def powerspectrum_1D(self, k_vec, z1, z2, numz):
r"""A vectorized routine for calculating the redshift space powerspectrum.
Parameters
----------
k_vec: array_like
The magnitude of the k-vector
redshift: scalar
Redshift at which to evaluate other parameters
Returns
-------
ps: array_like
The redshift space power spectrum at the given k-vector and redshift.
Note that this uses the same ps_vv as the realisation generator until
the full dd, dv, vv calculation is ready.
TODO: evaluate this using the same weight function in z as the data.
"""
c1 = self.cosmology.comoving_distance(z1)
c2 = self.cosmology.comoving_distance(z2)
# Construct an array of the redshifts on each slice of the cube.
comoving_inv = cosmo.inverse_approx(self.cosmology.comoving_distance,
z1, z2)
da = np.linspace(c1, c2, numz + 1, endpoint=True)
za = comoving_inv(da)
# Calculate the bias and growth factors for each slice of the cube.
mz = self.mean(za)
bz = self.bias_z(za)
fz = self.growth_rate(za)
Dz = self.growth_factor(za) / self.growth_factor(self.ps_redshift)
pz = self.prefactor(za)
dfactor = np.mean(Dz * pz * bz)
vfactor = np.mean(Dz * pz * fz)
return self.ps_vv(k_vec) * dfactor * dfactor
def powerspectrum_1D(self, k_vec, z1, z2, numz):
r"""A vectorized routine for calculating the redshift space powerspectrum.
Parameters
----------
k_vec: array_like
The magnitude of the k-vector
redshift: scalar
Redshift at which to evaluate other parameters
Returns
-------
ps: array_like
The redshift space power spectrum at the given k-vector and redshift.
Note that this uses the same ps_vv as the realisation generator until
the full dd, dv, vv calculation is ready.
TODO: evaluate this using the same weight function in z as the data.
"""
c1 = self.cosmology.comoving_distance(z1)
c2 = self.cosmology.comoving_distance(z2)
# Construct an array of the redshifts on each slice of the cube.
comoving_inv = cosmo.inverse_approx(self.cosmology.comoving_distance, z1, z2)
da = np.linspace(c1, c2, numz + 1, endpoint=True)
za = comoving_inv(da)
# Calculate the bias and growth factors for each slice of the cube.
mz = self.mean(za)
bz = self.bias_z(za)
fz = self.growth_rate(za)
Dz = self.growth_factor(za) / self.growth_factor(self.ps_redshift)
pz = self.prefactor(za)
dfactor = np.mean(Dz * pz * bz)
vfactor = np.mean(Dz * pz * fz)
return self.ps_vv(k_vec) * dfactor * dfactor
def physical_grid(input_array, refinement=2, pad=5, order=2):
r"""Project from freq, ra, dec into physical coordinates
Parameters
----------
input_array: np.ndarray
The freq, ra, dec map
Returns
-------
cube: np.ndarray
The cube projected back into physical coordinates
"""
freq_axis = input_array.get_axis('freq') / 1.e6
ra_axis = input_array.get_axis('ra')
dec_axis = input_array.get_axis('dec')
nu_lower, nu_upper = freq_axis.min(), freq_axis.max()
ra_fact = sp.cos(sp.pi * input_array.info['dec_centre'] / 180.0)
thetax, thetay = np.ptp(ra_axis), np.ptp(dec_axis)
thetax *= ra_fact
(numz, numx, numy) = input_array.shape
cosmology = cosmo.Cosmology()
z1 = units.nu21 / nu_upper - 1.0
z2 = units.nu21 / nu_lower - 1.0
d1 = cosmology.proper_distance(z1)
d2 = cosmology.proper_distance(z2)
c1 = cosmology.comoving_distance(z1)
c2 = cosmology.comoving_distance(z2)
c_center = (c1 + c2) / 2.
