/
kergain_sim_disk.py
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kergain_sim_disk.py
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import numpy as np
import matplotlib.pyplot as plt
import pysco
from pysco.core import *
import fitsio
from time import time as clock
from old_diffract_tools import *
import pymultinest
from pysco.diffract_tools import shift_image_ft
from pysco.common_tasks import shift_image
from swiftmask import swiftpupil
import matplotlib as mpl
from astropy.table import Table
mpl.rcParams['figure.figsize']=(8.0,6.0) #(6.0,4.0)
mpl.rcParams['font.size']= 18 #10
mpl.rcParams['savefig.dpi']=200 #72
mpl.rcParams['axes.labelsize'] = 16
mpl.rcParams['xtick.labelsize'] = 12
mpl.rcParams['ytick.labelsize'] = 12
shift = np.fft.fftshift
fft = np.fft.fft2
ifft = np.fft.ifft2
fftfreq = np.fft.fftfreq
fftn = np.fft.fftn
rfftn = np.fft.rfftn
dtor = np.pi/180.0
# =========================================================================
# =========================================================================
def print_time(t):
if t>3600:
print 'Time taken: %d h %d m %3f s'\
% (np.int(np.floor(t/3600)), np.int(np.floor(np.mod(t,3600)/60)),np.mod(t,60))
elif t>60:
print 'Time taken: %d m %3f s' % (np.int(np.floor(np.mod(t,3600)/60)),np.mod(t,60) )
else:
print 'Time taken: %3f s' % t
# =========================================================================
# =========================================================================
'''------------------------------------------------------------
kergain_sim.py
Automate a simulation of the effectiveness of raw visibility
fitting versus kernel amplitudes
------------------------------------------------------------'''
pupil = 'plain'
try:
a = pysco.kpi('./geometry/'+pupil+'model.pick')
print 'Loaded kernel phase object'
except:
a = pysco.kpi('./geometry/'+pupil+'.txt')
a.name = 'Test'
a.save_to_file('./geometry/'+pupil+'model.pick')
nbuv, nbh = a.nbuv, a.nbh
try:
KerGain = np.loadtxt('KerGain_plain.csv')
print 'Loaded kernel amplitude matrix'
except:
gtfm = np.abs(a.TFM)
U, S, Vh = np.linalg.svd(gtfm.T, full_matrices=1)
S1 = np.zeros(nbuv)
S1[0:nbh-1] = S
nkg = np.size(np.where(abs(S1) < 1e-3))
print nkg
KGCol = np.where(abs(S1) < 1e-3)[0]
KerGain = np.zeros((nkg, nbuv)) # allocate the array
for i in range(nkg):
KerGain[i,:] = (Vh)[KGCol[i],:]
np.savetxt('KerGain_plain.csv',KerGain)
print 'saved'
def make_ellipse(semi_axis,ecc,thick,sz=256,pscale=36.):
semi_axis, thick = semi_axis/pscale, thick/pscale
b = semi_axis*np.sqrt(1-ecc**2.)
bmin = (semi_axis-thick)*np.sqrt(1-ecc**2)
x = np.arange(sz)-sz/2.
xx, yy = np.meshgrid(x,x)
outer = (np.sqrt((xx/semi_axis)**2 + (yy/b)**2)< 1)
inner = (np.sqrt((xx/(semi_axis-thick))**2 + (yy/bmin)**2) >1)
plain = np.ones((sz,sz))
plain[~(outer*inner)] = 0
return plain/plain.sum()
from scipy.special import j1
def vis_gauss(d,u,v):
d = mas2rad(d)
return np.exp(-(np.pi*d*np.sqrt(u**2+v**2))**2/4./np.log(2))
def vis_ud(d,u,v):
r = np.sqrt(u**2+v**2)
t = 2*j1(np.pi*d*r)/(np.pi*d*r)
t[r <=(1/d*1e-5)] = 1.
