#!/usr/bin/env python
# coding: utf-8

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from ot.bregman import screenkhorn
from ot.datasets import make_1D_gauss as gauss
import ot.plot
import ot
import matplotlib.pylab as pl
import numpy as np
get_ipython().run_line_magic('matplotlib', 'inline')


#
# # 1D Screened optimal transport
#
#
# This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.
#
#

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# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
#
# License: MIT License


# Generate data
# -------------
#
#

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#%% 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
# ----------------------------------
#
#

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#%% 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 Screened Sinkhorn
# --------------
#
#

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# Screenkhorn

lambd = 1e-2  # entropy parameter
ns_budget = 30  # budget number of points to be keeped in the source distribution
nt_budget = 30  # budget number of points to be keeped in the target distribution

Gsc = screenkhorn(a, b, M, lambd, ns_budget, nt_budget, uniform=False, restricted=True, verbose=True)
pl.figure(4, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gs, 'OT matrix Screenkhorn')

pl.show()


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