"""
Interpolation
=====================

This example shows the types of interpolation used in the evaluation of
FDataGrids.
"""

# Author: Pablo Marcos Manchón
# License: MIT

# sphinx_gallery_thumbnail_number = 3

# %%
# The :class:`~skfda.representation.grid.FDataGrid` class is used for datasets
# containing discretized functions. For the evaluation between the points of
# discretization, or sample points, is necessary to interpolate.
#
# We will construct an example dataset with two curves with 6 points of
# discretization.

import matplotlib.pyplot as plt

import skfda

fd = skfda.datasets.make_sinusoidal_process(
    n_samples=2,
    n_features=6,
    random_state=1,
)
fig = fd.scatter()
fig.legend(["Sample 1", "Sample 2"])
plt.show()

# %%
# By default it is used linear interpolation, which is one of the simplest
# methods of interpolation and therefore one of the least computationally
# expensive, but has the disadvantage that the interpolant is not
# differentiable at the points of discretization.

fig = fd.plot()
fd.scatter(fig=fig)
plt.show()

# %%
# The interpolation method of the FDataGrid could be changed setting the
# attribute ``interpolation``. Once we have set an interpolation it is used for
# the evaluation of the object.
#
# Polynomial spline interpolation could be performed using the interpolation
# :class:`~skfda.representation.interpolation.SplineInterpolation`. In the
# following example a cubic interpolation is set.

from skfda.representation.interpolation import SplineInterpolation

fd.interpolation = SplineInterpolation(interpolation_order=3)

fig = fd.plot()
fd.scatter(fig=fig)
plt.show()

# %%
# Sometimes our samples are required to be monotone, in these cases it is
# possible to use monotone cubic interpolation with the attribute
# ``monotone``. A piecewise cubic hermite interpolating polynomial (PCHIP)
# will be used.

import numpy as np

fd = fd[1]

fd_monotone = fd.copy(data_matrix=np.sort(fd.data_matrix, axis=1))


fig = fd_monotone.plot(linestyle="--", label="cubic")


fd_monotone.interpolation = SplineInterpolation(
    interpolation_order=3,
    monotone=True,
)
fd_monotone.plot(fig=fig, label="PCHIP")

fd_monotone.scatter(fig=fig, c="C1")
fig.legend()
plt.show()

# %%
# All the interpolations will work regardless of the dimension of the image,
# but depending on the domain dimension some methods will not be available.
#
# For the next examples it is constructed a surface,
# :math:`x_i: \mathbb{R}^2 \longmapsto \mathbb{R}`. By default, as in
# unidimensional samples, it is used linear interpolation.

from mpl_toolkits.mplot3d import axes3d

X, Y, Z = axes3d.get_test_data(1.2)
data_matrix = [Z.T]
grid_points = [X[0, :], Y[:, 0]]


fd = skfda.FDataGrid(data_matrix, grid_points)

fig = fd.plot()
fd.scatter(fig=fig)
plt.show()

# %%
# In the following figure it is shown the result of the constant interpolation
# applied to the surface.

fd.interpolation = SplineInterpolation(interpolation_order=0)

fig = fd.plot()
fd.scatter(fig=fig)
plt.show()