def exampleNoNoise():
"""Plot information for a case without noise
Returns:
TYPE: None
"""
totalTime = 1.0 # s
dt = 0.001 # s
dtIntegration = 0.01 #s
betaIn = np.asarray([15.0, 100.0, 100., 100.0])
stokesIn = np.asarray([1.0, 1.2e-3, 5.e-3, 0.001])
lambdas = [5e-3, 5e-5, 5e-7]
pl.close('all')
f, ax = pl.subplots(nrows=3, ncols=3, figsize=(15,12), sharex='col')
stokesPar = ['I', 'Q', 'U', 'V']
for i in range(3):
out = rn.randomDemodulator(totalTime, dt, dtIntegration, stokesIn, betaIn, seed=123, signalToNoise=1e20)
coefFourier, stokes, beta, normL2, normL1, normL0 = out.FISTA(thresholdMethod = 'soft', niter = 1000, lambdaValue = lambdas[i])
stI, stQ, stU, stV = out.demodulateTrivial()
print "Q/I_original={0} - Q/I_inferred={1} - Q/I_trivial={2} - diff={3}".format(out.stokes[1] / out.stokes[0], stokes[1] / stokes[0], \
stQ/stI, out.stokes[1] / out.stokes[0]-stokes[1] / stokes[0])
print "U/I_original={0} - U/I_inferred={1} - U/I_trivial={2} - diff={3}".format(out.stokes[2] / out.stokes[0], stokes[2] / stokes[0], \
stU/stI, out.stokes[2] / out.stokes[0]-stokes[2] / stokes[0])
print "V/I_original={0} - V/I_inferred={1} - V/I_trivial={2} - diff={3}".format(out.stokes[3] / out.stokes[0], stokes[3] / stokes[0], \
stV/stI, out.stokes[3] / out.stokes[0]-stokes[3] / stokes[0])
coefFourier[0] = 0.0
Nt = rn.myIFFT(coefFourier)
Nt /= np.sqrt(rn.myTotalPower(coefFourier))
ax[i,0].plot(out.times, out.seeing, label='Original')
ax[i,0].plot(out.times, Nt, label='Reconstructed')
if (i == 2):
ax[i,0].set_xlabel('Time [s]')
ax[i,0].set_ylabel('Seeing random process')
ax[i,0].text(0.8, 0.07, '$\lambda={0}$'.format(lambdas[i]))
if (i == 0):
ax[i,0].legend(loc='upper left', fontsize=15)
ax[i,1].semilogy(out.freq, rn.myFFT(out.seeing) * np.conj(rn.myFFT(out.seeing)), '.', label='Original')
ax[i,1].semilogy(out.freq, rn.myFFT(Nt) * np.conj(rn.myFFT(Nt)), '.', label='Reconstructed')
ax[i,1].set_ylim([1e-9,1])
if (i == 2):
ax[i,1].set_xlabel('Frequency [Hz]')
ax[i,1].set_ylabel('Power spectrum')
if (i == 0):
ax[i,1].legend(fontsize=15)
for j in range(4):
ax[i,1].text(0.1,0.92-j*0.05,'{0}$_0$={1:10.7f}'.format(stokesPar[j],stokes[j] / stokes[0]), transform=ax[i,1].transAxes, fontsize=12)
ax[i,1].text(0.1,0.92-(j+4)*0.05,r'$\beta_{0}$={1:5.2f}'.format(stokesPar[j],beta[j]), transform=ax[i,1].transAxes, fontsize=12)
ax[i,2].loglog(normL2, label=r'$\ell_2$')
ax[i,2].loglog(normL1, label=r'$\ell_1$')
ax[i,2].loglog(normL0, label=r'$\ell_0$')
if (i == 2):
ax[i,2].set_xlabel('Iteration')
ax[i,2].set_ylabel('Error norm')
ax[i,2].set_xlim([1,1000])
if (i == 0):
ax[i,2].legend(fontsize=15)