# Make cube pixelisation finer, such that angular cube will
# have sufficient resolution on the closest face.
phys_dim = np.array([c2 - c1,
thetax * d2 * units.degree,
thetay * d2 * units.degree])
# Note that the ratio of deltas in Ra, Dec in degrees may
# be different than the Ra, Dec in physical coordinates due to
# rounding onto this grid
n = np.array([numz, int(d2 / d1 * numx), int(d2 / d1 * numy)])
# Enlarge cube size by `pad` in each dimension, so raytraced cube
# sits exactly within the gridded points.
phys_dim = phys_dim * (n + pad).astype(float) / n.astype(float)
c1 = c_center - (c_center - c1) * (n[0] + pad) / float(n[0])
c2 = c_center + (c2 - c_center) * (n[0] + pad) / float(n[0])
n = n + pad
# now multiply by scaling for a finer sub-grid
n = refinement * n
print "converting from obs. to physical coord refinement=%s, pad=%s" % \
(refinement, pad)
print "(%d, %d, %d)->(%f to %f) x %f x %f (%d, %d, %d) (h^-1 cMpc)^3" % \
(numz, numx, numy, c1, c2, \
phys_dim[1], phys_dim[2], \
n[0], n[1], n[2])
# this is wasteful in memory, but numpy can be pickled
phys_map_npy = np.zeros(n)
phys_map = algebra.make_vect(phys_map_npy, axis_names=('freq', 'ra', 'dec'))
#mask = np.ones_like(phys_map)
mask = np.ones_like(phys_map_npy)
# TODO: should this be more sophisticated? N-1 or N?
info = {}
info['axes'] = ('freq', 'ra', 'dec')
info['type'] = 'vect'
#info = {'freq_delta': abs(phys_dim[0])/float(n[0]),
# 'freq_centre': abs(c2+c1)/2.,
info['freq_delta'] = abs(c2 - c1) / float(n[0] - 1)
info['freq_centre'] = c1 + info['freq_delta'] * float(n[0] // 2)
info['ra_delta'] = abs(phys_dim[1]) / float(n[1] - 1)
#info['ra_centre'] = info['ra_delta'] * float(n[1] // 2)
info['ra_centre'] = 0.
info['dec_delta'] = abs(phys_dim[2]) / float(n[2] - 1)
#info['dec_centre'] = info['dec_delta'] * float(n[2] // 2)
info['dec_centre'] = 0.
phys_map.info = info
print info
# same as np.linspace(c1, c2, n[0], endpoint=True)
radius_axis = phys_map.get_axis("freq")
x_axis = phys_map.get_axis("ra")
y_axis = phys_map.get_axis("dec")
# Construct an array of the redshifts on each slice of the cube.
comoving_inv = cosmo.inverse_approx(cosmology.comoving_distance, z1, z2)
za = comoving_inv(radius_axis) # redshifts on the constant-D spacing
nua = units.nu21 / (1. + za)
gridy, gridx = np.meshgrid(y_axis, x_axis)
interpol_grid = np.zeros((3, n[1], n[2]))
for i in range(n[0]):
# nua[0] = nu_upper, nua[1] = nu_lower
#print nua[i], freq_axis[0], freq_axis[-1], (nua[i] - freq_axis[0]) / \
# (freq_axis[-1] - freq_axis[0]) * numz
interpol_grid[0, :, :] = (nua[i] - freq_axis[0]) / \
(freq_axis[-1] - freq_axis[0]) * numz
proper_z = cosmology.proper_distance(za[i])
angscale = proper_z * units.degree
interpol_grid[1, :, :] = gridx / angscale / thetax * numx + numx / 2
interpol_grid[2, :, :] = gridy / angscale / thetay * numy + numy / 2
phys_map_npy[i, :, :] = sp.ndimage.map_coordinates(input_array,
interpol_grid,
order=order)
interpol_grid[1, :, :] = np.logical_or(interpol_grid[1, :, :] > numx,
interpol_grid[1, :, :] < 0)
interpol_grid[2, :, :] = np.logical_or(interpol_grid[1, :, :] > numy,
interpol_grid[1, :, :] < 0)
mask = np.logical_not(np.logical_or(interpol_grid[1, :, :],
interpol_grid[2, :, :]))
phys_map_npy *= mask
return phys_map_npy, info
def realisation(
self,
z1,
z2,
thetax,
thetay,
numz,
numx,
numy,
zspace=True,
refinement=1,
report_physical=False,
density_only=False,
no_mean=False,
no_evolution=False,
pad=5,
):
r"""Simulate a redshift-space volume.
