def nsev_inverse_example2():
"""nsev_inverse_example: create a N=2.2 Satsuma-Yajima pulse from nonlinear spectrum."""
D = 1024
M = 2 * D
Tmax = 15
tvec = np.linspace(-Tmax, Tmax, D)
# calculate suitable frequency bonds (xi)
rv, xi = nsev_inverse_xi_wrapper(D, tvec[0], tvec[-1], M)
xivec = xi[0] + np.arange(M) * (xi[1] - xi[0]) / (M - 1)
# analytic field: chirp-free N=2.2 Satsuma-Yajima pulse
q = 2.2 / np.cosh(tvec)
# semi-analytic nonlinear spectrum
bound_states = np.array([0.7j, 1.7j])
disc_norming_const_ana = [1.0, -1.0]
cont_b_ana = 0.587783 / np.cosh(xivec * np.pi) * np.exp(1.0j * np.pi)
# call the function
res = nsev_inverse(xivec, tvec, cont_b_ana, bound_states, disc_norming_const_ana, cst=1, dst=0)
print("\n----- options used ----")
print(res['options'])
print("\n------ results --------")
print("FNFT return value: %d (should be 0)" % res['return_value'])
# compare result to analytic function
print("nsev-inverse example: Satsuma-Yajima N=2.2")
print("Difference analytic - numeric: sum((q_ana-q_num)**2) = %.2e (should be approx 0) " % np.sum(
np.abs(q - res['q']) ** 2))
return res
def nsev_inverse_example():
"""Mimics the C example for calling fnft_nsev_inverse."""
print("\nnsev inverse example")
# set values
M = 2048
D = 1024
tvec = np.linspace(-2, 2, D)
T1 = tvec[0]
T2 = tvec[-1]
alpha = 2.0
beta = 0.55
gamma = np.sqrt( np.abs(alpha)**2 + np.abs(beta)**2)
kappa = 1
# get the frequency intervall suited for the given time vector
rv, XI = nsev_inverse_xi_wrapper(D, T1, T2, M)
Xi1 = XI[0]
Xi2 = XI[1]
xivec = XI[0] + np.arange(M) * (XI[1] - XI[0]) / (M - 1)
# set continuous spectrum
contspec = alpha / (xivec - beta * 1.0j)
# set discrete spectrum
bound_states = np.array([1.0j * beta])
normconst_or_residues = np.array([-1.0j * alpha / (gamma + beta)])
# call function
res = nsev_inverse(xivec, tvec, contspec, bound_states, normconst_or_residues)
# print results
print("\n----- options used ----")
print(res['options'])
print("\n------ results --------")
print("FNFT return value: %d (should be 0)" % res['return_value'])
print("Total number of samples calculated: %d" % D)
print("some samples:")
for i in range(0, D, 64):
print(" %d : q(t=%.5f) = %.5e + %.5e j " % (i, tvec[i],
np.real(res['q'][i]),
np.imag(res['q'][i])))
res['Xi'] = np.array([Xi1,Xi2])
return res
def setUp(self):
D = 512
M = 2 * D
Tmax = 15
tvec = np.linspace(-Tmax, Tmax, D)
rv, xi = nsev_inverse_xi_wrapper(D, tvec[0], tvec[-1], M)
xivec = xi[0] + np.arange(M) * (xi[1] - xi[0]) / (M - 1)
# semi-analytic nonlinear spectrum
bound_states = np.array([0.7j, 1.7j])
disc_norming_const_ana = [1.0, -1.0]
cont_b_ana = 0.587783 / np.cosh(xivec * np.pi) * np.exp(1.0j * np.pi)
self.xivec = xivec
self.tvec = tvec
self.cont_b_ana = cont_b_ana
self.bound_states = bound_states
self.disc_norming_const_ana = disc_norming_const_ana
self.expected = {
'qsamprange': [0, -1, 40],
'q_both': np.array(
[1.34282821e-06 + 5.90905693e-16j, 1.40927340e-05 + 6.69759843e-16j,
1.47533087e-04 - 8.49415093e-16j, 1.54437857e-03 + 1.22641929e-16j,
1.61660017e-02 + 2.70942564e-15j, 1.68966183e-01 + 9.95269660e-15j,
1.52429449e+00 + 1.04462643e-14j, 9.88595941e-01 + 1.57705840e-14j,
9.97145517e-02 + 6.45254951e-15j, 9.53104365e-03 + 1.87953249e-15j,
9.10510486e-04 - 5.58634639e-16j, 8.69798167e-05 - 7.22303874e-16j,
8.30772437e-06 + 9.63333629e-16j]),
'q_disc': np.array(
[5.09548061e-09 - 0.j, 1.36459139e-07 - 0.j, 3.65443384e-06 - 0.j,
9.78673225e-05 - 0.j, 2.62101136e-03 - 0.j, 7.03972926e-02 - 0.j,
1.69330859e+00 - 0.j, 9.18642908e-01 + 0.j, 3.35346003e-02 + 0.j,
1.25083775e-03 + 0.j, 4.67066469e-05 + 0.j, 1.74405899e-06 + 0.j,
6.51243941e-08 + 0.j]),
'q_cont': np.array(
[1.15243924e-07 - 6.57512209e-16j, 1.27802639e-06 + 7.04459178e-16j,
1.34080356e-05 + 2.15209454e-16j, 1.40365068e-04 - 1.10360319e-15j,
1.46934384e-03 + 4.21307084e-16j, 1.53587945e-02 + 2.81885851e-15j,
1.38560954e-01 + 1.43110043e-14j, 8.98666443e-02 + 8.74350146e-15j,
9.06369089e-03 + 2.14242869e-15j, 8.66276590e-04 - 1.04369988e-16j,
8.27537156e-05 - 9.43644219e-16j, 7.90416963e-06 + 6.57722413e-16j,
7.51076324e-07 + 6.32640626e-16j]),
'q_none': np.array(
[[0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j, 0. + 0.j,
0. + 0.j, 0. + 0.j, 0. + 0.j]])}