def test_ns_mmq_2site_korzhnev_2005_15n_dq_data_complex128(self):
"""Test the matrix_exponential() function for higher dimensional data, and compare to matrix_exponential. This uses the data from systemtest Relax_disp.test_korzhnev_2005_15n_dq_data.
This test does the matrix exponential in complex128."""
fname = self.data + sep+ "test_korzhnev_2005_15n_dq_data"
M0, R20A, R20B, pA, dw, dwH, kex, inv_tcpmg, tcp, num_points, power, back_calc, pB, k_BA, k_AB = self.return_data_mmq_2site(fname)
# Extract the total numbers of experiments, number of spins, number of magnetic field strength, number of offsets, maximum number of dispersion point.
NS, NM, NO = num_points.shape
# Populate the m1 and m2 matrices (only once per function call for speed).
m1_mat = rmmq_2site_rankN(R20A=R20A, R20B=R20B, dw=dw, k_AB=k_AB, k_BA=k_BA, tcp=tcp)
m2_mat = rmmq_2site_rankN(R20A=R20A, R20B=R20B, dw=-dw, k_AB=k_AB, k_BA=k_BA, tcp=tcp)
# The A+/- matrices.
A_pos_mat = matrix_exponential(m1_mat)
A_neg_mat = matrix_exponential(m2_mat)
# Loop over spins.
for si in range(NS):
# Loop over the spectrometer frequencies.
for mi in range(NM):
# Loop over offsets:
for oi in range(NO):
# Extract number of points.
num_points_i = num_points[si, mi, oi]
# Loop over the time points, back calculating the R2eff values.
for i in range(num_points_i):
# Test the two different methods.
# The A+/- matrices.
A_pos_i = A_pos_mat[si, mi, oi, i]
A_neg_i = A_neg_mat[si, mi, oi, i]
# The lower dimensional matrix exponential.
A_pos = np_matrix_exponential(m1_mat[si, mi, oi, i])
A_neg = np_matrix_exponential(m2_mat[si, mi, oi, i])
# Calculate differences
diff_A_pos_real = A_pos_i.real - A_pos.real
diff_A_pos_real_sum = sum(diff_A_pos_real)
diff_A_pos_imag = A_pos_i.imag - A_pos.imag
diff_A_pos_imag_sum = sum(diff_A_pos_imag)
diff_A_neg_real = A_neg_i.real - A_neg.real
diff_A_neg_real_sum = sum(diff_A_neg_real)
diff_A_neg_imag = A_neg_i.imag - A_neg.imag
diff_A_neg_imag_sum = sum(diff_A_neg_imag)
# Test that the sum difference is zero.
self.assertAlmostEqual(diff_A_pos_real_sum, 0.0)
self.assertAlmostEqual(diff_A_pos_imag_sum, 0.0)
self.assertAlmostEqual(diff_A_neg_real_sum, 0.0)
self.assertAlmostEqual(diff_A_neg_imag_sum, 0.0)
def test_ns_cpmg_2site_3d_hansen_cpmg_data(self):
"""Test the matrix_exponential() function for higher dimensional data, and compare to matrix_exponential. This uses the data from systemtest Relax_disp.test_hansen_cpmg_data_to_ns_cpmg_2site_3D."""
fname = self.data + sep + "test_hansen_cpmg_data_to_ns_cpmg_2site_3D"
r180x, M0, r10a, r10b, r20a, r20b, pA, dw, dw_orig, kex, inv_tcpmg, tcp, num_points, power, back_calc, pB, k_BA, k_AB = self.return_data_ns_cpmg_2site_3d(
fname)
# Extract the total numbers of experiments, number of spins, number of magnetic field strength, number of offsets, maximum number of dispersion point.
NE, NS, NM, NO, ND = back_calc.shape
# The matrix R that contains all the contributions to the evolution, i.e. relaxation, exchange and chemical shift evolution.
R_mat = rcpmg_3d_rankN(R1A=r10a,
R1B=r10b,
R2A=r20a,
R2B=r20b,
pA=pA,
pB=pB,
dw=dw,
k_AB=k_AB,
k_BA=k_BA,
tcp=tcp)
# This matrix is a propagator that will evolve the magnetization with the matrix R for a delay tcp.
Rexpo_mat = matrix_exponential(R_mat)
# Loop over the spins
for si in range(NS):
# Loop over the spectrometer frequencies.
for mi in range(NM):
# Extract number of points.
num_points_si_mi = int(num_points[0, si, mi, 0])
# Loop over the time points, back calculating the R2eff values.
for di in range(num_points_si_mi):
# Test the two different methods.
R_mat_i = R_mat[0, si, mi, 0, di]
# The lower dimensional matrix exponential.
Rexpo = np_matrix_exponential(R_mat_i)
# The higher dimensional matrix exponential.
Rexpo_mat_i = Rexpo_mat[0, si, mi, 0, di]
diff = Rexpo - Rexpo_mat_i
diff_sum = sum(diff)
# Test that the sum difference is zero.
self.assertAlmostEqual(diff_sum, 0.0)
def test_ns_cpmg_2site_3d_hansen_cpmg_data(self):
"""Test the matrix_exponential() function for higher dimensional data, and compare to matrix_exponential. This uses the data from systemtest Relax_disp.test_hansen_cpmg_data_to_ns_cpmg_2site_3D."""
