#alt_ethane_fr = np.copy(ethane_fr) #alt_ethane_fi = np.copy(ethane_fi) #plt.loglog(ethane_periods,ethane_mag) #plt.show() #------------------------------------------------------------------ # #Do IFFT of altered spectra - with significant periods removed and gaps left in real and imag components linearly interpolated. # #altered spectra provides red noise estimation baseline # ##use ifft to get time series back from adjusted spectra1 # #complex Fourier spectrum which corresponds to the Lomb-Scargle periodogram: SAMP_R = 1./24 fft_periods,fft_mag,fft_fr,fft_fi,F2 = modules.take_fft_unwindowed(time,ethane,SAMP_R) closest_ha_index = min(range(len(fft_periods)), key=lambda i: abs(fft_periods[i]-182.625)) closest_annual_index = min(range(len(fft_periods)), key=lambda i: abs(fft_periods[i]-365.25)) rm_indices = [closest_ha_index,closest_annual_index] alt_ethane_mag,alt_ethane_fr,alt_ethane_fi,ethane_rm_inds = redfit.sidelobe_n_remove(np.copy(fft_mag),fft_fr,fft_fi,rm_indices,1,fft_periods) #alt_ethane_mag = np.copy(fft_mag) #alt_ethane_fr = np.copy(fft_fr) #alt_ethane_fi = np.copy(fft_fi) plt.loglog(fft_periods,alt_ethane_mag) plt.show()
def red_ar1_fit(nsim,t,x,ofac):
#average dt of entire time series
diffs = [t[i+1]-t[i] for i in range(len(t)-1)]
avgdt = np.average(diffs)
ave = np.mean(x)
#subtract mean from data
x = x - ave
#GET TAU
tau, rhoavg, ierr = gettau(t,x,1,avgdt)
nout = int(0.5*int(ofac)*1*len(t))
if tau == 'invalid':
model_periods,model_mag,corr_model_mag,model_fr,model_fi,red_periods,red_mag_avg,gredth,fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,tau,corr = np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),0,0,0,0,np.zeros(nout),np.zeros(nout),0,1
return model_periods,model_mag,corr_model_mag,model_fr,model_fi,red_periods,red_mag_avg,gredth,fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,tau,corr
#make sure that tau is non-negative
if (tau < 0.0):
print 'Negative tau is forced to zero.'
tau = 0.0
x = x + ave
#determine lag-1 autocorrelation coefficient
rho = np.exp(-avgdt / tau) # avg. autocorrelation coefficient
rhosq = rho * rho
xdif = np.max(t)-np.min(t)
#Calculate model spectrum
#model_periods,model_mag,model_ph,model_fr,model_fi = modules.take_lomb_unwindowed(t,x,ofac)
fft_periods_all,fft_mag_all,fft_fr,fft_fi,fft_array = modules.take_fft_unwindowed(t,x,avgdt)
fft_freq_all = 1./fft_periods_all
#full_n = len(model_periods)
#model_freq = 1./model_periods
# estimate data variance from data spectrum
# ----------------------------------------
#varx = (model_freq[0]) * np.sum(model_mag) # NB: freq[1] = df
varx_fft = (fft_freq_all[0]) * np.sum(fft_mag_all)
#red_mag = np.zeros((nsim,len(model_periods)))
#red_mag_sum = np.zeros(len(model_periods))
fft_mag = np.zeros((nsim,len(fft_periods_all)))
fft_mag_sum = np.zeros(len(fft_periods_all))
#create AR1 spectrum nsim times
for i in range(nsim):
print 'Nsim = ', i+1
red = makear1(t,len(x),tau)
#red_periods,red_mag[i,:],red_ph,red_fr,red_fi = modules.take_lomb_unwindowed(t,red,ofac,avgdt)
#red_freq = 1./red_periods
fft_periods,fft_mag[i,:],fft_fr,fft_fi,fft_array = modules.take_fft_unwindowed(t,red,avgdt)
fft_freq = 1./fft_periods
#scale and sum red-noise spectra
#-------------------------------
#varr = (red_freq[0]) * np.sum(red_mag[i,:]) # NB: freq[1] = df
#fac = varx / varr
#red_mag[i,:] = fac * red_mag[i,:]
#red_mag_sum = red_mag_sum + red_mag[i,:]
