def psffit(psf, frame, loc=None, w=None, scale=100, dframe=9, xoffs=None, yoffs=None, verbose=False):
"""
Conduct simple PRF model-fitting at a specified grid of positions
:INPUTS:
psf -- model PSF (or PRF), supersampled by factor 'scale'
frame -- science frame to which psf will be fit. best if it's odd-sized
:OPTIONS:
loc -- (x,y) integers, star location in data frame (e.g., data[x,y])
w -- [array] weights of pixels in data frame, (typ. 1/sigma^2)
scale -- supersampling level of PSF
dframe -- [odd int] diameter of square box around target
location. Errors may occur if this size is larger
than your binned-down PRF model.
xoffs -- [int array] subpixel x offsets to test.
yoffs -- [int array] subpixel y offsets to test.
:RETURNS:
modelpsf, data, chisq, background, fluxscale, xoffset, yoffset, chisq[ii,jj],background[ii,jj], fluxscale[ii,jj]
:EXAMPLE:
::
import k2
import phot
import pylab as py
fn = 'kplr060018142-2014044044430_lpd-targ.fits'
f = pyfits.open('kplr060018142-2014044044430_lpd-targ.fits')
image = f[1].data['flux'][0]
prf = k2.loadPRF(fn)
out = phot.psffit(prf, image, (33, 23), scale=50, dframe=7, verbose=True)
py.figure()
py.subplot(132)
py.imshow(out[0])
py.title('Best-fit Model PRF')
py.colorbar()
py.subplot(131)
py.imshow(out[1])
py.title('Observed Data')
py.clim([out[0].min(), out[0].max()])
py.colorbar()
py.subplot(133)
py.imshow(out[1] - out[0])
py.title('Data - Model')
py.colorbar()
"""
# 2009-10-07 14:18 IJC: Created.
# 2011-05-11 22:16 IJC: Added a try/except/pdb debugging step
# 2014-09-04 08:32 IJMC: Moderate overhaul! Updated
# documentation, changed numpy function
# calls to 'np.X', replaced np.nonzero()
# call with simple centroid.
#from numpy import arange, prod, zeros,vstack,dot, nonzero, diag,floor,abs,max,hstack
#from numpy.linalg import pinv
import analysis as an
from time import time
import pdb
tic = time()
if w is None:
w = np.zeros(frame.shape)+1
if loc is None:
loc = ((frame.shape[1]-1)/2,(frame.shape[0]-1)/2)
if xoffs is None:
xoffs = np.arange(scale) #arange(scale)
if yoffs is None:
yoffs = np.arange(scale) #arange(scale)
ycen = int(loc[0])
xcen = int(loc[1])
# Pick a thumbnail frame size to use, and cut it out of the larger frame
if verbose>0:
print "frame.shape>>", frame.shape
print "(xcen, ycen, dframe)>>", xcen,ycen,dframe
print "limits>>" , (ycen-(dframe-1)/2.), (ycen+(dframe+1)/2.), (xcen-(dframe-1)/2.), (xcen+(dframe+1)/2.)
print "xoffs, yoffs>>", xoffs, yoffs
data = frame[(ycen-(dframe-1)/2.):(ycen+(dframe+1)/2.),
(xcen-(dframe-1)/2.):(xcen+(dframe+1)/2.)]
weights = w[(ycen-(dframe-1)/2.):(ycen+(dframe+1)/2.),
(xcen-(dframe-1)/2.):(xcen+(dframe+1)/2.)]
wmat = np.diag(weights.ravel())
extrasize = 2*max(np.abs(np.floor(1.0*np.hstack((xoffs,yoffs))/scale)))
exs = 2*scale*dframe #extrasize*scale/2
if verbose>0: print "extrasize>> ",extrasize
# Determine how much of the PSF to cut out, and cut it out. If it
# is too small, then zero-pad it.
dpsf0 = (dframe+1)*scale-1
dpsf1 = dframe*scale-1
psfModelTooSmall = True
while psfModelTooSmall:
psf_x, psf_y = np.arange(psf.shape[0]), np.arange(psf.shape[1])
pycen = (psf_x*psf.sum(1)).sum()/psf.sum()
pxcen = (psf_y*psf.sum(0)).sum()/psf.sum()
#pycen, pxcen = (psf==psf.max()).nonzero() # Slower!!