# ax[loop].set_xlabel('Time [s]')
# ax[loop].set_ylabel('Stokes para{0}'.format(stokesPar[loop]))
# ax[loop].text(0.05,0.9,'{0}$_0$={1:10.7f}'.format(stokesPar[loop],stokesIn[loop] / stokesIn[0]), transform=ax[loop].transAxes, fontsize=15)
# ax[2,0].semilogy(np.abs(myFFT(out.seeing)))
# ax[2,0].semilogy(np.abs(myFFT(Nt)))
# ax[2,1].semilogy(normL21)
# ax[2,1].semilogy(normL11)
pl.tight_layout()
pl.savefig('../noNoise.pdf')
def exampleNoise():
"""Plot information for a case with noise
Returns:
TYPE: Description
"""
totalTime = 1.0 # s
dt = 0.001 # s
dtIntegration = 0.01 #s
beta = np.asarray([15.0, 100.0, 100., 100.0])
stokes = np.asarray([1.0, 1.2e-3, 5.e-3, 0.001])
out = rn.randomDemodulator(totalTime, dt, dtIntegration, stokes, beta, seed=123, signalToNoise=3e3)
coefFourier, stokes, beta, normL2, normL1, normL0 = out.FISTA(thresholdMethod = 'soft', niter = 1000, lambdaValue = 5e-6)
stI, stQ, stU, stV = out.demodulateTrivial()
print "Q/I_original={0} - Q/I_inferred={1} - Q/I_trivial={2} - diff={3}".format(out.stokes[1] / out.stokes[0], stokes[1] / stokes[0], \
stQ/stI, out.stokes[1] / out.stokes[0]-stokes[1] / stokes[0])
print "U/I_original={0} - U/I_inferred={1} - U/I_trivial={2} - diff={3}".format(out.stokes[2] / out.stokes[0], stokes[2] / stokes[0], \
stU/stI, out.stokes[2] / out.stokes[0]-stokes[2] / stokes[0])
print "V/I_original={0} - V/I_inferred={1} - V/I_trivial={2} - diff={3}".format(out.stokes[3] / out.stokes[0], stokes[3] / stokes[0], \
stV/stI, out.stokes[3] / out.stokes[0]-stokes[3] / stokes[0])
pl.close('all')
f, ax = pl.subplots(nrows=1, ncols=3, figsize=(18,6))
coefFourier[0] = 0.0
Nt = rn.myIFFT(coefFourier)
Nt /= np.sqrt(rn.myTotalPower(coefFourier))
stokesPar = ['I', 'Q', 'U', 'V']
loop = 0
ax[0].plot(out.times, out.seeing, label='Original')
ax[0].plot(out.times, Nt, label='Reconstructed')
ax[0].set_xlabel('Time [s]')
ax[0].set_ylabel('Seeing random process')
ax[0].legend(loc='upper left', fontsize=15)
ax[1].semilogy(out.freq, rn.myFFT(out.seeing) * np.conj(rn.myFFT(out.seeing)), '.', label='Original')
ax[1].semilogy(out.freq, rn.myFFT(Nt) * np.conj(rn.myFFT(Nt)), '.', label='Reconstructed')
ax[1].set_ylim([1e-9,1])
ax[1].set_xlabel('Frequency [Hz]')
ax[1].set_ylabel('Power spectrum')
ax[1].legend(fontsize=15)
for j in range(4):
ax[1].text(0.1,0.92-j*0.05,'{0}$_0$={1:10.7f}'.format(stokesPar[j],stokes[j] / stokes[0]), transform=ax[1].transAxes, fontsize=12)
ax[1].text(0.1,0.92-(j+4)*0.05,r'$\beta_{0}$={1:5.2f}'.format(stokesPar[j],beta[j]), transform=ax[1].transAxes, fontsize=12)
ax[2].loglog(normL2, label=r'$\ell_2$')
ax[2].loglog(normL1, label=r'$\ell_1$')
ax[2].loglog(normL0, label=r'$\ell_0$')
ax[2].set_xlabel('Iteration')
ax[2].set_ylabel('Error norm')
ax[2].set_xlim([1,1000])
ax[2].legend(fontsize=15)
pl.tight_layout()