Generates a 3D (angle-angle-redshift) volume from the given
power spectrum. Currently only works with simply biased power
spectra (i.e. vv_only). This routine uses a flat sky
approximation, and so becomes inaccurate when a large volume
of the sky is simulated.
Parameters
----------
z1, z2 : scalar
Lower and upper redshifts of the box.
thetax, thetay : scalar
The angular size (in degrees) of the box.
numz : integer
The number of bins in redshift.
numx, numy : integer
The number of angular pixels along each side.
zspace : boolean, optional
If True (default) redshift bins are equally spaced in
redshift. Otherwise space equally in the scale factor
(useful for generating an equal range in frequency).
density_only: boolean
no velocity contribution
no_mean: boolean
do not add the mean temperature
no_evolution: boolean
do not let b(z), D(z) etc. evolve: take their mean
pad: integer
number of pixels over which to pad the physical region for
interpolation onto freq, ra, dec; match spline order?
Returns
-------
cube : np.ndarray
The volume cube.
"""
d1 = self.cosmology.proper_distance(z1)
d2 = self.cosmology.proper_distance(z2)
c1 = self.cosmology.comoving_distance(z1)
c2 = self.cosmology.comoving_distance(z2)
c_center = (c1 + c2) / 2.0
# Make cube pixelisation finer, such that angular cube will
# have sufficient resolution on the closest face.
d = np.array([c2 - c1, thetax * d2 * units.degree, thetay * d2 * units.degree])
# Note that the ratio of deltas in Ra, Dec in degrees may
# be different than the Ra, Dec in physical coordinates due to
# rounding onto this grid
n = np.array([numz, int(d2 / d1 * numx), int(d2 / d1 * numy)])
# Enlarge cube size by 1 in each dimension, so raytraced cube
# sits exactly within the gridded points.
d = d * (n + pad).astype(float) / n.astype(float)
c1 = c_center - (c_center - c1) * (n[0] + pad) / float(n[0])
c2 = c_center + (c2 - c_center) * (n[0] + pad) / float(n[0])
n = n + pad
# now multiply by scaling for a finer sub-grid
n = refinement * n
print "Generating cube: (%f to %f) x %f x %f (%d, %d, %d) (h^-1 cMpc)^3" % (
c1,
c2,
d[1],
d[2],
n[0],
n[1],
n[2],
)
cube = self._realisation_dv(d, n)
# TODO: this is probably unnecessary now (realisation used to change
# shape through irfftn)
n = cube[0].shape
# Construct an array of the redshifts on each slice of the cube.
comoving_inv = cosmo.inverse_approx(self.cosmology.comoving_distance, z1, z2)
da = np.linspace(c1, c2, n[0], endpoint=True)
za = comoving_inv(da)
# Calculate the bias and growth factors for each slice of the cube.
mz = self.mean(za)
bz = self.bias_z(za)
fz = self.growth_rate(za)
Dz = self.growth_factor(za) / self.growth_factor(self.ps_redshift)
pz = self.prefactor(za)
# Construct the observable and velocity fields.
if not no_evolution:
df = cube[0] * (Dz * pz * bz)[:, np.newaxis, np.newaxis]
vf = cube[1] * (Dz * pz * fz)[:, np.newaxis, np.newaxis]
else:
df = cube[0] * np.mean(Dz * pz * bz)
vf = cube[1] * np.mean(Dz * pz * fz)
# Construct the redshift space cube.
rsf = df
if not density_only:
rsf += vf
if not no_mean:
rsf += mz[:, np.newaxis, np.newaxis]
