, label='_'):
"""Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes. refstd is
the reference standard deviation to be compared to.
"""
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
gl2_num = np.linspace(0, 1.5, 7)
gl2 = GF.FixedLocator(gl2_num)
gl2_ticks = [(x, str(x)) for x in gl2_num]
gl2_ticks[-1] = [gl2_num[-1], '']
gl2_ticks[0] = [gl2_num[0], '0']
tf1 = GF.DictFormatter(dict(list(zip(tlocs, list(map(str, rlocs))))))
tf2 = GF.DictFormatter(dict(gl2_ticks))
# Standard deviation axis extent
self.smin = min(gl2_num)
#self.smax = 1.5*self.refstd
self.smax = max(gl2_num)
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=(
0,
np.pi / 2, # 1st quadrant
self.smin,
self.smax),
grid_locator1=gl1,
grid_locator2=gl2,
tick_formatter1=tf1,
tick_formatter2=tf2)
# 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 (Normalized)")
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
# Contours along standard deviations
ax.grid(False)
# Shrink current axis by 20%
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width * 0.8, box.height * 0.8])
# Put a legend to the right of the current axis
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point and stddev contour
#print "Reference std:", self.refstd
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 setup_axes(self):
"""Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes.
"""
tr = PolarTransform()
# Intervals on the axis of the correlation coefficient
rlocs = np.concatenate(([-1.0, -0.99, -0.95], np.arange(-10, 0) / 10.0,
np.arange(10) / 10.0, [0.95, 0.99]))
# The same intervals as angles
tlocs = np.arccos(rlocs) # Conversion to polar angles
gl1 = GF.FixedLocator(tlocs) # Positions
tf1 = GF.DictFormatter(
dict(zip(tlocs, map(str, rlocs)))
) # maps coefficient angles to string representation of correlation coefficient
x_max = np.pi if self.show_negative_corrcoeff else np.pi / 2
x_axis_range = (0, x_max)
y_axis_range = (0, self.max_stddev)
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=(x_axis_range[0], x_axis_range[1], y_axis_range[0],
y_axis_range[1]),
grid_locator1=gl1,
tick_formatter1=tf1,
)
ax = FA.FloatingSubplot(
self.fig, 111, grid_helper=ghelper
) # 111 -> plot contains 1 row, 1 col and shall be located at position 1 (1-based!) in the resulting grid
self.fig.add_subplot(ax)
if self.show_negative_corrcoeff:
self.fig.text(0.41, 0.178, 'Standard Deviation'
) # magic numbers: place label central below plot
# Setup 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 coefficient")
if not self.show_negative_corrcoeff:
ax.axis["left"].set_axis_direction("bottom") # "X axis"
ax.axis["left"].label.set_text("Standard deviation")
else:
ax.axis["left"].set_axis_direction("bottom") # "X axis"
ax.axis["right"].set_axis_direction("top") # "Y axis"
ax.axis["right"].toggle(ticklabels=True, label=True)
tick_axis_direction = "bottom" if self.show_negative_corrcoeff else "left"
ax.axis["right"].major_ticklabels.set_axis_direction(
tick_axis_direction)
label_axis_direction = "bottom" if self.show_negative_corrcoeff else "left"
ax.axis["right"].label.set_axis_direction(label_axis_direction)
if not self.show_negative_corrcoeff:
ax.axis["right"].label.set_text("Standard deviation")
ax.axis["bottom"].set_visible(False) # Hide useless axis
# Grid
ax.grid()
# This defines how to draw the data -- putting the polar transform here forces the plot to draw the data on
# the polar plot instead of a rectangular one
self.ax = ax.get_aux_axes(tr)
# Add reference points
# [0] = x-value
# stddev = y-value
for name, ref_stddev, unit in self.ref:
dataset = self.ax.plot([0], ref_stddev,
'%so' % self.get_color())[0]
if hasattr(self, 'sample_names'):
self.sample_points.append(dataset)
self.sample_names.append(
create_sample_name(name, unit, self.use_absolute_stddev))
else:
self.sample_points = [dataset]
self.sample_names = [
create_sample_name(name, unit, self.use_absolute_stddev)
]
# Add stddev contours
t = np.linspace(0, x_max, num=50)
for name, ref_stddev, unit in self.ref:
if not np.isnan(ref_stddev):
r = np.zeros_like(t) + ref_stddev # 50 times the stddev
self.ax.plot(t, r, 'k--', label='_', linewidth=0.5)
# Add rmse contours
rs, ts = np.meshgrid(np.linspace(0, y_axis_range[1], num=50),
np.linspace(0, x_max, num=50))
for name, ref_stddev, unit in self.ref:
if not np.isnan(ref_stddev):
# Unfortunately, I don't understand the next line AT ALL,
# it's copied from http://matplotlib.1069221.n5.nabble.com/Taylor-diagram-2nd-take-td28070.html
# but it leads to the right results (contours of the centered pattern RMS), so I keep it
rmse = np.sqrt(ref_stddev**2 + rs**2 -
2 * ref_stddev * rs * np.cos(ts))
colors = ('#7F0000', '#6F0000', '#5F0000', '#4F0000',
'#3F0000', '#2F0000', '#1F0000', '#0F0000')
rmse_contour = self.ax.contour(ts,
rs,
rmse,
8,
linewidths=0.5,
colors=colors)
plt.clabel(rmse_contour, inline=1, fmt='%1.2f', fontsize=8)
def taylor_ax(fig, *args, **kw):
#th1=0., th2=np.pi/3, rd1=0., rd2=1.2, tloc1=None, tloc2=None)
tr = PolarAxes.PolarTransform()
# Correlation labels
if kw.has_key("tloc1"):
rlocs = kw["tloc1"]
else:
rlocs = np.concatenate((np.arange(10) / 10., [0.95, 0.99]))
tlocs = np.arccos(rlocs)
gl1 = GF.FixedLocator(tlocs)
tf1 = GF.DictFormatter(dict(zip(tlocs, map(str, rlocs))))
if kw.has_key("tloc2"):
gl2 = GF.FixedLocator(kw["tloc2"])
else:
gl2 = GF.MaxNLocator(10)
if kw.has_key("th1"):
th1 = kw["th1"]
else:
th1 = 0.