return t
def vis_ellipse_disk(semi_axis,ecc,theta,u,v):
semi_axis = mas2rad(semi_axis)
thetad = np.pi*theta/180.
u1, v1 = u*np.cos(thetad)+v*np.sin(thetad), -u*np.sin(thetad)+v*np.cos(thetad)
ad, bd = semi_axis, semi_axis*np.sqrt(1-ecc**2.)
u1, v1 = u1*ad, v1*bd
return vis_ud(0.5,u1,v1)
def vis_ellipse_thin(semi_axis,ecc,theta,thick,u,v):
ad, bd = semi_axis, semi_axis*np.sqrt(1.-ecc**2.)
a2, b2 = semi_axis-thick, (semi_axis-thick)*np.sqrt(1.-ecc**2)
n1, n2 = ad*bd, a2*b2
return vis_ellipse_disk(semi_axis,ecc,theta,u,v)-n2/n1*vis_ellipse_disk(semi_axis-thick,ecc,theta,u,v)
def vis_ellipse_gauss(semi_axis,thick,gausswidth,ecc,theta,u,v):
return vis_gauss(gausswidth,u,v)*vis_ellipse_thin(semi_axis,thick,ecc,theta,u,v)
def my_convolve_2d(array1,array2):
return shift(ifft(fft(shift(array1))*fft(shift(array2))))
def my_gauss_blur(array1,gausswidth):
gausswidth *= spaxel
s = np.shape(array1)[0]
x = np.arange(s)-s/2.
xx,yy = np.meshgrid(x,x)
rr = np.sqrt(xx**2 + yy**2)
gauss = np.exp(-(rr/gausswidth)**2)
return np.abs(my_convolve_2d(array1,gauss))
def mk_star_with_ring(psf_temp,ring,con):
dummy = np.abs(my_convolve_2d(ring,psf_temp))
dummy /= dummy.sum()
ff = psf_temp/psf_temp.sum()+dummy/con
return ff/ff.sum()
def make_disk(psf_temp,params,contrast):
dummy = make_ellipse(*params)
return mk_star_with_ring(psf_temp,dummy,contrast)
###-----------------------------------------
### now initialize a simulation
###-----------------------------------------
'''------------------------------
First, set all your parameters.
------------------------------'''
print '\nSimulating a basic PSF'
wavel = 2.5e-6
rprim = 5.093/2.#36903.e-3/2.
rsec= 1.829/2.
pos = [0,0] #m, deg
spaxel = 36.
piston = 0
nimages = 200
reso = rad2mas(wavel/(2*rprim))
print 'Minimum Lambda/D = %.3g mas' % reso
image, imagex = diffract(wavel,rprim,rsec,pos,piston=piston,spaxel=spaxel,seeing=None,verbose=False,\
show_pupil=False,mode=None)
# image = recenter(image,sg_rad=25)
imsz = image.shape[0]
images = np.zeros((nimages,imsz,imsz))
psfs = np.zeros((nimages,imsz,imsz))
'''----------------------------------------
Loop over a range of contrasts
----------------------------------------'''
contrast_list = np.linspace(10,4000.,39)
ncalcs = len(contrast_list)
ksemis, keccs, kthetas, kthicks, kcons = np.zeros(ncalcs), np.zeros(ncalcs),np.zeros(ncalcs), np.zeros(ncalcs), np.zeros(ncalcs)
dksemis, dkeccs, dkthetas, dkthicks, dkcons = np.zeros(ncalcs), np.zeros(ncalcs),np.zeros(ncalcs), np.zeros(ncalcs), np.zeros(ncalcs)
vsemis, veccs, vthetas, vthicks, vcons = np.zeros(ncalcs), np.zeros(ncalcs),np.zeros(ncalcs), np.zeros(ncalcs), np.zeros(ncalcs)
dvsemis, dveccs, dvthetas, dvthicks, dvcons = np.zeros(ncalcs), np.zeros(ncalcs),np.zeros(ncalcs), np.zeros(ncalcs), np.zeros(ncalcs)
t0 = clock()
true_vals = (300.,0.95,100)
amp = 0.1
try:
dummy = fitsio.FITS('psf_cube_scint_%.2f_wavel_%.2f.fits' % (amp,wavel*1e6))
