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#!/usr/bin/env python
# coding: utf-8
# In[ ]:
get_ipython().run_line_magic('matplotlib', 'inline')
#
# # 1D Screened optimal transport
#
#
# This example illustrates the computation of Screenkhorn: Screening Sinkhorn Algorithm for Optimal transport.
#
#
# In[13]:
# Author: Mokhtar Z. Alaya <mokhtarzahdi.alaya@gmail.com>
#
# License: MIT License
import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot
from ot.datasets import make_1D_gauss as gauss
from ot.bregman import screenkhorn
# Generate data
# -------------
#
#
# In[14]:
#%% 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
# ----------------------------------
#
#
# In[15]:
#%% 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
# --------------
#
#
# In[21]:
# 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()
# In[ ]:
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