pxmin = int(pxcen-(dpsf0-1)/2-exs)
pxmax = int(pxcen+(dpsf0+1)/2+exs)
pymin = int(pycen-(dpsf0-1)/2-exs)
pymax = int(pycen+(dpsf0+1)/2+exs)
if verbose>0: print "shape & indices>>", psf.shape, pymin, pymax, pxmin, pxmax
if pxmin<0 or pymin<0 or pxmax>=psf.shape[1] or pymax>=psf.shape[0]:
psfModelTooSmall = True
psf = an.pad(psf, 2*psf.shape[0], 2*psf.shape[1])
else:
psfModelTooSmall = False
smpsf = psf[pymin:pymax, pxmin:pxmax]
if verbose>0: print "data.shape>>" , data.shape
ndata = data.size
if verbose>0: print "ndata>> %i" % ndata
const = np.zeros(ndata,float)+1
background = np.zeros((len(xoffs),len(yoffs)), float)
fluxscale = np.zeros((len(xoffs),len(yoffs)), float)
chisq = np.zeros((len(xoffs),len(yoffs)), float)
if verbose>0:
print "wmat.shape>>", wmat.shape
print "data.ravel().shape>>", data.ravel().shape
dfs = dframe * scale
initoffset_min = scale - 1 + exs
initoffset_max = scale - 1 + exs + dfs
nx = len(xoffs)
ny = len(yoffs)
rangeny = range(ny)
for ii in range(nx):
xoffset = xoffs[ii]
xmin, xmax = int(initoffset_min-xoffset), int(initoffset_max-xoffset)
for jj in rangeny:
# Cut out the correct portion of the model PSF
yoffset = yoffs[jj]
ymin, ymax = int(initoffset_min-yoffset), int(initoffset_max-yoffset)
# Bin down the PSF by the correct factor. Sizes should now match!
#pdb.set_trace()
#binpsf = an.binarray(smpsf[ymin:ymax, xmin:xmax],scale)
binpsfs = [an.binarray(smpsf[ymin:ymax, xmin:xmax],scale), \
an.binarray(smpsf[ymin+1:ymax+1, xmin:xmax],scale), \
an.binarray(smpsf[ymin:ymax, xmin+1:xmax+1],scale), \
an.binarray(smpsf[ymin+1:ymax+1, xmin+1:xmax+1],scale)]
xfrac, yfrac = xoffset - int(xoffset), yoffset - int(yoffset)
binpsf_weights = [(1. - xfrac)*(1.-yfrac), yfrac*(1.-xfrac), (1.-yfrac)*xfrac, xfrac*yfrac]
binpsf = np.array([bp*bpw for bp, bpw in zip(binpsfs, binpsf_weights)]).sum(0) / np.sum(binpsf_weights)
#pdb.set_trace()
# Compute the best-fit background & PSF scaling factor
if verbose>0:
print "xmat shapes>> ",const.shape, binpsf.ravel().shape
print "ymin,ymax,xmin,xmax>> ",ymin,ymax, xmin,xmax
print "binpsf.shape>> ",binpsf.shape
try:
xmat = np.vstack((const,binpsf.ravel())).transpose()
fitvec, efitvec = an.lsq(xmat, data.ravel(), w=weights.ravel())
background[ii,jj], fluxscale[ii,jj] = fitvec
if c_chisq:
chisq[ii,jj] = _chi2.chi2(np.dot(xmat, fitvec), data.ravel(), weights.ravel())
else:
chisq[ii,jj] = (weights.ravel() * (np.dot(xmat, fitvec) - data.ravel())**2).sum()
except:
print "error occurred"
chisq[ii,jj] = 9e99
pdb.set_trace()
ii,jj = (chisq==chisq.min()).nonzero()
if len(ii)>1: # more than one chisquared minimum found!
ii = ii[0]
jj = jj[0]
xoffset = xoffs[ii]
xmin, xmax = int(scale-xoffset-1+exs), int(scale-xoffset-1 + dfs+exs)
yoffset = yoffs[jj]
ymin, ymax = int(scale-yoffset-1+exs), int(scale-yoffset-1 + dfs+exs)
# Bin down the PSF by the correct factor. Sizes should now match!
binpsf = an.binarray(smpsf[ymin:ymax, xmin:xmax],scale)
modelpsf = background[ii,jj] + fluxscale[ii,jj]*binpsf
#print "%f seconds for completion!" % (time()-tic)
return modelpsf, data, chisq, background, fluxscale, xoffset, yoffset, chisq[ii,jj],background[ii,jj], fluxscale[ii,jj]
import numpy as np
from _chi2 import chi2
if __name__ == '__main__':
mu_y = 0.
sig_y = 5.
mu_x = 0.21
sig_x = 3.