if kw.has_key("th2"):
th2 = kw["th2"]
else:
th2 = np.pi / 2
if kw.has_key("rd1"):
rd1 = kw["rd1"]
else:
rd1 = 0.
if kw.has_key("rd2"):
rd2 = kw["rd2"]
else:
rd2 = 1.65
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=(th1, th2, rd1, rd2),
grid_locator1=gl1,
grid_locator2=gl2,
tick_formatter1=tf1,
tick_formatter2=None,
)
ax = FA.FloatingSubplot(fig, *args, grid_helper=ghelper)
fig.add_subplot(ax)
# Adjust axes
fontsize = 9
ax.axis["top"].set_axis_direction("bottom") # "Angle axis"
ax.axis["top"].toggle(ticklabels=True, label=True)
ax.axis["top"].major_ticklabels.set_size('xx-small')
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["top"].label.set_fontsize(fontsize)
ax.axis["left"].set_axis_direction("right") # "X axis"
ticks_font = 2
ax.axis["left"].major_ticklabels.set_size('xx-small')
ax.axis["left"].major_ticks.set_ticksize(ticks_font) # "X axis"
ax.axis["left"].label.set_text("Normalized standard deviation")
ax.axis["left"].label.set_fontsize(fontsize)
ax.axis["right"].major_ticklabels.set_size('xx-small')
ax.axis["right"].set_axis_direction("top") # "Y axis"
ax.axis["right"].toggle(ticklabels=True)
ax.axis["right"].major_ticks.set_ticksize(ticks_font) # "Y axis"
ax.axis["right"].major_ticklabels.set_axis_direction("left")
ax.axis["right"].label.set_fontsize(fontsize)
ax.axis["bottom"].set_visible(False) # turn off overlaying tickmark
ax.grid(linewidth=0.5, color='gray')
aux_ax = ax.get_aux_axes(tr) # Polar coordinates
aux_ax.th1 = th1
aux_ax.th2 = th2
aux_ax.rd1 = rd1
aux_ax.rd2 = rd2
ax.th1 = th1
ax.th2 = th2
ax.rd1 = rd1
ax.rd2 = rd2
return ax, aux_ax
def __init__(self, refstd, fig=None, rect=111, label='_'):
"""
Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes. refstd is
the reference standard deviation to be compared to.
"""
from matplotlib.projections import PolarAxes
from mpl_toolkits.axisartist import floating_axes
from mpl_toolkits.axisartist import grid_finder
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 = grid_finder.FixedLocator(tlocs) # Positions.
dict_formatter = dict(list(zip(tlocs, map(str, rlocs))))
tf1 = grid_finder.DictFormatter(dict_formatter)
# Standard deviation axis extent.
self.smin = 0
self.smax = 1.5 * self.refstd
extremes = (
0,
np.pi / 2, # 1st quadrant.
self.smin,
self.smax)
ghelper = floating_axes.GridHelperCurveLinear(tr,
extremes=extremes,
grid_locator1=gl1,
tick_formatter1=tf1)
if fig is None:
fig = plt.figure()
ax = floating_axes.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.
# Contours along standard deviations.
ax.grid(False)
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, 'ko', 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 setup_axes(self,
fig,
rect=111,
extra_graph=1.5,
quadrant=1,
print_bool=False,
*args,
**kwargs):
"""Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes.
Wouldn't the ideal be to define its own non-linear
transformation, so that coordinates are directly r=stddev and
theta=correlation? I guess it would allow
"""
self.extra_graph = extra_graph
tr = PolarAxes.PolarTransform()
# Correlation labels
if quadrant == 1:
rlocs = np.concatenate((np.arange(0, 10, 1) / 10., [0.95, 0.99]))
extremes = (0, np.pi / 2, 0, extra_graph * self.ref_STD)
elif quadrant == 2:
rlocs = np.concatenate(
([-0.99, -0.95], np.arange(-9, 10, 1) / 10., [0.95, 0.99]))
extremes = (0, np.pi, 0, extra_graph * self.ref_STD)
else:
raise ValueError("'quadrant' should be 1 or 2.")
tlocs = np.arccos(rlocs) # Conversion to polar angles
gl1 = GF.FixedLocator(tlocs) # Positions
tf1 = GF.DictFormatter(dict(zip(tlocs, map(str, rlocs))))
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=extremes,
grid_locator1=gl1,
tick_formatter1=tf1,
)
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["right"].label.set_text("Standard deviation")
ax.axis["right"].label._visible = True
ax.axis["bottom"].set_visible(False) # Useless
# Grid
ax.grid()
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point and stddev contour
if print_bool:
print "Reference std:", self.ref_STD
self.ax.plot([0],
self.ref_STD,
'bo',
label=self.ref_label,
markersize=2. * markersize)
self.ax.text(-0.045,
self.ref_STD,
"\\textbf{%s}" % self.ref_label,
color='b',
fontsize=fontsize,
horizontalalignment='left',
verticalalignment='top')
if quadrant == 1:
t = np.linspace(0., np.pi / 2)
elif quadrant == 2:
t = np.linspace(0., np.pi)
else:
raise ValueError("'quadrant' should be 1 or 2.")
