"""
Simulation of clusters of multivariate functional data
======================================================

Examples of simulation of clusters of multivariate functional data.
"""

# Author: Steven Golovkine <steven_golovkine@icloud.com>
# License: MIT

# Load packages
import numpy as np

from FDApy.simulation.karhunen import KarhunenLoeve
from FDApy.visualization.plot import plot_multivariate

# Set general parameters
rng = 42
n_obs = 20

# Define the random state
random_state = np.random.default_rng(rng)

# Parameters of the basis
name = ['fourier', 'wiener']
n_functions = 5  # Set an odd number of functions for Fourier basis

# Parameters of the clusters
n_clusters = 2
mean = np.array([0, 0])
covariance = np.array([[1, -0.6], [-0.6, 1]])
centers = random_state.multivariate_normal(mean, covariance, size=n_functions)

###############################################################################
#
# **First example**
# ---
# We simulate :math:`N = 20` curves of a 2-dimensional process. The first
# component of the process is defined on the one-dimensional observation grid
# :math:`\{0, 0.01, 0.02, \cdots, 1\}`, based on the first :math:`K = 5`
# Fourier basis functions on :math:`[0, 1]` and the decreasing of the variance
# of the scores is exponential. The second component of the process is defined
# on the one-dimensional observation grid :math:`\{0, 0.01, 0.02, \cdots, 1\}`,
# based on the first :math:`K = 5` Wiener basis functions on :math:`[0, 1]`
# and the decreasing of the variance of the scores is exponential. The clusters
# are defined through the coefficients in the Karhunen-Loève decomposition. The
# centers of the clusters are generated as Gaussian random variables with
# parameters defined by `mean` and `covariance`.
kl = KarhunenLoeve(
    basis_name=name, n_functions=n_functions, random_state=rng
)
kl.new(
    n_obs=n_obs,
    n_clusters=n_clusters,
    centers=centers,
    clusters_std='exponential'
)

_ = plot_multivariate(kl.data, kl.labels)

###############################################################################
#
# **Second example**
# ---
# We simulate :math:`N = 20` curves of a 2-dimensional process. The first
# component of the process is defined on the one-dimensional observation grid
# :math:`\{0, 0.01, 0.02, \cdots, 1\}`, based on the first :math:`K = 5`
# Fourier basis functions on :math:`[0, 1]` and the decreasing of the variance
# of the scores is linear. The second component of the process is defined
# on the one-dimensional observation grid :math:`\{0, 0.01, 0.02, \cdots, 1\}`,
# based on the first :math:`K = 5` Wiener basis functions on :math:`[0, 1]`
# and the decreasing of the variance of the scores is linear. The clusters
# are defined through the coefficients in the Karhunen-Loève decomposition. The
# centers of the clusters are generated as Gaussian random variables with
# parameters defined by `mean` and `covariance`.
kl = KarhunenLoeve(
    basis_name=name, n_functions=n_functions, random_state=rng
)
kl.new(
    n_obs=n_obs,
    n_clusters=n_clusters,
    centers=centers,
    clusters_std='linear'
)

_ = plot_multivariate(kl.data, kl.labels)