def test_normalization_time():
ut = 10
tmin = 0
tmax = 100
int0 = integrate.quad(
lambda t: qtdmri.qtdmri_temporal_normalization(ut)**2 * qtdmri.
temporal_basis(0, ut, t) * qtdmri.temporal_basis(0, ut, t), tmin,
tmax)[0]
int1 = integrate.quad(
lambda t: qtdmri.qtdmri_temporal_normalization(ut)**2 * qtdmri.
temporal_basis(1, ut, t) * qtdmri.temporal_basis(1, ut, t), tmin,
tmax)[0]
int2 = integrate.quad(
lambda t: qtdmri.qtdmri_temporal_normalization(ut)**2 * qtdmri.
temporal_basis(2, ut, t) * qtdmri.temporal_basis(2, ut, t), tmin,
tmax)[0]
assert_almost_equal(int0, 1.)
assert_almost_equal(int1, 1.)
assert_almost_equal(int2, 1.)
def test_orthogonality_temporal_basis_functions():
# numerical integration parameters
ut = 10
tmin = 0
tmax = 100
int1 = integrate.quad(
lambda t: qtdmri.temporal_basis(1, ut, t) * qtdmri.temporal_basis(
2, ut, t), tmin, tmax)
int2 = integrate.quad(
lambda t: qtdmri.temporal_basis(2, ut, t) * qtdmri.temporal_basis(
3, ut, t), tmin, tmax)
int3 = integrate.quad(
lambda t: qtdmri.temporal_basis(3, ut, t) * qtdmri.temporal_basis(
4, ut, t), tmin, tmax)
int4 = integrate.quad(
lambda t: qtdmri.temporal_basis(4, ut, t) * qtdmri.temporal_basis(
5, ut, t), tmin, tmax)
assert_almost_equal(int1, 0.)
assert_almost_equal(int2, 0.)
assert_almost_equal(int3, 0.)
assert_almost_equal(int4, 0.)
def test_orthogonality_temporal_basis_functions():
# numerical integration parameters
ut = 10
tmin = 0
tmax = 100
int1 = integrate.quad(lambda t:
qtdmri.temporal_basis(1, ut, t) *
qtdmri.temporal_basis(2, ut, t), tmin, tmax)
int2 = integrate.quad(lambda t:
qtdmri.temporal_basis(2, ut, t) *
qtdmri.temporal_basis(3, ut, t), tmin, tmax)
int3 = integrate.quad(lambda t:
qtdmri.temporal_basis(3, ut, t) *
qtdmri.temporal_basis(4, ut, t), tmin, tmax)
int4 = integrate.quad(lambda t:
qtdmri.temporal_basis(4, ut, t) *
qtdmri.temporal_basis(5, ut, t), tmin, tmax)
assert_almost_equal(int1, 0.)
assert_almost_equal(int2, 0.)
assert_almost_equal(int3, 0.)
assert_almost_equal(int4, 0.)
def test_normalization_time():
ut = 10
tmin = 0
tmax = 100
int0 = integrate.quad(lambda t:
qtdmri.qtdmri_temporal_normalization(ut) ** 2 *
qtdmri.temporal_basis(0, ut, t) *
qtdmri.temporal_basis(0, ut, t), tmin, tmax)[0]
int1 = integrate.quad(lambda t:
qtdmri.qtdmri_temporal_normalization(ut) ** 2 *
qtdmri.temporal_basis(1, ut, t) *
qtdmri.temporal_basis(1, ut, t), tmin, tmax)[0]
int2 = integrate.quad(lambda t:
qtdmri.qtdmri_temporal_normalization(ut) ** 2 *
qtdmri.temporal_basis(2, ut, t) *
qtdmri.temporal_basis(2, ut, t), tmin, tmax)[0]
assert_almost_equal(int0, 1.)
assert_almost_equal(int1, 1.)
assert_almost_equal(int2, 1.)
