def mapFromFFT(self,
kFilter=None,
kFilterFromList=None,
showFilter=False,
setMeanToZero=False,
returnFFT=False):
"""
@brief Performs inverse fft (map from FFT) with an optional filter.
@param kFilter Optional; If applied, resulting map = IFFT(fft*kFilter)
@return (optinally filtered) 2D real array
"""
kMap = self.kMap.copy()
kFilter0 = np.real(kMap.copy()) * 0. + 1.
if kFilter != None:
kFilter0 *= kFilter
if kFilterFromList != None:
kFilter = kMap.copy() * 0.
l = kFilterFromList[0]
Fl = kFilterFromList[1]
FlSpline = splrep(l, Fl, k=3)
ll = np.ravel(self.modLMap)
kk = (splev(ll, FlSpline))
kFilter = np.reshape(kk, [self.Ny, self.Nx])
kFilter0 *= kFilter
if setMeanToZero:
id = np.where(self.modLMap == 0.)
kFilter0[id] = 0.
#showFilter = True
if showFilter:
pylab.semilogy(l, Fl, 'r', ll, kk, 'b.')
#utils.saveAndShow()
#sys.exit()
pylab.matshow(fftshift(kFilter0),origin="down",extent=[np.min(self.lx),\
np.max(self.lx),\
np.min(self.ly),\
np.max(self.ly)])
pylab.show()
kMap[:, :] *= kFilter0[:, :]
if returnFFT:
ftMap = self.copy()
ftMap.kMap = kMap.copy()
return np.real(fftfast.ifft(kMap, axes=[-2, -1],
normalize=True)), ftMap
else:
return np.real(fftfast.ifft(kMap, axes=[-2, -1], normalize=True))
def kappaToAlpha(self, kappaMap, test=False):
fKappa = fft(kappaMap, axes=[-2, -1])
fAlpha = self.ftkernels * fKappa
pixScaleY, pixScaleX = kappaMap.pixshape()
Ny, Nx = kappaMap.shape
#retAlpha = (np.fft.ifftshift(enmap.ifft(fAlpha,normalize=False).real)+kappaMap*0.)*pixScaleY*pixScaleX/Nx/Ny
retAlpha = -(np.fft.ifftshift(
ifft(fAlpha, axes=[-2, -1], normalize=False).real[::-1]) +
kappaMap * 0.) * pixScaleY * pixScaleX / Nx / Ny
if test:
newKap = -np.nan_to_num(0.5 * enmap.div(retAlpha))
thetaMap = kappaMap.posmap()
thetaModMap = 60. * 180. * (np.sum(thetaMap**2, 0)**0.5) / np.pi
print "newkappaint ", np.nanmean(newKap[thetaModMap < 10.])
pl = Plotter()
pl.plot2d(kappaMap)
pl.done("output/oldKap.png")
pl = Plotter()
pl.plot2d(newKap)
pl.done("output/newKap.png")
ratio = np.nan_to_num(newKap / kappaMap)
print thetaMap.shape
print ratio[thetaModMap < 5].mean()
pl = Plotter()
pl.plot2d(ratio[200:-200, 200:-200])
pl.done("output/testratio.png")
return retAlpha
def mapFromFFT(self,kFilter=None,kFilterFromList=None,showFilter=False,setMeanToZero=False,returnFFT=False):
"""
@brief Performs inverse fft (map from FFT) with an optional filter.
@param kFilter Optional; If applied, resulting map = IFFT(fft*kFilter)
@return (optinally filtered) 2D real array
"""
kMap = self.kMap.copy()
kFilter0 = np.real(kMap.copy())*0.+ 1.
if kFilter != None:
kFilter0 *= kFilter
if kFilterFromList != None:
kFilter = kMap.copy()*0.
l = kFilterFromList[0]
Fl = kFilterFromList[1]
FlSpline = splrep(l,Fl,k=3)
ll = np.ravel(self.modLMap)
kk = (splev(ll,FlSpline))
kFilter = np.reshape(kk,[self.Ny,self.Nx])
kFilter0 *= kFilter
if setMeanToZero:
id = np.where(self.modLMap == 0.)
kFilter0[id] = 0.
