# -*- coding: utf-8 -*-
"""
================================
Smooth optimal transport example
================================

This example illustrates the computation of EMD, Sinkhorn and smooth OT plans
and their visualization.

"""

# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License

# sphinx_gallery_thumbnail_number = 6

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

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 = 2e-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()

##############################################################################
# Solve Smooth OT
# ---------------


#%% Smooth OT with KL regularization

lambd = 2e-3
Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='kl')

pl.figure(5, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT KL reg.')

pl.show()


#%% Smooth OT with KL regularization

lambd = 1e-1
Gsm = ot.smooth.smooth_ot_dual(a, b, M, lambd, reg_type='l2')

pl.figure(6, figsize=(5, 5))
ot.plot.plot1D_mat(a, b, Gsm, 'OT matrix Smooth OT l2 reg.')

pl.show()
