#!/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 = [coeff, 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 = [50, 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 = [40, 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)