# Find the distances that correspond to a regular redshift
# spacing (or regular spacing in a).
if zspace:
za = np.linspace(z1, z2, numz, endpoint=False)
else:
za = 1.0 / np.linspace(1.0 / (1 + z2), 1.0 / (1 + z1), numz, endpoint=False)[::-1] - 1.0
da = self.cosmology.proper_distance(za)
xa = self.cosmology.comoving_distance(za)
# Construct the angular offsets into cube
tx = np.linspace(-thetax / 2.0, thetax / 2.0, numx) * units.degree
ty = np.linspace(-thetay / 2.0, thetay / 2.0, numy) * units.degree
# tgridx, tgridy = np.meshgrid(tx, ty)
tgridy, tgridx = np.meshgrid(ty, tx)
tgrid2 = np.zeros((3, numx, numy))
acube = np.zeros((numz, numx, numy))
# Iterate over redshift slices, constructing the coordinates
# and interpolating into the 3d cube. Note that the multipliers scale
# from 0 to 1, or from i=0 to i=N-1
for i in range(numz):
tgrid2[0, :, :] = (xa[i] - c1) / (c2 - c1) * (n[0] - 1.0)
tgrid2[1, :, :] = (tgridx * da[i]) / d[1] * (n[1] - 1.0) + 0.5 * (n[1] - 1.0)
tgrid2[2, :, :] = (tgridy * da[i]) / d[2] * (n[2] - 1.0) + 0.5 * (n[2] - 1.0)
# if(zi > numz - 2):
# TODO: what order here?; do end-to-end P(k) study
# acube[i,:,:] = scipy.ndimage.map_coordinates(rsf, tgrid2, order=2)
acube[i, :, :] = scipy.ndimage.map_coordinates(rsf, tgrid2, order=1)
if report_physical:
return acube, rsf, (c1, c2, d[1], d[2])
else:
return acube
from utils import cosmology from simulations import corr from utils.cosmology import Cosmology redshift = 1. cosmo = Cosmology() proper = cosmo.proper_distance(redshift) comoving = cosmo.comoving_distance(redshift) comoving_inv = cosmology.inverse_approx(cosmo.comoving_distance, 0.6, 1.) print proper, comoving, comoving_inv(2355.35909781)
def physical_grid(input_array, refinement=2, pad=5, order=2):
r"""Project from freq, ra, dec into physical coordinates
Parameters
----------
input_array: np.ndarray
The freq, ra, dec map
Returns
-------
cube: np.ndarray
The cube projected back into physical coordinates
"""
freq_axis = input_array.get_axis('freq') / 1.e6
ra_axis = input_array.get_axis('ra')
dec_axis = input_array.get_axis('dec')
nu_lower, nu_upper = freq_axis.min(), freq_axis.max()
ra_fact = sp.cos(sp.pi * input_array.info['dec_centre'] / 180.0)
thetax, thetay = np.ptp(ra_axis), np.ptp(dec_axis)
thetax *= ra_fact
(numz, numx, numy) = input_array.shape
cosmology = cosmo.Cosmology()
z1 = units.nu21 / nu_upper - 1.0
z2 = units.nu21 / nu_lower - 1.0
d1 = cosmology.proper_distance(z1)
d2 = cosmology.proper_distance(z2)
c1 = cosmology.comoving_distance(z1)
c2 = cosmology.comoving_distance(z2)
c_center = (c1 + c2) / 2.
# Make cube pixelisation finer, such that angular cube will
# have sufficient resolution on the closest face.
phys_dim = np.array(
[c2 - c1, thetax * d2 * units.degree, thetay * d2 * units.degree])
# Note that the ratio of deltas in Ra, Dec in degrees may
# be different than the Ra, Dec in physical coordinates due to
# rounding onto this grid
n = np.array([numz, int(d2 / d1 * numx), int(d2 / d1 * numy)])
# Enlarge cube size by `pad` in each dimension, so raytraced cube
# sits exactly within the gridded points.
phys_dim = phys_dim * (n + pad).astype(float) / n.astype(float)
c1 = c_center - (c_center - c1) * (n[0] + pad) / float(n[0])
c2 = c_center + (c2 - c_center) * (n[0] + pad) / float(n[0])
n = n + pad
# now multiply by scaling for a finer sub-grid
n = refinement * n
print "converting from obs. to physical coord refinement=%s, pad=%s" % \
(refinement, pad)
print "(%d, %d, %d)->(%f to %f) x %f x %f (%d, %d, %d) (h^-1 cMpc)^3" % \
(numz, numx, numy, c1, c2, \
phys_dim[1], phys_dim[2], \
n[0], n[1], n[2])
# this is wasteful in memory, but numpy can be pickled
phys_map_npy = np.zeros(n)
phys_map = algebra.make_vect(phys_map_npy,
axis_names=('freq', 'ra', 'dec'))
#mask = np.ones_like(phys_map)
mask = np.ones_like(phys_map_npy)
