def gather_patches_plain(self):
"""Assemble patch statistics relevant to lensing at small scales.
Compute the small scale (ell > lmin) temperature power at different
patches across the sky as well as the average amplitude of the
background temperature gradient (ell < ldT).
"""
self._edge = 0 # Not throwing away edge pixels
m_fft = enmap.fft(self.map_in)
hp = np.zeros(self.map_in.shape)
hp[np.where((self._lmod > self.lmin) & (self._lmod < self.lmax))] = 1.
self._Tss = enmap.ifft(m_fft * hp)
self._dTy, self._dTx = gradient_flat(self.map_in, self.ldT)
# Scale geometry for lower res map of patches
pshp, pwcs = enmap.scale_geometry(self.map_in.shape, self.map_in.wcs,
1. / self._p)
if not self.savesteps:
del self.map_in, m_fft
self._T2patch = enmap.zeros(pshp, pwcs)
self._dTxpatch = enmap.zeros(pshp, pwcs)
self._dTypatch = enmap.zeros(pshp, pwcs)
Trs = self._Tss[:pshp[-2] * self._p, :pshp[-1] * self._p].reshape(
[pshp[-2], self._p, pshp[-1], self._p])
dTxrs = self._dTx[:pshp[-2] * self._p, :pshp[-1] * self._p].reshape(
[pshp[-2], self._p, pshp[-1], self._p])
dTyrs = self._dTy[:pshp[-2] * self._p, :pshp[-1] * self._p].reshape(
[pshp[-2], self._p, pshp[-1], self._p])
self._T2patch[:, :] = np.var(Trs, axis=(1, 3))
self._dTypatch[:, :] = np.mean(dTyrs, axis=(1, 3))
self._dTxpatch[:, :] = np.mean(dTxrs, axis=(1, 3))
self._dT2patch = self._dTxpatch**2 + self._dTypatch**2
if not self.savesteps:
del self._dTypatch, self._dTxpatch, self._dTy, self._dTx, self._Tss
def gather_patches_cos(self):
"""Assemble patch statistics for small scale lensing with cos filter.
Compute the small scale (ell > 3000) temperature power at different
patches across the sky as well as the average amplitude of the
background temperature gradient (ell < 2000). For the small scale
statistics, also apply a filter in Fourier space such that:
.. math::
f_\\ell = \\cos(\\hat{\\ell}\\cdot\\hat{\\nabla T})
"""
self._edge = 5 # Edge pixels to throw away
p = self._p
m_fft = enmap.fft(self.map_in)
hp = np.zeros(self.map_in.shape)
hp[np.where((self._lmod > self.lmin) & (self._lmod < self.lmax))] = 1.
# Apply pre-whitening or Wiener/inverse variance filters, then top hat
if self._aW and self.fid is not None:
cs = CubicSpline(self.fid[0], self.fid[1]) # (ell, Cl)
m_fft = m_fft / cs(self._lmod)
self._Tss = enmap.ifft(m_fft * hp)
self._dTy, self._dTx = gradient_flat(self.map_in, self.ldT)
# Scale geometry for lower res map of patches
pshp, pwcs = enmap.scale_geometry(self.map_in.shape, self.map_in.wcs,
1. / self._p)
if not self.savesteps:
del self.map_in, m_fft
self._T2patch = enmap.zeros(pshp, pwcs)
self._dTxpatch = enmap.zeros(pshp, pwcs)
self._dTypatch = enmap.zeros(pshp, pwcs)
self._T_sub = np.zeros((pshp[-2], pshp[-1], p, p))
for i in range(self._T2patch.shape[-2]):
for j in range(self._T2patch.shape[-1]):
self._dTypatch[i, j] = np.mean(self._dTy[i * p:(i + 1) * p,
j * p:(j + 1) * p])
self._dTxpatch[i, j] = np.mean(self._dTx[i * p:(i + 1) * p,
j * p:(j + 1) * p])
Tp = self._Tss[i * p:(i + 1) * p, j * p:(j + 1) * p]
lsuby, lsubx = Tp.lmap()
lsubmod = Tp.modlmap()
lsubmod[0, 0] = 1.
fl = 1.j*(lsubx*self._dTxpatch[i,j] + \
lsuby*self._dTypatch[i,j]) / \
(lsubmod * np.sqrt(self._dTxpatch[i,j]**2 + \
self._dTypatch[i,j]**2))
fl[0, 0] = 0.
