/
fig8a_irreg_fourier_samp.py
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/
fig8a_irreg_fourier_samp.py
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from __future__ import division
import datetime
import os
import numpy as np
from scipy import linalg
import matplotlib
if os.environ.get('DISPLAY') is None:
matplotlib.use('Agg')
else:
matplotlib.use('Qt5Agg')
from matplotlib import rcParams
import matplotlib.pyplot as plt
# import bokeh.plotting as b_plt
# from bokeh.io import vplot, hplot, output_file, show
# from bokeh.models.tools import WheelZoomTool
from alg_tools_1d import distance, build_G_fourier, dirac_recon_irreg_fourier
# for latex rendering
os.environ['PATH'] = os.environ['PATH'] + ':/usr/texbin' + \
':/opt/local/bin' + ':/Library/TeX/texbin/'
rcParams['text.usetex'] = True
rcParams['text.latex.unicode'] = True
if __name__ == '__main__':
# various experiment settings
save_fig = True # save figure or not
stop_cri = 'max_iter' # stopping criteria: 1) mse; or 2) max_iter
fig_format = r'png' # file type used to save the figure, e.g., pdf, png, etc.
interp_kernel = 'triangular' # interpolation kernel used: 1) dirichlet; 2) triangular; 3) cubic; 4) keys
periodic_spectrum = False # whether the spectrum is periodic or not
web_fig = False # generate html file for the figures
# check and correct interpolation kernel if the spectrum is periodic
# should use dirichlet kernel in this case
if periodic_spectrum:
interp_kernel = 'dirichlet'
K = 5 # number of Diracs
M = 21 # period of the spectrum: M * tau must be an ODD number
tau = 1. # time support of the signal is from -0.5 * tau to 0.5 * tau
'''
# generate random values for Dirac amplitudes and locations
# amplitudes of the Diracs
ak = np.sign(np.random.randn(K)) * (1 + (np.random.rand(K) - 0.5) / 1.)
# locations of the Diracs
if periodic_spectrum:
delta_t = 1. / M
tk = np.sort(
np.random.permutation(np.uint(np.floor(0.5 * tau / delta_t) * 2))[0:K] *
delta_t) - np.floor(0.5 * tau / delta_t) * delta_t
else:
if K == 1:
tk = np.random.rand()
else:
a = 4. / M
uk = np.random.exponential(scale=1. / K, size=(K - 1, 1))
tk = np.cumsum(a + (1. - K * a) * (1 - 0.1 * np.random.rand()) / uk.sum() * uk)
tk = np.sort(np.hstack((np.random.rand() * tk[0] / 2., tk)) + (1 - tk[-1]) / 2.) * tau - 0.5 * tau
# save Dirac parameter
time_stamp = datetime.datetime.now().strftime("%d-%m_%H_%M")
if periodic_spectrum:
file_name = './data/freq_Dirac_Data_p' + time_stamp + '.npz'
else:
file_name = './data/freq_Dirac_Data_ap' + time_stamp + '.npz'
np.savez(file_name, tk=tk, ak=ak, K=K, M=M, time_stamp=time_stamp)
'''
# load saved data
if periodic_spectrum:
time_stamp = r'20-12_11_48' # for the periodic case
else:
time_stamp = r'20-12_11_55' # for the aperiodic case
if periodic_spectrum:
stored_param = np.load('./data/freq_Dirac_Data_p' + time_stamp + '.npz')
else:
stored_param = np.load('./data/freq_Dirac_Data_ap' + time_stamp + '.npz')
tk = stored_param['tk']
ak = stored_param['ak']
K = stored_param['K'].tolist()
M = stored_param['M'].tolist()
print(r'time stamp: ' + time_stamp +
'\n=======================================\n')
# number of random Fourier domain measurements (over sample in the noisy case)
L = 2 * M
# generate random frequencies to take samples
omega_ell = np.pi * (np.random.rand(L) * (2 * M - 1) - M)
# Fourier transform of the Diracs
tk_grid, omega_grid = np.meshgrid(tk, omega_ell)
Xomega_ell = np.dot(np.exp(-1j * omega_grid * tk_grid), ak)
# add noise
P = float('inf')
noise = np.random.randn(L) + 1j * np.random.randn(L)
noise = noise / linalg.norm(noise) * linalg.norm(Xomega_ell) * 10 ** (-P / 20.)