varr = (fft_freq[0]) * np.sum(fft_mag[i,:]) # NB: freq[1] = df
fac = varx_fft / varr
fft_mag[i,:] = fac * fft_mag[i,:]
fft_mag_sum = fft_mag_sum + fft_mag[i,:]
#determine average red-noise spectrum; scale average again to
#make sure that roundoff errors do not affect the scaling
#------------------------------------------------------------
#red_mag_avg = red_mag_sum / float(nsim)
#varr = (red_freq[0]) * np.sum(red_mag_avg)
#fac = varx / varr
#red_mag_avg = fac * red_mag_avg
fft_mag_avg = fft_mag_sum / float(nsim)
varr = (fft_freq[0]) * np.sum(fft_mag_avg)
fac = varx_fft / varr
fft_mag_avg = fac * fft_mag_avg
#plt.plot(model_freq,model_mag)
#plt.plot(red_freq,red_mag_avg)
#plt.loglog(fft_periods_all,fft_mag_all)
#plt.loglog(fft_periods,fft_mag_avg)
corr = [1.]*len(fft_freq)
fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,ci99 = significance_tests(x,fft_periods,fft_mag,nsim,1,corr,True)
#plt.loglog(fft_periods,fft_mag_avg*fac95)
#plt.loglog(fft_periods,fft_mag_avg*fac99)
#plt.loglog(fft_periods,fft_mag_avg*faccrit)
#plt.show()
model_periods = np.copy(fft_periods_all)
model_mag = np.copy(fft_mag_all)
red_periods = np.copy(fft_periods)
red_mag_avg = np.copy(fft_mag_avg)
return model_periods,model_mag,red_periods,red_mag_avg,fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,tau,corr
#alt_ethane_mag = np.copy(ethane_mag)
#alt_ethane_fr = np.copy(ethane_fr)
#alt_ethane_fi = np.copy(ethane_fi)
#plt.loglog(ethane_periods,ethane_mag)
#plt.show()
#------------------------------------------------------------------
# #Do IFFT of altered spectra - with significant periods removed and gaps left in real and imag components linearly interpolated.
# #altered spectra provides red noise estimation baseline
# ##use ifft to get time series back from adjusted spectra1
# #complex Fourier spectrum which corresponds to the Lomb-Scargle periodogram:
SAMP_R = 1. / 24
fft_periods, fft_mag, fft_fr, fft_fi, F2 = modules.take_fft_unwindowed(
time, ethane, SAMP_R)
closest_ha_index = min(range(len(fft_periods)),
key=lambda i: abs(fft_periods[i] - 182.625))
closest_annual_index = min(range(len(fft_periods)),
key=lambda i: abs(fft_periods[i] - 365.25))
rm_indices = [closest_ha_index, closest_annual_index]
alt_ethane_mag, alt_ethane_fr, alt_ethane_fi, ethane_rm_inds = redfit.sidelobe_n_remove(
np.copy(fft_mag), fft_fr, fft_fi, rm_indices, 1, fft_periods)
#alt_ethane_mag = np.copy(fft_mag)
#alt_ethane_fr = np.copy(fft_fr)
#alt_ethane_fi = np.copy(fft_fi)
plt.loglog(fft_periods, alt_ethane_mag)
def red_background(nsim,mctest,t,x,ofac,all_t,all_x ):
#average dt of entire time series
diffs = [t[i+1]-t[i] for i in range(len(t)-1)]
avgdt = np.average(diffs)
ave = np.mean(x)
#subtract mean from data
x = x - ave
#GET TAU
tau, rhoavg, ierr = gettau(t,x,1,avgdt)
nout = int(0.5*int(ofac)*1*len(t))
if tau == 'invalid':
model_periods,model_mag,corr_model_mag,model_fr,model_fi,red_periods,red_mag_avg,gredth,fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,tau,corr = np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),np.zeros(nout),0,0,0,0,np.zeros(nout),np.zeros(nout),0,1
return model_periods,model_mag,corr_model_mag,model_fr,model_fi,red_periods,red_mag_avg,gredth,fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,tau,corr
#make sure that tau is non-negative
if (tau < 0.0):
print 'Negative tau is forced to zero.'