# TODO: should this be more sophisticated? N-1 or N?
info = {}
info['axes'] = ('freq', 'ra', 'dec')
info['type'] = 'vect'
#info = {'freq_delta': abs(phys_dim[0])/float(n[0]),
# 'freq_centre': abs(c2+c1)/2.,
info['freq_delta'] = abs(c2 - c1) / float(n[0] - 1)
info['freq_centre'] = c1 + info['freq_delta'] * float(n[0] // 2)
info['ra_delta'] = abs(phys_dim[1]) / float(n[1] - 1)
#info['ra_centre'] = info['ra_delta'] * float(n[1] // 2)
info['ra_centre'] = 0.
info['dec_delta'] = abs(phys_dim[2]) / float(n[2] - 1)
#info['dec_centre'] = info['dec_delta'] * float(n[2] // 2)
info['dec_centre'] = 0.
phys_map.info = info
print info
# same as np.linspace(c1, c2, n[0], endpoint=True)
radius_axis = phys_map.get_axis("freq")
x_axis = phys_map.get_axis("ra")
y_axis = phys_map.get_axis("dec")
# Construct an array of the redshifts on each slice of the cube.
comoving_inv = cosmo.inverse_approx(cosmology.comoving_distance, z1, z2)
za = comoving_inv(radius_axis) # redshifts on the constant-D spacing
nua = units.nu21 / (1. + za)
gridy, gridx = np.meshgrid(y_axis, x_axis)
interpol_grid = np.zeros((3, n[1], n[2]))
for i in range(n[0]):
# nua[0] = nu_upper, nua[1] = nu_lower
#print nua[i], freq_axis[0], freq_axis[-1], (nua[i] - freq_axis[0]) / \
# (freq_axis[-1] - freq_axis[0]) * numz
interpol_grid[0, :, :] = (nua[i] - freq_axis[0]) / \
(freq_axis[-1] - freq_axis[0]) * numz
proper_z = cosmology.proper_distance(za[i])
angscale = proper_z * units.degree
interpol_grid[1, :, :] = gridx / angscale / thetax * numx + numx / 2
interpol_grid[2, :, :] = gridy / angscale / thetay * numy + numy / 2
phys_map_npy[i, :, :] = sp.ndimage.map_coordinates(input_array,
interpol_grid,
order=order)
interpol_grid[1, :, :] = np.logical_or(interpol_grid[1, :, :] > numx,
interpol_grid[1, :, :] < 0)
interpol_grid[2, :, :] = np.logical_or(interpol_grid[1, :, :] > numy,
interpol_grid[1, :, :] < 0)
mask = np.logical_not(
np.logical_or(interpol_grid[1, :, :], interpol_grid[2, :, :]))
phys_map_npy *= mask
return phys_map_npy, info
def realisation(self,
z1,
z2,
thetax,
thetay,
numz,
numx,
numy,
zspace=True,
refinement=1,
report_physical=False,
density_only=False,
no_mean=False,
no_evolution=False,
pad=5):
r"""Simulate a redshift-space volume.
Generates a 3D (angle-angle-redshift) volume from the given
power spectrum. Currently only works with simply biased power
spectra (i.e. vv_only). This routine uses a flat sky
approximation, and so becomes inaccurate when a large volume
of the sky is simulated.
Parameters
----------
z1, z2 : scalar
Lower and upper redshifts of the box.
thetax, thetay : scalar
The angular size (in degrees) of the box.
numz : integer
The number of bins in redshift.
numx, numy : integer
The number of angular pixels along each side.
zspace : boolean, optional
If True (default) redshift bins are equally spaced in
redshift. Otherwise space equally in the scale factor
(useful for generating an equal range in frequency).
density_only: boolean
no velocity contribution
no_mean: boolean
do not add the mean temperature
no_evolution: boolean
do not let b(z), D(z) etc. evolve: take their mean
pad: integer
number of pixels over which to pad the physical region for
interpolation onto freq, ra, dec; match spline order?
Returns
-------
cube : np.ndarray
The volume cube.
"""
d1 = self.cosmology.proper_distance(z1)
d2 = self.cosmology.proper_distance(z2)
c1 = self.cosmology.comoving_distance(z1)
c2 = self.cosmology.comoving_distance(z2)
c_center = (c1 + c2) / 2.