r = np.zeros_like(t) + self.ref_STD
self.ax.plot(t, r, 'k--')
return ax
def __init__(self,
datastd,
fig=None,
rect=111,
normalize='Y',
sd_axis_frac=1.5,
fontsize=10):
#Impot the things we need
from matplotlib.projections import PolarAxes
import mpl_toolkits.axisartist.floating_axes as fa
import mpl_toolkits.axisartist.grid_finder as gf
# Check if we are going to be normalizing values or not, and set
# values appropriately.
if normalize == 'Y':
self.datastd = datastd / datastd
self.normfactor = datastd
else:
self.datastd = datastd
self.normfactor = 1
# Standard deviation axis extent
self.smin = 0
self.smax = sd_axis_frac * self.datastd
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))))
# Std. Dev. labels
sdlocs = np.linspace(self.smin, self.smax, 7)
# Round the output (particularly import when normalize='N')
sdlocs = [
round(sd, -int(np.floor(np.log10(sd))) + 2) for sd in sdlocs[1:]
]
sdlocs.append(0)
gl2 = gf.FixedLocator(sdlocs)
tf2 = gf.DictFormatter(dict(zip(sdlocs, map(str, sdlocs))))
ghelper = fa.GridHelperCurveLinear(
tr,
extremes=(
0,
np.pi / 2, # 1st quadrant
self.smin,
self.smax),
grid_locator1=gl1,
grid_locator2=gl2,
tick_formatter1=tf1,
tick_formatter2=tf2)
# Check if an existing figure has been passed to the program
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") # Azimuthal 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"].major_ticklabels.set_color("darkgreen")
ax.axis["top"].label.set_color("darkgreen")
ax.axis["top"].label.set_text("Correlation")
ax.axis["top"].label.set_fontsize(fontsize)
ax.axis["left"].set_axis_direction("bottom") # X axis
ax.axis["left"].toggle(ticklabels=True)
ax.axis["right"].set_axis_direction("top") # Y axis
ax.axis["right"].toggle(ticklabels=True, label=True)
ax.axis["right"].major_ticklabels.set_axis_direction("left")
if normalize == 'Y':
ax.axis["right"].label.set_text("Normalised standard deviation")
else:
ax.axis["right"].label.set_text("Standard deviation")
ax.axis["right"].label.set_fontsize(fontsize)
ax.axis["bottom"].set_visible(False) # Don't want it
# Contours for each standard deviation
ax.grid(False)
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point and ref stddev contour
l, = self.ax.plot([0], self.datastd, 'k*', ls='', ms=10)
t = np.linspace(0, np.pi / 2)
r = np.zeros_like(t) + self.datastd
self.ax.plot(t, r, 'k--', label='_', alpha=0.75)
# Collect data points for latter use (e.g. legend)
self.samplePoints = [l]
#Add "correlation lines"
for i in np.concatenate((np.arange(1, 10) / 10., [0.99])):
self.ax.plot([np.arccos(i), np.arccos(i)], [0, self.smax],
c='darkgreen',
alpha=0.35)
def __init__(self,
refstd,
fig=None,
rect=111,
label=None,
cors=[0.3, 0.6, 0.9]):
"""Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes. refstd is
the reference standard deviation to be compared to.
"""
from matplotlib.projections import PolarAxes
import mpl_toolkits.axisartist.floating_axes as FA
import mpl_toolkits.axisartist as axisartist
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., 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
self.smin = 0.0
self.smax = 1.6 * self.refstd
gl2 = GF.MaxNLocator(10) #[0, 0.2,0.4,0.6, 0.8,1.0,1.2,1.4]
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=(
0,
NP.pi / 2.0, # 1st quadrant
self.smin,
self.smax),
grid_locator1=gl1,
grid_locator2=gl2,
tick_formatter1=tf1,
tick_formatter2=None,
)
ghelper.grid_finder.grid_locator2._nbins = 4
if fig is None:
fig = PLT.figure()
ax = FA.FloatingSubplot(fig, rect, grid_helper=ghelper)
fig.add_subplot(ax)
# Adjust axes
PLT.setp(ax.spines.values(), visible=False)
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["top"].label.set_fontsize(9)
ax.axis[:].major_ticklabels.set_fontsize(12)
ax.axis["left"].set_axis_direction("right") # "X axis"
ax.axis["left"].toggle(ticklabels=True, label=True)
ax.axis["left"].toggle(ticklabels=False, label=False)
ax.axis["left"].label.set_text("Normalized std.")
ax.axis["left"].label.set_fontsize(9)
ax.axis["right"].set_axis_direction("top") # "Y axis"
ax.axis["right"].toggle(ticklabels=True, label=True)
ax.axis["right"].major_ticklabels.set_axis_direction("left")
ax.axis["right"].label.set_fontsize(9)
ax.axis["bottom"].set_visible(False) # Useless
# Contours along standard deviations
ax.grid(False)
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,
color='black',
marker='o',
ls='',
ms=10,
label="OBS")
t = NP.linspace(0, NP.pi / 2.0)
r = NP.zeros_like(t) + self.refstd
lines = self.ax.plot(t,
r,
color='darkgray',
ls='--',
label='_',
zorder=0,
lw=0.8)
for isec in cors:
rad = NP.arccos(isec)
stds = NP.linspace(self.smin, self.smax)
rad0 = [rad for x in stds]
lines = self.ax.plot(rad0,
stds,
color='darkgray',
ls='--',
zorder=0,
lw=0.8)
self.samplePoints = [l]
def Taylor_diag(series, names):
""" Taylor Diagram : obs is reference data sample
in a full diagram (0 --> npi)
--------------------------------------------------------------------------
Input: series - dict with all time series (lists) to analyze
series[0] - is the observation, the reference by default.
