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# %%
# -*- coding: utf-8 -*-
"""
======================================
Optimal Transport for 1D distributions
======================================
This example illustrates the computation of EMD and Sinkhorn transport plans
and their visualization.
"""
# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License
# sphinx_gallery_thumbnail_number = 3
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
from ot.datasets import make_1D_gauss as gauss
##############################################################################
# Generate data
# -------------
# %% parameters
n = 100 # nb bins
# bin positions
x = np.arange(n, dtype=np.float64)
# Gaussian distributions
a = gauss(n, m=20, s=5) # m= mean, s= std
b = gauss(n, m=60, s=10)
# loss matrix
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))
M /= M.max()
##############################################################################
# Plot distributions and loss matrix
# ----------------------------------
# %% plot the distributions
pl.figure(1, figsize=(6.4, 3))
pl.plot(x, a, "b", label="Source distribution")
pl.plot(x, b, "r", label="Target distribution")
pl.legend()
# %% plot distributions and loss matrix
pl.figure(2, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, M, "Cost matrix M")
##############################################################################
# Solve EMD
# ---------
# %% EMD
# use fast 1D solver
G0 = ot.emd_1d(x, x, a, b)
# Equivalent to
# G0 = ot.emd(a, b, M)
pl.figure(3, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, G0, "OT matrix G0")
##############################################################################
# Solve Sinkhorn
# --------------
# %% Sinkhorn
lambd = 1e-3
Gs = ot.sinkhorn(a, b, M, lambd, verbose=True)
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gs, "OT matrix Sinkhorn")
pl.show()
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