tau = 0.0
x = x + ave
#determine lag-1 autocorrelation coefficient
rho = np.exp(-avgdt / tau) # avg. autocorrelation coefficient
rhosq = rho * rho
#t = np.copy(all_t)
#x = np.copy(all_x)
xdif = np.max(t)-np.min(t)
#Calculate model spectrum
model_periods,model_mag,model_ph,model_fr,model_fi = modules.take_lomb_unwindowed(t,x,ofac,avgdt)
fft_periods_all,fft_mag_all,fft_fr,fft_fi,fft_array = modules.take_fft_unwindowed(t,x,avgdt)
fft_freq_all = 1./fft_periods_all
full_n = len(model_periods)
model_freq = 1./model_periods
# estimate data variance from data spectrum
# ----------------------------------------
varx = (model_freq[0]) * np.sum(model_mag) # NB: freq[1] = df
varx_fft = (fft_freq_all[0]) * np.sum(fft_mag_all)
red_mag = np.zeros((nsim,len(model_periods)))
red_mag_sum = np.zeros(len(model_periods))
fft_mag = np.zeros((nsim,len(fft_periods_all)))
fft_mag_sum = np.zeros(len(fft_periods_all))
#create AR1 spectrum nsim times
for i in range(nsim):
print 'Nsim = ', i+1
red = makear1(t,len(x),tau)
if mctest == True:
#red_periods,red_mag[i,:],red_ph,red_fr,red_fi = modules.take_lomb_unwindowed(t,red,ofac,avgdt)
#red_freq = 1./red_periods
fft_periods,fft_mag[i,:],fft_fr,fft_fi,fft_array = modules.take_fft_unwindowed(t,red,avgdt)
fft_freq = 1./fft_periods
else:
#red_periods,red_mag[0,:],red_ph,red_fr,red_fi = modules.take_lomb_unwindowed(t,red,ofac,avgdt)
#red_freq = 1./red_periods
fft_periods,fft_mag[0,:],fft_fr,fft_fi,fft_array = modules.take_fft_unwindowed(t,red,avgdt)
fft_freq = 1./fft_periods
#plt.loglog(red_periods,red_mag[0,:],color='black')
#plt.loglog(fft_periods,fft_mag[0,:],color='red')
#plt.show()
#red_periods = red_periods[cp:]
#red_mag = red_mag[0,cp:]
#scale and sum red-noise spectra
#-------------------------------
if mctest == True:
#varr = (red_freq[0]) * np.sum(red_mag[i,:]) # NB: freq[1] = df
#fac = varx / varr
#red_mag[i,:] = fac * red_mag[i,:]
#red_mag_sum = red_mag_sum + red_mag[i,:]
varr = (fft_freq[0]) * np.sum(fft_mag[i,:]) # NB: freq[1] = df
fac = varx_fft / varr
fft_mag[i,:] = fac * fft_mag[i,:]
fft_mag_sum = fft_mag_sum + fft_mag[i,:]
else:
#varr = (red_freq[0]) * np.sum(red_mag[0,:]) # NB: freq[1] = df
#fac = varx / varr
#red_mag_sum = red_mag_sum + fac * red_mag[0,:]
varr = (fft_freq[0]) * np.sum(fft_mag[0,:]) # NB: freq[1] = df
fac = varx_fft / varr
fft_mag_sum = fft_mag_sum + fac * fft_mag[0,:]
#determine average red-noise spectrum; scale average again to
#make sure that roundoff errors do not affect the scaling
#------------------------------------------------------------
#red_mag_avg = red_mag_sum / float(nsim)
#varr = (red_freq[0]) * np.sum(red_mag_avg)
#fac = varx / varr
#red_mag_avg = fac * red_mag_avg
fft_mag_avg = fft_mag_sum / float(nsim)
varr = (fft_freq[0]) * np.sum(fft_mag_avg)
fac = varx_fft / varr
fft_mag_avg = fac * fft_mag_avg