self._T_sub[i, j, :, :] = enmap.ifft(enmap.fft(Tp) * fl).real
# Throw away pixels with edge effects
self._T2patch[i, j] = np.var(self._T_sub[i, j, 5:-5, 5:-5])
self._dT2patch = self._dTxpatch**2 + self._dTypatch**2
if not self.savesteps:
del self._dTypatch, self._dTxpatch, self._dTy, self._dTx, self._Tss
del self._T_sub
def test_scale(self):
# Test (with a plain geometry) that scale_geometry
# will result in geometries with the same bounding box
# but different area pixel
pres = 0.5
ufact = 2
dfact = 0.5
shape,wcs = enmap.geometry(pos=(0,0),shape=(30,30),res=pres*u.arcmin,proj='plain')
ushape,uwcs = enmap.scale_geometry(shape,wcs,ufact)
dshape,dwcs = enmap.scale_geometry(shape,wcs,dfact)
box = enmap.box(shape,wcs)
ubox = enmap.box(ushape,uwcs)
dbox = enmap.box(dshape,dwcs)
parea = enmap.pixsize(shape,wcs)
uparea = enmap.pixsize(ushape,uwcs)
dparea = enmap.pixsize(dshape,dwcs)
assert np.all(np.isclose(box,ubox))
assert np.all(np.isclose(box,dbox))
assert np.isclose(parea/(ufact**2),uparea)
assert np.isclose(parea/(dfact**2),dparea)
def gather_patches_cos2(self):
"""Assemble patch statistics for small scale lensing with cos^2 filter.
Compute the small scale (ell > 3000) temperature power at different
patches across the sky as well as the average amplitude of the
background temperature gradient (ell < 2000). For the small scale
statistics, also apply a filter in Fourier space such that:
.. math::
f_\\ell = \\cos^2(\\hat{\\ell}\\cdot\\hat{\\nabla T})
"""
self._edge = 3 # Edge pixels to throw away
p = self._p
m_fft = enmap.fft(self.map_in)
hp = np.zeros(self.map_in.shape)
hp[np.where((self._lmod > self.lmin) & (self._lmod < self.lmax))] = 1.
self._Tss = enmap.ifft(m_fft * hp)
self._dTy, self._dTx = gradient_flat(self.map_in, self.ldT)
# Scale geometry for lower res map of patches
pshp, pwcs = enmap.scale_geometry(self.map_in.shape, self.map_in.wcs,
1. / self._p)
if not self.savesteps:
del self.map_in, m_fft
self._T2patch = enmap.zeros(pshp, pwcs)
self._dTxpatch = enmap.zeros(pshp, pwcs)
self._dTypatch = enmap.zeros(pshp, pwcs)
self._T_sub = np.zeros((pshp[-2], pshp[-1], p, p))
for i in range(self._T2patch.shape[-2]):
for j in range(self._T2patch.shape[-1]):
self._dTypatch[i, j] = np.mean(self._dTy[i * p:(i + 1) * p,
j * p:(j + 1) * p])
self._dTxpatch[i, j] = np.mean(self._dTx[i * p:(i + 1) * p,
j * p:(j + 1) * p])
Tp = self._Tss[i * p:(i + 1) * p, j * p:(j + 1) * p]
lsuby, lsubx = Tp.lmap()
lsubmod = Tp.modlmap()
lsubmod[0, 0] = 1. # Avoid divide by 0; set fl here to 0 later
fl = (lsubx*self._dTxpatch[i,j] + \
lsuby*self._dTypatch[i,j])**2 / \
(lsubmod * np.sqrt(self._dTxpatch[i,j]**2 + \
self._dTypatch[i,j]**2))**2
fl[0, 0] = 0.
self._T_sub[i, j, :, :] = enmap.ifft(enmap.fft(Tp) * fl).real
# Throw away pixels with edge effects
self._T2patch[i, j] = np.var(self._T_sub[i, j, 3:-3, 3:-3])
self._dT2patch = self._dTxpatch**2 + self._dTypatch**2
if not self.savesteps:
del self._dTypatch, self._dTxpatch, self._dTy, self._dTx, self._Tss
del self._T_sub