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wave_tools_test.py
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wave_tools_test.py
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#!/usr/bin/env python3
import sys, os
import unittest
import numpy as np
from wave_tools import shoaling_1d, surface_core
from help_tools import convolution, plotting_interface
import matplotlib.pyplot as plt
#TODO make sure all dimensions are tested!
class SeaSurface(unittest.TestCase):
def setUp(self, plot_it=False):
self.name = r'$\eta$'
self.Nx = 64#1024
self.Ny = 64#2*1024
self.x = np.linspace(-250, 250, self.Nx, endpoint=True)
self.y = np.linspace(0, 500, self.Ny, endpoint=True)
self.kx = 0.0#66
self.ky = 0.066
self.k = np.sqrt(self.kx**2 + self.ky**2)
grid_cut_off = [0.15, 0.15]
self.xx, self.yy = np.meshgrid(self.x, self.y, indexing='ij')
self.eta = 5*np.sin(self.kx*self.xx + self.ky*self.yy)
self.surf2d = surface_core.Surface(self.name, self.eta, [self.x,self.y])
self.spec2d = self.surf2d.define_SpectralAnalysis(grid_cut_off)
if plot_it:
plt.figure()
plt.imshow(self.eta)
plt.figure()
plt.imshow(self.surf2d.etaND.eta)
plt.show()
def test_inversion(self):
surf2d_inversion = self.spec2d.invert('inversion_test', grid_offset=[self.x[0], self.y[0]])
for i in range(0, self.Nx):
for j in range(0, self.Ny):
self.assertAlmostEqual(surf2d_inversion.etaND.eta[i,j], self.eta[i,j])
for i in range(0, self.Nx):
self.assertAlmostEqual(self.x[i], surf2d_inversion.etaND.x[i])
for i in range(0, self.Ny):
self.assertAlmostEqual(self.y[i], surf2d_inversion.etaND.y[i])
def test_name(self):
self.assertEqual(self.name, self.surf2d.get_name())
def test_1dconvolution(self, plot_it=False):
N = len(self.x)
mat1 = np.sin(self.kx*self.x)
mat2 = self.x**2
mat2 /= np.max(mat2)
Res1 = np.fft.fftshift(np.fft.fft(mat1 * mat2))/N
mat1_hat = np.fft.fftshift(np.fft.fft(mat1))/N
mat2_hat = np.fft.fftshift(np.fft.fft(mat2))/N
Res2 = np.convolve(mat1_hat, mat2_hat)[self.Nx//2:self.Nx//2+self.Nx]
if plot_it:
plt.subplot(2,1,1)
plt.plot(Res1.real)
plt.plot(Res2.real)
plt.subplot(2,1,2)
plt.plot(Res1.imag)
plt.plot(Res2.imag)
plt.show()
for i in range(0, self.Nx):
self.assertAlmostEqual(Res1[i], Res2[i])
def test_2dconvolution(self, plot_it=False):
mat2 = self.xx + self.yy
mat2 /= np.max(mat2)
Res1 = np.fft.fftshift(np.fft.fft2(self.eta*mat2))/(self.Nx*self.Ny)
F_mat1 = np.fft.fftshift(np.fft.fft2(self.eta))/(self.Nx*self.Ny)
F_mat2 = np.fft.fftshift(np.fft.fft2(mat2))/(self.Nx*self.Ny)
Res2 = convolution.convolve2d(F_mat1, F_mat2)
if plot_it:
plt.imshow(np.abs(Res1))
plt.figure()
plt.imshow(np.abs(Res2))
plt.show()
for i in range(0, self.Nx):
for j in range(0, self.Ny):
self.assertAlmostEqual(Res1[i,j], Res2[i,j])
def test_fft_interpol(self, plot_it=False):
inter_factor_x = 4
inter_factor_y = 4
Nx = 1000
Ny = 1000
x = np.linspace(0,10*np.pi, inter_factor_x * Nx )
eta = np.sin(x)
x_coarse = x[::inter_factor_x]
eta_coarse = np.sin(x_coarse)
surf1d = surface_core.Surface('test', eta_coarse, [x_coarse])