"""
corr, std = {}, {}
for i in series.keys():
corr[i] = ma.corrcoef(series[0], series[i])[1, 0]
std[i] = ma.std(series[i]) / ma.std(series[0])
ref = 1 # ma.std(series[0])
#print corr
rlocs = np.concatenate((np.arange(0, -10, -0.25), [-0.95, -0.99],
np.arange(0, 10, 0.25), [0.95, 0.99]))
str_rlocs = np.concatenate(
(np.arange(0, 10, 0.25), [0.95, 0.99], np.arange(0, 10,
0.25), [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))))
str_locs2 = np.arange(-10, 11, 0.5)
tlocs2 = np.arange(-10, 11, 0.5) # Conversion to polar angles
g22 = GF.FixedLocator(tlocs2)
tf2 = GF.DictFormatter(dict(zip(tlocs2, map(str, str_locs2))))
tr = PolarAxes.PolarTransform()
smin = 0
smax = 2.5
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=(
0,
np.pi, # 1st quadrant
smin,
smax),
grid_locator1=gl1,
#grid_locator2=g11,
tick_formatter1=tf1,
tick_formatter2=tf2,
)
fig = plt.figure(figsize=(10, 5), dpi=100)
ax = FA.FloatingSubplot(fig, 111, grid_helper=ghelper)
fig.add_subplot(ax)
ax.axis["top"].set_axis_direction("bottom")
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 Coefficient")
ax.axis["left"].set_axis_direction("bottom")
ax.axis["left"].label.set_text("Standard Deviation")
ax.axis["right"].set_axis_direction("top")
ax.axis["right"].toggle(ticklabels=True, label=True)
ax.axis["right"].set_visible(True)
ax.axis["right"].major_ticklabels.set_axis_direction("bottom")
#ax.axis["right"].label.set_text("Standard Deviation")
ax.axis["bottom"].set_visible(False)
ax.grid(True)
ax = ax.get_aux_axes(tr)
t = np.linspace(0, np.pi)
r = np.zeros_like(t) + ref
ax.plot(t, r, 'k--', label='_')
rs, ts = np.meshgrid(np.linspace(smin, smax), np.linspace(0, np.pi))
rms = np.sqrt(ref**2 + rs**2 - 2 * ref * rs * np.cos(ts))
CS = ax.contour(ts, rs, rms, cmap=cm.bone)
plt.clabel(CS, inline=1, fontsize=10)
ax.plot(np.arccos(0.9999), ref, 'k', marker='*', ls='', ms=10)
aux = range(1, len(corr))
#del aux[ref]
colors = plt.matplotlib.cm.jet(np.linspace(0, 1, len(corr)))
for i in aux:
ax.plot(np.arccos(corr[i]),
std[i],
c=colors[i],
alpha=0.7,
ms=15,
marker='o',
label="%s" % names[i])
ax.text(np.arccos(corr[i]), std[i], "%s" % i)
legend(bbox_to_anchor=(1.5, 1), prop=dict(size='large'), loc='best')
plt.savefig('example.png', dpi=300)
return
def taylorDiagram(benchmarks, savepath='', fname='', debug=False):
"""
References:
Taylor, K.E.: Summarizing multiple aspects of model performance in a single diagram.
J. Geophys. Res., 106, 7183-7192, 2001
(also see PCMDI Report 55, http://www-pcmdi.llnl.gov/publications/ab55.html)
IPCC, 2001: Climate Change 2001: The Scientific Basis,
Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change
Houghton, J.T., Y. Ding, D.J. Griggs, M. Noguer, P.J. van der Linden, X. Dai, K. Maskell, and C.A. Johnson (eds.)
Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 881 pp.
(see http://www.grida.no/climate/ipcc_tar/wg1/317.htm#fig84)
Code inspired by Yannick Copin's code (see https://github.com/ycopin)
"""
if debug: print "Plotting time-series..."
# Setting up graph
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
smin = 0
smax = 1.5
ghelper = fa.GridHelperCurveLinear(tr,
extremes=(0, np.pi / 2, smin, smax),
grid_locator1=gl1,
tick_formatter1=tf1)
fig = plt.figure(figsize=(18, 10))
rect = 111
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
# Contours along standard deviations
ax.grid(False)
_ax = ax # Graphical axes
ax = ax.get_aux_axes(tr) # Polar coordinates
# Reference lines
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]
ax.plot(x95, y95, color='k')
ax.plot(x99, y99, color='k')
# Add reference point and stddev contour
l, = ax.plot(0.0, 1.0, 'k*', ls='', ms=10, label='Reference')
t = np.linspace(0, np.pi / 2)
r = np.zeros_like(t) + 1.0
ax.plot(t, r, 'k--', label='_')
samplePoints = [l]
# Plot points
sampleLenght = benchmarks['Type'].shape[0]
colors = plt.matplotlib.cm.jet(np.linspace(0, 1, sampleLenght))
for i in range(sampleLenght):
l, = ax.plot(benchmarks['NRMSE'][i] / 100.0,
benchmarks['r2'][i],
marker='$%d$' % (i + 1),
ms=10,
ls='',
mfc=colors[i],
mec=colors[i],
label=benchmarks['Type'][i] + " " + benchmarks['gear'][i])
samplePoints.append(l)
t = np.linspace(0, np.pi / 2)
r = np.zeros_like(t) + 1.0
ax.plot(t, r, 'k--', label='_')
# Add NRMS contours, and label them
rs, ts = np.meshgrid(np.linspace(smin, smax), np.linspace(0, np.pi / 2))
# Compute centered RMS difference
rms = np.sqrt(1.0 + rs**2 - 2 * rs * np.cos(ts))
contours = ax.contour(ts, rs, rms, 5, colors='0.5')
ax.clabel(contours, inline=1, fontsize=10, fmt='%.1f')
# Add a figure legend
fig.legend(samplePoints, [p.get_label() for p in samplePoints],
numpoints=1,
prop=dict(size='small'),
loc='upper right')
fig.tight_layout()
if savepath.strip() and fname.strip():
if os.exists(savepath):
fig.savefig(savepath + fname)
plt.close(fig)
else:
fig.show()
plt.show()
def generateGrid(self, fig=None, srange=(0,1.5), rect=111):
from matplotlib.projections import PolarAxes
import mpl_toolkits.axisartist.floating_axes as FA
import mpl_toolkits.axisartist.grid_finder as GF
tr = PolarAxes.PolarTransform()
# Correlation labels
rlocs = NP.concatenate((NP.arange(10)/10.,[0.95,0.99],-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
steps = NP.round((self.smax - self.smin) / 10,1)
xticks = NP.arange(self.smin, self.smax, steps)
tf2 = GF.DictFormatter(dict(zip(xticks, map(str, xticks))))
gl2= GF.FixedLocator(xticks)
ghelper = FA.GridHelperCurveLinear(tr,
extremes=(0, self.width,
self.smin, self.smax),
grid_locator1=gl1,
tick_formatter1=tf1,
tick_formatter2=tf2,
grid_locator2=gl2)
if fig is None:
fig = plt.figure(figsize=(10, 10))
self.figure = fig
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["left"].label.set_ha(self.labelPosition)
ax.axis["right"].set_axis_direction("top") # "Y axis"
ax.axis["right"].toggle(ticklabels=True)
ax.axis["right"].major_ticklabels.set_axis_direction(self.labelDirection)
ax.axis["bottom"].set_visible(False) # Useless
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
self._add_contours(colors = '0.5')
plt.title("Taylor diagram") # Figure title
return fig
def taylorDiagram(predicted,
observed,
norm=False,
addTo=None,
modelName='',
isoSTD=True):
"""Taylor diagrams for comparing model performance
Parameters
==========
predicted : array-like
predicted data
observed : array-like
observation vector
Other Parameters
================
norm : boolean or float
Selects whether the values should be normalized (default is False).
