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#!/usr/bin/python
import brill_data
import numpy as np
import sys
def eval_residual_coeffs(bd, x, z):
X, Z = np.meshgrid(x, z)
psi = bd.eval_psi(x, z)
d2psi_x = bd.eval_psi(x, z, (2, 0))
d2psi_z = bd.eval_psi(x, z, (0, 2))
dpsi_x = bd.eval_psi(x, z, (1, 0))
d2psi_y = np.where(np.abs(X) < 1e-12, d2psi_x, dpsi_x / X)
d2q = bd.eval_q(x, z, (2, 0)) + bd.eval_q(x, z, (0, 2))
d2psi = d2psi_x + d2psi_y + d2psi_z
return d2psi + 0.25 * psi * d2q
coeffs = (10, 15, 20, 25, 30, 40, 50, 60, 80, 100)
amplitudes = (1, 2, 4, 6)
x = np.linspace(0, 10, 100)
z = np.linspace(0, 10, 100)
err_coeffs = [
[ 1, 0.01, 0.001, 5e-7, 1e-8, 1e-11, 1e-12, 5e-13, 1e-13, 1e-13 ], # amplitude 1
[ 5, 0.1, 5e-4, 5e-7, 5e-8, 5e-11, 5e-12, 5e-11, 1e-13, 1e-13 ], # amplitude 2
[ 5, 1, 5e-3, 1e-6, 5e-8, 1e-10, 1e-11, 5e-12, 5e-13, 5e-13 ], # amplitude 4
[ 5, 15, 1e-2, 1e-5, 1e-7, 5e-10, 5e-11, 5e-12, 5e-13, 1e-12 ], # amplitude 6
]
sys.stderr.write('Testing convergence of the residual calculated by spectral derivatives\n')
for amplitude, err_row in zip(amplitudes, err_coeffs):
sys.stderr.write('amplitude: %d\n' % amplitude)
for coeff, err_ref in zip(coeffs, err_row):
sys.stderr.write('coeffs: %dx%d ' % (coeff, coeff))
BD = brill_data.BrillData(nb_coeffs_rho = coeff, amplitude = amplitude)
error = np.max(np.abs(eval_residual_coeffs(BD, x, z)))
sys.stderr.write('calculated error %g, reference %g\n' % (error, err_ref))
if error > err_ref:
sys.stderr.write('Test FAILED\n')
sys.exit(1)
def eval_residual_fd(bd, x, y, z):
Z, Y, X = np.meshgrid(z, y, x, indexing = 'ij')
psi = np.empty_like(Z)
d2q = np.empty_like(Z)
for i, yy in enumerate(y):
rho = np.sqrt(x ** 2 + yy ** 2)
stuff = bd.eval_psi(rho, z)
psi[:, i] = bd.eval_psi(rho, z)
d2q[:, i] = bd.eval_q(rho, z, (2, 0)) + bd.eval_q(rho, z, (0, 2))
dpsi_z, dpsi_y, dpsi_x = np.gradient(psi, z[1] - z[0], y[1] - y[0], x[1] - x[0])
d2psi_z, foo, foo = np.gradient(dpsi_z, z[1] - z[0], y[1] - y[0], x[1] - x[0])
foo, d2psi_y, foo = np.gradient(dpsi_y, z[1] - z[0], y[1] - y[0], x[1] - x[0])
foo, foo, d2psi_x = np.gradient(dpsi_x, z[1] - z[0], y[1] - y[0], x[1] - x[0])
d2psi = d2psi_x + d2psi_y + d2psi_z
return (d2psi + 0.25 * psi * d2q)[2:-2, 2:-2, 2:-2]
return (d2psi + 0.25 * psi * d2q)[2:-2, 2:-2, 2:-2]
points = [ 100, 500, 1000 ]
err_fd = [ 1e-2, 5e-4, 1e-4 ]
sys.stderr.write('Testing convergence of the residual calculated by finite difference derivatives\n')
BD = brill_data.BrillData(nb_coeffs_rho = 50, amplitude = 5)
for point, err_ref in zip(points, err_fd):
x = np.linspace(-1, 1, point)
y = np.linspace(-3 * (x[1] - x[0]), 3 * (x[1] - x[0]), 7)
z = np.linspace(-1, 1, point)
sys.stderr.write('number of points: %d\n' % point)
error = np.max(np.abs(eval_residual_fd(BD, x, y, z)))
sys.stderr.write('calculated error %g, reference %g\n' % (error, err_ref))
if error > err_ref:
sys.stderr.write('Test FAILED\n')
sys.exit(1)
sys.stderr.write('Testing metric evaluation\n')
rho = np.linspace(0, 1, 100)
z = np.linspace(0, 1, 100)
err_metric = [
[ 5e-3, 5e-4, 1e-2, 5e-3, 1e-3 ], # component 00
[ 5e-3, 5e-4, 1e-2, 5e-3, 1e-3 ], # component 11
[ 5e-4, 5e-5, 5e-4, 1e-4, 1e-4 ], # component 22
]
BD = brill_data.BrillData(nb_coeffs_rho = 40, amplitude = 3)
for c, err_row in zip(xrange(3), err_metric):
sys.stderr.write('component %d%d\n' % (c, c))
metric = BD.eval_metric(rho, z, (c, c))
dmetric_rho = BD.eval_metric(rho, z, (c, c), (1, 0))
dmetric_z = BD.eval_metric(rho, z, (c, c), (0, 1))
d2metric_rho_z = BD.eval_metric(rho, z, (c, c), (1, 1))
d2metric_rho = BD.eval_metric(rho, z, (c, c), (2, 0))
d2metric_z = BD.eval_metric(rho, z, (c, c), (0, 2))
emetric_z, emetric_rho = np.gradient(metric, z[1] - z[0], rho[1] - rho[0])
e2metric_rho_z, e2metric_rho = np.gradient(dmetric_rho, z[1] - z[0], rho[1] - rho[0])
e2metric_z, foo = np.gradient(dmetric_z, z[1] - z[0], rho[1] - rho[0])
err = np.max(np.abs((dmetric_rho - emetric_rho)[3:-3, 3:-3]))
err_ref = err_row[0]
sys.stderr.write('calculated error for d/drho %g, reference %g\n' % (err, err_ref))
if err > err_ref:
sys.stderr.write('Test FAILED\n')
sys.exit(1)
err = np.max(np.abs((dmetric_z - emetric_z)[3:-3, 3:-3]))
err_ref = err_row[1]
sys.stderr.write('calculated error for d/dz %g, reference %g\n' % (err, err_ref))
if err > err_ref:
sys.stderr.write('Test FAILED\n')
sys.exit(1)
err = np.max(np.abs((d2metric_rho - e2metric_rho)[3:-3, 3:-3]))
err_ref = err_row[2]
sys.stderr.write('calculated error for d2/drho2 %g, reference %g\n' % (err, err_ref))
if err > err_ref:
sys.stderr.write('Test FAILED\n')
sys.exit(1)
err = np.max(np.abs((d2metric_z - e2metric_z)[3:-3, 3:-3]))
err_ref = err_row[3]
sys.stderr.write('calculated error for d2/dz2 %g, reference %g\n' % (err, err_ref))
if err > err_ref:
sys.stderr.write('Test FAILED\n')
sys.exit(1)
err = np.max(np.abs((d2metric_rho_z - e2metric_rho_z)[3:-3, 3:-3]))
err_ref = err_row[4]
sys.stderr.write('calculated error for d2/drhodz %g, reference %g\n' % (err, err_ref))
if err > err_ref:
sys.stderr.write('Test FAILED\n')
sys.exit(1)
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