surf1d_interpol = surf1d.fft_interpolate(inter_factor_x)
if plot_it:
plt.plot(x,eta)
plt.plot(surf1d_interpol.x, surf1d_interpol.eta)
for i in range(int(0.1*Nx*inter_factor_x), int(0.9*Nx*inter_factor_x-10)):
self.assertAlmostEqual(np.round(eta[i],1), np.round(surf1d_interpol.eta[i],1))
self.assertAlmostEqual(np.round(x[i],2), np.round(surf1d_interpol.x[i],2))
y = np.linspace(0,10*np.pi, inter_factor_y * Ny)
y_coarse = y[::inter_factor_y]
kx = 1
ky = 1
xx, yy = np.meshgrid(x, y, indexing='ij')
xx_coarse, yy_coarse = np.meshgrid(x_coarse, y_coarse, indexing='ij')
eta2d = np.sin(kx*xx + ky*yy)
eta2d_coarse = np.sin(kx*xx_coarse + ky*yy_coarse)
surf2d_coarse = surface_core.Surface('test2d', eta2d_coarse, [x_coarse, y_coarse])
surf2d_interpol = surf2d_coarse.fft_interpolate(inter_factor_x, inter_factor_y)
if plot_it:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(x,eta2d[:,50])
plt.plot(surf2d_interpol.x, surf2d_interpol.eta[:,50])
plt.figure()
plt.plot(y, eta2d[20,:])
plt.plot(surf2d_interpol.y, surf2d_interpol.eta[20,:])
plt.show()
for i in range(int(0.1*inter_factor_x*Nx), int(0.9*inter_factor_x*Nx)):
self.assertAlmostEqual(np.round(x[i],2), np.round(surf2d_interpol.x[i],2))
for j in range(int(0.1*inter_factor_y*Ny), int(0.9*inter_factor_y*Ny)):
self.assertAlmostEqual(np.round(eta2d[50,j],1), np.round(surf2d_interpol.eta[50,j],1))
self.assertAlmostEqual(np.round(y[j],2), np.round(surf2d_interpol.y[j],2))
def test_get_sub_surface(self):
Nx = 128
Ny = 128
x = np.linspace(-500, 500, Nx, endpoint=True)
y = np.linspace(0, 500, Ny, endpoint=True)
xx, yy = np.meshgrid(x, y, indexing='ij')
eta2d = 5*np.sin(self.kx*xx + self.ky*yy)
surf2d = surface_core.Surface('test', eta2d, [x,y])
sub_surf = surf2d.get_sub_surface('sub_surf', [-250, 250, 0, 500], dx_new=self.surf2d.etaND.dx, dy_new=self.surf2d.etaND.dy)
# 3D
Nt = 3
eta3d = np.zeros((Nt, Nx, Ny))
fake_t = np.arange(0,Nt)
for i in range(0, Nt):
eta3d[i,:,:] = 5*np.sin(self.kx*xx + self.ky*yy )
surf3d = surface_core.Surface('surf3d', eta3d, [fake_t, x, y])
sub_3d = surf3d.get_sub_surface('sub_surf2', [-250, 250, 0, 500], dx_new=self.surf2d.etaND.dx, dy_new=self.surf2d.etaND.dy)
# Test
for i in range(0, self.Nx):
self.assertAlmostEqual(sub_surf.etaND.x[i], self.x[i], 2, 0.01)
self.assertAlmostEqual(sub_3d.etaND.x[i], self.x[i], 2, 0.01)
self.assertAlmostEqual(sub_surf.eta[i, 50], self.surf2d.eta[i, 50], 2, 0.01)
self.assertAlmostEqual(sub_3d.eta[0, i, 50], self.surf2d.eta[i, 50], 3, 0.001)
for i in range(0, self.Ny):
self.assertAlmostEqual(sub_surf.etaND.y[i], self.y[i], 1, 0.1)
self.assertAlmostEqual(sub_3d.etaND.y[i], self.y[i], 1, 0.1)
self.assertAlmostEqual(sub_surf.eta[30,i], self.surf2d.eta[30,i], 2, 0.01)
self.assertAlmostEqual(sub_3d.eta[0,30,i], self.surf2d.eta[30,i], 3, 0.001)
def test_shadowing(self):
H = 45.0
#self.surf2d.get_shadowing_mask('shad', H)
def test_incidence_angle(self):
y_grid_offset = 200
self.surf2d.replace_grid([self.x, self.y+y_grid_offset])
HP_limit = 0.05
#grid_offset = [self.x[0], y_grid_offset]