If a value is given this will be used to normalize the inputs.
xyline : boolean
Toggles the display of a line of y=x (perfect model). Default True.
addTo : axes, or None
The object on which plotting will happen. If **None** (default)
then a figure and axes will be created. If matplotlib axes are
given then the plot will be made on those axes, assuming that the
point is being added to a previously generated Taylor diagram.
modelName : string
Name of model to label the point on the Taylor diagram with.
isoSTD : boolean
Toggle for isocontours of standard deviation. Default is True, but
turning them off can reduce visual clutter or prevent intereference
with custom plot styles that alter background grid behavior.
Returns
=======
out_dict : dict
A dictionary containing the Figure, the Axes, and 'Norm' (the value
used to normalize the inputs/outputs).
Example
=======
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from verify.plot import taylorDiagram
>>> model1 = np.random.randint(0,40,101).astype(float)
>>> model2 = model1*(1 + np.arange(101)/70)
>>> obs = model1 + np.random.randn(101)
>>> obs[[2,3,8,9,15,16,30,31]] = obs[[31,30,16,15,9,8,3,2]]
>>> obs *= 0.25 + (5-(np.arange(101)/30.))/4
>>> result1 = taylorDiagram(model1, obs, norm=True, modelName='A')
>>> result2 = taylorDiagram(model2, obs, norm=result1['Norm'],
>>> modelName='B', addTo=result1['Axes'])
>>> plt.show()
Notes
=====
Based on ''Summarizing multiple aspects of model performance in a single
diagram' by K.E. Taylor (Radio Science, 2001; doi: 10.1029/2000JD900719)
and 'Taylor Diagram Primer' by Taylor (document at
https://pcmdi.llnl.gov/staff/taylor/CV/Taylor_diagram_primer.pdf)
With some implementation aspects inspired by the public domain code of
github user ycopin at https://gist.github.com/ycopin/3342888
"""
#fancy plotting imports
from mpl_toolkits.axisartist import floating_axes, angle_helper, grid_finder
from matplotlib.projections import PolarAxes
pred = _maskSeries(predicted)
obse = _maskSeries(observed)
pstd = pred.std(ddof=1) #unbiased sample std.dev. model
ostd = obse.std(ddof=1) #unbiased sample std.dev. observed
pcorr = numpy.corrcoef(obse, pred)[0, 1] # Pearson's r
pbias = bias(pred, obse) #mean error
# Normalize on request
if norm:
setNormed = True
normfac = ostd
ostd = ostd / normfac
pstd = pstd / normfac
else:
setNormed = False
normfac = 1
tr = PolarAxes.PolarTransform()
# Correlation labels
corrtickvals = numpy.asarray(list(range(10)) + [9.5, 9.9]) / 10.
corrtickvals_polar = numpy.arccos(corrtickvals)
# Round labels to nearest N digits
corrticklabs = []
for cval in corrtickvals:
lab = '{0:0.2f}'.format(cval) if str(cval)[2] != '0' else \
'{0:0.1f}'.format(cval)
corrticklabs.append('{0:0.2f}'.format(cval))
valsAndLabs = list(zip(corrtickvals_polar, corrticklabs))
corrgrid = grid_finder.FixedLocator(corrtickvals_polar)
corrticks = grid_finder.DictFormatter(dict(valsAndLabs))
# Std. Dev. tick values and labels
smin, smax = 0, numpy.ceil(0.8335 * ostd) * 2
stdtickvals = numpy.linspace(smin, smax, 9)
# Round labels to nearest N digits
stdticklabs = []
for stdval in stdtickvals:
stdticklabs.append('{0:0.2f}'.format(stdval))
valsAndLabs = list(zip(stdtickvals, stdticklabs))
stdgrid = grid_finder.FixedLocator(stdtickvals)
stdticks = grid_finder.DictFormatter(dict(valsAndLabs))
gh_curvegrid = floating_axes.GridHelperCurveLinear(
tr,
extremes=(0, numpy.pi / 2, smin, smax),
grid_locator1=corrgrid,
grid_locator2=stdgrid,
tick_formatter1=corrticks,
tick_formatter2=stdticks)
artists = []
#if addTo isn't None then assume we've been given a previously returned
#axes object
if addTo is None:
fig = plt.figure()
ax = floating_axes.FloatingSubplot(fig,
'111',
grid_helper=gh_curvegrid)
fig.add_subplot(ax)
#Adjust axes following matplotlib gallery example
#Correlation is angular coord
ax.axis['top'].set_axis_direction('bottom')
ax.axis['top'].toggle(ticklabels=True, label=True)
ax.axis['top'].major_ticklabels.set_axis_direction('top')
ax.axis['top'].major_ticklabels.set_color('royalblue')
ax.axis['top'].label.set_axis_direction('top')
ax.axis['top'].label.set_color('royalblue')
ax.axis['top'].label.set_text("Pearson's r")
#X-axis
ax.axis['left'].set_axis_direction('bottom')
ax.axis['left'].toggle(ticklabels=True)
#Y-axis
ax.axis['right'].set_axis_direction('top')
ax.axis['right'].toggle(ticklabels=True, label=True)
ax.axis['right'].major_ticklabels.set_axis_direction('left')
if setNormed:
xylabel = 'Normalized standard deviation'
else:
xylabel = 'Standard deviation'
ax.axis['right'].label.set_text(xylabel)
ax.axis['left'].label.set_text(xylabel)
ax.axis['bottom'].set_visible(False)
_ax = ax # Display axes
#Figure set up, done we work with the transformed axes
ax = ax.get_aux_axes(tr) # Axes referenced in polar coords
#Add reference point, ref stddev contour and other stddev contours