N = int(1000)
m = float(1.)
b = float(0.)
x = np.random.normal(mu_x, sig_x, N).astype('float64')
y = np.random.normal(mu_y, sig_y, N).astype('float64')
yerr = np.array([sig_y] * N, 'float64')
result = chi2(m, b, x, y, yerr) # The module determines N from the arguments.
print(result)
def psffit(psf, frame, loc=None, w=None, scale=100, dframe=9, xoffs=None, yoffs=None, verbose=False):
"""
Conduct simple PRF model-fitting at a specified grid of positions
:INPUTS:
psf -- model PSF (or PRF), supersampled by factor 'scale'
frame -- science frame to which psf will be fit. best if it's odd-sized
:OPTIONS:
loc -- (x,y) integers, star location in data frame (e.g., data[x,y])
w -- [array] weights of pixels in data frame, (typ. 1/sigma^2)
scale -- supersampling level of PSF
dframe -- [odd int] diameter of square box around target
location. Errors may occur if this size is larger
than your binned-down PRF model.
xoffs -- [int array] subpixel x offsets to test.
yoffs -- [int array] subpixel y offsets to test.
:RETURNS:
modelpsf, data, chisq, background, fluxscale, xoffset, yoffset, chisq[ii,jj],background[ii,jj], fluxscale[ii,jj]
:EXAMPLE:
::
import k2
import phot
import pylab as py
fn = 'kplr060018142-2014044044430_lpd-targ.fits'
f = pyfits.open('kplr060018142-2014044044430_lpd-targ.fits')
image = f[1].data['flux'][0]
prf = k2.loadPRF(fn)
out = phot.psffit(prf, image, (33, 23), scale=50, dframe=7, verbose=True)
py.figure()
py.subplot(132)
py.imshow(out[0])
py.title('Best-fit Model PRF')
py.colorbar()
py.subplot(131)
py.imshow(out[1])
py.title('Observed Data')
py.clim([out[0].min(), out[0].max()])
py.colorbar()
py.subplot(133)
py.imshow(out[1] - out[0])
py.title('Data - Model')
py.colorbar()
"""
# 2009-10-07 14:18 IJC: Created.
# 2011-05-11 22:16 IJC: Added a try/except/pdb debugging step
# 2014-09-04 08:32 IJMC: Moderate overhaul! Updated
# documentation, changed numpy function
# calls to 'np.X', replaced np.nonzero()
# call with simple centroid.
#from numpy import arange, prod, zeros,vstack,dot, nonzero, diag,floor,abs,max,hstack
#from numpy.linalg import pinv
import analysis as an
from time import time
import pdb
tic = time()
if w==None:
w = np.zeros(frame.shape)+1
if loc==None:
loc = ((frame.shape[1]-1)/2,(frame.shape[0]-1)/2)
if xoffs==None:
xoffs = np.arange(scale) #arange(scale)
if yoffs==None:
yoffs = np.arange(scale) #arange(scale)
ycen = int(loc[0])
xcen = int(loc[1])
# Pick a thumbnail frame size to use, and cut it out of the larger frame
if verbose>0:
print "frame.shape>>", frame.shape
print "(xcen, ycen, dframe)>>", xcen,ycen,dframe
print "limits>>" , (ycen-(dframe-1)/2.), (ycen+(dframe+1)/2.), (xcen-(dframe-1)/2.), (xcen+(dframe+1)/2.)
print "xoffs, yoffs>>", xoffs, yoffs
data = frame[(ycen-(dframe-1)/2.):(ycen+(dframe+1)/2.),
(xcen-(dframe-1)/2.):(xcen+(dframe+1)/2.)]
weights = w[(ycen-(dframe-1)/2.):(ycen+(dframe+1)/2.),
(xcen-(dframe-1)/2.):(xcen+(dframe+1)/2.)]
wmat = np.diag(weights.ravel())
extrasize = 2*max(np.abs(np.floor(1.0*np.hstack((xoffs,yoffs))/scale)))
exs = 2*scale*dframe #extrasize*scale/2
if verbose>0: print "extrasize>> ",extrasize
# Determine how much of the PSF to cut out, and cut it out. If it
# is too small, then zero-pad it.
dpsf0 = (dframe+1)*scale-1
dpsf1 = dframe*scale-1
psfModelTooSmall = True
while psfModelTooSmall:
psf_x, psf_y = np.arange(psf.shape[0]), np.arange(psf.shape[1])
pycen = (psf_x*psf.sum(1)).sum()/psf.sum()
pxcen = (psf_y*psf.sum(0)).sum()/psf.sum()
#pycen, pxcen = (psf==psf.max()).nonzero() # Slower!!