#showFilter = True
if showFilter:
pylab.semilogy(l,Fl,'r',ll,kk,'b.')
#utils.saveAndShow()
#sys.exit()
pylab.matshow(fftshift(kFilter0),origin="down",extent=[np.min(self.lx),\
np.max(self.lx),\
np.min(self.ly),\
np.max(self.ly)])
pylab.show()
kMap[:,:] *= kFilter0[:,:]
if returnFFT:
ftMap = self.copy()
ftMap.kMap = kMap.copy()
return np.real(fftfast.ifft(kMap,axes=[-2,-1],normalize=True)),ftMap
else:
return np.real(fftfast.ifft(kMap,axes=[-2,-1],normalize=True))
def fillWithGaussianRandomField(self,ell,Cell,bufferFactor = 1):
"""
Generates a GRF from an input power spectrum specified as ell, Cell
BufferFactor =1 means the map will be periodic boundary function
BufferFactor > 1 means the map will be genrated on a patch bufferFactor times
larger in each dimension and then cut out so as to have non-periodic bcs.
Fills the data field of the map with the GRF realization
"""
ft = fftFromLiteMap(self)
Ny = self.Ny*bufferFactor
Nx = self.Nx*bufferFactor
bufferFactor = int(bufferFactor)
realPart = np.zeros([Ny,Nx])
imgPart = np.zeros([Ny,Nx])
ly = np.fft.fftfreq(Ny,d = self.pixScaleY)*(2*np.pi)
lx = np.fft.fftfreq(Nx,d = self.pixScaleX)*(2*np.pi)
#print ly
modLMap = np.zeros([Ny,Nx])
iy, ix = np.mgrid[0:Ny,0:Nx]
modLMap[iy,ix] = np.sqrt(ly[iy]**2+lx[ix]**2)
s = splrep(ell,Cell,k=3)
ll = np.ravel(modLMap)
kk = splev(ll,s)
id = np.where(ll>ell.max())
kk[id] = 0.
#add a cosine ^2 falloff at the very end
#id2 = np.where( (ll> (ell.max()-500)) & (ll<ell.max()))
#lEnd = ll[id2]
#kk[id2] *= np.cos((lEnd-lEnd.min())/(lEnd.max() -lEnd.min())*np.pi/2)
#pylab.loglog(ll,kk)
area = Nx*Ny*self.pixScaleX*self.pixScaleY
p = np.reshape(kk,[Ny,Nx]) /area * (Nx*Ny)**2
assert np.all(p>=0)
realPart = np.sqrt(p)*np.random.randn(Ny,Nx)
imgPart = np.sqrt(p)*np.random.randn(Ny,Nx)
kMap = realPart+1j*imgPart
data = np.real(fftfast.ifft(kMap,axes=[-2,-1],normalize=True))
b = bufferFactor
self.data = data[(b-1)/2*self.Ny:(b+1)/2*self.Ny,(b-1)/2*self.Nx:(b+1)/2*self.Nx]
def fillWithGaussianRandomField(self,ell,Cell,bufferFactor = 1):
"""
Generates a GRF from an input power spectrum specified as ell, Cell
BufferFactor =1 means the map will be periodic boundary function
BufferFactor > 1 means the map will be genrated on a patch bufferFactor times
larger in each dimension and then cut out so as to have non-periodic bcs.
Fills the data field of the map with the GRF realization
"""
ft = fftFromLiteMap(self)
Ny = self.Ny*bufferFactor
Nx = self.Nx*bufferFactor
bufferFactor = int(bufferFactor)
realPart = np.zeros([Ny,Nx])
imgPart = np.zeros([Ny,Nx])
ly = np.fft.fftfreq(Ny,d = self.pixScaleY)*(2*np.pi)
lx = np.fft.fftfreq(Nx,d = self.pixScaleX)*(2*np.pi)
#print ly
modLMap = np.zeros([Ny,Nx])
iy, ix = np.mgrid[0:Ny,0:Nx]
modLMap[iy,ix] = np.sqrt(ly[iy]**2+lx[ix]**2)
s = splrep(ell,Cell,k=3)
ll = np.ravel(modLMap)
kk = splev(ll,s)
id = np.where(ll>ell.max())
kk[id] = 0.
