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signal.py
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signal.py
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import numpy as np;
import matplotlib.pyplot as plt;
import scipy;
from scipy.ndimage import gaussian_filter, uniform_filter, median_filter;
from scipy.special import gammainc, gamma;
from scipy.interpolate import interp1d
from . import log, files, headers, setup, oifits;
def airy (x):
''' Airy function, with its zero at x = 1.22'''
return 2.*scipy.special.jn (1,np.pi*x) / (np.pi*x);
def gaussian_filter_cpx (input,sigma,**kwargs):
''' Gaussian filter of a complex array '''
return gaussian_filter (input.real,sigma,**kwargs) + \
gaussian_filter (input.imag,sigma,**kwargs) * 1.j;
def uniform_filter_cpx (input,sigma,**kwargs):
''' Uniform filter of a complex array '''
return uniform_filter (input.real,sigma,**kwargs) + \
uniform_filter (input.imag,sigma,**kwargs) * 1.j;
def getwidth (curve, threshold=None):
'''
Compute the width of curve around its maximum,
given a threshold. Return the tuple (center,fhwm)
'''
if threshold is None:
threshold = 0.5*np.max (curve);
# Find rising point
f = np.argmax (curve > threshold) - 1;
if f == -1:
log.warning ('Width detected outside the spectrum');
first = 0;
else:
first = f + (threshold - curve[f]) / (curve[f+1] - curve[f]);
# Find lowering point
l = len(curve) - np.argmax (curve[::-1] > threshold) - 1;
if l == len(curve)-1:
log.warning ('Width detected outside the spectrum');
last = l;
else:
last = l + (threshold - curve[l]) / (curve[l+1] - curve[l]);
return 0.5*(last+first), 0.5*(last-first);
def bootstrap_matrix (snr, gd):
'''
Compute the best SNR and GD of each baseline when considering
also the boostraping capability of the array.
snr and gd shall be of shape (...,nb)
Return (snr_b, gd_b) of same size, but including bootstrap.
'''
log.info ('Bootstrap baselines with linear matrix');
# User a power to implement a type of min/max of SNR
power = 4.0;
# Reshape
shape = snr.shape;
snr = snr.reshape ((-1,shape[-1]));
gd = gd.reshape ((-1,shape[-1]));
ns,nb = gd.shape;
# Ensure no zero and no nan
snr[~np.isfinite (snr)] = 0.0;
snr = np.maximum (snr,1e-1);
snr = np.minimum (snr,1e3);
log.info ('Compute OPD_TO_OPD');
# The OPL_TO_OPD matrix
OPL_TO_OPD = setup.beam_to_base;
# OPD_TO_OPL = (OPL_TO_OPD^T.snr.OPL_TO_OPD)^-1 . OPL_TO_OPD^T.W_OPD
# o is output OPL
JtW = np.einsum ('tb,sb->stb',OPL_TO_OPD.T,snr**power);
JtWJ = np.einsum ('stb,bo->sto',JtW,OPL_TO_OPD);
JtWJ_inv = np.array([ np.linalg.pinv (JtWJ[s]) for s in range(ns)]);# 'sot'
OPD_TO_OPL = np.einsum ('sot,stb->sob', JtWJ_inv, JtW);
# OPD_TO_OPD = OPL_TO_OPD.OPD_TO_OPL (m is output OPD)
OPD_TO_OPD = np.einsum ('mo,sob->smb', OPL_TO_OPD, OPD_TO_OPL);
log.info ('Compute gd_b and snr_b');
# GDm = OPD_TO_OPD . GD
gd_b = np.einsum ('smb,sb->sm',OPD_TO_OPD,gd);
# Cm = OPD_TO_OPD . C_OPD . OPD_TO_OPD^T
OPD_TO_OPD_W = np.einsum ('smb,sb->smb',OPD_TO_OPD,snr**-power);
cov_b = np.einsum ('smb,snb->smn',OPD_TO_OPD_W, OPD_TO_OPD);
# Reform SNR from covariance
snr_b = np.diagonal (cov_b, axis1=1, axis2=2)**-(1./power);
snr_b[snr_b < 1e-2] = 0.0;
# Reshape
snr = snr.reshape (shape);
gd = gd.reshape (shape);
snr_b = snr_b.reshape (shape);
gd_b = gd_b.reshape (shape);
return (snr_b,gd_b);
def bootstrap_triangles (snr,gd):
'''
Compute the best SNR and GD of each baseline when considering
also the boostraping capability of the array.
snr and gd shall be of shape (...,nb)
Return (snr_b, gd_b) of same size, but including bootstrap.
