def chi2PolarFunc(params,nmax,im,nm):
"""Function which is to be minimized in the chi^2 analysis for Polar shapelets
params = [beta, xc, yc]
beta: characteristic size of shapelets, fit parameter
xc: x centroid of shapelets, fit parameter
yc: y centroid of shapelets, fit parameter
nmax: number of coefficents to use in the Laguerre polynomials
im: observed image
nm: noise map
"""
import sys
beta=params[0]
xc=params[1]
yc=params[2]
if beta<0.:
print 'warning: beta going negative, setting to 0.0'
beta=0.
print 'beta: %f\txc: (%f,%f)'%(beta,xc,yc)
size=im.shape
r,th=shapelet.polarArray([xc,yc],size)
bvals=fgenPolarBasisMatrix(beta,nmax,r,th)
coeffs=solveCoeffs(bvals,im)
mdl=np.abs(img.constructModel(bvals,coeffs,[xc,yc],size))
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2betaFunc(params,xc,yc,nmax,im,nm):
"""Function which is to be minimized in the chi^2 analysis
params = [beta]
beta: characteristic size of shapelets, fit parameter
xc: x centroid of shapelets
yc: y centroid of shapelets
nmax: number of coefficents to use in x,y
im: observed image
nm: noise map
"""
betaX=params[0]
betaY=params[1]
if betaX<0.:
print 'warning: betaX going negative, setting to 0.0'
betaX=0.
if betaY<0.:
print 'warning: betaY going negative, setting to 0.0'
betaY=0.
print 'beta: (%f,%f)'%(betaX,betaY)
size=im.shape
#shift the (0,0) point to the centroid
rx=np.array(range(0,size[0]),dtype=float)-xc
ry=np.array(range(0,size[1]),dtype=float)-yc
bvals=genBasisMatrix([betaX,betaY],nmax,rx,ry)
coeffs=solveCoeffs(bvals,im)
mdl=img.constructModel(bvals,coeffs,[xc,yc],size)
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2nmaxPolarFunc(params,im,nm,beta,xc):
"""
params = [nmax]
nmax: number of coefficents
im: observed image
nm: noise map
beta: fit beta value
xc: fit centroid position
"""
print params
nmax=params
size=im.shape
r,th=shapelet.polarArray(xc,size)
bvals=genPolarBasisMatrix(beta,nmax,r,th)
coeffs=solveCoeffs(bvals,im)
mdl=np.abs(img.constructModel(bvals,coeffs,xc,size))
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2nmaxPolarFunc(params,im,nm,beta0,beta1,phi,xc):
"""
params = [nmax]
nmax: number of coefficents
im: observed image
nm: noise map
beta0: fit beta value
beta1: fit beta value
phi: rotation angle
xc: fit centroid position
"""
#nmax=params[0]
nmax=[params, params]
size=im.shape
r,th=shapelet.polarArray(xc,size)
bvals=genPolarBasisMatrix([beta0,beta1],nmax,phi,r,th)
coeffs=solveCoeffs(bvals,im)
mdl=np.abs(img.constructModel(bvals,coeffs,size))
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2nmaxPolarFunc(params, im, nm, beta0, beta1, phi, xc):
"""
params = [nmax]
nmax: number of coefficents
im: observed image
nm: noise map
beta0: fit beta value
beta1: fit beta value
phi: rotation angle
xc: fit centroid position
"""
#nmax=params[0]
nmax = [params, params]
size = im.shape
r, th = shapelet.polarArray(xc, size)
bvals = genPolarBasisMatrix([beta0, beta1], nmax, phi, r, th)
coeffs = solveCoeffs(bvals, im)
mdl = np.abs(img.constructModel(bvals, coeffs, size))
return np.sum((im - mdl)**2 / nm**2) / (size[0] * size[1])
def chi2nmaxFunc(params,im,nm,beta,xc):
"""
params = [nmax]
nmax: number of coefficents to use in x,y
im: observed image
nm: noise map
beta: fit beta values
xc: fit centroid position
"""
print params
nmax=[params,params]
size=im.shape
#shift the (0,0) point to the centroid
rx=np.array(range(0,size[0]),dtype=float)-xc[0]
ry=np.array(range(0,size[1]),dtype=float)-xc[1]
bvals=genBasisMatrix(beta,nmax,rx,ry)
coeffs=solveCoeffs(bvals,im)
mdl=img.constructModel(bvals,coeffs,xc,size)
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2nmaxFunc(params,im,nm,betaY,betaX,phi,xc):
"""
params = [nmaxX,nmaxY]
nmax: number of coefficents to use in x,y
im: observed image
nm: noise map
betaY: characteristic size of shapelet
betaX: characteristic size of shapelet
phi: rotation angle of shapelets
xc: fit centroid position
