"""
Functions for plotting OT matrices
.. warning::
Note that by default the module is not import in :mod:`ot`. In order to
use it you need to explicitly import :mod:`ot.plot`
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
from matplotlib import gridspec
[docs]
def plot1D_mat(
a,
b,
M,
title="",
plot_style="yx",
a_label="",
b_label="",
color_source="b",
color_target="r",
coupling_cmap="gray_r",
):
r"""Plot matrix :math:`\mathbf{M}` with the source and target 1D distributions.
Creates a subplot with the source distribution :math:`\mathbf{a}` and target
distribution :math:`\mathbf{b}`t.
In 'yx' mode (default), the source is on the left and
the target on the top, and in 'xy' mode, source on the bottom (upside
down) and the target on the left.
The matrix :math:`\mathbf{M}` is shown in between.
Parameters
----------
a : ndarray, shape (na,)
Source distribution
b : ndarray, shape (nb,)
Target distribution
M : ndarray, shape (na, nb)
Matrix to plot
title : str, optional
Title of the plot
plot_style : str, optional
Style of the plot, 'yx' or 'xy'. 'yx' places the source on the left and
the target on the top, 'xy' places the source on the bottom (upside
down) and the target on the left.
a_label : str, optional
Label for source distribution
b_label : str, optional
Label for target distribution
color_source : str, optional
Color of the source distribution
color_target : str, optional
Color of the target distribution
coupling_cmap : str, optional
Colormap for the coupling matrix
Returns
-------
ax1 : source plot ax
ax2 : target plot ax
ax3 : coupling plot ax
.. seealso::
:func:`rescale_for_imshow_plot`
"""
assert plot_style in ["yx", "xy"], "plot_style should be 'yx' or 'xy'"
na, nb = M.shape
gs = gridspec.GridSpec(
3, 3, height_ratios=[1, 1, 1], width_ratios=[1, 1, 1], hspace=0, wspace=0
)
xa = np.arange(na)
xb = np.arange(nb)
# helper function for code factorisation
def _set_ticks_and_spines(ax, empty_ticks=True, visible_spines=False):
if empty_ticks:
ax.set_xticks(())
ax.set_yticks(())
ax.spines["top"].set_visible(visible_spines)
ax.spines["right"].set_visible(visible_spines)
ax.spines["bottom"].set_visible(visible_spines)
ax.spines["left"].set_visible(visible_spines)
if plot_style == "xy":
# horizontal source on the bottom, flipped vertically
ax1 = pl.subplot(gs[2, 1:])
ax1.plot(xa, np.max(a) - a, color=color_source, linewidth=2)
ax1.fill(
xa,
np.max(a) - a,
np.max(a) * np.ones_like(a),
color=color_source,
alpha=0.5,
)
ax1.set_title(a_label, y=-0.15)
# vertical target on the left
ax2 = pl.subplot(gs[0:2, 0])
ax2.plot(b, xb, color=color_target, linewidth=2)
ax2.fill(b, xb, color=color_target, alpha=0.5)
ax2.invert_xaxis()
ax2.invert_yaxis()
ax2.set_title(b_label)
_set_ticks_and_spines(ax1, empty_ticks=True, visible_spines=False)
_set_ticks_and_spines(ax2, empty_ticks=True, visible_spines=False)
# coupling matrix in the middle
ax3 = pl.subplot(gs[0:2, 1:], sharey=ax2, sharex=ax1)
ax3.imshow(M.T, interpolation="nearest", origin="lower", cmap=coupling_cmap)
ax3.set_title(title)
_set_ticks_and_spines(ax3, empty_ticks=False, visible_spines=True)
pl.subplots_adjust(hspace=0, wspace=0)
return ax1, ax2, ax3
else: # plot_style == 'yx'
# vertical source on the left
ax1 = pl.subplot(gs[1:, 0])
ax1.plot(a, xa, color=color_source, linewidth=2)
ax1.fill(a, xa, color=color_source, alpha=0.5)
ax1.invert_xaxis()
ax1.set_title(a_label)
# horizontal target on the top
ax2 = pl.subplot(gs[0, 1:])
ax2.plot(xb, b, color=color_target, linewidth=2)
ax2.fill(xb, b, color=color_target, alpha=0.5)
ax2.set_title(b_label)
_set_ticks_and_spines(ax1, empty_ticks=True, visible_spines=False)
_set_ticks_and_spines(ax2, empty_ticks=True, visible_spines=False)
# coupling matrix in the middle
ax3 = pl.subplot(gs[1:, 1:], sharey=ax1, sharex=ax2)
ax3.imshow(M, interpolation="nearest", cmap=coupling_cmap)
# Set title below matrix plot
ax3.text(
0.5,
-0.025,
title,
ha="center",
va="top",
transform=ax3.transAxes,
fontsize="large",
)
_set_ticks_and_spines(ax3, empty_ticks=False, visible_spines=True)
pl.subplots_adjust(hspace=0, wspace=0)
return ax1, ax2, ax3
[docs]
def rescale_for_imshow_plot(x, y, n, m=None, a_y=None, b_y=None):
r"""
Gives arrays xr, yr that can be plotted over an (n, m)
imshow plot (in 'xy' coordinates). If `a_y` or `b_y` is provided,
y is sliced over its indices such that y stays in [ay, by].
Parameters
----------
x : ndarray, shape (nx,)
y : ndarray, shape (nx,)
n : int
x-axis size of the imshow plot on which to plot (x, y)
m : int, optional
y-axis size of the imshow plot, defaults to n
a_y : float, optional
Lower bound for y
b_y : float, optional
Upper bound for y
Returns
-------
xr : ndarray, shape (nx,)
Rescaled x values (due to slicing, may have less elements than x)
yr : ndarray, shape (nx,)
Rescaled y values (due to slicing, may have less elements than y)
.. seealso::
:func:`plot1D_mat`
"""
# slice over the y values that are in the y range
a_x, b_x = np.min(x), np.max(x)
assert x.shape[0] == y.shape[0], "x and y arrays should have the same size"
if a_y is None:
a_y = np.min(y)
if b_y is None:
b_y = np.max(y)
if m is None:
m = n
idx = (y >= a_y) & (y <= b_y)
x_rescaled = (x[idx] - a_x) * (n - 1) / (b_x - a_x)
y_rescaled = (y[idx] - a_y) * (m - 1) / (b_y - a_y)
return x_rescaled, y_rescaled
[docs]
def plot2D_samples_mat(xs, xt, G, thr=1e-8, **kwargs):
r"""Plot matrix :math:`\mathbf{G}` in 2D with lines using alpha values
Plot lines between source and target 2D samples with a color
proportional to the value of the matrix :math:`\mathbf{G}` between samples.
Parameters
----------
xs : ndarray, shape (ns,2)
Source samples positions
b : ndarray, shape (nt,2)
Target samples positions
G : ndarray, shape (na,nb)
OT matrix
thr : float, optional
threshold above which the line is drawn
**kwargs : dict
parameters given to the plot functions (default color is black if
nothing given)
"""
if ("color" not in kwargs) and ("c" not in kwargs):
kwargs["color"] = "k"
mx = G.max()
if "alpha" in kwargs:
scale = kwargs["alpha"]
del kwargs["alpha"]
else:
scale = 1
for i in range(xs.shape[0]):
for j in range(xt.shape[0]):
if G[i, j] / mx > thr:
pl.plot(
[xs[i, 0], xt[j, 0]],
[xs[i, 1], xt[j, 1]],
alpha=G[i, j] / mx * scale,
**kwargs,
)
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