'''
log.info ('Bootstrap baselines with triangles');
# Reshape
shape = snr.shape;
snr = snr.reshape ((-1,shape[-1]));
gd = gd.reshape ((-1,shape[-1]));
ns,nb = gd.shape;
# Ensure no zero and no nan
snr[~np.isfinite (snr)] = 0.0;
snr = np.maximum (snr,1e-1);
snr = np.minimum (snr,1e3);
# Create output
gd_b = gd.copy ();
snr_b = snr.copy ();
# Sign of baseline in triangles
sign = np.array ([1.0,1.0,-1.0]);
# Loop several time over triplet to also
# get the baseline tracked by quadruplets.
for i in range (7):
for tri in setup.triplet_base ():
for s in range (ns):
i0,i1,i2 = np.argsort (snr_b[s,tri]);
# Set SNR as the worst of the two best
snr_b[s,tri[i0]] = snr_b[s,tri[i1]];
# Set the GD as the sum of the two best
mgd = gd_b[s,tri[i1]] * sign[i1] + gd_b[s,tri[i2]] * sign[i2];
gd_b[s,tri[i0]] = - mgd * sign[i0];
# Reshape
snr = snr.reshape (shape);
gd = gd.reshape (shape);
snr_b = snr_b.reshape (shape);
gd_b = gd_b.reshape (shape);
return (snr_b,gd_b);
def bootstrap_triangles_jdm (snr,gd):
'''
MIRC/JDM Method: Compute the best SNR and GD of each baseline when considering
also the boostraping capability of the array.
snr and gd shall be of shape (...,nb)
Return (snr_b, gd_b) of same size, but including bootstrap.
'''
log.info ('Bootstrap baselines with triangles using MIRC/JDM method');
w=snr.copy()
opd0=gd.copy()
ns,nf,ny,nb=snr.shape
a=np.zeros((ns,nf,ny,5,5))
b=np.zeros((ns,nf,ny,5))
gd_jdm = np.zeros((ns,nf,ny,15))
# Reshape
shape = snr.shape;
snr = snr.reshape ((-1,shape[-1]));
gd = gd.reshape ((-1,shape[-1]));
ns,nb = gd.shape;
# Ensure no zero and no nan
snr[~np.isfinite (snr)] = 0.0;
snr = np.maximum (snr,1e-1);
snr = np.minimum (snr,1e3);
# Create output
gd_b = gd.copy ();
snr_b = snr.copy ();
# Sign of baseline in triangles
sign = np.array ([1.0,1.0,-1.0]);
# Loop several time over triplet to also
# get the baseline tracked by quadruplets.
for i in range (7):
for tri in setup.triplet_base ():
for s in range (ns):
i0,i1,i2 = np.argsort (snr_b[s,tri]);
# Set SNR as the worst of the two best
snr_b[s,tri[i0]] = snr_b[s,tri[i1]];
# Set the GD as the sum of the two best
mgd = gd_b[s,tri[i1]] * sign[i1] + gd_b[s,tri[i2]] * sign[i2];
gd_b[s,tri[i0]] = - mgd * sign[i0];
# Reshape
snr = snr.reshape (shape);
gd = gd.reshape (shape);
snr_b = snr_b.reshape (shape);
gd_b = gd_b.reshape (shape);
OPD=opd0.copy()
OPD=np.where(w <=1., 0.0, OPD)
w=np.where(w <=1., .01, w)
#inzero=np.argwhere(w <= 100.)
