def power_spectrum_multipoles(input_array, kbins = 10, box_dims = None,\
los_axis = 0):
'''
Calculate the power spectrum of an array and
expand it in the first three Legendre polynomials.
Parameters:
* input_array (numpy array): the array to calculate the
power spectrum of. Can be of any dimensions.
* kbins = 10 (integer or array-like): The number of bins,
or a list containing the bin edges. If an integer is given, the bins
are logarithmically spaced.
* box_dims = None (float or array-like): the dimensions of the
box. If this is None, the current box volume is used along all
dimensions. If it is a float, this is taken as the box length
along all dimensions. If it is an array-like, the elements are
taken as the box length along each axis.
* los_axis = 0 (integer): the line-of-sight axis
Returns:
A tuple with (P0, P2, P4, k) where P0, P2 and P4
are the multipole moments as a function of k and
k contains the midpoints of the k bins.
All four arrays have the same length
'''
assert (los_axis >= 0 and los_axis <= len(input_array.shape))
#First calculate the power spectrum
box_dims = _get_dims(box_dims, input_array.shape)
ps = power_spectrum_nd(input_array, box_dims)
#Get k values and bins
k_comp, k = _get_k(input_array, box_dims)
kbins = _get_kbins(kbins, box_dims, k)
dk = (kbins[1:] - kbins[:-1]) / 2.
mu = _get_mu(k_comp, k, los_axis)
#Legendre polynomials
P0 = np.ones_like(mu)
P2 = 0.5 * (3. * mu**2 - 1.)
P4 = 4.375 * (mu**2 - 0.115587) * (mu**2 - 0.741556)
#Bin data
n_kbins = len(kbins) - 1
outdata_P0 = np.zeros(n_kbins)
outdata_P2 = np.zeros_like(outdata_P0)
outdata_P4 = np.zeros_like(outdata_P0)
for i in range(n_kbins):
idx = (k > kbins[i]) * (k <= kbins[i + 1])
outdata_P0[i] = np.sum(ps[idx] * P0[idx]) / np.sum(P0[idx]**2)
outdata_P2[i] = np.sum(ps[idx] * P2[idx]) / np.sum(P2[idx]**2)
outdata_P4[i] = np.sum(ps[idx] * P4[idx]) / np.sum(P4[idx]**2)
return outdata_P0, outdata_P2, outdata_P4, kbins[:-1] + dk
def make_gaussian_random_field(dims,
box_dims,
power_spectrum,
random_seed=None):
'''
Generate a Gaussian random field with the specified
power spectrum.
Parameters:
* dims (tuple): the dimensions of the field in number
of cells. Can be 2D or 3D.
* box_dims (float or tuple): the dimensions of the field
in cMpc.
* power_spectrum (callable, one parameter): the desired
spherically-averaged power spectrum of the output.
Given as a function of k
* random_seed (int): the seed for the random number generation
Returns:
The Gaussian random field as a numpy array
'''
#Verify input
assert len(dims) == 2 or len(dims) == 3
#Generate FT map
if random_seed != None:
np.random.seed(random_seed)
map_ft_real = np.random.normal(loc=0., scale=1., size=dims)
map_ft_imag = np.random.normal(loc=0., scale=1., size=dims)
map_ft = map_ft_real + 1j * map_ft_imag
#Get k modes
box_dims = _get_dims(box_dims, map_ft_real.shape)
assert len(box_dims) == len(dims)
k_comp, k = _get_k(map_ft_real, box_dims)
#k[np.abs(k) < 1.e-6] = 1.e-6
#Scale factor
boxvol = np.product(map(float, box_dims))
pixelsize = boxvol / (np.product(map_ft_real.shape))
scale_factor = pixelsize**2 / boxvol
#Scale to power spectrum
map_ft *= np.sqrt(power_spectrum(k) / scale_factor)
#Inverse FT
map_ift = fftpack.ifftn(fftpack.fftshift(map_ft))
#Return real part
map_real = np.real(map_ift)
return map_real
def make_gaussian_random_field(dims, box_dims, power_spectrum, random_seed=None):
'''
Generate a Gaussian random field with the specified
power spectrum.
Parameters:
* dims (tuple): the dimensions of the field in number
of cells. Can be 2D or 3D.
* box_dims (float or tuple): the dimensions of the field
in cMpc.
* power_spectrum (callable, one parameter): the desired
spherically-averaged power spectrum of the output.