Xomega_ell_noisy = Xomega_ell + noise
# noise energy, in the noiseless case 1e-14 is considered as 0
noise_level = np.max([1e-14, linalg.norm(noise)])
max_ini = 50 # maximum number of random initialisations
tk_ref, ak_recon, Xomega_Uniform_ref = \
dirac_recon_irreg_fourier(Xomega_ell_noisy, K, tau, omega_ell, M,
noise_level, max_ini, stop_cri,
interp_kernel)
# location estimation error
t_error = distance(tk_ref, tk)[0]
# plot reconstruction
plt.close()
fig = plt.figure(num=1, figsize=(5, 4), dpi=90)
subplt_height = 0.2
subplt_width = 0.87
subplt_left_corner = 0.115
# sub-figure 1
ax1 = plt.axes([subplt_left_corner, 0.71, subplt_width, subplt_height])
markerline311_1, stemlines311_1, baseline311_1 = ax1.stem(tk, ak, label='Original Diracs')
plt.setp(stemlines311_1, linewidth=1.5, color=[0, 0.447, 0.741])
plt.setp(markerline311_1, marker='^', linewidth=1.5, markersize=8,
markerfacecolor=[0, 0.447, 0.741], mec=[0, 0.447, 0.741])
plt.setp(baseline311_1, linewidth=0)
markerline311_2, stemlines311_2, baseline311_2 = \
plt.stem(tk_ref, ak_recon, label='Estimated Diracs')
plt.setp(stemlines311_2, linewidth=1.5, color=[0.850, 0.325, 0.098])
plt.setp(markerline311_2, marker='*', linewidth=1.5, markersize=10,
markerfacecolor=[0.850, 0.325, 0.098], mec=[0.850, 0.325, 0.098])
plt.setp(baseline311_2, linewidth=0)
ax1.yaxis.set_tick_params(labelsize=8.5)
plt.axhline(0, color='k')
plt.xlim([-tau / 2, tau / 2])
plt.ylim([1.18 * np.min(np.concatenate((ak, ak_recon, np.array(0)[np.newaxis]))),
1.18 * np.max(np.concatenate((ak, ak_recon, np.array(0)[np.newaxis])))])
plt.xlabel(r'$t$', fontsize=12)
plt.ylabel(r'amplitudes', fontsize=12)
ax1.xaxis.set_label_coords(0.5, -0.21)
plt.legend(numpoints=1, loc=0, fontsize=9, framealpha=0.3,
columnspacing=1.7, labelspacing=0.1)
t_error_pow = np.int(np.floor(np.log10(t_error)))
plt.title(r'$K={0}$, $L={1}$, '
r'$\mbox{{SNR}}={2}$dB, '
r'$t_{{\mbox{{\footnotesize error}}}}={3:.2f}\times10^{other}$'.format(repr(K), repr(L), repr(P),
t_error / 10 ** t_error_pow,
other='{' + str(t_error_pow) + '}'),
fontsize=12)
# sub-figure 2
omega_continuous = np.linspace(-np.pi * M, np.pi * M, num=np.max([10 * L, 10000]))
tk_grid_conti, omega_grid_conti = np.meshgrid(tk, omega_continuous)
Xomegas_conti = np.dot(np.exp(-1j * omega_grid_conti * tk_grid_conti), ak)
m_limit = np.floor(M * tau / 2.)