psfs = dummy[0][:,:,:]
print 'Loaded PSFs'
except:
print 'Creating PSFs'
for j in range(nimages):
psfs[j,:,:], imagex = diffract(wavel,rprim,rsec,pos,piston=piston,spaxel=spaxel,
verbose=False,show_pupil=show,mode='amp',
perturbation=None,amp=amp)
fitsio.write('psf_cube_scint_%.2f_wavel_%.2f.fits' % (amp,wavel*1e6),psfs)
imsz = image.shape[0]
print_time(clock()-t0)
'''----------------------------------------
Initialise pysco with a pupil model
----------------------------------------'''
# meter to pixel conversion factor
scale = 1.0
m2pix = mas2rad(spaxel) * imsz/ wavel * scale
uv_samp = a.uv * m2pix + imsz/2 # uv sample coordinates in pixels
x = a.mask[:,0]
y = a.mask[:,1]
rev = 1
ac = shift(fft(shift(image)))
ac /= (np.abs(ac)).max() / a.nbh
uv_samp_rev=np.cast['int'](np.round(uv_samp))
uv_samp_rev[:,0]*=rev
data_cplx=ac[uv_samp_rev[:,1], uv_samp_rev[:,0]]
vis2 = np.abs(data_cplx)
vis2 /= vis2.max() #normalise to the origin
'''----------------------------------------
Now loop over simulated disks
----------------------------------------'''
for trial, contrast in enumerate(contrast_list):
print '\nSimulating for contrast %f' % contrast
thistime = clock()
true_params = [true_vals[0]*4.,true_vals[1],0.,true_vals[2]/float(true_vals[0]),contrast]
for j in range(nimages):
images[j,:,:] = make_disk(psfs[j,:,:],true_vals,contrast)
imsz = images.shape[1]
'''----------------------------------------
Extract Visibilities
----------------------------------------'''
kervises = np.zeros((nimages,KerGain.shape[0]))
vis2s = np.zeros((nimages,vis2.shape[0]))
for j in range(nimages):
image2 = images[j,:,:]
ac2 = shift(fft(shift(image2)))
ac2 /= (np.abs(ac2)).max() / a.nbh
data_cplx2=ac2[uv_samp_rev[:,1], uv_samp_rev[:,0]]
vis2b = np.abs(data_cplx2)
vis2b /= vis2b.max() #normalise to the origin
vis2s[j,:]=vis2b
kervises[j,:] = np.dot(KerGain,vis2b/vis2-1.)
'''----------------------------------------
Now Model
----------------------------------------'''
paramlimits = [50.,10000.,0.,0.99,-90.,90.,0.02,0.49,contrast/4.,contrast*4.]
hdr = {'tel':'HST',
'filter':wavel,
'orient':0}
def vis_model(cube,kpi):
con = 1./cube[4]
u, v = (kpi.uv/wavel).T
unresolved = 1./(1.+con)
flux_ratio = con/(1.+con)
vises = vis_ellipse_thin(cube[0],cube[1],cube[2],cube[0]*cube[3],u,v)
norm = vis_ellipse_thin(cube[0],cube[1],cube[2],cube[0]*cube[3],np.array([1e-5]),np.array([1e-5]))
vises = (vises/norm *flux_ratio + unresolved)
return vises
### define prior and loglikelihood
def kg_loglikelihood(cube,kgd,kge,kpi):
'''Calculate chi2 for single band kernel phase data.
Used both in the MultiNest and MCMC Hammer implementations.'''
vises = vis_model(cube,kpi)
kergains = np.dot(KerGain,vises-1.)
chi2 = np.sum(((kgd-kergains)/kge)**2)
return -chi2/2.
def vis_loglikelihood(cube,vdata,ve,kpi):
'''Calculate chi2 for single band kernel phase data.