artists.append(
ax.scatter(0,
ostd,
marker='o',
linewidths=2,
edgecolors='black',
facecolors='None',
label='Observation',
zorder=99))
azim = numpy.linspace(0, numpy.pi / 2)
rad = numpy.zeros_like(azim)
rad.fill(ostd)
ax.plot(azim, rad, 'k--', alpha=0.75)
if isoSTD:
for sd in stdtickvals[::2]:
rad.fill(sd)
ax.plot(azim,
rad,
linestyle=':',
color='dimgrey',
alpha=0.75,
zorder=3)
#Add radial markers at correlation ticks
for i in corrtickvals[1:]:
ax.plot([numpy.arccos(i), numpy.arccos(i)], [0, smax],
c='royalblue',
alpha=0.5,
zorder=40)
#Add contours of centered RMS error
rs, ts = numpy.meshgrid(numpy.linspace(smin, smax),
numpy.linspace(0, numpy.pi / 2))
rms = numpy.sqrt(ostd**2 + rs**2 - 2 * ostd * rs * numpy.cos(ts))
contours = ax.contour(ts,
rs,
rms,
4,
alpha=0.75,
zorder=30,
colors='dimgray')
plt.clabel(contours, inline=True, fontsize='smaller', fmt='%1.2f')
else:
#TODO: add some testing/error handling here
ax = addTo
fig = ax.figure
#add present model
stdextent = smax - smin
twopercent = stdextent / 50.0
artists.append(
ax.scatter(numpy.arccos(pcorr),
pstd,
marker='o',
label=modelName,
zorder=99))
dum = ax.text(numpy.arccos(pcorr),
pstd + twopercent,
modelName,
fontsize='larger')
out = dict()
out['Figure'] = fig
out['Axes'] = ax
out['Norm'] = normfac
out['Artists'] = artists
return out
def __init__(self,
refstd=1,
fig=None,
rect=111,
label='REF',
std_range=(0, 1.65),
std_level=np.arange(0, 1.51, 0.25)):
"""Create base Taylor Diagram.
Parameters
----------
refstd : float, optional
reference standard deviation
fig : matplotlib.figure.Figure, optional
Optional input figure. Default is None
rect : int, optional
Optional subplot definition
label : string, optional
Optional reference label string indentifier
std_range : Tuple, optional
Optional stddev axis extent
std_level : list, optional
Optional list of tick locations for stddev axis
"""
from matplotlib.projections import PolarAxes
import mpl_toolkits.axisartist.floating_axes as fa
import mpl_toolkits.axisartist.grid_finder as gf
# Pull and set optional constructor variables
# Set figure
self.fig = fig
if fig is None:
self.fig = plt.figure(figsize=(8, 8))
# Reference standard deviation
self.refstd = refstd
# Standard deviation axis extent (in units of reference stddev)
self.smin = std_range[0]
self.smax = std_range[1]
# Set polar transform
tr = PolarAxes.PolarTransform()
# Set correlation labels
rlocs = np.concatenate((np.arange(10) / 10., [0.95, 0.99, 1]))
tlocs = np.arccos(rlocs) # Conversion to polar angles
gl1 = gf.FixedLocator(tlocs) # Positions
tf1 = gf.DictFormatter(dict(list(zip(tlocs, list(map(str, rlocs))))))
# Set standard deviation labels
gl2 = gf.FixedLocator(std_level)
# format each label with 2 decimal places
format_string = list(map(lambda x: "{0:0.2f}".format(x), std_level))
index = np.where(std_level == self.refstd)[0][0]
format_string[index] = label
tf2 = gf.DictFormatter(dict(list(zip(std_level, format_string))))
# Use customized GridHelperCurveLinear to define curved axis
ghelper = fa.GridHelperCurveLinear(
tr,
extremes=(
0,
np.pi / 2, # 1st quadrant only
self.smin,
self.smax),
grid_locator1=gl1,
tick_formatter1=tf1,
grid_locator2=gl2,
tick_formatter2=tf2)
# Create graphical axes
ax = fa.FloatingSubplot(self.fig, rect, grid_helper=ghelper)
self.fig.add_subplot(ax)
# Adjust axes for Correlation
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("right")
ax.axis["top"].label.set_axis_direction("top")
ax.axis["top"].label.set_text("Correlation")
# Standard deviation ("X axis")
ax.axis["left"].set_axis_direction("bottom")
# Standard deviation ("Y axis")
ax.axis["right"].set_axis_direction("top")
ax.axis["right"].toggle(ticklabels=True, label=True)
ax.axis["right"].major_ticklabels.set_axis_direction("left")
ax.axis["right"].label.set_text("Standard deviation (Normalized)")
# Set font sizes, tick sizes, and padding
ax.axis['top', 'right'].label.set_fontsize(18)
ax.axis['top', 'right', 'left'].major_ticklabels.set_fontsize(16)
ax.axis['top', 'right', 'left'].major_ticks.set_ticksize(10)
ax.axis['top', 'right', 'left'].major_ticklabels.set_pad(8)
ax.axis['top', 'right'].label.set_pad(6)
# Bottom axis is not needed
ax.axis["bottom"].set_visible(False)
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point stddev contour
t = np.linspace(0, np.pi / 2)
r = np.zeros_like(t) + self.refstd
h, = self.ax.plot(t,
r,
linewidth=1,
linestyle=(0, (9, 5)),
color='black',
zorder=1)
# Set aspect ratio
self.ax.set_aspect('equal')
# Store the reference line
self.referenceLine = h
# Collect sample points for latter use (e.g. legend)
self.modelMarkerSet = []
# Set number for models outside axes
self.modelOutside = -1
def __init__(self, refstd, fig=None, rect=111, label='_'):
"""Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes. refstd is
the reference standard deviation to be compared to.
