def csd(self,xstr,ystr,nfft=256,noverlap=0,coarsable=False):
"""Return CSD(cross spectral density) of the time-series.
Positional parameters:
xstr -- string naming one observable, either 'A' or 'E'
ystr -- string naming one observable, either 'A' or 'E'
Keyword parameters:
nfft -- length of fast fourier transform(fft) (default 256)
noverlap -- number of data points overlapping between segments (default 0)
coarsable -- return the CSD as a Coarsable object (default False)
OUTPUT:
f -- frequencies
P -- CSD
Note:
The CPSD is calculated using pl.csd() with an additional factor of dt in the normalisation.
If xstr='A' and ystr='E', then the CSD between A and E is returned.
"""
x = getattr(self,xstr)
y = getattr(self,ystr)
fs = 1. / x.Cadence1
P , f = pl.csd( x.data , y.data , nfft , fs , noverlap=noverlap )
P = P / fs
if coarsable:
scale = {'Offset1' : f[0] ,
'Cadence1': f[1] - f[0] }
f = ASI.Coarsable( f , **scale )
P = ASI.Coarsable( P , **scale )
return f , P
def csd(self, xstr, ystr, nfft=256, noverlap=0, coarsable=False):
"""Return CSD(cross spectral density) of the time-series.
Positional parameters:
xstr -- string naming one observable, either 'A' or 'E'
ystr -- string naming one observable, either 'A' or 'E'
Keyword parameters:
nfft -- length of fast fourier transform(fft) (default 256)
noverlap -- number of data points overlapping between segments (default 0)
coarsable -- return the CSD as a Coarsable object (default False)
OUTPUT:
f -- frequencies
P -- CSD
Note:
The CPSD is calculated using pl.csd() with an additional factor of dt in the normalisation.
If xstr='A' and ystr='E', then the CSD between A and E is returned.
"""
x = getattr(self, xstr)
y = getattr(self, ystr)
fs = 1. / x.Cadence1
P, f = pl.csd(x.data, y.data, nfft, fs, noverlap=noverlap)
P = P / fs
if coarsable:
scale = {'Offset1': f[0], 'Cadence1': f[1] - f[0]}
f = ASI.Coarsable(f, **scale)
P = ASI.Coarsable(P, **scale)
return f, P
power_max = 3
Nsegs = 10**np.arange( power_max + 1 )
P12s = [] ; P12s_legend = [] ; C12s = [] ; C12s_legend = []
P13s = [] ; P13s_legend = [] ; C13s = [] ; C13s_legend = []
P23s = [] ; P23s_legend = [] ; C23s = [] ; C23s_legend = []
for i , Nseg in enumerate( Nsegs ) :
print "Taking %d averages to esimate spectral densities ... " % ( 2*Nseg )
nfft = int( np.round( N / Nseg ) )
noverlap = nfft / 2
P11 , f = pl.psd( n1 , nfft , fs , noverlap = noverlap )
P22 , f = pl.psd( n2 , nfft , fs , noverlap = noverlap )
P33 , f = pl.psd( n3 , nfft , fs , noverlap = noverlap )
P12 , f = pl.csd( n1 , n2 , nfft , fs , noverlap = noverlap )
P23 , f = pl.csd( n2 , n3 , nfft , fs , noverlap = noverlap )
P13 , f = pl.csd( n1 , n3 , nfft , fs , noverlap = noverlap )
C12 = np.abs( P12 )**2 / ( P11*P22 )
C23 = np.abs( P23 )**2 / ( P22*P33 )
C13 = np.abs( P13 )**2 / ( P11*P33 )
for k in range( C12.shape[0] ) :
if C12[k] < 0 :
print 'C12[%d] < 0' % k
P12s += [ f , np.abs( P12 ) ] ; C12s += [ f , C12 ] ; C12s_legend += [ '%d' % Nseg ]
P23s += [ f , np.abs( P23 ) ] ; C23s += [ f , C23 ] ; C23s_legend += [ '%d' % Nseg ]
P13s += [ f , np.abs( P13 ) ] ; C13s += [ f , C13 ] ; C13s_legend += [ '%d' % Nseg ]
print 'done'
print 'C12'
f = csddict['f'].data
P12 = csddict['AE'].data
P13 = csddict['AT'].data
P23 = csddict['ET'].data
print 'Estimating power spectral densities from some simulated time-series...'