Used both in the MultiNest and MCMC Hammer implementations.'''
vises = vis_model(cube,kpi)**2.
chi2 = np.sum(((vdata-vises)/ve)**2)
return -chi2/2.
def myprior(cube, ndim, n_params,paramlimits=paramlimits):
cube[0] = (paramlimits[1] - paramlimits[0])*cube[0]+paramlimits[0]
cube[1] = (paramlimits[3] - paramlimits[2])*cube[1]+paramlimits[2]
cube[2] = (paramlimits[5] - paramlimits[4])*cube[2]+paramlimits[4]
cube[3] = (paramlimits[7] - paramlimits[6])*cube[3]+paramlimits[6]
cube[4] = (paramlimits[9] - paramlimits[8])*cube[4]+paramlimits[8]
'''-----------------------------------------------
First do kernel amplitudes
-----------------------------------------------'''
my_observable = np.mean(kervises,axis=0)
addederror = 0.000001 # in case there are bad frames
my_error = np.sqrt((np.std(kervises,axis=0))**2+addederror**2)
print 'Error:', my_error
def myloglike_kg(cube,ndim,n_params):
try:
loglike = kg_loglikelihood(cube,my_observable,my_error,a)
return loglike
except:
return -np.inf
parameters = ['Semi-major axis','Eccentricity','Position Angle', 'Thickness','Contrast']
n_params = len(parameters)
resume=False
eff=0.3
multi=True,
max_iter= 10000
ndim = n_params
pymultinest.run(myloglike_kg, myprior, n_params,wrapped_params=[2],
verbose=False,resume=False,max_iter=max_iter)
thing = pymultinest.Analyzer(n_params = n_params)
try:
s = thing.get_stats()
ksemis[trial], dksemis[trial] = s['marginals'][0]['median']/4., s['marginals'][0]['sigma']/4.
keccs[trial], dkeccs[trial] = s['marginals'][1]['median'], s['marginals'][1]['sigma']
kthetas[trial], dkthetas[trial] = s['marginals'][2]['median'], s['marginals'][2]['sigma']
kthicks[trial], dkthicks[trial] = s['marginals'][3]['median'], s['marginals'][3]['sigma']
kcons[trial], dkcons[trial] = s['marginals'][4]['median'], s['marginals'][4]['sigma']
stuff = thing.get_best_fit()
best_params = stuff['parameters']
print 'Best params (kg):', best_params
ksemis[trial] = best_params[0]/4.
keccs[trial] = best_params[1]
kthetas[trial] = best_params[2]
kthicks[trial] = best_params[3]
kcons[trial] = best_params[4]
model = np.dot(KerGain,vis_model(best_params,a)-1.)
true_model = np.dot(KerGain,vis_model(true_params,a)-1.)
plt.clf()
plt.errorbar(my_observable,true_model,xerr=my_error,color='b',alpha=0.5,
ls='',markersize=10,linewidth=2.5)
plt.errorbar(my_observable,model,xerr=my_error,color='k',
ls='',markersize=10,linewidth=2.5)
plt.xlabel('Measured Kernel Amplitudes')
plt.ylabel('Model Kernel Amplitudes')
plt.title('Model Fit: Kernel Amplitudes, Contrast %.1f' % contrast)
plt.savefig('kpfit_%.1f_con.png' % contrast)
except:
print 'Failed!'