pxmin = int(pxcen-(dpsf0-1)/2-exs)
pxmax = int(pxcen+(dpsf0+1)/2+exs)
pymin = int(pycen-(dpsf0-1)/2-exs)
pymax = int(pycen+(dpsf0+1)/2+exs)
if verbose>0: print "shape & indices>>", psf.shape, pymin, pymax, pxmin, pxmax
if pxmin<0 or pymin<0 or pxmax>=psf.shape[1] or pymax>=psf.shape[0]:
psfModelTooSmall = True
psf = an.pad(psf, 2*psf.shape[0], 2*psf.shape[1])
else:
psfModelTooSmall = False
smpsf = psf[pymin:pymax, pxmin:pxmax]
if verbose>0: print "data.shape>>" , data.shape
ndata = data.size
if verbose>0: print "ndata>> %i" % ndata
const = np.zeros(ndata,float)+1
background = np.zeros((len(xoffs),len(yoffs)), float)
fluxscale = np.zeros((len(xoffs),len(yoffs)), float)
chisq = np.zeros((len(xoffs),len(yoffs)), float)
if verbose>0:
print "wmat.shape>>", wmat.shape
print "data.ravel().shape>>", data.ravel().shape
dfs = dframe * scale
initoffset_min = scale - 1 + exs
initoffset_max = scale - 1 + exs + dfs
nx = len(xoffs)
ny = len(yoffs)
rangeny = range(ny)
for ii in range(nx):
xoffset = xoffs[ii]
xmin, xmax = int(initoffset_min-xoffset), int(initoffset_max-xoffset)
for jj in rangeny:
# Cut out the correct portion of the model PSF
yoffset = yoffs[jj]
ymin, ymax = int(initoffset_min-yoffset), int(initoffset_max-yoffset)
# Bin down the PSF by the correct factor. Sizes should now match!
#pdb.set_trace()
#binpsf = an.binarray(smpsf[ymin:ymax, xmin:xmax],scale)
binpsfs = [an.binarray(smpsf[ymin:ymax, xmin:xmax],scale), \
an.binarray(smpsf[ymin+1:ymax+1, xmin:xmax],scale), \
an.binarray(smpsf[ymin:ymax, xmin+1:xmax+1],scale), \
an.binarray(smpsf[ymin+1:ymax+1, xmin+1:xmax+1],scale)]
xfrac, yfrac = xoffset - int(xoffset), yoffset - int(yoffset)
binpsf_weights = [(1. - xfrac)*(1.-yfrac), yfrac*(1.-xfrac), (1.-yfrac)*xfrac, xfrac*yfrac]
binpsf = np.array([bp*bpw for bp, bpw in zip(binpsfs, binpsf_weights)]).sum(0) / np.sum(binpsf_weights)
#pdb.set_trace()
# Compute the best-fit background & PSF scaling factor
if verbose>0:
print "xmat shapes>> ",const.shape, binpsf.ravel().shape
print "ymin,ymax,xmin,xmax>> ",ymin,ymax, xmin,xmax
print "binpsf.shape>> ",binpsf.shape
try:
xmat = np.vstack((const,binpsf.ravel())).transpose()
fitvec, efitvec = an.lsq(xmat, data.ravel(), w=weights.ravel())
background[ii,jj], fluxscale[ii,jj] = fitvec
if c_chisq:
chisq[ii,jj] = _chi2.chi2(np.dot(xmat, fitvec), data.ravel(), weights.ravel())
else:
chisq[ii,jj] = (weights.ravel() * (np.dot(xmat, fitvec) - data.ravel())**2).sum()
except:
print "error occurred"
chisq[ii,jj] = 9e99
pdb.set_trace()
ii,jj = (chisq==chisq.min()).nonzero()
if len(ii)>1: # more than one chisquared minimum found!
ii = ii[0]
jj = jj[0]
xoffset = xoffs[ii]
xmin, xmax = int(scale-xoffset-1+exs), int(scale-xoffset-1 + dfs+exs)
yoffset = yoffs[jj]
ymin, ymax = int(scale-yoffset-1+exs), int(scale-yoffset-1 + dfs+exs)
# Bin down the PSF by the correct factor. Sizes should now match!
binpsf = an.binarray(smpsf[ymin:ymax, xmin:xmax],scale)
modelpsf = background[ii,jj] + fluxscale[ii,jj]*binpsf
#print "%f seconds for completion!" % (time()-tic)
return modelpsf, data, chisq, background, fluxscale, xoffset, yoffset, chisq[ii,jj],background[ii,jj], fluxscale[ii,jj]
import numpy as np
from _chi2 import chi2
if __name__ == '__main__':
mu_y = 0.
sig_y = 5.
mu_x = 0.21
sig_x = 3.
N = int(1000)
m = float(1.)
b = float(0.)
x = np.random.normal(mu_x, sig_x, N).astype('float64')
y = np.random.normal(mu_y, sig_y, N).astype('float64')
yerr = np.array([sig_y] * N, 'float64')
result = chi2(m, b, x, y,
yerr) # The module determines N from the arguments.
print(result)
#!/usr/bin/env python import _chi2 print _chi2.chi2(2.0, 1.0, [-1.0, 4.2, 30.6], [-1.5, 8.0, 63.0], [1.0, 1.5, 0.6])
#!/usr/bin/env python
import _chi2
print _chi2.chi2(2.0, 1.0, [-1.0, 4.2, 30.6], [-1.5, 8.0, 63.0],
[1.0, 1.5, 0.6])