def test_orthogonality_basis_functions():
# numerical integration parameters
diffusivity = 0.0015
qmin = 0
qmax = 1000
int1 = integrate.quad(
lambda x: np.real(mapmri.mapmri_phi_1d(0, x, diffusivity)) * np.real(
mapmri.mapmri_phi_1d(2, x, diffusivity)), qmin, qmax)[0]
int2 = integrate.quad(
lambda x: np.real(mapmri.mapmri_phi_1d(2, x, diffusivity)) * np.real(
mapmri.mapmri_phi_1d(4, x, diffusivity)), qmin, qmax)[0]
int3 = integrate.quad(
lambda x: np.real(mapmri.mapmri_phi_1d(4, x, diffusivity)) * np.real(
mapmri.mapmri_phi_1d(6, x, diffusivity)), qmin, qmax)[0]
int4 = integrate.quad(
lambda x: np.real(mapmri.mapmri_phi_1d(6, x, diffusivity)) * np.real(
mapmri.mapmri_phi_1d(8, x, diffusivity)), qmin, qmax)[0]
# checking for first 5 basis functions if they are indeed orthogonal
assert_almost_equal(int1, 0.)
assert_almost_equal(int2, 0.)
assert_almost_equal(int3, 0.)
assert_almost_equal(int4, 0.)
# do the same for the isotropic mapmri basis functions
# we already know the spherical harmonics are orthonormal
# only check j>0, l=0 basis functions
C1 = mapmri.mapmri_isotropic_radial_pdf_basis(1, 0, diffusivity, 0)
C2 = mapmri.mapmri_isotropic_radial_pdf_basis(2, 0, diffusivity, 0)
C3 = mapmri.mapmri_isotropic_radial_pdf_basis(3, 0, diffusivity, 0)
C4 = mapmri.mapmri_isotropic_radial_pdf_basis(4, 0, diffusivity, 0)
C5 = mapmri.mapmri_isotropic_radial_pdf_basis(4, 0, diffusivity, 0)
int1 = integrate.quad(
lambda q: mapmri.mapmri_isotropic_radial_signal_basis(
1, 0, diffusivity, q) * mapmri.
mapmri_isotropic_radial_signal_basis(2, 0, diffusivity, q) * q**2,
qmin, qmax)[0]
int2 = integrate.quad(
lambda q: mapmri.mapmri_isotropic_radial_signal_basis(
2, 0, diffusivity, q) * mapmri.
mapmri_isotropic_radial_signal_basis(3, 0, diffusivity, q) * q**2,
qmin, qmax)[0]
int3 = integrate.quad(
lambda q: mapmri.mapmri_isotropic_radial_signal_basis(
3, 0, diffusivity, q) * mapmri.
mapmri_isotropic_radial_signal_basis(4, 0, diffusivity, q) * q**2,
qmin, qmax)[0]
int4 = integrate.quad(
lambda q: mapmri.mapmri_isotropic_radial_signal_basis(
4, 0, diffusivity, q) * mapmri.
mapmri_isotropic_radial_signal_basis(5, 0, diffusivity, q) * q**2,
qmin, qmax)[0]
# checking for first 5 basis functions if they are indeed orthogonal
assert_almost_equal(int1, 0.)
assert_almost_equal(int2, 0.)
assert_almost_equal(int3, 0.)
assert_almost_equal(int4, 0.)
def test_orthogonality_basis_functions():
# numerical integration parameters
diffusivity = 0.0015
qmin = 0
qmax = 1000
int1 = integrate.quad(lambda x:
np.real(mapmri.mapmri_phi_1d(0, x, diffusivity)) *
np.real(mapmri.mapmri_phi_1d(2, x, diffusivity)),
qmin, qmax)[0]
int2 = integrate.quad(lambda x:
np.real(mapmri.mapmri_phi_1d(2, x, diffusivity)) *
np.real(mapmri.mapmri_phi_1d(4, x, diffusivity)),
qmin, qmax)[0]
int3 = integrate.quad(lambda x:
np.real(mapmri.mapmri_phi_1d(4, x, diffusivity)) *
np.real(mapmri.mapmri_phi_1d(6, x, diffusivity)),
qmin, qmax)[0]
int4 = integrate.quad(lambda x:
np.real(mapmri.mapmri_phi_1d(6, x, diffusivity)) *
np.real(mapmri.mapmri_phi_1d(8, x, diffusivity)),
qmin, qmax)[0]
# checking for first 5 basis functions if they are indeed orthogonal
assert_almost_equal(int1, 0.)
assert_almost_equal(int2, 0.)
assert_almost_equal(int3, 0.)
assert_almost_equal(int4, 0.)
# do the same for the isotropic mapmri basis functions
# we already know the spherical harmonics are orthonormal
# only check j>0, l=0 basis functions
int1 = integrate.quad(lambda q:
mapmri.mapmri_isotropic_radial_signal_basis(
1, 0, diffusivity, q) *
mapmri.mapmri_isotropic_radial_signal_basis(
2, 0, diffusivity, q) * q ** 2, qmin, qmax)[0]
int2 = integrate.quad(lambda q:
mapmri.mapmri_isotropic_radial_signal_basis(
2, 0, diffusivity, q) *
mapmri.mapmri_isotropic_radial_signal_basis(
3, 0, diffusivity, q) * q ** 2, qmin, qmax)[0]
int3 = integrate.quad(lambda q:
mapmri.mapmri_isotropic_radial_signal_basis(
3, 0, diffusivity, q) *
mapmri.mapmri_isotropic_radial_signal_basis(
4, 0, diffusivity, q) * q ** 2, qmin, qmax)[0]
int4 = integrate.quad(lambda q:
mapmri.mapmri_isotropic_radial_signal_basis(
4, 0, diffusivity, q) *
mapmri.mapmri_isotropic_radial_signal_basis(
5, 0, diffusivity, q) * q ** 2, qmin, qmax)[0]
# checking for first 5 basis functions if they are indeed orthogonal
assert_almost_equal(int1, 0.)
assert_almost_equal(int2, 0.)
assert_almost_equal(int3, 0.)
assert_almost_equal(int4, 0.)