ksemis[trial], dksemis[trial] = 0,0
keccs[trial], dkeccs[trial] = 0,0
kthetas[trial], dkthetas[trial] = 0,0
kthicks[trial], dkthicks[trial] = 0,0
kcons[trial], dkcons[trial] = 0,0
print 'Kernel amplitudes done'
print_time(clock()-thistime)
print ''
'''-----------------------------------------------
Now do visibilities
-----------------------------------------------'''
my_observable = np.mean((vis2s/vis2)**2,axis=0)
print '\nDoing raw visibilities'
my_error = np.sqrt((np.std((vis2s/vis2)**2,axis=0))**2+addederror**2)
print 'Error:', my_error
def myloglike_vis(cube,ndim,n_params):
try:
loglike = vis_loglikelihood(cube,my_observable,my_error,a)
return loglike
except:
return -np.inf
thistime = clock()
pymultinest.run(myloglike_vis, myprior, n_params,wrapped_params=[2],
verbose=False,resume=False,max_iter=max_iter)
thing = pymultinest.Analyzer(n_params = n_params)
try:
s = thing.get_stats()
vsemis[trial], dvsemis[trial] = s['marginals'][0]['median']/4., s['marginals'][0]['sigma']/4.
veccs[trial], dveccs[trial] = s['marginals'][1]['median'], s['marginals'][1]['sigma']
vthetas[trial], dvthetas[trial] = s['marginals'][2]['median'], s['marginals'][2]['sigma']
vthicks[trial], dvthicks[trial] = s['marginals'][3]['median'], s['marginals'][3]['sigma']
vcons[trial], dvcons[trial] = s['marginals'][4]['median'], s['marginals'][4]['sigma']
stuff = thing.get_best_fit()
best_params = stuff['parameters']
print 'Best params (vis):', best_params
vsemis[trial] = best_params[0]/4.
veccs[trial] = best_params[1]
vthetas[trial] = best_params[2]
vthicks[trial] = best_params[3]
vcons[trial] = best_params[4]
model = vis_model(best_params,a)**2.
true_model = vis_model(true_params,a)**2.
plt.clf()
plt.errorbar(my_observable,true_model,xerr=my_error,color='b',alpha=0.5,
ls='',markersize=10,linewidth=2.5)
plt.errorbar(my_observable,model,xerr=my_error,color='k',
ls='',markersize=10,linewidth=2.5)
plt.xlabel('Measured Square Visibilities')
plt.ylabel('Model Square Visibilities')
plt.title('Model Fit: Visibilities, Contrast %.1f' % contrast)
plt.savefig('visfit_%.1f_con.png' % contrast)
except:
print 'Failed'
vsemis[trial], dvsemis[trial] = 0,0
veccs[trial], dveccs[trial] = 0,0
vthetas[trial], dvthetas[trial] = 0,0
vthicks[trial], dvthicks[trial] = 0,0
vcons[trial], dvcons[trial] = 0,0
print 'Visibilities done'
print_time(clock()-thistime)
'''------------------------------------
Now save!
------------------------------------'''
cmin, cmax = np.min(contrast_list), np.max(contrast_list)
vdata = Table({'Semis':vsemis,
'Eccs':veccs,
'Thetas':vthetas,
'Thicks':vthicks,
'Cons':vcons,
'Dsemis':dvsemis,
'Deccs':dveccs,
'Dthetas':dvthetas,
'Dthicks':dvthicks,
'Dcons':dvcons})
vdata.write('raw_vis_disk_sims_%.0f_%.0f.csv' % (cmin,cmax))
print 'Visibility fits saved to raw_vis_disk_sims_%.0f_%.0f.csv' % (cmin,cmax)
kdata = Table({'Semis':ksemis,
'Eccs':keccs,
'Thetas':kthetas,
'Thicks':kthicks,
'Cons':kcons,
'Dsemis':dksemis,
'Deccs':dkeccs,
'Dthetas':dkthetas,
'Dthicks':dkthicks,
'Dcons':dkcons})
kdata.write('kernel_amplitude_disk_sims_%.0f_%.0f.csv' % (cmin,cmax))
print 'Kernel amplitude fits saved to kernel_amplitude_disk_sims_%.0f_%.0f.csv' \
% (cmin,cmax)
print 'Finished contrast loop'
print_time(clock()-t0)