"""
nmax=params
size=im.shape
#shift the (0,0) point to the centroid
ry=np.array(range(0,size[0]),dtype=float)-xc[0]
rx=np.array(range(0,size[1]),dtype=float)-xc[1]
yy,xx=shapelet.xy2Grid(ry,rx)
bvals=genBasisMatrix([betaY,betaX],[nmax,nmax],phi,yy,xx)
coeffs=solveCoeffs(bvals,im)
mdl=img.constructModel(bvals,coeffs,size)
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2nmaxFunc(params, im, nm, betaY, betaX, phi, xc):
"""
params = [nmaxX,nmaxY]
nmax: number of coefficents to use in x,y
im: observed image
nm: noise map
betaY: characteristic size of shapelet
betaX: characteristic size of shapelet
phi: rotation angle of shapelets
xc: fit centroid position
"""
nmax = params
size = im.shape
#shift the (0,0) point to the centroid
ry = np.array(range(0, size[0]), dtype=float) - xc[0]
rx = np.array(range(0, size[1]), dtype=float) - xc[1]
yy, xx = shapelet.xy2Grid(ry, rx)
bvals = genBasisMatrix([betaY, betaX], [nmax, nmax], phi, yy, xx)
coeffs = solveCoeffs(bvals, im)
mdl = img.constructModel(bvals, coeffs, size)
return np.sum((im - mdl)**2 / nm**2) / (size[0] * size[1])
def chi2xcFunc(params,beta,nmax,im,nm):
"""Function which is to be minimized in the chi^2 analysis
params = [xc, yc]
xc: x centroid of shapelets, fit parameter
yc: y centroid of shapelets, fit parameter
beta: characteristic size of shapelet
nmax: number of coefficents to use in x,y
im: observed image
nm: noise map
"""
xc=params[2]
yc=params[3]
print xc,yc
size=im.shape
#shift the (0,0) point to the centroid
rx=np.array(range(0,size[0]),dtype=float)-xc
ry=np.array(range(0,size[1]),dtype=float)-yc
bvals=genBasisMatrix(beta,nmax,rx,ry)
coeffs=solveCoeffs(bvals,im)
mdl=img.constructModel(bvals,coeffs,[xc,yc],size)
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2betaPolarFunc(params,xc,yc,r,th,nmax,im,nm):
"""Function which is to be minimized in the chi^2 analysis for Polar shapelets
params = [beta]
beta: characteristic size of shapelets, fit parameter
xc: x centroid of shapelets
yc: y centroid of shapelets
r: radius from centroid, array of im.shape
th: angle from centroid, array of im.shape
nmax: number of coefficents to use in the Laguerre polynomials
im: observed image
nm: noise map
"""
beta=params[0]
if beta<0.:
print 'warning: beta going negative, setting to 0.0'
beta=0.
print 'beta: %f'%(beta)
size=im.shape
bvals=genPolarBasisMatrix(beta,nmax,r,th)
coeffs=solveCoeffs(bvals,im)
mdl=np.abs(img.constructModel(bvals,coeffs,[xc,yc],size))
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2Func(params,nmax,im,nm,order=['beta0','beta1','phi','yc','xc'],set_beta=[None,None],set_phi=None,set_xc=[None,None],xx=None,yy=None):
"""Function which is to be minimized in the chi^2 analysis for Cartesian shapelets
params = [beta0, beta1, phi, xc, yc] or some subset
beta0: characteristic size of shapelets, fit parameter
beta1: characteristic size of shapelets, fit parameter
phi: rotation angle of shapelets, fit parameter
yc: y centroid of shapelets, fit parameter
xc: x centroid of shapelets, fit parameter
nmax: number of coefficents to use in the Hermite polynomials
im: observed image
nm: noise map
order: order of parameters
fixed parameters: set_beta, set_phi, set_xc
xx: X position grid, array of im.shape, not required if xc and yc being fit
yy: Y position grid, array of im.shape, not required if xc and yc being fit
"""
#determine which parameters are being fit for, and which are not
betaY=set_beta[0]
betaX=set_beta[1]
phi=set_phi
yc=set_xc[0]
xc=set_xc[1]
fitParams={'beta':False,'phi':False,'xc':False}
for pid,paramName in enumerate(order):
if paramName=='beta0':
betaY=params[pid]
fitParams['beta']=True
elif paramName=='beta1':
betaX=params[pid]
fitParams['beta']=True
elif paramName=='phi':
phi=params[pid]
fitParams['phi']=True
elif paramName=='xc':
xc=params[pid]
fitParams['xc']=True
elif paramName=='yc':
yc=params[pid]
fitParams['xc']=True
#if betaX<0.:
