def test_fdatabasis_derivative_monomial(self):
monomial = FDataBasis(Monomial(nbasis=8),
[1, 5, 8, 9, 7, 8, 4, 5])
monomial2 = FDataBasis(Monomial(nbasis=5),
[[4, 9, 7, 4, 3],
[1, 7, 9, 8, 5],
[4, 6, 6, 6, 8]])
np.testing.assert_equal(monomial.derivative(),
FDataBasis(Monomial(nbasis=7),
[5, 16, 27, 28, 40, 24, 35]))
np.testing.assert_equal(monomial.derivative(order=0), monomial)
np.testing.assert_equal(monomial.derivative(order=6),
FDataBasis(Monomial(nbasis=2),
[2880, 25200]))
np.testing.assert_equal(monomial2.derivative(),
FDataBasis(Monomial(nbasis=4),
[[9, 14, 12, 12],
[7, 18, 24, 20],
[6, 12, 18, 32]]))
np.testing.assert_equal(monomial2.derivative(order=0), monomial2)
np.testing.assert_equal(monomial2.derivative(order=3),
FDataBasis(Monomial(nbasis=2),
[[24, 72],
[48, 120],
[36, 192]]))
def test_fdatabasis_derivative_constant(self):
constant = FDataBasis(Constant(), [[1], [2], [3], [4]])
self.assertTrue(constant.derivative().equals(
FDataBasis(Constant(), [[0], [0], [0], [0]])))
self.assertTrue(
constant.derivative(order=0).equals(
FDataBasis(Constant(), [[1], [2], [3], [4]])))
def test_fdatabasis_derivative_bspline(self):
bspline = FDataBasis(BSpline(n_basis=8), [1, 5, 8, 9, 7, 8, 4, 5])
bspline2 = FDataBasis(
BSpline(n_basis=5),
[[4, 9, 7, 4, 3], [1, 7, 9, 8, 5], [4, 6, 6, 6, 8]])
bs0 = bspline.derivative(order=0)
bs1 = bspline.derivative()
bs2 = bspline.derivative(order=2)
np.testing.assert_equal(bs1.basis, BSpline(n_basis=7, order=3))
np.testing.assert_almost_equal(
bs1.coefficients, np.atleast_2d([60, 22.5, 5, -10, 5, -30, 15]))
np.testing.assert_equal(bs0, bspline)
np.testing.assert_equal(bs2.basis, BSpline(n_basis=6, order=2))
np.testing.assert_almost_equal(
bs2.coefficients, np.atleast_2d([-375, -87.5, -75, 75, -175, 450]))
bs0 = bspline2.derivative(order=0)
bs1 = bspline2.derivative()
bs2 = bspline2.derivative(order=2)
np.testing.assert_equal(bs1.basis, BSpline(n_basis=4, order=3))
np.testing.assert_almost_equal(
bs1.coefficients,
[[30, -6, -9, -6], [36, 6, -3, -18], [12, 0, 0, 12]])
np.testing.assert_equal(bs0, bspline2)
np.testing.assert_equal(bs2.basis, BSpline(n_basis=3, order=2))
np.testing.assert_almost_equal(
bs2.coefficients, [[-144, -6, 12], [-120, -18, -60], [-48, 0, 48]])
def test_evaluation_derivative_monomial(self):
"""Test the evaluation of the derivative of a FDataBasis"""
monomial = Monomial(domain_range=(0, 1), n_basis=3)
coefficients = [[1, 2, 3], [0.5, 1.4, 1.3]]
f = FDataBasis(monomial, coefficients)
t = np.linspace(0, 1, 4)
f_deriv = f.derivative()
np.testing.assert_array_almost_equal(
f_deriv(t).round(3),
np.array([[2., 4., 6., 8.], [1.4, 2.267, 3.133, 4.]])[...,
np.newaxis])
def test_evaluation_derivative_bspline(self):
"""Test the evaluation of the derivative of a FDataBasis"""
bspline = BSpline(domain_range=(0, 1), n_basis=5, order=3)
coefficients = [[0.00078238, 0.48857741, 0.63971985, 0.23, 0.33],
[0.01778079, 0.73440271, 0.20148638, 0.54, 0.12]]
f = FDataBasis(bspline, coefficients)
t = np.linspace(0, 1, 4)
f_deriv = f.derivative()
np.testing.assert_array_almost_equal(
f_deriv(t).round(3),
np.array([[2.927, 0.453, -1.229, 0.6], [4.3, -1.599, 1.016,
-2.52]])[..., np.newaxis])
def test_evaluation_derivative_fourier(self):
"""Test the evaluation of the derivative of a FDataBasis"""
fourier = Fourier(domain_range=(0, 1), n_basis=3)
coefficients = np.array([[0.00078238, 0.48857741, 0.63971985],
[0.01778079, 0.73440271, 0.20148638]])
f = FDataBasis(fourier, coefficients)
t = np.linspace(0, 1, 4)
res = np.array([
4.34138447771721, -7.09352774867064, 2.75214327095343,
4.34138447771721, 6.52573053999253, -4.81336320468984,
-1.7123673353027, 6.52573053999253
]).reshape((2, 4, 1)).round(3)
f_deriv = f.derivative()
np.testing.assert_array_almost_equal(f_deriv(t).round(3), res)
def test_fdatabasis_derivative_fourier(self):
fourier = FDataBasis(Fourier(n_basis=7), [1, 5, 8, 9, 8, 4, 5])
fourier2 = FDataBasis(
Fourier(n_basis=5),
[[4, 9, 7, 4, 3], [1, 7, 9, 8, 5], [4, 6, 6, 6, 8]])
fou0 = fourier.derivative(order=0)
fou1 = fourier.derivative()
fou2 = fourier.derivative(order=2)
np.testing.assert_equal(fou1.basis, fourier.basis)
np.testing.assert_almost_equal(
fou1.coefficients.round(5),
np.atleast_2d([
0, -50.26548, 31.41593, -100.53096, 113.09734, -94.24778,
75.39822
]))
np.testing.assert_equal(fou0, fourier)
np.testing.assert_equal(fou2.basis, fourier.basis)
np.testing.assert_almost_equal(
fou2.coefficients.round(5),
np.atleast_2d([
0, -197.39209, -315.82734, -1421.22303, -1263.30936,
-1421.22303, -1776.52879
]))
fou0 = fourier2.derivative(order=0)
fou1 = fourier2.derivative()
fou2 = fourier2.derivative(order=2)
np.testing.assert_equal(fou1.basis, fourier2.basis)
np.testing.assert_almost_equal(
fou1.coefficients.round(5),
[[0, -43.98230, 56.54867, -37.69911, 50.26548],
[0, -56.54867, 43.98230, -62.83185, 100.53096],
[0, -37.69911, 37.69911, -100.53096, 75.39822]])
np.testing.assert_equal(fou0, fourier2)
np.testing.assert_equal(fou2.basis, fourier2.basis)
np.testing.assert_almost_equal(
fou2.coefficients.round(5),
[[0, -355.30576, -276.34892, -631.65468, -473.74101],
[0, -276.34892, -355.30576, -1263.30936, -789.56835],
[0, -236.87051, -236.87051, -947.48202, -1263.30936]])