"""
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, [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
self.smin = 0
self.smax = 1.5 * self.refstd
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=(0, np.pi / 2, self.smin, self.smax), # 1stquadrant
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'].label.set_text('Standard deviation')
ax.axis['right'].toggle(ticklabels=True)
ax.axis['right'].major_ticklabels.set_axis_direction('left')
ax.axis['bottom'].set_visible(False) # Useless
# Contours along standard deviations
ax.grid(False)
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point and stddev contour
# print("Reference std:", self.refstd)
# l, = self.ax.plot([0], self.refstd, 'k*', rem by saeed
# ls='', ms=10, label=label) rem by saeed
# t = np.linspace(0, np.pi/2) rem by saeed
# r = np.zeros_like(t) + self.refstd rem by saeed
# self.ax.plot(t,r, 'k--', label='_') rem by saeed
for ip in range(len(rlocs)):
x = [self.smin, self.smax]
y = [np.arccos(rlocs[ip]), np.arccos(rlocs[ip])]
self.ax.plot(y, x, 'grey', linewidth=0.25)
# Collect sample points for latter use (e.g. legend)
# self.samplePoints = [l] rem by saeed
self.samplePoints = [] # add by saeed
def setup_axes(self, fig, rect=111):
"""Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes.
Wouldn't the ideal be to define its own non-linear
transformation, so that coordinates are directly r=stddev and
theta=correlation? I guess it would allow
"""
from matplotlib.projections import PolarAxes
import mpl_toolkits.axisartist.floating_axes as FA
import mpl_toolkits.axisartist.grid_finder as GF
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))))
ghelper = FA.GridHelperCurveLinear(tr,
extremes=(0,NP.pi/2, # 1st quadrant
0,1.5*self.ref.std()),
grid_locator1=gl1,
tick_formatter1=tf1,
)
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
# Grid
ax.grid()
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point and stddev contour
print("Reference std:", self.ref.std())
self.ax.plot([0],self.ref.std(),'ko', label='_')
t = NP.linspace(0,NP.pi/2)
r = NP.zeros_like(t) + self.ref.std()
self.ax.plot(t,r,'k--', label='_')
return self.ax
def __init__(self, refstd, fig=None, rect=111, label='_', norm=False, full=False, grid=True):
"""Set up Taylor diagram axes, i.e. polar plot,
using mpl_toolkits.axisartist.floating_axes. refstd is
the reference standard deviation to be compared to.
norm : flag to normalize with respect to refstd.
full : flag to create single quadrant or semi-circle
"""
from matplotlib.projections import PolarAxes as _PolarAxes
import mpl_toolkits.axisartist.floating_axes as _FA
import mpl_toolkits.axisartist.grid_finder as _GF
self.refstd = refstd # Reference standard deviation
self.norm = norm # Normalized or Absolute
self.full = full # Full or Single-quadrant Taylor
self.grid = grid # Cyan grid-lines at correlation theta
tr = _PolarAxes.PolarTransform()
# Correlation labels
rlocs = _np.concatenate((_np.arange(10)/10.,[0.95,0.99]))
if self.full:
rlocs = _np.concatenate([-1.*_np.flipud(rlocs)[:-1],rlocs])
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 and labels
self.smin = 0
if self. norm:
self.smax = 1.5
slocs = _np.arange(self.smax*10)[::2]/10.
gl2 = _GF.FixedLocator(slocs)
tf2 = _GF.DictFormatter(dict(zip(slocs, map(str,slocs))))
else:
self.smax = 1.5*self.refstd
gl2 = None
tf2 = None
self.ext_max = _np.pi if self.full else _np.pi/2.
ghelper = _FA.GridHelperCurveLinear(tr,
extremes=(0.,self.ext_max,
self.smin,self.smax),
grid_locator1=gl1,
tick_formatter1=tf1,
grid_locator2=gl2,
tick_formatter2=tf2,
)
if fig is None:
fig = _plt.figure()
self.fig = fig
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["top"].label.set_fontsize(12)
ax.axis["top"].label.set_fontweight("normal")
ax.axis["left"].set_axis_direction("bottom") # "X axis"
ax.axis["left"].label.set_text("Normalized Standard Deviation" if self.norm else "Standard Deviation")
ax.axis["left"].label.set_fontsize(12)
ax.axis["left"].label.set_fontweight("normal")
ax.axis["right"].set_axis_direction("top") # "Y axis"
ax.axis["right"].toggle(ticklabels=True)
if self.full:
ax.axis["right"].major_ticklabels.set_axis_direction("bottom")
ax.axis["bottom"].toggle(ticklabels=False)
ax.axis["bottom"].set_axis_direction("bottom")
else:
ax.axis["right"].major_ticklabels.set_axis_direction("left")
ax.axis["bottom"].set_visible(False) # Useless
# Contours along standard deviations
ax.grid(False)
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point and stddev contour
#print "Reference std:", self.refstd
l, = self.ax.plot([0], 1.0 if self.norm else self.refstd, 'k*',
ls='', ms=10, label=label)
t = _np.linspace(0, self.ext_max)
r = _np.zeros_like(t) + ( 1.0 if self.norm else self.refstd )
self.ax.plot(t,r, 'k--', label='_')
# Collect sample points for latter use (e.g. legend)
self.samplePoints = [l]
# Add 0 line if full Taylor
if self.full:
r = _np.linspace(0.,self.smax)
t = _np.zeros_like(r) + _np.pi/2.