m_grid_conti, omega_grid_conti_recon = np.meshgrid(np.arange(-m_limit, m_limit + 1), omega_continuous)
G_conti_recon = build_G_fourier(omega_continuous, M, tau, interp_kernel, tk_ref=tk_ref)
Xomegas_conti_recon = np.dot(G_conti_recon, Xomega_Uniform_ref)
ax2 = plt.axes([subplt_left_corner, 0.358, subplt_width, subplt_height])
line312_1 = ax2.plot(omega_ell, np.real(Xomega_ell_noisy), label='Measurements')
plt.setp(line312_1, marker='.', linestyle='None', markersize=5, color=[0, 0.447, 0.741])
line312_2 = plt.plot(omega_continuous, np.real(Xomegas_conti), label='Ground Truth')
plt.setp(line312_2, linestyle='-', color=[0.850, 0.325, 0.098], linewidth=1)
line312_3 = plt.plot(omega_continuous, np.real(Xomegas_conti_recon), label='Reconstruction')
plt.setp(line312_3, linestyle='--', color=[0.466, 0.674, 0.188], linewidth=1.5)
plt.ylim([1.1 * np.min(np.concatenate((np.real(Xomegas_conti), np.real(Xomega_ell_noisy)))),
1.1 * np.max(np.concatenate((np.real(Xomegas_conti), np.real(Xomega_ell_noisy))))])
ax2.yaxis.major.locator.set_params(nbins=7)
plt.ylabel(r'$\Re\left\{X(\omega)\right\}$', fontsize=13)
plt.legend(numpoints=1, loc=4, bbox_to_anchor=(1.013, 0.975), fontsize=9,
handletextpad=.2, columnspacing=1.7, labelspacing=0.1, ncol=3)
# sub-figure 3
ax3 = plt.axes([subplt_left_corner, 0.10, subplt_width, subplt_height])
line313_1 = ax3.plot(omega_ell, np.imag(Xomega_ell_noisy), label='Measurements')
plt.setp(line313_1, marker='.', linestyle='None', markersize=5, color=[0, 0.447, 0.741])
line313_2 = plt.plot(omega_continuous, np.imag(Xomegas_conti), label='Ground Truth')
plt.setp(line313_2, linestyle='-', color=[0.850, 0.325, 0.098], linewidth=1)
line313_3 = plt.plot(omega_continuous, np.imag(Xomegas_conti_recon), label='Reconstruction')
plt.setp(line313_3, linestyle='--', color=[0.466, 0.674, 0.188], linewidth=1.5)
plt.ylim([1.1 * np.min(np.concatenate((np.imag(Xomegas_conti), np.imag(Xomega_ell_noisy)))),
1.1 * np.max(np.concatenate((np.imag(Xomegas_conti), np.imag(Xomega_ell_noisy))))])
ax3.yaxis.major.locator.set_params(nbins=7)
plt.ylabel(r'$\Im\left\{X(\omega)\right\}$', fontsize=12)
plt.xlabel(r'$\omega$', fontsize=12)
ax3.xaxis.set_label_coords(0.5, -0.21)
if save_fig:
if periodic_spectrum:
file_name = (r'./result/TSP_eg2_K_{0}_L_{1}_M_{2}_noise_{3}dB_' +
interp_kernel + r'_periodic' +
r'.' + fig_format).format(repr(K), repr(L), repr(M), repr(P))
else:
file_name = (r'./result/TSP_eg2_K_{0}_L_{1}_M_{2}_noise_{3}dB_' +
interp_kernel + r'_aperiodic' +
r'.' + fig_format).format(repr(K), repr(L), repr(M), repr(P))
plt.savefig(file_name, format=fig_format, dpi=300, transparent=True)
plt.show()
# for web rendering
# if web_fig:
# output_file('./html/eg2.html')
# TOOLS = 'pan, reset'
# p_hdl1 = b_plt.figure(title='K={0}, L={1}, SNR={2:.1f}dB, error={3:.2e}'.format(repr(K), repr(L), P, t_error),
# tools=TOOLS,
# x_axis_label='time', y_axis_label='amplitudes',
# plot_width=550, plot_height=220,
# x_range=(-0.5 * tau, 0.5 * tau),
# y_range=(1.18 * np.min(np.concatenate((ak, ak_recon, np.array(0)[np.newaxis]))),
# 1.18 * np.max(np.concatenate((ak, ak_recon, np.array(0)[np.newaxis])))
# )
# )
# p_hdl1.title.text_font_size = '12pt'
# p_hdl1.add_tools(WheelZoomTool(dimensions=["width"]))
# p_hdl1.triangle(x=tk, y=ak,
# color='#0072BD',