# Make cube pixelisation finer, such that angular cube will
# have sufficient resolution on the closest face.
d = np.array(
[c2 - c1, thetax * d2 * units.degree, thetay * d2 * units.degree])
# Note that the ratio of deltas in Ra, Dec in degrees may
# be different than the Ra, Dec in physical coordinates due to
# rounding onto this grid
n = np.array([numz, int(d2 / d1 * numx), int(d2 / d1 * numy)])
# Enlarge cube size by 1 in each dimension, so raytraced cube
# sits exactly within the gridded points.
d = d * (n + pad).astype(float) / n.astype(float)
c1 = c_center - (c_center - c1) * (n[0] + pad) / float(n[0])
c2 = c_center + (c2 - c_center) * (n[0] + pad) / float(n[0])
n = n + pad
# now multiply by scaling for a finer sub-grid
n = refinement * n
print "Generating cube: (%f to %f) x %f x %f (%d, %d, %d) (h^-1 cMpc)^3" % \
(c1, c2, d[1], d[2], n[0], n[1], n[2])
cube = self._realisation_dv(d, n)
# TODO: this is probably unnecessary now (realisation used to change
# shape through irfftn)
n = cube[0].shape
# Construct an array of the redshifts on each slice of the cube.
comoving_inv = cosmo.inverse_approx(self.cosmology.comoving_distance,
z1, z2)
da = np.linspace(c1, c2, n[0], endpoint=True)
za = comoving_inv(da)
# Calculate the bias and growth factors for each slice of the cube.
mz = self.mean(za)
bz = self.bias_z(za)
fz = self.growth_rate(za)
Dz = self.growth_factor(za) / self.growth_factor(self.ps_redshift)
pz = self.prefactor(za)
# Construct the observable and velocity fields.
if not no_evolution:
df = cube[0] * (Dz * pz * bz)[:, np.newaxis, np.newaxis]
vf = cube[1] * (Dz * pz * fz)[:, np.newaxis, np.newaxis]
else:
df = cube[0] * np.mean(Dz * pz * bz)
vf = cube[1] * np.mean(Dz * pz * fz)
# Construct the redshift space cube.
rsf = df
if not density_only:
rsf += vf
if not no_mean:
rsf += mz[:, np.newaxis, np.newaxis]
# Find the distances that correspond to a regular redshift
# spacing (or regular spacing in a).
if zspace:
za = np.linspace(z1, z2, numz, endpoint=False)
else:
za = 1.0 / np.linspace(
1.0 / (1 + z2), 1.0 /
(1 + z1), numz, endpoint=False)[::-1] - 1.0
da = self.cosmology.proper_distance(za)
xa = self.cosmology.comoving_distance(za)
# Construct the angular offsets into cube
tx = np.linspace(-thetax / 2., thetax / 2., numx) * units.degree
ty = np.linspace(-thetay / 2., thetay / 2., numy) * units.degree
#tgridx, tgridy = np.meshgrid(tx, ty)
tgridy, tgridx = np.meshgrid(ty, tx)
tgrid2 = np.zeros((3, numx, numy))
acube = np.zeros((numz, numx, numy))
# Iterate over redshift slices, constructing the coordinates
# and interpolating into the 3d cube. Note that the multipliers scale
# from 0 to 1, or from i=0 to i=N-1
for i in range(numz):
tgrid2[0, :, :] = (xa[i] - c1) / (c2 - c1) * (n[0] - 1.)
tgrid2[1,:,:] = (tgridx * da[i]) / d[1] * (n[1] - 1.) + \
0.5*(n[1] - 1.)
tgrid2[2,:,:] = (tgridy * da[i]) / d[2] * (n[2] - 1.) + \
0.5*(n[2] - 1.)
#if(zi > numz - 2):
# TODO: what order here?; do end-to-end P(k) study
#acube[i,:,:] = scipy.ndimage.map_coordinates(rsf, tgrid2, order=2)
acube[i, :, :] = scipy.ndimage.map_coordinates(rsf,
tgrid2,
order=1)
if report_physical:
return acube, rsf, (c1, c2, d[1], d[2])
else:
return acube