#add a cosine ^2 falloff at the very end
#id2 = np.where( (ll> (ell.max()-500)) & (ll<ell.max()))
#lEnd = ll[id2]
#kk[id2] *= np.cos((lEnd-lEnd.min())/(lEnd.max() -lEnd.min())*np.pi/2)
#pylab.loglog(ll,kk)
area = Nx*Ny*self.pixScaleX*self.pixScaleY
p = np.reshape(kk,[Ny,Nx]) /area * (Nx*Ny)**2
assert np.all(p>=0)
realPart = np.sqrt(p)*np.random.randn(Ny,Nx)
imgPart = np.sqrt(p)*np.random.randn(Ny,Nx)
kMap = realPart+1j*imgPart
data = np.real(fftfast.ifft(kMap,axes=[-2,-1],normalize=True))
b = bufferFactor
self.data = data[(b-1)/2*self.Ny:(b+1)/2*self.Ny,(b-1)/2*self.Nx:(b+1)/2*self.Nx]
def upgradePixelPitch( m, N = 1 ):
"""
@brief go to finer pixels with fourier interpolation
@param m a liteMap
@param N go to 2^N times smaller pixels
@return the map with smaller pixels
"""
Ny = m.Ny*2**N
Nx = m.Nx*2**N
npix = Ny*Nx
ft = fftfast.fft(m.data,axes=[-2,-1])
ftShifted = np.fft.fftshift(ft)
newFtShifted = np.zeros((Ny, Nx), dtype=np.complex128)
# From the np.fft.fftshift help:
# """
# Shift zero-frequency component to center of spectrum.
#
# This function swaps half-spaces for all axes listed (defaults to all).
# If len(x) is even then the Nyquist component is y[0].
# """
#
# So in the case that we have an odd dimension in our map, we want to put
# the extra zero at the beginning
if m.Nx % 2 != 0:
offsetX = (Nx-m.Nx)/2 + 1
else:
offsetX = (Nx-m.Nx)/2
if m.Ny % 2 != 0:
offsetY = (Ny-m.Ny)/2 + 1
else:
offsetY = (Ny-m.Ny)/2
newFtShifted[offsetY:offsetY+m.Ny,offsetX:offsetX+m.Nx] = ftShifted
del ftShifted
ftNew = np.fft.ifftshift(newFtShifted)
del newFtShifted
# Finally, deconvolve by the pixel window
mPix = np.copy(np.real(ftNew))
mPix[:] = 0.0
mPix[mPix.shape[0]/2-(2**(N-1)):mPix.shape[0]/2+(2**(N-1)),mPix.shape[1]/2-(2**(N-1)):mPix.shape[1]/2+(2**(N-1))] = 1./(2.**N)**2
ftPix = fftfast.fft(mPix,axes=[-2,-1])
del mPix
inds = np.where(ftNew != 0)
ftNew[inds] /= np.abs(ftPix[inds])
newData = fftfast.ifft(ftNew,axes=[-2,-1],normalize=True)*(2**N)**2
del ftNew
del ftPix
x0_new,y0_new = m.pixToSky(0,0)
m = m.copy() # don't overwrite original
m.wcs.header['NAXIS1'] = 2**N*m.wcs.header['NAXIS1']
m.wcs.header['NAXIS2'] = 2**N*m.wcs.header['NAXIS2']
m.wcs.header['CDELT1'] = m.wcs.header['CDELT1']/2.**N
m.wcs.header['CDELT2'] = m.wcs.header['CDELT2']/2.**N
m.wcs.updateFromHeader()
p_x, p_y = m.skyToPix(x0_new, y0_new)
m.wcs.header['CRPIX1'] = m.wcs.header['CRPIX1'] - p_x
m.wcs.header['CRPIX2'] = m.wcs.header['CRPIX2'] - p_y
m.wcs.updateFromHeader()
mNew = liteMapFromDataAndWCS(np.real(newData), m.wcs)
mNew.data[:] = newData[:]
return mNew
def upgradePixelPitch( m, N = 1 ):
"""
@brief go to finer pixels with fourier interpolation
@param m a liteMap
@param N go to 2^N times smaller pixels
@return the map with smaller pixels
"""
Ny = m.Ny*2**N
Nx = m.Nx*2**N
npix = Ny*Nx
ft = fftfast.fft(m.data,axes=[-2,-1])
ftShifted = np.fft.fftshift(ft)
newFtShifted = np.zeros((Ny, Nx), dtype=np.complex128)
