def test_rational_chebyshev_interpolation(show=False):
"""Test the inperpolation routine of ChebyshevRationalGrid"""
import numpy as np
from psecas import ChebyshevRationalGrid
def psi(x, c):
from numpy.polynomial.hermite import hermval
return hermval(x, c) * np.exp(-x**2 / 2)
N = 95
grid = ChebyshevRationalGrid(N, C=4)
grid_fine = ChebyshevRationalGrid(N * 4, C=1)
z = grid_fine.zg
y = psi(grid.zg, np.array(np.ones(4)))
y_fine = psi(z, np.array(np.ones(4)))
y_interpolated = grid.interpolate(z, y)
if show:
import matplotlib.pyplot as plt
plt.figure(3)
plt.clf()
plt.title("Interpolation with rational Chebyshev")
plt.plot(z, y_fine, "-")
plt.plot(z, y_interpolated, "--")
plt.plot(grid.zg, y, "+")
plt.xlim(-15, 15)
plt.show()
np.testing.assert_allclose(y_fine, y_interpolated, atol=1e-12)
return (y_fine, y_interpolated)
fig, axes = plt.subplots(num=1, ncols=2, nrows=modes, sharex=True,
sharey='col')
for mode in range(modes):
# List of resolutions to try
Ns = np.hstack((np.arange(3, 6) * 32, np.arange(4, 12) * 64))
# Solve the system to a given tolerance
K2, vec, err = solver.iterate_solver(
Ns, mode=mode, verbose=True, tol=1e-8, guess_tol=1e-3
)
# Plottting
phi = np.arctan(vec[2].imag / vec[2].real)
A = np.max(np.abs(vec))
solver.keep_result(K2, vec * np.exp(-1j * phi)/A, mode=mode)
axes[mode, 1].set_title(
r"$K_n H = ${:1.4f}".format(np.sqrt(K2.real)), fontsize=10
)
zfine = np.linspace(-4, 4, 5000)
axes[mode, 1].plot(zfine, grid.interpolate(zfine, system.result['G'].real))
axes[mode, 1].plot(grid.zg, system.result['G'].real, '.')
axes[mode, 1].set_xlim(-4, 4)
axes[mode, 1].set_ylim(-1.3, 1.3)
F = -1/(system.h*np.sqrt(K2.real))*grid.der(system.result['G'])
axes[mode, 0].plot(grid.zg, F.real, '-')
axes[mode, 0].set_xlim(-4, 4)
axes[mode, 0].set_ylim(-3, 3)
axes[mode, 0].set_label(r'$z$')
axes[mode, 1].set_label(r'$z$')
plt.show()