#OPD[inzero]=0.0
#w[inzero]=.01
opd12=OPD[:,:,:,0];
opd13=OPD[:,:,:,1];
opd14=OPD[:,:,:,2];
opd15=OPD[:,:,:,3];
opd16=OPD[:,:,:,4];
opd23=OPD[:,:,:,5];
opd24=OPD[:,:,:,6];
opd25=OPD[:,:,:,7];
opd26=OPD[:,:,:,8];
opd34=OPD[:,:,:,9];
opd35=OPD[:,:,:,10];
opd36=OPD[:,:,:,11];
opd45=OPD[:,:,:,12];
opd46=OPD[:,:,:,13];
opd56=OPD[:,:,:,14];
w12=w[:,:,:,0]+0.001;
w13=w[:,:,:,1]+0.002;
w14=w[:,:,:,2]+0.005;
w15=w[:,:,:,3]+0.007;
w16=w[:,:,:,4]+0.003;
w23=w[:,:,:,5]+0.004;
w24=w[:,:,:,6]+0.008;
w25=w[:,:,:,7]+0.009;
w26=w[:,:,:,8]+0.002;
w34=w[:,:,:,9]+0.003;
w35=w[:,:,:,10]+0.006;
w36=w[:,:,:,11]+0.008;
w45=w[:,:,:,12]+0.009;
w46=w[:,:,:,13]+0.004;
w56=w[:,:,:,14]+0.005;
a[:,:,:,0,0] = w12+w23+w24+w25+w26;
a[:,:,:,1,1] = w13+w23+w34+w35+w36;
a[:,:,:,2,2] = w14+w24+w34+w45+w46;
a[:,:,:,3,3] = w15+w25+w35+w45+w56;
a[:,:,:,4,4] = w16+w26+w36+w46+w56;
a[:,:,:,0,1] = -w23;
a[:,:,:,0,2] = -w24;
a[:,:,:,0,3] = -w25;
a[:,:,:,0,4] = -w26;
a[:,:,:,1,0] = -w23;
a[:,:,:,1,2] = -w34;
a[:,:,:,1,3] = -w35;
a[:,:,:,1,4] = -w36;
a[:,:,:,2,0] = -w24;
a[:,:,:,2,1] = -w34;
a[:,:,:,2,3] = -w45;
a[:,:,:,2,4] = -w46;
a[:,:,:,3,0] = -w25;
a[:,:,:,3,1] = -w35;
a[:,:,:,3,2] = -w45;
a[:,:,:,3,4] = -w56;
a[:,:,:,4,0] = -w26;
a[:,:,:,4,1] = -w36;
a[:,:,:,4,2] = -w46;
a[:,:,:,4,3] = -w56;
b[:,:,:,0] = w12*opd12 - w23*opd23 - w24*opd24 - w25*opd25 - w26*opd26;
b[:,:,:,1] = w13*opd13 + w23*opd23 - w34*opd34 - w35*opd35 - w36*opd36;
b[:,:,:,2] = w14*opd14 + w24*opd24 + w34*opd34 - w45*opd45 - w46*opd46;
b[:,:,:,3] = w15*opd15 + w25*opd25 + w35*opd35 + w45*opd45 - w56*opd56;
b[:,:,:,4] = w16*opd16 + w26*opd26 + w36*opd36 + w46*opd46 + w56*opd56;
#invert!
result=np.linalg.solve(a, b)
gd_jdm[:,:,:,0]=result[:,:,:,0]
gd_jdm[:,:,:,1]=result[:,:,:,1]
gd_jdm[:,:,:,2]=result[:,:,:,2]
gd_jdm[:,:,:,3]=result[:,:,:,3]
gd_jdm[:,:,:,4]=result[:,:,:,4]
gd_jdm[:,:,:,5]=result[:,:,:,1]-result[:,:,:,0]
gd_jdm[:,:,:,6]=result[:,:,:,2]-result[:,:,:,0]
gd_jdm[:,:,:,7]=result[:,:,:,3]-result[:,:,:,0]
gd_jdm[:,:,:,8]=result[:,:,:,4]-result[:,:,:,0]
gd_jdm[:,:,:,9]=result[:,:,:,2]-result[:,:,:,1]
gd_jdm[:,:,:,10]=result[:,:,:,3]-result[:,:,:,1]
gd_jdm[:,:,:,11]=result[:,:,:,4]-result[:,:,:,1]
gd_jdm[:,:,:,12]=result[:,:,:,3]-result[:,:,:,2]
gd_jdm[:,:,:,13]=result[:,:,:,4]-result[:,:,:,2]
gd_jdm[:,:,:,14]=result[:,:,:,4]-result[:,:,:,3]
return (snr_b,gd_jdm,result);
def gd_tracker(opds_trial,input_snr,gd_key):
'''
Used for fitting a self-consistent set of opds. input 5 telscope delays
and compare to the snr vectors in opds space.