# print 'warning: beta going negative, setting to 0.0'
# betaX=0.
#if betaY<0.:
# print 'warning: beta going negative, setting to 0.0'
# betaY=0.
if betaX<0.:
print 'warning: beta going negative, taking absolute value'
betaX = np.abs(betaY)
if betaY<0.:
print 'warning: beta going negative, taking absolute value'
betaY = np.abs(betaX)
print 'beta: (%f,%f)\t phi: %f\txc: (%f,%f)'%(betaX,betaY,phi,xc,yc)
#update noise map
nm=img.makeNoiseMap(nm.shape,np.mean(nm),np.std(nm))
size=im.shape
if fitParams['xc'] or xx is None:
#shift the (0,0) point to the centroid
ry=np.array(range(0,size[0]),dtype=float)-yc
rx=np.array(range(0,size[1]),dtype=float)-xc
yy,xx=shapelet.xy2Grid(ry,rx)
bvals=genBasisMatrix([betaY,betaX],nmax,phi,yy,xx)
coeffs=solveCoeffs(bvals,im)
mdl=img.constructModel(bvals,coeffs,size)
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2PolarFunc(params,nmax,im,nm,order=['beta0','beta1','phi','yc','xc'],set_beta=[None,None],set_phi=None,set_xc=[None,None],r=None,th=None):
"""Function which is to be minimized in the chi^2 analysis for Polar shapelets
params = [beta0, beta1, phi, xc, yc] or some subset
beta0: characteristic size of shapelets, fit parameter
beta1: characteristic size of shapelets, fit parameter
phi: rotation angle of shapelets, fit parameter
yc: y centroid of shapelets, fit parameter
xc: x centroid of shapelets, fit parameter
nmax: number of coefficents to use in the Laguerre polynomials
im: observed image
nm: noise map
order: order of parameters
fixed parameters: set_beta, set_phi, set_xc
r: radius from centroid, array of im.shape, not required if xc and yc being fit
th: angle from centroid, array of im.shape, not required if xc and yc being fit
"""
#determine which parameters are being fit for, and which are not
beta0=set_beta[0]
beta1=set_beta[1]
phi=set_phi
yc=set_xc[0]
xc=set_xc[1]
fitParams={'beta':False,'phi':False,'xc':False}
for pid,paramName in enumerate(order):
if paramName=='beta0':
beta0=params[pid]
fitParams['beta']=True
elif paramName=='beta1':
beta1=params[pid]
fitParams['beta']=True
elif paramName=='phi':
phi=params[pid]
fitParams['phi']=True
elif paramName=='xc':
xc=params[pid]
fitParams['xc']=True
elif paramName=='yc':
yc=params[pid]
fitParams['xc']=True
#if beta0<0.:
# print 'warning: beta going negative, setting to 0.0'
# beta0=0.
#if beta1<0.:
# print 'warning: beta going negative, setting to 0.0'
# beta1=0.
if beta0<0.:
print 'warning: beta going negative, taking absolute value'
beta0 = np.abs(beta0)
if beta1<0.:
print 'warning: beta going negative, taking absolute value'
beta1 = np.abs(beta1)
print 'beta: (%f,%f)\t phi: %f\txc: (%f,%f)'%(beta0,beta1,phi,xc,yc)
#update noise map
nm=img.makeNoiseMap(nm.shape,np.mean(nm),np.std(nm))
size=im.shape
if fitParams['xc'] or r is None:
r,th=shapelet.polarArray([yc,xc],size) #the radius,theta pairs need to updated if fitting for the xc centre or if not using the r,th inputs
bvals=genPolarBasisMatrix([beta0,beta1],nmax,phi,r,th)
coeffs=solveCoeffs(bvals,im)
mdl=np.abs(img.constructModel(bvals,coeffs,size))
return np.sum((im-mdl)**2 / nm**2)/(size[0]*size[1])
def chi2Func(params,
nmax,
im,
nm,
order=['beta0', 'beta1', 'phi', 'yc', 'xc'],
set_beta=[None, None],
set_phi=None,
set_xc=[None, None],
xx=None,
yy=None):
"""Function which is to be minimized in the chi^2 analysis for Cartesian shapelets
params = [beta0, beta1, phi, xc, yc] or some subset
beta0: characteristic size of shapelets, fit parameter
beta1: characteristic size of shapelets, fit parameter
phi: rotation angle of shapelets, fit parameter
yc: y centroid of shapelets, fit parameter
xc: x centroid of shapelets, fit parameter
nmax: number of coefficents to use in the Hermite polynomials
im: observed image
nm: noise map
order: order of parameters
fixed parameters: set_beta, set_phi, set_xc
xx: X position grid, array of im.shape, not required if xc and yc being fit
yy: Y position grid, array of im.shape, not required if xc and yc being fit
"""
#determine which parameters are being fit for, and which are not
betaY = set_beta[0]
betaX = set_beta[1]
phi = set_phi
yc = set_xc[0]
xc = set_xc[1]
fitParams = {'beta': False, 'phi': False, 'xc': False}
for pid, paramName in enumerate(order):
if paramName == 'beta0':
betaY = params[pid]
fitParams['beta'] = True
elif paramName == 'beta1':
betaX = params[pid]
fitParams['beta'] = True
elif paramName == 'phi':
phi = params[pid]
fitParams['phi'] = True
elif paramName == 'xc':
xc = params[pid]
fitParams['xc'] = True
elif paramName == 'yc':
yc = params[pid]
fitParams['xc'] = True
#if betaX<0.:
# print 'warning: beta going negative, setting to 0.0'
# betaX=0.
#if betaY<0.:
# print 'warning: beta going negative, setting to 0.0'
# betaY=0.
if betaX < 0.:
print 'warning: beta going negative, taking absolute value'
betaX = np.abs(betaY)
if betaY < 0.:
print 'warning: beta going negative, taking absolute value'
betaY = np.abs(betaX)
print 'beta: (%f,%f)\t phi: %f\txc: (%f,%f)' % (betaX, betaY, phi, xc, yc)
#update noise map
nm = img.makeNoiseMap(nm.shape, np.mean(nm), np.std(nm))
size = im.shape
if fitParams['xc'] or xx is None:
#shift the (0,0) point to the centroid
ry = np.array(range(0, size[0]), dtype=float) - yc
rx = np.array(range(0, size[1]), dtype=float) - xc
yy, xx = shapelet.xy2Grid(ry, rx)
bvals = genBasisMatrix([betaY, betaX], nmax, phi, yy, xx)
coeffs = solveCoeffs(bvals, im)
mdl = img.constructModel(bvals, coeffs, size)
return np.sum((im - mdl)**2 / nm**2) / (size[0] * size[1])
def chi2PolarFunc(params,
nmax,
im,
nm,
order=['beta0', 'beta1', 'phi', 'yc', 'xc'],
set_beta=[None, None],
set_phi=None,
set_xc=[None, None],
r=None,
th=None):
"""Function which is to be minimized in the chi^2 analysis for Polar shapelets
params = [beta0, beta1, phi, xc, yc] or some subset
beta0: characteristic size of shapelets, fit parameter
beta1: characteristic size of shapelets, fit parameter
phi: rotation angle of shapelets, fit parameter
yc: y centroid of shapelets, fit parameter
xc: x centroid of shapelets, fit parameter
nmax: number of coefficents to use in the Laguerre polynomials
im: observed image
nm: noise map
order: order of parameters
fixed parameters: set_beta, set_phi, set_xc
r: radius from centroid, array of im.shape, not required if xc and yc being fit
th: angle from centroid, array of im.shape, not required if xc and yc being fit
"""
#determine which parameters are being fit for, and which are not
beta0 = set_beta[0]
beta1 = set_beta[1]
phi = set_phi
yc = set_xc[0]
xc = set_xc[1]
fitParams = {'beta': False, 'phi': False, 'xc': False}
for pid, paramName in enumerate(order):
if paramName == 'beta0':
beta0 = params[pid]
fitParams['beta'] = True
elif paramName == 'beta1':
beta1 = params[pid]
fitParams['beta'] = True
elif paramName == 'phi':
phi = params[pid]
fitParams['phi'] = True
elif paramName == 'xc':
xc = params[pid]
fitParams['xc'] = True
elif paramName == 'yc':
yc = params[pid]
fitParams['xc'] = True
#if beta0<0.:
# print 'warning: beta going negative, setting to 0.0'
# beta0=0.
#if beta1<0.:
# print 'warning: beta going negative, setting to 0.0'
# beta1=0.
if beta0 < 0.:
print 'warning: beta going negative, taking absolute value'
beta0 = np.abs(beta0)
if beta1 < 0.:
print 'warning: beta going negative, taking absolute value'
beta1 = np.abs(beta1)
print 'beta: (%f,%f)\t phi: %f\txc: (%f,%f)' % (beta0, beta1, phi, xc, yc)
#update noise map
nm = img.makeNoiseMap(nm.shape, np.mean(nm), np.std(nm))
size = im.shape
if fitParams['xc'] or r is None:
r, th = shapelet.polarArray(
[yc, xc], size
) #the radius,theta pairs need to updated if fitting for the xc centre or if not using the r,th inputs
bvals = genPolarBasisMatrix([beta0, beta1], nmax, phi, r, th)
coeffs = solveCoeffs(bvals, im)
mdl = np.abs(img.constructModel(bvals, coeffs, size))
return np.sum((im - mdl)**2 / nm**2) / (size[0] * size[1])