fname = self.data + sep+ "test_hansen_cpmg_data_to_ns_cpmg_2site_3D"
r180x, M0, r10a, r10b, r20a, r20b, pA, dw, dw_orig, kex, inv_tcpmg, tcp, num_points, power, back_calc, pB, k_BA, k_AB = self.return_data_ns_cpmg_2site_3d(fname)
# Extract the total numbers of experiments, number of spins, number of magnetic field strength, number of offsets, maximum number of dispersion point.
NE, NS, NM, NO, ND = back_calc.shape
# The matrix R that contains all the contributions to the evolution, i.e. relaxation, exchange and chemical shift evolution.
R_mat = rcpmg_3d_rankN(R1A=r10a, R1B=r10b, R2A=r20a, R2B=r20b, pA=pA, pB=pB, dw=dw, k_AB=k_AB, k_BA=k_BA, tcp=tcp)
# This matrix is a propagator that will evolve the magnetization with the matrix R for a delay tcp.
Rexpo_mat = matrix_exponential(R_mat)
# Loop over the spins
for si in range(NS):
# Loop over the spectrometer frequencies.
for mi in range(NM):
# Extract number of points.
num_points_si_mi = int(num_points[0, si, mi, 0])
# Loop over the time points, back calculating the R2eff values.
for di in range(num_points_si_mi):
# Test the two different methods.
R_mat_i = R_mat[0, si, mi, 0, di]
# The lower dimensional matrix exponential.
Rexpo = np_matrix_exponential(R_mat_i)
# The higher dimensional matrix exponential.
Rexpo_mat_i = Rexpo_mat[0, si, mi, 0, di]
diff = Rexpo - Rexpo_mat_i
diff_sum = sum(diff)
# Test that the sum difference is zero.
self.assertAlmostEqual(diff_sum, 0.0)
def test_ns_mmq_2site_korzhnev_2005_15n_dq_data_complex128(self):
"""Test the matrix_exponential() function for higher dimensional data, and compare to matrix_exponential. This uses the data from systemtest Relax_disp.test_korzhnev_2005_15n_dq_data.
This test does the matrix exponential in complex128."""
fname = self.data + sep + "test_korzhnev_2005_15n_dq_data"
M0, R20A, R20B, pA, dw, dwH, kex, inv_tcpmg, tcp, num_points, power, back_calc, pB, k_BA, k_AB = self.return_data_mmq_2site(
fname)
# Extract the total numbers of experiments, number of spins, number of magnetic field strength, number of offsets, maximum number of dispersion point.
NS, NM, NO = num_points.shape
# Populate the m1 and m2 matrices (only once per function call for speed).
m1_mat = rmmq_2site_rankN(R20A=R20A,
R20B=R20B,
dw=dw,
k_AB=k_AB,
k_BA=k_BA,
tcp=tcp)
m2_mat = rmmq_2site_rankN(R20A=R20A,
R20B=R20B,
dw=-dw,
k_AB=k_AB,
k_BA=k_BA,
tcp=tcp)
# The A+/- matrices.
A_pos_mat = matrix_exponential(m1_mat)
A_neg_mat = matrix_exponential(m2_mat)
# Loop over spins.
for si in range(NS):
# Loop over the spectrometer frequencies.
for mi in range(NM):
# Loop over offsets:
for oi in range(NO):
# Extract number of points.
num_points_i = num_points[si, mi, oi]
# Loop over the time points, back calculating the R2eff values.
for i in range(num_points_i):
# Test the two different methods.
# The A+/- matrices.
A_pos_i = A_pos_mat[si, mi, oi, i]
A_neg_i = A_neg_mat[si, mi, oi, i]
# The lower dimensional matrix exponential.
A_pos = np_matrix_exponential(m1_mat[si, mi, oi, i])
A_neg = np_matrix_exponential(m2_mat[si, mi, oi, i])
# Calculate differences
diff_A_pos_real = A_pos_i.real - A_pos.real
diff_A_pos_real_sum = sum(diff_A_pos_real)
diff_A_pos_imag = A_pos_i.imag - A_pos.imag
diff_A_pos_imag_sum = sum(diff_A_pos_imag)
diff_A_neg_real = A_neg_i.real - A_neg.real
diff_A_neg_real_sum = sum(diff_A_neg_real)
diff_A_neg_imag = A_neg_i.imag - A_neg.imag
diff_A_neg_imag_sum = sum(diff_A_neg_imag)
# Test that the sum difference is zero.
self.assertAlmostEqual(diff_A_pos_real_sum, 0.0)
self.assertAlmostEqual(diff_A_pos_imag_sum, 0.0)
self.assertAlmostEqual(diff_A_neg_real_sum, 0.0)
self.assertAlmostEqual(diff_A_neg_imag_sum, 0.0)