def xlm_to_qlm( self ):
indxpn = LISAresponse.getMLvec( self.ntrunc , 'pn' )
qlm = numpy.zeros( self.xlm.shape , dtype='complex' )
for i,ml in enumerate( indxpn ) :
m , l = ml[0] , ml[1]
k = indxpn.index( (-m,l) )
qlm[i] = ( self.xlm[i] - (-1)**m * numpy.conj( self.xlm[k] ) ) / 2j
indxp = LISAresponse.getMLvec( self.ntrunc , 'p' )
self._SkyMap__qlm = numpy.copy( qlm[ :len(indxp) ] )
return
def xlm_to_qlm(self):
indxpn = LISAresponse.getMLvec(self.ntrunc, 'pn')
qlm = numpy.zeros(self.xlm.shape, dtype='complex')
for i, ml in enumerate(indxpn):
m, l = ml[0], ml[1]
k = indxpn.index((-m, l))
qlm[i] = (self.xlm[i] - (-1)**m * numpy.conj(self.xlm[k])) / 2j
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
self._SkyMap__qlm = numpy.copy(qlm[:len(indxp)])
return
def plmqlm_to_xlm( self ):
indxp = LISAresponse.getMLvec( self.ntrunc , 'p' )
indxpn = LISAresponse.getMLvec( self.ntrunc , 'pn' )
xlm = numpy.zeros( ( len(indxpn), ) , dtype='complex' )
for i,ml in enumerate( indxpn ):
m , l = ml
k = indxp.index( ( abs(m),l ) )
if m >= 0:
xlm[i] = self.plm[k] + 1j*self.qlm[k]
else:
xlm[i] = (-1)**m * ( numpy.conj( self.plm[k] ) + 1j*numpy.conj( self.qlm[k] ) )
self._SkyMap__xlm = numpy.copy( xlm )
return
def plmqlm_to_xlm(self):
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
indxpn = LISAresponse.getMLvec(self.ntrunc, 'pn')
xlm = numpy.zeros((len(indxpn), ), dtype='complex')
for i, ml in enumerate(indxpn):
m, l = ml
k = indxp.index((abs(m), l))
if m >= 0:
xlm[i] = self.plm[k] + 1j * self.qlm[k]
else:
xlm[i] = (-1)**m * (numpy.conj(self.plm[k]) +
1j * numpy.conj(self.qlm[k]))
self._SkyMap__xlm = numpy.copy(xlm)
return
def __init__( self , nlat=3 , nlon=4 , X=None ):
super( XSkyMap , self ).__init__()
if X == None:
if nlat < 3 or nlon < 4:
print "Make sure that nlat >=3, and nlon >=4."
raise ValueError
else:
self._SkyMap__X = numpy.zeros( ( nlat , nlon ) , dtype='complex' )
self._SkyMap__sky = LISAresponse.mySpharmt( nlon , nlat )
else:
nlat , nlon = X.shape
self._SkyMap__X = numpy.copy( X )
self._SkyMap__sky = LISAresponse.mySpharmt( nlon , nlat )
return
def __init__(self, nlat=3, nlon=4, X=None):
super(XSkyMap, self).__init__()
if X == None:
if nlat < 3 or nlon < 4:
print "Make sure that nlat >=3, and nlon >=4."