tsdirz = '/gpfs1/JC0311443/workhere/stochasGW/Mapp/runs/EccenctricInclined_eta0_0_xi0_0_sw_1_t0_0/output/signal/point_sources/lon_263_lat_-35_plus_P00_GWslope_0/TDI/Michelson/G2/AET/noise/TDI/Michelson/G2/AET/simulation/by_me/stime_1.0_N_86400_for_days/data/'
tspathz = tsdirz + 'd%03d.pkl' % day
file = open( tspathz , 'rb' ) ; tsdictz = cpkl.load( file ) ; file.close()
tz = tsdictz['t'].data
s1z , s2z , s3z = tsdictz['1'].data , tsdictz['2'].data , tsdictz['3'].data
stimez = tz[1] - tz[0] ; inittimez = tz[0] ; Nz = tz.shape[0]
nfftz = int( np.round( Nz / 100 ) )
noverlapz = nfftz / 2
fsz = 1. / stimez
P12z , fz = pl.csd( s1z , s2z , nfftz , fsz , noverlap=noverlapz )
P13z , fz = pl.csd( s1z , s3z , nfftz , fsz , noverlap=noverlapz )
P23z , fz = pl.csd( s2z , s3z , nfftz , fsz , noverlap=noverlapz )
print 'done'
fig = plt.figure()
fig.suptitle( 'Cross Spectral Densities' )
ax1 = fig.add_subplot(311)
ax1.plot( fz , np.real( P12z ) , fz , np.imag( P12z ) , f , np.real( P12 ) , f , np.imag( P12 ) , 'y' )
# ax1.plot( f , np.real( P12 ) , f , np.imag( P12 ) , 'y' )
# ax1.plot( fz , np.real( P12z ) , fz , np.imag( P12z ) )
ax1.legend( ( 'real' , 'imag' ) )
ax1.set_ylabel( 'P12' )
ax2 = fig.add_subplot(312)
ax2.plot( fz , np.real( P13z ) , fz , np.imag( P13z ) , f , np.real( P13 ) , f , np.imag( P13 ) , 'y' )
# ax2.plot( f , np.real( P13 ) , f , np.imag( P13 ) , 'y' )
tspath = tsdir + 'd%03d.pkl' % day
file = open( tspath , 'rb' )
tsdict = cpkl.load( file ) ; file.close()
t = tsdict['t'].data
n1 , n2 , n3 = tsdict['1'].data , tsdict['2'].data , tsdict['3'].data
stime = t[1] - t[0] ; inittime = t[0] ; N = t.shape[0]
print "Taking %d averages to estimate spectral densities ... " % ( 2*Nseg )
nfft = int( np.round( N / Nseg ) )
noverlap = nfft / 2
fs = 1. / stime
P12 , f = pl.csd( n1 , n2 , nfft , fs , noverlap = noverlap )
P13 , f = pl.csd( n1 , n3 , nfft , fs , noverlap = noverlap )
P23 , f = pl.csd( n2 , n3 , nfft , fs , noverlap = noverlap )
fig = plt.figure()
ax = fig.add_subplot( 311 )
ax.plot( f , np.real( P12 ) , f , np.imag( P12 ) )
ax.legend( ( 'real' , 'imag' ) )
ax.set_ylabel( 'P12' )
ax.set_title( 'Day %d' % day )
ax = fig.add_subplot( 312 )
ax.plot( f , np.real( P13 ) , f , np.imag( P13 ) )
ax.legend( ( 'real' , 'imag' ) )
ax.set_ylabel( 'P13' )
ax = fig.add_subplot( 313 )
ax.plot( f , np.real( P23 ) , f , np.imag( P23 ) )