self.ax.plot(t,r,'k--',label='_')
# Add cyan radii at all correlations:
if self.grid:
r = _np.linspace(0.,self.smax)
for th in tlocs:
th_deg = 180.*th/_np.pi
if not (20. < th_deg < 160. and th_deg != 90.): continue
t = _np.zeros_like(r) + th
self.ax.plot(t,r,'c-',label='_')
return
def __init__(self,
refstd,
refcorrcoef=1.0,
fig=None,
rect=111,
label='_',
srange=(0, 1.5)):
"""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(NP.arccos(refcorrcoef),
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 __init__(self,
true,
fig=None,
rect=111,
label='_',
srange=(0, 1.5),
extend=False,
axis_fontdict: dict = None):
"""
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
:param axis_fontdict: dictionary must consist of at least three dictionaries 'left', 'right', 'top'
"""
#self.refstd = refstd # Reference standard deviation
self.refstd = np.std(true)
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['top'].label.set_fontsize(axis_fontdict['top'].get(
'fontsize', 18))
ax.axis['top'].label.set_color(axis_fontdict['top'].get('color', 'k'))
ax.axis['top'].major_ticklabels.set_fontsize(axis_fontdict['top'].get(
'ticklabel_fs', 10))
ax.axis["left"].set_axis_direction("bottom") # "X axis"
ax.axis["left"].label.set_text("Standard deviation")
ax.axis['left'].label.set_fontsize(axis_fontdict['bottom'].get(
'fontsize', 18))
ax.axis['left'].label.set_color(axis_fontdict['bottom'].get(
'color', 'k'))
ax.axis['left'].major_ticklabels.set_fontsize(
axis_fontdict['bottom'].get('ticklabel_fs', 10))
ax.axis["right"].set_axis_direction("top") # "Y-axis"
ax.axis["right"].toggle(ticklabels=True)
ax.axis['right'].label.set_fontsize(axis_fontdict['left'].get(
'fontsize', 18))
ax.axis['right'].label.set_color(axis_fontdict['left'].get(
'color', 'k'))
ax.axis['right'].major_ticklabels.set_fontsize(
axis_fontdict['left'].get('ticklabel_fs', 10))
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 __init__(self, refstd, fig=None, rect=111, label='_'):
"""Set up Taylor diagram axes, i.e. single quadrant polar
plot, using mpl_toolkits.axisartist.floating_axes. refstd is
the reference standard deviation to be compared to.
"""
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
self.smin = 0
self.smax = 1.4 * 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)
# for plot number > 9
ax = FA.FloatingSubplot(fig, rect[0], rect[1], rect[2], \
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
# Contours along standard deviations
ax.grid(False)
self._ax = ax # Graphical axes
self.ax = ax.get_aux_axes(tr) # Polar coordinates
# Add reference point and stddev contour
print "Reference std:", self.refstd
l, = self.ax.plot([0], self.refstd, 'k*', ls='', ms=10, label=label)
# ms is the marker size
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 Taylor_diag(series, names, styles, colors):
""" Taylor Diagram : obs is reference data sample
in a full diagram (0 --> npi)
--------------------------------------------------------------------------
Input: series - dict with all time series (lists) to analyze
series[0] - is the observation, the reference by default.
"""
from matplotlib.projections import PolarAxes
taylor_stats = np.array([
AnDA_Taylor_stats(series[i], series[list(series.keys())[0]])
for i in series.keys()
])
crmsd, corr, std = taylor_stats.T
ref = std[0]
rlocs = np.concatenate((np.arange(0, 10, 0.25), [0.95, 0.99]))
str_rlocs = np.concatenate((np.arange(0, 10, 0.25), [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))))
str_locs2 = np.arange(0, 11, 0.5)
tlocs2 = np.arange(0, 11, 0.5) # Conversion to polar angles
g22 = GF.FixedLocator(tlocs2)
tf2 = GF.DictFormatter(dict(zip(tlocs2, map(str, str_locs2))))
tr = PolarAxes.PolarTransform()
smin = 0
smax = (120 / 100) * np.max(std)
ghelper = FA.GridHelperCurveLinear(
tr,
extremes=(
0,
np.pi / 2, # 1st quadrant
smin,
smax),
grid_locator1=gl1,
#grid_locator2=g11,
tick_formatter1=tf1,
tick_formatter2=tf2,
)
fig = plt.figure(figsize=(10, 5), dpi=100)
ax = FA.FloatingSubplot(fig, 111, grid_helper=ghelper)
fig.add_subplot(ax)
ax.axis["top"].set_axis_direction("bottom")
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 Coefficient")
ax.axis["left"].set_axis_direction("bottom")
ax.axis["left"].label.set_text("Standard Deviation")
ax.axis["right"].set_axis_direction("top")
ax.axis["right"].toggle(ticklabels=True, label=True)
ax.axis["right"].set_visible(True)
ax.axis["right"].major_ticklabels.set_axis_direction("bottom")
ax.axis["right"].label.set_text("Standard Deviation")
ax.axis["bottom"].set_visible(False)
ax.grid(True)
ax = ax.get_aux_axes(tr)
t = np.linspace(0, np.pi / 2)
r = np.zeros_like(t) + ref
ax.plot(t, r, 'k--', label='_')
rs, ts = np.meshgrid(np.linspace(smin, smax), np.linspace(0, np.pi / 2))
rms = np.sqrt(ref**2 + rs**2 - 2 * ref * rs * np.cos(ts))
CS = ax.contour(ts, rs, rms, cmap=cm.bone)
plt.clabel(CS, inline=1, fontsize=10)
ax.plot(np.arccos(0.9999), ref, 'k', marker='*', ls='', ms=10)
aux = range(1, len(corr))
#colors = plt.matplotlib.cm.jet(np.linspace(0,1,len(corr)))
for i in reversed(aux):
ax.plot(np.arccos(corr[i]),
std[i],
c=colors[i],
alpha=0.7,
marker=styles[i],
label="%s" % names[i])
#ax.text(np.arccos(corr[i]), std[i],"%s"%i)
# inset axes....
'''axins = ax.inset_axes([1.1, 0, 0.3, 0.3])
def pol2cart(phi, rho):
x = rho * np.cos(phi)
y = rho * np.sin(phi)
return(x, y)
x = np.empty(len(aux))
y = np.empty(len(aux))
for i in reversed(aux):
x[i-1], y[i-1] = pol2cart(np.arccos(corr[i]), std[i])
axins.plot(x[i-1], y[i-1], c=colors[i],alpha=0.7,marker=styles[i],label="%s" %names[i])
#axins.text(x[i-1], y[i-1],"%s"%i)
# sub region of the original image
x1, x2, y1, y2 = np.min(x)-(1/50)*np.min(x), np.max(x)+(1/50)*np.max(x),\
np.min(y)-(1)*np.min(y), np.max(y)+(1)*np.max(y)
axins.set_xlim(x1,x2)
axins.set_ylim(y1,y2)
axins.set_xticks([])
axins.set_yticks([])
axins.set_xticklabels('')
axins.set_yticklabels('')'''
plt.legend(bbox_to_anchor=(1.5, 1), prop=dict(size='small'), loc='best')