raise ValueError
else:
self._SkyMap__X = numpy.zeros((nlat, nlon), dtype='complex')
self._SkyMap__sky = LISAresponse.mySpharmt(nlon, nlat)
else:
nlat, nlon = X.shape
self._SkyMap__X = numpy.copy(X)
self._SkyMap__sky = LISAresponse.mySpharmt(nlon, nlat)
return
def checkPIXELCONVERSION( lmax , nlat , nlon ) :
"""
INPUT:
lmax -- maximum degree of SpH, l
nlat -- number of latitudes
nlon -- number of longitudes
OUTPUT:
U -- matrix for converting a matrix from SpH to PIXELS
lats -- latitudes, repeated nlon times
lons -- longitudes, repeated nlat times
"""
indxpn = LISAresponse.getMLvec( lmax , 'pn' )
U = numpy.empty( ( nlat*nlon , len(indxpn) ) , dtype='complex' )
for i,ml in enumerate( indxpn ) :
M = xlmSkyMap( ntrunc=ml[-1] )
M.alter_ml( False , ( ml[0] , ml[-1] , 1 ) )
M.xlm_to_plm()
M.xlm_to_qlm()
M.create_sky( nlat=nlat , nlon=nlon )
M.plm_to_P()
M.qlm_to_Q()
M.PQ_to_X()
U[ :,i ] = numpy.reshape( M.X , ( nlat*nlon, ) )
lats = numpy.outer( M.sky.lats , numpy.ones( nlon ) )
lons = numpy.outer( numpy.ones( nlat ) , M.sky.lons )
lats = numpy.reshape( lats , ( nlat*nlon , ) )
lons = numpy.reshape( lons , ( nlat*nlon , ) )
return U , lats , lons
def checkPIXELCONVERSION(lmax, nlat, nlon):
"""
INPUT:
lmax -- maximum degree of SpH, l
nlat -- number of latitudes
nlon -- number of longitudes
OUTPUT:
U -- matrix for converting a matrix from SpH to PIXELS
lats -- latitudes, repeated nlon times
lons -- longitudes, repeated nlat times
"""
indxpn = LISAresponse.getMLvec(lmax, 'pn')
U = numpy.empty((nlat * nlon, len(indxpn)), dtype='complex')
for i, ml in enumerate(indxpn):
M = xlmSkyMap(ntrunc=ml[-1])
M.alter_ml(False, (ml[0], ml[-1], 1))
M.xlm_to_plm()
M.xlm_to_qlm()
M.create_sky(nlat=nlat, nlon=nlon)
M.plm_to_P()
M.qlm_to_Q()
M.PQ_to_X()
U[:, i] = numpy.reshape(M.X, (nlat * nlon, ))
lats = numpy.outer(M.sky.lats, numpy.ones(nlon))
lons = numpy.outer(numpy.ones(nlat), M.sky.lons)
lats = numpy.reshape(lats, (nlat * nlon, ))
lons = numpy.reshape(lons, (nlat * nlon, ))
return U, lats, lons
def qlm_to_Q( self ):
indxp = LISAresponse.getMLvec( self.ntrunc , 'p' )
to_pyspharm = numpy.zeros( ( len(indxp), ) )
for i,ml in enumerate( indxp ):
to_pyspharm[i] = (-1)**ml[0] / numpy.sqrt( 2*numpy.pi )
self._SkyMap__Q = self.sky.spectogrd( to_pyspharm * self.qlm )
return
def qlm_to_Q(self):
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
to_pyspharm = numpy.zeros((len(indxp), ))
for i, ml in enumerate(indxp):
to_pyspharm[i] = (-1)**ml[0] / numpy.sqrt(2 * numpy.pi)
self._SkyMap__Q = self.sky.spectogrd(to_pyspharm * self.qlm)
return
def getImagMultipleMoments(self,msign='pn'):
try:
assert msign=='p' or msign=='pn'
except AssertionError:
print "Keyword parameter 'msign' must either be 'p' for only positive m's or 'pn' for all m's."
indxpn = LISAresponse.getMLvec( self.ntrunc , 'pn' )
qlm = numpy.zeros( numpy.shape(self.xlm) , dtype = complex )
for i,ml in enumerate(indxpn):
m = ml[0]
l = ml[1]
k = indxpn.index((-m,l))
qlm[i] = ( self.xlm[i] - (-1)**m*numpy.conj(self.xlm[k]) ) / 2j
if ( msign=='p' ):
indxp = LISAresponse.getMLvec( self.ntrunc , 'p' )
qlm = qlm[:len(indxp)]
else:
qlm = qlm
return qlm
def getImagMultipleMoments(self, msign='pn'):
try:
assert msign == 'p' or msign == 'pn'
except AssertionError:
print "Keyword parameter 'msign' must either be 'p' for only positive m's or 'pn' for all m's."
indxpn = LISAresponse.getMLvec(self.ntrunc, 'pn')
qlm = numpy.zeros(numpy.shape(self.xlm), dtype=complex)
for i, ml in enumerate(indxpn):
m = ml[0]
l = ml[1]
k = indxpn.index((-m, l))
qlm[i] = (self.xlm[i] - (-1)**m * numpy.conj(self.xlm[k])) / 2j
if (msign == 'p'):
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
qlm = qlm[:len(indxp)]
else:
qlm = qlm
return qlm
def Q_to_qlm( self ):
indxp =LISAresponse.getMLvec( self.ntrunc , 'p' )
to_standard = numpy.zeros( ( len(indxp), ) )
for i, ml in enumerate( indxp ):
to_standard[i] = (-1)**ml[0] * numpy.sqrt( 2*numpy.pi )
self._SkyMap__qlm = to_standard * self.sky.grdtospec( self.Q , self.ntrunc )
return
def Q_to_qlm(self):
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
to_standard = numpy.zeros((len(indxp), ))
for i, ml in enumerate(indxp):
to_standard[i] = (-1)**ml[0] * numpy.sqrt(2 * numpy.pi)
self._SkyMap__qlm = to_standard * self.sky.grdtospec(
self.Q, self.ntrunc)
return
def getMultipleMoments(self, msign='pn'):
try:
assert msign == 'p' or msign == 'pn'
except AssertionError:
print "Keyword parameter 'msign' must either be 'p' for only positive m's or 'pn' for all m's."