grid_cut_off=[0.2, 0.2]
#'''
surf_theta_l_10 = self.surf2d.get_local_incidence_surface('theta_l_10', 10, approx=False)
surf_theta_l_10_approx = self.surf2d.get_local_incidence_surface('theta_l_10_approx', 10, approx=True)
surf_theta_l_45 = self.surf2d.get_local_incidence_surface('theta_l_45', 45, approx=False)
surf_theta_l_45_approx = self.surf2d.get_local_incidence_surface('theta_l_10_approx', 45, approx=True)
spec_theta_l_10 = surf_theta_l_10.define_SpectralAnalysis()
spec_theta_l_10.apply_HP_filter(HP_limit)
surf_theta_l_10_filtered = spec_theta_l_10.invert('test1')
spec_theta_l_45 = surf_theta_l_45.define_SpectralAnalysis()
spec_theta_l_45.apply_HP_filter(HP_limit)
surf_theta_l_45_filtered = spec_theta_l_45.invert('test2')
spec_theta_l_45_approx = surf_theta_l_45_approx.define_SpectralAnalysis(grid_cut_off)
#spec_theta_l_45_approx.apply_HP_filter(HP_limits)
surf_theta_l_45_approx_filtered = spec_theta_l_45_approx.invert('test3')
test1 = surf_theta_l_10.etaND.eta
test1 -= np.mean(test1)
test2 = surf_theta_l_10_approx.etaND.eta
test2 -= np.mean(test2)
rms_error = np.sqrt(np.mean((test1 - test2)**2))
sigma = np.sqrt(np.var(test1))
print('rms_error/sigma = ', rms_error/sigma)
#''''''
#'''
'''
import matplotlib.pyplot as plt
plt.figure()
plt.imshow(surf_theta_l_10_filtered.etaND.eta*180/np.pi)
plt.colorbar()
plt.figure()
plt.imshow(surf_theta_l_10_approx.etaND.eta*180/np.pi)
plt.figure()
plt.imshow(surf_theta_l_45_approx_filtered.etaND.eta*180/np.pi)
plt.colorbar()
plt.figure()
plt.imshow(surf_theta_l_45_approx.etaND.eta*180/np.pi)
plt.colorbar()
plt.show()
'''
'''
surf_theta_l_10.plot_3d_surface()
surf_theta_l_10_approx.plot_3d_surface()
plt.show()
# test
kx_mesh, F_cos_theta, ky_mesh, F_sin_theta = spec_theta_l_45_approx.get_2d_MTF(grid_offset)
#plt.figure()
#plt.imshow(np.abs(1.0j*kx_mesh * self.spec2d.spectrumND.coeffs))
should_work = convolution.convolve2d(F_cos_theta, (1.0j*kx_mesh * self.spec2d.spectrumND.coeffs))
please_work = 1.0j*kx_mesh * convolution.convolve2d( F_cos_theta, (self.spec2d.spectrumND.coeffs))
#magic = convolution.convolve2d( F_cos_theta, 1.0j*kx_mesh) * self.spec2d.spectrumND.coeffs
#magic = convolution.convolve2d(1.0j*kx_mesh * F_cos_theta, self.spec2d.spectrumND.coeffs)
magic = (F_cos_theta[self.Nx//2, self.Ny//2]*1.0j*kx_mesh + F_sin_theta[self.Nx//2, self.Ny//2]*1.0j*ky_mesh)* self.spec2d.spectrumND.coeffs
#plt.figure()
#plt.imshow(np.abs(should_work))
#plt.figure()
#plt.imshow(np.abs(please_work))
plt.figure()
plt.imshow(np.abs(magic))
#MTF = spec_theta_l_45_approx.get_2d_MTF(self.x[0], self.y[0])
#plt.imshow(np.abs(convolution.convolve2d(MTF, ( self.spec2d.spectrumND.coeffs))))
#plt.figure()
#plt.imshow(np.abs(MTF))
plt.figure()
spec_theta_l_45_approx.spectrumND.coeffs[self.Nx//2, self.Ny//2] = 0
plt.imshow(np.abs(spec_theta_l_45_approx.spectrumND.coeffs))
#plt.figure()
#plt.plot(np.abs(spec_theta_l_45_approx.spectrumND.coeffs[:, self.Ny//2]))
#plt.plot(np.abs(please_work)[:, self.Ny//2], '--')
#plt.plot(np.abs(should_work)[:, self.Ny//2], '-.')