# set theoretical spectrum (e.g., Mann and Lees, 1996, Eq. 4)
# make area equal to that of the input time series
# -----------------------------------------------------------
#print red_freq[-1]
#fnyq = red_freq[-1]
#gredth = (1.0-rhosq) / (1.0-2.0*rho*np.cos(np.pi*red_freq/fnyq)+rhosq)
#varr = red_freq[0] * np.sum(gredth)
#fac = varx / varr
#gredth = fac * gredth
print fft_freq[-1]
fnyq = fft_freq[-1]
gredth_fft = (1.0-rhosq) / (1.0-2.0*rho*np.cos(np.pi*fft_freq/fnyq)+rhosq)
varr = fft_freq[0] * np.sum(gredth_fft)
fac = varx_fft / varr
gredth_fft = fac * gredth_fft
#ratio = float(len(act_periods))/float(len(model_periods))
#print 'ratio = ', ratio
#model_mag = model_mag/ratio
#red_mag_avg = red_mag_avg/ratio
#gredth = gredth/ratio
#determine correction factor
#---------------------------
#corr = red_mag_avg / gredth
#correct for bias in autospectrum
#--------------------------------
#corr_model_mag = model_mag / corr
#corr_model_mag = model_mag
#gredth = gredth*corr
#print 'model freq 0 = ', model_freq[1]
print 'varx = ', varx
print 'ofac = ', ofac
print 'avgdt = ', avgdt
print 'Avg. autocorr. coeff., rho = ', rho
print 'Avg. tau = ', tau
npoints = len(t) # of data points
nseg = int(2 * npoints / (1 + 1)) # points per segment
#avgdt = (t[-1] - t[0]) / (npoints-1.0) # average sampling interval
tp = avgdt * nseg # average period of a segment
#df = 1.0 / (ofac * tp) # freq. spacing
df = model_freq[0]
wz = 2.0 * np.pi * df # omega = 2*pi*f
fnyq = 1.0 * 1.0 / (2.0 * avgdt) # average Nyquist freq.
nfreq = fnyq / df + 1 # f(1) = f0; f(nfreq) = fNyq
lfreq = nfreq * 2
nout = nfreq
scal = 2.0 / (1.0 * nseg * df * ofac)
print 'df = ', df
print 'Nseg = ', nseg
print 'Scal = ', scal
print model_freq[0:20]
print model_freq[-10:]
#fft_mag_all = fft_mag_all*scal
#fft_mag_all = fft_mag_all/4.
#winbw = (model_freq[1]-model_freq[0]) * ofac * 1.21
#model_mag = model_mag*len(t)
#model_mag = 20*np.log10(model_mag)
#gredth = 20*np.log10(gredth)
#plt.loglog(red_periods,red_mag_avg)
#plt.loglog(fft_periods,fft_mag_avg)
#plt.loglog(fft_periods_all,fft_mag_avg)
#plt.loglog(fft_periods,gredth_fft)
#plt.plot(model_freq,model_mag)
#plt.plot(red_freq,red_mag_avg)
plt.loglog(fft_periods_all,fft_mag_all)
plt.loglog(fft_periods,fft_mag_avg)
#plt.plot(red_freq,gredth)
#plt.loglog(fft_periods,gredth_fft)
#plt.plot(model_freq,corr_model_mag)
#plt.show()
corr = [1.]*len(fft_freq)
fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,ci99 = significance_tests(x,fft_periods,fft_mag,nsim,1,corr,mctest)
plt.loglog(fft_periods,fft_mag_avg*fac95)
plt.loglog(fft_periods,fft_mag_avg*fac99)
plt.loglog(fft_periods,fft_mag_avg*faccrit)
plt.show()
return model_periods,model_mag,corr_model_mag,model_fr,model_fi,red_periods,red_mag_avg,gredth,fac95,fac99,fac99_9,faccrit,fac_grid,sig_levels,tau,corr