if (msign == 'p'):
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
xlm = self.xlm[:len(indxp)]
else:
xlm = self.xlm
return xlm
def getMultipleMoments(self,msign='pn'):
try:
assert msign=='p' or msign=='pn'
except AssertionError:
print "Keyword parameter 'msign' must either be 'p' for only positive m's or 'pn' for all m's."
if ( msign == 'p' ):
indxp = LISAresponse.getMLvec( self.ntrunc , 'p' )
xlm = self.xlm[:len(indxp)]
else:
xlm = self.xlm
return xlm
def getMultipleMoments(self, msign='pn'):
if not hasattr(self, 'ntrunc'):
self.getntrunc()
try:
assert msign == 'p' or msign == 'pn'
except AssertionError:
print "Keyword parameter 'msign' must either be 'p' for only positive m's or 'pn' for all m's."
numf = self.Length
sqrt2pi = numpy.sqrt(2 * numpy.pi)
if (msign == 'p'):
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
p = self.realr - 1j * self.reali # + 1j*self.reali
q = self.imagr - 1j * self.imagi # + 1j*self.imagi
g = numpy.zeros((len(indxp), numf), complex)
for i, ml in enumerate(indxp):
g[i] = (-1)**ml[0] * sqrt2pi * (p[i] + 1j * q[i])
self.indxp = indxp
self.Moments_pm = g
else:
indxp = LISAresponse.getMLvec(self.ntrunc, 'p')
indxpn = LISAresponse.getMLvec(self.ntrunc, 'pn')
p = self.realr - 1j * self.reali # + 1j*self.reali
q = self.imagr - 1j * self.imagi # + 1j*self.imagi
g = numpy.zeros((len(indxpn), numf), complex)
for i, ml in enumerate(indxpn):
m = ml[0]
l = ml[1]
if m >= 0:
k = indxp.index(ml)
g[i, :] = (-1)**m * sqrt2pi * (p[k, :] + 1j * q[k, :])
else:
ml = (-m, l)
k = indxp.index(ml)
g[i, :] = sqrt2pi * (numpy.conj(p[k, :]) +
1j * numpy.conj(q[k, :]))
self.indxpn = indxpn
self.Moments = g
return g
def getMultipleMoments(self,msign='pn'):
if not hasattr(self,'ntrunc'):
self.getntrunc()
try:
assert msign=='p' or msign=='pn'
except AssertionError:
print "Keyword parameter 'msign' must either be 'p' for only positive m's or 'pn' for all m's."
numf = self.Length
sqrt2pi = numpy.sqrt( 2*numpy.pi )
if (msign == 'p'):
indxp = LISAresponse.getMLvec(self.ntrunc,'p')
p = self.realr - 1j*self.reali # + 1j*self.reali
q = self.imagr - 1j*self.imagi # + 1j*self.imagi
g = numpy.zeros( ( len(indxp),numf ) , complex )
for i,ml in enumerate( indxp ):
g[i] = (-1)**ml[0] * sqrt2pi * ( p[i] + 1j*q[i] )
self.indxp = indxp
self.Moments_pm = g
else:
indxp = LISAresponse.getMLvec(self.ntrunc,'p')
indxpn = LISAresponse.getMLvec(self.ntrunc,'pn')
p = self.realr - 1j*self.reali # + 1j*self.reali
q = self.imagr - 1j*self.imagi # + 1j*self.imagi
g = numpy.zeros( ( len(indxpn),numf ) ,complex)
for i,ml in enumerate(indxpn):
m = ml[0]
l = ml[1]
if m >= 0:
k = indxp.index(ml)
g[i,:] = (-1)**m * sqrt2pi * ( p[k,:] + 1j*q[k,:] )
else:
ml = (-m,l)
k = indxp.index(ml)
g[i,:] = sqrt2pi * ( numpy.conj(p[k,:]) + 1j*numpy.conj(q[k,:]) )
self.indxpn = indxpn
self.Moments = g
return g
def getPixels(self):
nlat = self.ntrunc + 30
nlon = 2 * (nlat - 1)
self.sky = LISAresponse.mySpharmt(nlon, nlat)
if self.maptype in ['X', 'XX']:
norm = 1e-45
elif self.maptype in ['P']:
norm = 1
xlm = self.getMultipleMoments('p') * norm
plm = self.getRealMultipleMoments('p') * norm
qlm = self.getImagMultipleMoments('p') * norm
self.pix = self.sky.spectogrd(xlm)