# From the np.fft.fftshift help:
# """
# Shift zero-frequency component to center of spectrum.
#
# This function swaps half-spaces for all axes listed (defaults to all).
# If len(x) is even then the Nyquist component is y[0].
# """
#
# So in the case that we have an odd dimension in our map, we want to put
# the extra zero at the beginning
if m.Nx % 2 != 0:
offsetX = (Nx-m.Nx)/2 + 1
else:
offsetX = (Nx-m.Nx)/2
if m.Ny % 2 != 0:
offsetY = (Ny-m.Ny)/2 + 1
else:
offsetY = (Ny-m.Ny)/2
newFtShifted[offsetY:offsetY+m.Ny,offsetX:offsetX+m.Nx] = ftShifted
del ftShifted
ftNew = np.fft.ifftshift(newFtShifted)
del newFtShifted
# Finally, deconvolve by the pixel window
mPix = np.copy(np.real(ftNew))
mPix[:] = 0.0
mPix[mPix.shape[0]/2-(2**(N-1)):mPix.shape[0]/2+(2**(N-1)),mPix.shape[1]/2-(2**(N-1)):mPix.shape[1]/2+(2**(N-1))] = 1./(2.**N)**2
ftPix = fftfast.fft(mPix,axes=[-2,-1])
del mPix
inds = np.where(ftNew != 0)
ftNew[inds] /= np.abs(ftPix[inds])
newData = fftfast.ifft(ftNew,axes=[-2,-1],normalize=True)*(2**N)**2
del ftNew
del ftPix
x0_new,y0_new = m.pixToSky(0,0)
m = m.copy() # don't overwrite original
m.wcs.header['NAXIS1'] = 2**N*m.wcs.header['NAXIS1']
m.wcs.header['NAXIS2'] = 2**N*m.wcs.header['NAXIS2']
m.wcs.header['CDELT1'] = m.wcs.header['CDELT1']/2.**N
m.wcs.header['CDELT2'] = m.wcs.header['CDELT2']/2.**N
m.wcs.updateFromHeader()
p_x, p_y = m.skyToPix(x0_new, y0_new)
m.wcs.header['CRPIX1'] = m.wcs.header['CRPIX1'] - p_x
m.wcs.header['CRPIX2'] = m.wcs.header['CRPIX2'] - p_y
m.wcs.updateFromHeader()
mNew = liteMapFromDataAndWCS(np.real(newData), m.wcs)
mNew.data[:] = newData[:]
return mNew
def NFWMatchedFilterSN(clusterCosmology,log10Moverh,c,z,ells,Nls,kellmax,overdensity=500.,critical=True,atClusterZ=True,arcStamp=100.,pxStamp=0.05,saveId=None,verbose=False,rayleighSigmaArcmin=None,returnKappa=False,winAtLens=None):
if rayleighSigmaArcmin is not None: assert rayleighSigmaArcmin>=pxStamp
M = 10.**log10Moverh
lmap = lm.makeEmptyCEATemplate(raSizeDeg=arcStamp/60., decSizeDeg=arcStamp/60.,pixScaleXarcmin=pxStamp,pixScaleYarcmin=pxStamp)
kellmin = 2.*np.pi/arcStamp*np.pi/60./180.