return a globabl metric base don logs of the snrs with thresholds.
'''
#log.info ('Bootstrap baselines with triangles using MIRC/JDM method');
# probably replace as matrix in future for vectorizing.
gd_jdm,snr_jdm = get_gds(opds_trial,input_snr,gd_key)
#fit_metric = np.sum(np.log10(snr_jdm))
fit_metric = np.sum(snr_jdm)
return (-fit_metric);
def get_gds(topds,input_snr,gd_key):
'''
Used for fitting a self-consistent set of opds. input 5 telscope delays
and compare to the snr vectors in opds space.
return a gds and snrs for self-consistent set of delays.
'''
nscan,nb=input_snr.shape
gd_jdm=np.zeros(nb)
snr_jdm=np.zeros(nb)
gd_jdm[0]=topds[0]
gd_jdm[1]=topds[1]
gd_jdm[2]=topds[2]
gd_jdm[3]=topds[3]
gd_jdm[4]=topds[4]
gd_jdm[5]=topds[1]-topds[0]
gd_jdm[6]=topds[2]-topds[0]
gd_jdm[7]=topds[3]-topds[0]
gd_jdm[8]=topds[4]-topds[0]
gd_jdm[9]=topds[2]-topds[1]
gd_jdm[10]=topds[3]-topds[1]
gd_jdm[11]=topds[4]-topds[1]
gd_jdm[12]=topds[3]-topds[2]
gd_jdm[13]=topds[4]-topds[2]
gd_jdm[14]=topds[4]-topds[3]
# interpolate into the snr.
for i in range(nb):
#snr_func=interp1d(gd_key,input_snr[:,i],kind='cubic',bounds_error=False,fill_value=(input_snr[:,i]).min(),assume_sorted=True)
snr_func=interp1d(gd_key,input_snr[:,i],kind='cubic',bounds_error=False,fill_value=1.,assume_sorted=True)
snr_jdm[i]=snr_func(gd_jdm[i])
return(gd_jdm,snr_jdm)
def get_gd_gravity(topds, bestsnr_snrs,bestsnr_indices,softlength=2.,nscan=None):
'''
Used for fitting a self-consistent set of opds. input 5 telscope delays
and compare to the snr vectors in opds space.
return a gds and snrs for self-consistent set of delays.
topds = (nramps,nframes, ntels=5)
bestsnr_snrs = (nramps, nframes, npeaks, nbaselines )
bestsnr_indices = (nramps, nframes, npeaks, nbaselines ) ; integers
'''
nr,nf,npeak,nt=topds.shape
nr,nf,npeak,nb=bestsnr_snrs.shape
OPL_TO_OPD = setup.beam_to_base;
temp = setup.base_beam ()
#photo_power = photo[:,:,:,setup.base_beam ()];
#totflux = np.nansum(photo,axis=(1,3))
#bp=np.nanmean(bias_power,axis=2)
topds1= topds[:,:,:,setup.base_beam ()]
gd_jdm= topds1[:,:,:,:,1] - topds1[:,:,:,:,0]
