def test_error_degree(self):
with np.testing.assert_raises(ValueError):
interpolation = SplineInterpolation(7)
f = FDataGrid(self.data_matrix_1_1, grid_points=np.arange(10),
interpolation=interpolation)
f(1)
with np.testing.assert_raises(ValueError):
interpolation = SplineInterpolation(0)
f = FDataGrid(self.data_matrix_1_1, grid_points=np.arange(10),
interpolation=interpolation)
f(1)
def setUp(self):
"""Initialization of samples"""
self.time = np.linspace(-1, 1, 50)
interpolation = SplineInterpolation(3, monotone=True)
self.polynomial = FDataGrid([self.time**3, self.time**5],
self.time,
interpolation=interpolation)
def test_evaluation_nodes(self):
"""Test interpolation in nodes for all dimensions"""
for degree in range(1, 6):
interpolation = SplineInterpolation(degree)
f = FDataGrid(self.data_matrix_1_n, grid_points=np.arange(10),
interpolation=interpolation)
# Test interpolation in nodes
np.testing.assert_array_almost_equal(f(np.arange(10)),
self.data_matrix_1_n)
def test_evaluation_cubic_point(self):
"""Test the evaluation of a single point"""
f = FDataGrid(self.data_matrix_1_1, grid_points=np.arange(10),
interpolation=SplineInterpolation(3))
# Test a single point
np.testing.assert_array_almost_equal(f(5.3).round(3),
np.array([[[28.09]], [[13.69]]]))
np.testing.assert_array_almost_equal(
f([3]).round(3), np.array([[[9.]], [[36.]]]))
np.testing.assert_array_almost_equal(
f((2,)).round(3), np.array([[[4.]], [[49.]]]))
def test_evaluation_cubic_simple(self):
"""Test basic usage of evaluation"""
f = FDataGrid(self.data_matrix_1_1, grid_points=np.arange(10),
interpolation=SplineInterpolation(3))
# Test interpolation in nodes
np.testing.assert_array_almost_equal(f(np.arange(10)).round(1)[..., 0],
self.data_matrix_1_1)
# Test evaluation in a list of times
np.testing.assert_array_almost_equal(
f([0.5, 1.5, 2.5]).round(2),
np.array([[[0.25], [2.25], [6.25]],
[[72.25], [56.25], [42.25]]]))
def setUp(self):
# Data matrix of a datagrid with a dimension of domain and image equal
# to 1.
# Matrix of functions (x**2, (9-x)**2)
self.t = np.arange(10)
data_1 = np.array([np.arange(10)**2,
np.arange(start=9, stop=-1, step=-1)**2])
data_2 = np.sin(np.pi / 81 * data_1)
self.data_matrix_1_n = np.dstack((data_1, data_2))
self.interpolation = SplineInterpolation(interpolation_order=2)
def test_evaluation_cubic_composed(self):
f = FDataGrid(self.data_matrix_1_1, grid_points=np.arange(10),
interpolation=SplineInterpolation(3))
# Evaluate (x**2, (9-x)**2) in (1,8)
np.testing.assert_array_almost_equal(
f([[1], [8]], aligned=False).round(3),
np.array([[[1.]], [[1.]]]))
t = np.linspace(4, 6, 4)
np.testing.assert_array_almost_equal(
f([t, 9 - t], aligned=False).round(2),
np.array([[[16.], [21.78], [28.44], [36.]],
[[16.], [21.78], [28.44], [36.]]]))
# Same length than nsample
t = np.linspace(4, 6, 2)
np.testing.assert_array_almost_equal(
f([t, 9 - t], aligned=False).round(3),
np.array([[[16.], [36.]], [[16.], [36.]]]))
def test_evaluation_cubic_grid(self):
"""Test grid evaluation. With domain dimension = 1"""
f = FDataGrid(self.data_matrix_1_1, grid_points=np.arange(10),
interpolation=SplineInterpolation(3))
t = [0.5, 1.5, 2.5]
res = np.array([[[0.25], [2.25], [6.25]],
[[72.25], [56.25], [42.25]]])
# Test evaluation in a list of times
np.testing.assert_array_almost_equal(f(t, grid=True).round(3), res)
np.testing.assert_array_almost_equal(f((t,), grid=True).round(3), res)
np.testing.assert_array_almost_equal(f([t], grid=True).round(3), res)
# Single point with grid
np.testing.assert_array_almost_equal(
f(3, grid=True), np.array([[[9.]], [[36.]]]))
# Check erroneous axis
with np.testing.assert_raises(ValueError):
f((t, t), grid=True)
def test_evaluation_grid(self):
"""Test grid evaluation. With domain dimension = 1"""
f = FDataGrid(self.data_matrix_1_n, grid_points=np.arange(10),
interpolation=SplineInterpolation(2))
t = [1.5, 2.5, 3.5]
res = np.array([[[2.25, 0.08721158],
[6.25, 0.24020233],
[12.25, 0.4577302]],
[[56.25, 0.81614206],
[42.25, 0.99758925],
[30.25, 0.92214607]]])
# Test evaluation in a list of times
np.testing.assert_array_almost_equal(f(t, grid=True), res)
np.testing.assert_array_almost_equal(f((t,), grid=True), res)
np.testing.assert_array_almost_equal(f([t], grid=True), res)
# Check erroneous axis
with np.testing.assert_raises(ValueError):
f((t, t), grid=True)
# differentiable at the points of discretization.
#
fig = fd.plot()
fd.scatter(fig=fig)
##############################################################################
# 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.
fd.interpolation = SplineInterpolation(interpolation_order=3)
fig = fd.plot()
fd.scatter(fig=fig)
##############################################################################
# Smooth interpolation could be performed with the attribute
# ``smoothness_parameter`` of the spline interpolation.
#
# Sample with noise
fd_smooth = skfda.datasets.make_sinusoidal_process(n_samples=1,
n_features=30,
random_state=1,
error_std=.3)
# In this representation, the data can be arranged as a matrix.
print(fd.data_matrix)
##############################################################################
# By default, the data points are interpolated using a linear interpolation,
# but this is configurable.
dataset = skfda.datasets.fetch_medflies()
fd = dataset['data']
first_curve = fd[0]
first_curve.plot()
##############################################################################
# The interpolation used can however be changed. Here, we will use an
# interpolation with degree 3 splines.
first_curve.interpolation = SplineInterpolation(3)
first_curve.plot()
##############################################################################
# This representation allows also functions with arbitrary dimensions of the
# domain and codomain.
fd = skfda.datasets.make_multimodal_samples(n_samples=1,
dim_domain=2,
dim_codomain=2)
print(fd.dim_domain)
print(fd.dim_codomain)
fd.plot()
##############################################################################
