"""
Surface Boxplot
====================

Shows the use of the surface boxplot, which is a generalization of the
functional boxplot for FDataGrid whose domain dimension is 2.
"""

# Author: Amanda Hernando Bernabé
# License: MIT

# sphinx_gallery_thumbnail_number = 3

# %%
# In order to instantiate a
# :class:`~skfda.exploratory.visualization.SurfaceBoxplot`, a functional data
# object with bidimensional domain must be generated. In this example, a
# FDataGrid representing a function
# :math:`f : \mathbb{R}^2\longmapsto\mathbb{R}` is constructed,
# using as an example a Brownian process extruded into another dimension.
#
# The values of the Brownian process are generated using
# :func:`~skfda.datasets.make_gaussian_process`,
# Those functions return FDataGrid objects whose ``data_matrix``
# store the values needed.

from skfda.datasets import make_gaussian_process

n_samples = 10
n_features = 10

fd = make_gaussian_process(
    n_samples=n_samples,
    n_features=n_features,
    random_state=1,
)
fd.dataset_name = "Brownian process"

# %%
# After, those values generated for one dimension on the domain are extruded
# along another dimension, obtaining a three-dimensional matrix or cube
# (two-dimensional domain and one-dimensional image).

import numpy as np

cube = np.repeat(fd.data_matrix, n_features).reshape(
    (n_samples, n_features, n_features),
)

# %%
# We can plot now the extruded trajectories.

import matplotlib.pyplot as plt

from skfda import FDataGrid

fd_2 = FDataGrid(
    data_matrix=cube,
    grid_points=np.tile(fd.grid_points, (2, 1)),
    dataset_name="Extruded Brownian process",
)

fd_2.plot()
plt.show()

# %%
# Since matplotlib was initially designed with only two-dimensional plotting
# in mind, the three-dimensional plotting utilities were built on top of
# matplotlib's two-dimensional display, and the result is a convenient (if
# somewhat limited) set of tools for three-dimensional data visualization as
# we can observe.
#
# For this reason, the profiles of the surfaces, which are contained in the
# first two generated functional data objects, are plotted below, to help to
# visualize the data.

fd.plot()
plt.show()

# %%
# To terminate the example, the instantiation of the
# :class:`~skfda.exploratory.visualization.SurfaceBoxplot` object is
# made, showing the surface boxplot which corresponds to our FDataGrid

from skfda.exploratory.visualization import SurfaceBoxplot

surface_boxplot = SurfaceBoxplot(fd_2)
surface_boxplot.plot()
plt.show()

# %%
# The surface boxplot contains the median, the central envelope and the
# outlying envelope plotted from darker to lighter colors, although they can
# be customized.
#
# Analogous to the procedure followed before of plotting the three-dimensional
# data and their correponding profiles, we can obtain also the functional
# boxplot for one-dimensional data with the
# :class:`~skfda.exploratory.visualization.Boxplot` passing as arguments the
# first FdataGrid object. The profile of the surface boxplot is obtained.

from skfda.exploratory.visualization import Boxplot

boxplot1 = Boxplot(fd)
boxplot1.plot()
plt.show()