# if gd_jdm > nscan/2 than wraparond. but.. does sign work in fordce equation.. will have to check.
##if nscan != None:
# gd_jdm= np.where( gd_jdm >nscan/2, gd_jdm-nscan ,gd_jdm)
# gd_jdm= np.where( gd_jdm < -nscan/2, nscan + gd_jdm, gd_jdm)
# alternatively instead of adding in a discontunity, we could copy the force centers +/- nscan and apply
# global down-weight.
if nscan != None:
bestsnr_snrs=np.concatenate((bestsnr_snrs,bestsnr_snrs,bestsnr_snrs),axis=2)
bestsnr_indices=np.concatenate((bestsnr_indices,bestsnr_indices+nscan,bestsnr_indices-nscan),axis=2)
bestsnr_snrs = bestsnr_snrs*np.exp(-.5*((bestsnr_indices/(nscan/2.))**2))
snr_wt = np.log10(np.maximum(bestsnr_snrs,1.0))
#snr_wt = np.sqrt(bestsnr_snrs)
gd_forces=np.empty( (nr,nf,1,0))
gd_pot =np.empty( (nr,nf,1,0))
gd_offsets =gd_jdm-bestsnr_indices
for i_b in range(nt):
factor0=OPL_TO_OPD[:,i_b][None,None,None,:]
F0 = np.sum(factor0*snr_wt *np.sign(gd_offsets)*softlength**2/ (gd_offsets**2+softlength**2) ,axis=(2,3))
gd_forces =np.append(gd_forces,F0[:,:,None,None],axis=3)
F1 = np.sum(-2*np.abs(factor0)*snr_wt *softlength/ np.sqrt(gd_offsets**2+softlength**2) ,axis=(2,3)) # approximate!
gd_pot = np.append(gd_pot,F1[:,:,None,None],axis=3)
return(gd_forces,gd_pot,gd_jdm )
def topd_to_gds(topds):
'''
Used for fitting a self-consistent set of opds. input 5 telscope delays
and compare to the snr vectors in opds space.
return a gds and snrs for self-consistent set of delays.
topds = (nramps,nframes, ntels = 6)
bestsnr_snrs = (nramps, nframes, npeaks, nbaselines )
bestsnr_indices = (nramps, nframes, npeaks, nbaselines ) ; integers
'''
#photo_power = photo[:,:,:,setup.base_beam ()];
#totflux = np.nansum(photo,axis=(1,3))
#bp=np.nanmean(bias_power,axis=2)
topds1= topds[:,:,:,setup.base_beam ()]
gd_jdm= topds1[:,:,:,:,0] - topds1[:,:,:,:,1]
return(gd_jdm)
def psd_projection (scale, freq, freq0, delta0, data):
'''
Project the PSD into a scaled theoretical model,
Return the merit function 1. - D.M / sqrt(D.D*M.M)
'''
# Scale the input frequencies
freq_s = freq * scale;
# Compute the model of PSD
model = np.sum (np.exp (- (freq_s[:,None] - freq0[None,:])**2 / delta0**2), axis=-1);
if data is None:
return model;
# Return the merit function from the normalised projection
weight = np.sqrt (np.sum (model * model) * np.sum (data * data));
return 1. - np.sum (model*data) / weight;
def decoherence_free (x, vis2, cohtime, expo):
'''
Decoherence loss due to phase jitter, from Monnier equation:
vis2*2.*cohtime/(expo*x) * ( igamma(1./expo,(x/cohtime)^(expo))*gamma(1./expo) -
(cohtime/x)*gamma(2./expo)*igamma(2./expo,(x/cohtime)^(expo)) )
vis2 is the cohence without jitter, cohtime is the coherence time, expo is the exponent
of the turbulent jitter (5/3 for Kolmogorof)
'''
xc = x/cohtime;
xce = (xc)**expo;
y = gammainc (1./expo, xce) * gamma (1./expo) - gamma (2./expo) / xc * gammainc (2./expo, xce);
y *= 2. * vis2 / expo / xc;
return y;
def decoherence (x, vis2, cohtime):
'''
decoherence function with a fixed exponent
'''
expo = 1.5;
xc = x/cohtime;
xce = (xc)**expo;
y = gammainc (1./expo, xce) * gamma (1./expo) - gamma (2./expo) / xc * gammainc (2./expo, xce);
y *= 2. * vis2 / expo / xc;
return y;