# This is the 1d Kernel for High Pass (last scale)
h1d_H = firwin(Nf[m],F_Bank_r[m],pass_zero=False)
List_h.append(h1d_H)
plt.plot(Freq,np.fft.fftshift(np.abs(np.fft.fft(h1d_H,n_t))),linewidth=1.5)
plt.xlim([0,0.4])
plt.xlabel('$\hat{f}[-]$',fontsize=18)
plt.ylabel('Normalized Spectra',fontsize=18)
plt.tight_layout()
plt.savefig('Frequency_Splitting.pdf', dpi=100)
Ex=201
# Compute the mPOD Temporal Basis
PSI_M = mPOD_K(K,dt,Nf,Ex,F_V,Keep,'nearest','reduced');
# Save as numpy array all the data
np.savez('Psis_mPOD',PSI_M=PSI_M)
# To make a comparison later, we also compute the POD basis
# Temporal structures are eigenvectors of K
Psi_P, Lambda_P, _ = np.linalg.svd(K)
# The POD has the unique feature of providing the amplitude of the modes
# with no need of projection. The amplitudes are:
Sigma_P=(Lambda_P)**0.5;
# Obs: svd and eig on a symmetric positive matrix are equivalent.
np.savez('Psis_POD',Psi_P=Psi_P,Sigma_P=Sigma_P)
plt.plot(Freq,
np.fft.fftshift(np.abs(np.fft.fft(h1d_H, n_t))),
linewidth=1.5)
plt.xlim([0, 0.4])
plt.rc('text', usetex=True) # This is Miguel's customization
plt.rc('font', family='serif')
plt.xlabel('$\hat{f}[-]$', fontsize=18)
plt.ylabel('Normalized Spectra', fontsize=18)
plt.tight_layout()
plt.savefig('Frequency_Splitting.png', dpi=200)
# Compute the mPOD Temporal Basis
PSI_M, Ks = mPOD_K(data['K'], dt, Nf, Ex, F_V, Keep, 'nearest', 'reduced')
# Save the correlation matrices of each scale:
for i in range(0, Ks.shape[2]):
K = Ks[:, :, i]
K_HAT_ABS = np.fliplr(np.abs(np.fft.fftshift(np.fft.fft2(K - np.mean(K)))))
fig, ax = plt.subplots(figsize=(4, 4))
#ax.set_xlim([-0.5,0.5])
#ax.set_ylim([-0.5,0.5])
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
plt.rc('xtick', labelsize=12)
plt.rc('ytick', labelsize=12)
plt.pcolor(Freq, Freq, K_HAT_ABS / np.size(D)) # We normalize the result
ax.set_aspect('equal') # Set equal aspect ratio