# fill_color='#0072BD',
# line_width=1.5, size=8,
# legend='Original Diracs')
# p_hdl1.multi_line(xs=np.vstack((tk, tk)).T.tolist(),
# ys=np.vstack((np.zeros(ak.shape), ak)).T.tolist(),
# color='#0072BD',
# line_width=1.5,
# line_color='#0072BD')
# p_hdl1.diamond(x=tk_recon, y=ak_recon,
# color='#D95319',
# line_width=1.5, size=10,
# legend='Estimated Diracs')
# p_hdl1.multi_line(xs=np.vstack((tk_recon, tk_recon)).T.tolist(),
# ys=np.vstack((np.zeros(ak_recon.shape), ak_recon)).T.tolist(),
# color='#D95319',
# line_width=1.5,
# line_color='#D95319')
# p_hdl1.legend.location = 'bottom_right'
# p_hdl1.legend.border_line_alpha = 0.6
# p_hdl1.xaxis.axis_label_text_font_size = "11pt"
# p_hdl1.yaxis.axis_label_text_font_size = "11pt"
# p_hdl1.legend.legend_spacing = 1
# p_hdl1.legend.legend_padding = 5
# p_hdl1.legend.label_text_font_size = "9pt"
#
# # subplot 2
# TOOLS2 = 'pan, reset'
# p_hdl2 = b_plt.figure(tools=TOOLS2, x_axis_label='omega',
# y_axis_label='Spectrum (Real)',
# plot_width=550, plot_height=220,
# y_range=(1.1 * np.min(np.concatenate((np.real(Xomegas_conti),
# np.real(Xomega_ell_noisy)))
# ),
# 1.1 * np.max(np.concatenate((np.real(Xomegas_conti),
# np.real(Xomega_ell_noisy)))
# )
# )
# )
# p_hdl2.add_tools(WheelZoomTool())
# p_hdl2.line(x=omega_continuous, y=np.real(Xomegas_conti),
# color='#D95319',
# line_color='#D95319',
# line_width=1.5,
# legend='Ground Truth')
# p_hdl2.line(x=omega_continuous, y=np.real(Xomegas_conti_recon),
# color='#77AC30',
# line_color='#77AC30',
# line_width=1.5,
# legend='Reconstruction')
# p_hdl2.circle(x=omega_ell, y=np.real(Xomega_ell_noisy),
# color='#0072BD',
# fill_color='#0072BD',
# line_width=1.5, size=2,
# legend='Measurements')
# p_hdl2.xaxis.axis_label_text_font_size = "11pt"
# p_hdl2.yaxis.axis_label_text_font_size = "10pt"
# p_hdl2.legend.location = 'bottom_right'
# p_hdl2.legend.border_line_alpha = 0.6
# p_hdl2.legend.legend_spacing = 1
# p_hdl2.legend.legend_padding = 5
# p_hdl2.legend.label_text_font_size = "8pt"
#
# # subplot 3
# TOOLS3 = 'pan, reset'
# p_hdl3 = b_plt.figure(tools=TOOLS3, x_axis_label='omega',
# y_axis_label='Spectrum (Imaginary)',
# plot_width=550, plot_height=220,
# x_range=p_hdl2.x_range,
# y_range=(1.1 * np.min(np.concatenate((np.imag(Xomegas_conti),
# np.imag(Xomega_ell_noisy)))
# ),
# 1.1 * np.max(np.concatenate((np.imag(Xomegas_conti),
# np.imag(Xomega_ell_noisy)))
# )
# )
# )
# p_hdl3.add_tools(WheelZoomTool())
# p_hdl3.line(x=omega_continuous, y=np.imag(Xomegas_conti),
# color='#D95319',
# line_color='#D95319',
# line_width=1.5,
# legend='Ground Truth')
# p_hdl3.line(x=omega_continuous, y=np.imag(Xomegas_conti_recon),
# color='#77AC30',
# line_color='#77AC30',
# line_width=1.5,
# legend='Reconstruction')
# p_hdl3.circle(x=omega_ell, y=np.imag(Xomega_ell_noisy),
# color='#0072BD',
# fill_color='#0072BD',
# line_width=1.5, size=2,
# legend='Measurements')
# p_hdl3.xaxis.axis_label_text_font_size = "11pt"
# p_hdl3.yaxis.axis_label_text_font_size = "10pt"
# p_hdl3.legend.location = 'bottom_right'
# p_hdl3.legend.border_line_alpha = 0.6
# p_hdl3.legend.legend_spacing = 1
# p_hdl3.legend.legend_padding = 5
# p_hdl3.legend.label_text_font_size = "8pt"
#
# p_hdl = b_plt.gridplot([[p_hdl1], [p_hdl2], [p_hdl3]], toolbar_location='above')
# show(p_hdl)