xMap,yMap,modRMap,xx,yy = fmaps.getRealAttributes(lmap)
lxMap,lyMap,modLMap,thetaMap,lx,ly = fmaps.getFTAttributesFromLiteMap(lmap)
cc = clusterCosmology
cmb = False
if winAtLens is None:
cmb = True
comS = cc.results.comoving_radial_distance(cc.cmbZ)*cc.h
comL = cc.results.comoving_radial_distance(z)*cc.h
winAtLens = (comS-comL)/comS
kappaReal, r500 = NFWkappa(cc,M,c,z,modRMap*180.*60./np.pi,winAtLens,overdensity=overdensity,critical=critical,atClusterZ=atClusterZ)
dAz = cc.results.angular_diameter_distance(z) * cc.h
th500 = r500/dAz
#fiveth500 = 10.*np.pi/180./60. #5.*th500
fiveth500 = 5.*th500
# print "5theta500 " , fiveth500*180.*60./np.pi , " arcminutes"
# print "maximum theta " , modRMap.max()*180.*60./np.pi, " arcminutes"
kInt = kappaReal.copy()
kInt[modRMap>fiveth500] = 0.
# print "mean kappa inside theta500 " , kInt[modRMap<fiveth500].mean()
# print "area of th500 disc " , np.pi*fiveth500**2.*(180.*60./np.pi)**2.
# print "estimated integral " , kInt[modRMap<fiveth500].mean()*np.pi*fiveth500**2.
k500 = simps(simps(kInt, yy), xx)
if verbose: print "integral of kappa inside disc ",k500
kappaReal[modRMap>fiveth500] = 0. #### !!!!!!!!! Might not be necessary!
# if cmb: print z,fiveth500*180.*60./np.pi
Ukappa = kappaReal/k500
# pl = Plotter()
# pl.plot2d(Ukappa)
# pl.done("output/kappa.png")
ellmax = kellmax
ellmin = kellmin
Uft = fftfast.fft(Ukappa,axes=[-2,-1])
if rayleighSigmaArcmin is not None:
Prayleigh = rayleigh(modRMap*180.*60./np.pi,rayleighSigmaArcmin)
outDir = "/gpfs01/astro/www/msyriac/plots/"
# io.quickPlot2d(Prayleigh,outDir+"rayleigh.png")
rayK = fftfast.fft(ifftshift(Prayleigh),axes=[-2,-1])
rayK /= rayK[modLMap<1.e-3]
Uft = Uft.copy()*rayK
Upower = np.real(Uft*Uft.conjugate())
# pl = Plotter()
# pl.plot2d(fftshift(Upower))
# pl.done("output/upower.png")
Nls[Nls<0.]=0.
s = splrep(ells,Nls,k=3)
Nl2d = splev(modLMap,s)
Nl2d[modLMap<ellmin]=np.inf
Nl2d[modLMap>ellmax] = np.inf
area = lmap.Nx*lmap.Ny*lmap.pixScaleX*lmap.pixScaleY
Upower = Upower *area / (lmap.Nx*lmap.Ny)**2
filter = np.nan_to_num(Upower/Nl2d)
#filter = np.nan_to_num(1./Nl2d)
filter[modLMap>ellmax] = 0.
filter[modLMap<ellmin] = 0.
# pl = Plotter()
# pl.plot2d(fftshift(filter))
# pl.done("output/filter.png")
# if (cmb): print Upower.sum()
# if not(cmb) and z>2.5:
# bin_edges = np.arange(500,ellmax,100)
# binner = bin2D(modLMap, bin_edges)
# centers, nl2dells = binner.bin(Nl2d)
# centers, upowerells = binner.bin(np.nan_to_num(Upower))
# centers, filterells = binner.bin(filter)
# from orphics.tools.io import Plotter
# pl = Plotter(scaleY='log')
# pl.add(centers,upowerells,label="upower")
# pl.add(centers,nl2dells,label="noise")
# pl.add(centers,filterells,label="filter")
# pl.add(ells,Nls,ls="--")
# pl.legendOn(loc='upper right')
# #pl._ax.set_ylim(0,1e-8)
# pl.done("output/filterells.png")
# sys.exit()
varinv = filter.sum()
std = np.sqrt(1./varinv)
sn = k500/std
if verbose: print sn
if saveId is not None:
np.savetxt("data/"+saveId+"_m"+str(log10Moverh)+"_z"+str(z)+".txt",np.array([log10Moverh,z,1./sn]))
if returnKappa:
return sn,fftfast.ifft(Uft,axes=[-2,-1],normalize=True).real*k500
return sn, k500, std