#plt.plot(np.abs(1.0j*kx_mesh*self.spec2d.spectrumND.coeffs), '-')
#plt.plot(np.abs(magic)[:, self.Ny//2], ':')
plt.figure()
plt.plot(np.abs(spec_theta_l_45_approx.spectrumND.coeffs[self.Nx//2, :]))
plt.plot(np.abs(magic)[self.Nx//2, :], ':')
'''
plt.show()
def test_deta_dx(self):
xt = np.linspace(-50, 50, self.Nx*3)
yt = np.linspace(0, 100, self.Ny*3)
xxt, yyt = np.meshgrid(xt, yt, indexing='ij')
etat = 10*np.exp(-0.05*(xxt**2 + yyt**2))
tsts = surface_core.Surface('tsts', etat, [xt, yt])
dxapprox = tsts.get_deta_dx()
dyapprox = tsts.get_deta_dy()
dxexact = -0.5*2*xxt*np.exp(-0.05*(xxt**2 + yyt**2))
dyexact = -0.5*2*yyt*np.exp(-0.05*(xxt**2 + yyt**2))
for i in range(0, self.Nx):
for j in range(0, self.Ny):
self.assertAlmostEqual(dxapprox[i,j], dxexact[i,j], places=1)
for i in range(0, self.Nx):
for j in range(0, self.Ny):
self.assertAlmostEqual(dyapprox[i,j], dyexact[i,j], places=1)
def test_deta_dx1(self):
xt1 = np.linspace(-50, 50, self.Nx*3)
etat1 = 10*np.exp(-0.05*xt1**2)
tsts1 = surface_core.Surface('tsts1', etat1, [xt1])
dapprox = tsts1.get_deta_dx()
dexact = -0.5*2*xt1*np.exp(-0.05*xt1**2)
for i in range(0, self.Nx):
self.assertAlmostEqual(dapprox[i], dexact[i], places=1)
def test_inversion_with_1d_MTF(self):
y_grid_offset = 500
self.surf2d.replace_grid([self.x, self.y+y_grid_offset])
#self.surf2d.plot_3d_surface()
HP_limit = 0.04
surf_theta_l_45 = self.surf2d.get_local_incidence_surface('theta_l_45', 45, approx=False)
spec_theta_l_45 = surf_theta_l_45.define_SpectralAnalysis()
spec_theta_l_45.apply_HP_filter(HP_limit)
spec_theta_l_45.apply_1d_MTF()
retrieved_surf = spec_theta_l_45.invert('retrieved_surf', grid_offset=[self.surf2d.x[0], self.surf2d.y[0]])
#retrieved_surf.plot_3d_surface()
plt.show()
def test_shoaling_1d(self):
ti = np.array([1])
dx = 0.5
a = np.array([1])
f_r = np.array([0.1])
x = np.arange(200, 2200+dx, dx)
Nx = len(x)
bathy1 = -10 * (x<=700)
bathy2 = (-0.05*x + 25)*(np.logical_and(x>700, x<=1700))
bathy3 = -60*(x>1700)
b = bathy1 + bathy2 + bathy3
def calc_wavenumbert(f_r):
k_out = np.zeros(Nx)
eps = 10**(-6)
N_max = 100
w = 2*np.pi*f_r
ki = w**2/(9.81)
wt = np.sqrt(9.81*ki*np.tanh(ki*(-b)))
count = 0
while np.max(np.abs(w-wt))>eps and count<N_max:
latter = 9.81*np.tanh(ki*(-b))
ki = w**2/(latter)
wt = np.sqrt(latter)
count += 1
k_out[:] = ki
return k_out
k = calc_wavenumbert(f_r)
w = 2*np.pi*f_r
H = -b
zetat = np.zeros(Nx)
k2H_by_sinh_2kH = np.where(k*H < 50, 2*k*H / np.sinh(2*k*H), 0)
ksh = np.cumsum(k*dx)
Cgx = w/(2*k*(1+k2H_by_sinh_2kH))
Cg0x = w[-1]/(2*k*(1+k2H_by_sinh_2kH[-1]))
phase = np.array([np.random.uniform()*np.pi*2])
zetat += a*np.abs(np.sqrt(Cg0x/Cgx))*np.cos(phase+w*ti+ksh)
bc = shoaling_1d.Bathymetry(x, bathy_filename=0, test=True)
test = shoaling_1d.SpectralRealization(0, 0, 0, 1, dx, test=True, phase=phase)
zetac = test.invert(bc, np.array([0, 1, 2]), x)
for i in range(0, len(zetac)):
self.assertAlmostEqual(zetat[i], zetac[1,i])
if __name__ == '__main__':
unittest.main()