self.pixp = self.sky.spectogrd(plm)
self.pixq = self.sky.spectogrd(qlm)
self.gotpix = True
return self.pix, self.pixp, self.pixq
def getPixels(self):
nlat = self.ntrunc + 30
nlon = 2*(nlat - 1)
self.sky = LISAresponse.mySpharmt(nlon,nlat)
if self.maptype in ['X','XX']:
norm = 1e-45
elif self.maptype in ['P']:
norm = 1
xlm = self.getMultipleMoments('p') * norm
plm = self.getRealMultipleMoments('p') * norm
qlm = self.getImagMultipleMoments('p') * norm
self.pix = self.sky.spectogrd(xlm)
self.pixp = self.sky.spectogrd(plm)
self.pixq = self.sky.spectogrd(qlm)
self.gotpix = True
return self.pix, self.pixp, self.pixq
def AngularPower(self, l=0, realimag='real'):
if realimag == 'real':
xlm = numpy.copy(self.plm)
elif realimag == 'imag':
xlm = numpy.copy(self.qlm)
else:
raise Exception, "realimag must either be 'real' or 'imag'."
mlvec = LISAresponse.getMLvec(self.ntrunc)
angpower = 0
for m in range(l + 1):
dangpower = abs(xlm[mlvec.index((m, l))])**2
if m == 0:
angpower += dangpower
else:
angpower += 2 * dangpower
return angpower
def AngularPower( self , l=0 , realimag='real' ) :
if realimag == 'real' :
xlm = numpy.copy( self.plm )
elif realimag == 'imag' :
xlm = numpy.copy( self.qlm )
else :
raise Exception , "realimag must either be 'real' or 'imag'."
mlvec = LISAresponse.getMLvec( self.ntrunc )
angpower = 0
for m in range( l+1 ) :
dangpower = abs( xlm[ mlvec.index( (m,l) ) ] )**2
if m == 0 :
angpower += dangpower
else :
angpower += 2 * dangpower
return angpower
def alter_ml( self , add_on=False , *mlvs ):
if mlvs == ():
print "No (m,l) to add/overwrite."
return
mlvec = LISAresponse.getMLvec( self.ntrunc )
for mlv in mlvs:
m , l , value = mlv
if (m,l) not in mlvec:
print "(%d,%d) is out of range. lmax = %d . " % ( m , l ,self.ntrunc )
continue
indx = mlvec.index( (m,l) )
if add_on==False:
self._SkyMap__xlm[ indx ] = value
elif add_on==True:
self._SkyMap__xlm[ indx ] = self._SkyMap__xlm[ indx ] + value
return
def alter_ml(self, add_on=False, *mlvs):
if mlvs == ():
print "No (m,l) to add/overwrite."
return
mlvec = LISAresponse.getMLvec(self.ntrunc)
for mlv in mlvs:
m, l, value = mlv
if (m, l) not in mlvec:
print "(%d,%d) is out of range. lmax = %d . " % (m, l,
self.ntrunc)
continue
indx = mlvec.index((m, l))
if add_on == False:
self._SkyMap__xlm[indx] = value
elif add_on == True:
self._SkyMap__xlm[indx] = self._SkyMap__xlm[indx] + value
return
def create_sky( self , nlon=6 , nlat=4 ):
self._SkyMap__sky = LISAresponse.mySpharmt( nlon , nlat )
return
def create_sky(self, nlon=6, nlat=4):
self._SkyMap__sky = LISAresponse.mySpharmt(nlon, nlat)
return
import cPickle
import LISAresponse
import Utilities4 as U4
sourcename = '' #Name your custom function something.
mapdir = ''
nlon =
nlat =
ntrunc = 20
sky = LISAresponse.mySpharmt( nlon , nlat )
X = numpy.zeros( ( nlat , nlon ) )
for i,lat in enumerate( sky.lats ):
theta = ( 90 - lat ) / 180 * numpy.pi
for k,lon in enumerate( sky.lons ):
lon = lon / 180 * numpy.pi
X[ i,k ] = #Enter your function here in terms of theta and lon
skymap = U4.XSkyMap( X=X )
skymap.X_to_P()
skymap.X_to_Q()
skymap.ntrunc_equals( ntrunc )
skymap.P_to_plm()
skymap.Q_to_qlm()
skymap.plmqlm_to_xlm()
