# -*- coding: utf-8 -*-
"""
=================================
Wasserstein Discriminant Analysis
=================================

This example illustrate the use of WDA as proposed in [11].


[11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016).
Wasserstein Discriminant Analysis.

"""

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

# sphinx_gallery_thumbnail_number = 2

import numpy as np
import matplotlib.pylab as pl

from ot.dr import wda, fda


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

# %% parameters

n = 1000  # nb samples in source and target datasets
nz = 0.2

np.random.seed(1)

# generate circle dataset
t = np.random.rand(n) * 2 * np.pi
ys = np.floor((np.arange(n) * 1.0 / n * 3)) + 1
xs = np.concatenate((np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)
xs = xs * ys.reshape(-1, 1) + nz * np.random.randn(n, 2)

t = np.random.rand(n) * 2 * np.pi
yt = np.floor((np.arange(n) * 1.0 / n * 3)) + 1
xt = np.concatenate((np.cos(t).reshape((-1, 1)), np.sin(t).reshape((-1, 1))), 1)
xt = xt * yt.reshape(-1, 1) + nz * np.random.randn(n, 2)

nbnoise = 8

xs = np.hstack((xs, np.random.randn(n, nbnoise)))
xt = np.hstack((xt, np.random.randn(n, nbnoise)))

##############################################################################
# Plot data
# ---------

# %% plot samples
pl.figure(1, figsize=(6.4, 3.5))

pl.subplot(1, 2, 1)
pl.scatter(xt[:, 0], xt[:, 1], c=ys, marker="+", label="Source samples")
pl.legend(loc=0)
pl.title("Discriminant dimensions")

pl.subplot(1, 2, 2)
pl.scatter(xt[:, 2], xt[:, 3], c=ys, marker="+", label="Source samples")
pl.legend(loc=0)
pl.title("Other dimensions")
pl.tight_layout()

##############################################################################
# Compute Fisher Discriminant Analysis
# ------------------------------------

# %% Compute FDA
p = 2

Pfda, projfda = fda(xs, ys, p)

##############################################################################
# Compute Wasserstein Discriminant Analysis
# -----------------------------------------

# %% Compute WDA
p = 2
reg = 1e0
k = 10
maxiter = 100

P0 = np.random.randn(xs.shape[1], p)

P0 /= np.sqrt(np.sum(P0**2, 0, keepdims=True))

Pwda, projwda = wda(xs, ys, p, reg, k, maxiter=maxiter, P0=P0)


##############################################################################
# Plot 2D projections
# -------------------

# %% plot samples

xsp = projfda(xs)
xtp = projfda(xt)

xspw = projwda(xs)
xtpw = projwda(xt)

pl.figure(2)

pl.subplot(2, 2, 1)
pl.scatter(xsp[:, 0], xsp[:, 1], c=ys, marker="+", label="Projected samples")
pl.legend(loc=0)
pl.title("Projected training samples FDA")

pl.subplot(2, 2, 2)
pl.scatter(xtp[:, 0], xtp[:, 1], c=ys, marker="+", label="Projected samples")
pl.legend(loc=0)
pl.title("Projected test samples FDA")

pl.subplot(2, 2, 3)
pl.scatter(xspw[:, 0], xspw[:, 1], c=ys, marker="+", label="Projected samples")
pl.legend(loc=0)
pl.title("Projected training samples WDA")

pl.subplot(2, 2, 4)
pl.scatter(xtpw[:, 0], xtpw[:, 1], c=ys, marker="+", label="Projected samples")
pl.legend(loc=0)
pl.title("Projected test samples WDA")
pl.tight_layout()

pl.show()