Given as a function of k
* random_seed (int): the seed for the random number generation
Returns:
The Gaussian random field as a numpy array
'''
#Verify input
assert len(dims) == 2 or len(dims) == 3
#Generate FT map
if random_seed != None:
np.random.seed(random_seed)
map_ft_real = np.random.normal(loc=0., scale=1., size=dims)
map_ft_imag = np.random.normal(loc=0., scale=1., size=dims)
map_ft = map_ft_real + 1j*map_ft_imag
#Get k modes
box_dims = _get_dims(box_dims, map_ft_real.shape)
assert len(box_dims) == len(dims)
k_comp, k = _get_k(map_ft_real, box_dims)
#k[np.abs(k) < 1.e-6] = 1.e-6
#Scale factor
boxvol = np.product(map(float,box_dims))
pixelsize = boxvol/(np.product(map_ft_real.shape))
scale_factor = pixelsize**2/boxvol
#Scale to power spectrum
map_ft *= np.sqrt(power_spectrum(k)/scale_factor)
#Inverse FT
map_ift = fftpack.ifftn(fftpack.fftshift(map_ft))
#Return real part
map_real = np.real(map_ift)
return map_real
def power_spectrum_multipoles(input_array, kbins = 10, box_dims = None,\
los_axis = 0, output=['P0', 'P2', 'P4', 'nmodes'], exclude_zero_modes=False):
'''
Calculate the power spectrum of an array and
expand it in the first three Legendre polynomials.
Parameters:
* input_array (numpy array): the array to calculate the
power spectrum of. Can be of any dimensions.
* kbins = 10 (integer or array-like): The number of bins,
or a list containing the bin edges. If an integer is given, the bins
are logarithmically spaced.
* box_dims = None (float or array-like): the dimensions of the
box. If this is None, the current box volume is used along all
dimensions. If it is a float, this is taken as the box length
along all dimensions. If it is an array-like, the elements are
taken as the box length along each axis.
* los_axis = 0 (integer): the line-of-sight axis
* output = ['P0', 'P2', 'P4', 'nmodes'] (list): the multipole moments to
include in the output. For example, to get only the P2 moment,
pass in ['P2']. Can also contain 'nmodes' to return the number of
Fourier modes per bin
* exlude_zero_modes = True (bool): if true, modes with any components
of k equal to zero will be excluded.
Returns:
A tuple with (multipoles, k) where multipoles is a
dictionary containing the multipoles (the keys are the
values passed to the output parameter) and
k contains the midpoints of the k bins.
All arrays have the same dimension
'''
assert(los_axis >= 0 and los_axis <= len(input_array.shape))
#First calculate the power spectrum
box_dims = _get_dims(box_dims, input_array.shape)
ps = power_spectrum_nd(input_array, box_dims)
#Get k values and bins
k_comp, k = _get_k(input_array, box_dims)
kbins = _get_kbins(kbins, box_dims, k)
dk = (kbins[1:]-kbins[:-1])/2.
mu = _get_mu(k_comp, k, los_axis)
#Exclude k_perp = 0 modes
if exclude_zero_modes:
good_idx = _get_nonzero_idx(ps.shape, los_axis)
else:
good_idx = np.ones_like(ps)
#Legendre polynomials
if 'P0' in output:
P0 = np.ones_like(mu)
if 'P2' in output:
P2 = 0.5*(3.*mu**2 - 1.)
if 'P4' in output:
P4 = 4.375*(mu**2-0.115587)*(mu**2-0.741556)
#Bin data
n_kbins = len(kbins)-1
multipoles = {}
if 'P0' in output:
multipoles['P0'] = np.zeros(n_kbins)
if 'P2' in output:
multipoles['P2'] = np.zeros(n_kbins)
if 'P4' in output:
multipoles['P4'] = np.zeros(n_kbins)
nmodes = np.zeros(n_kbins)
for i in range(n_kbins):
kmin = kbins[i]
kmax = kbins[i+1]
idx = get_eval()('(k >= kmin) & (k < kmax)')
idx *= good_idx
nmodes[i] = len(np.nonzero(idx))
if 'P0' in output:
multipoles['P0'][i] = np.sum(ps[idx]*P0[idx])/np.sum(P0[idx]**2)
if 'P2' in output:
multipoles['P2'][i] = np.sum(ps[idx]*P2[idx])/np.sum(P2[idx]**2)
if 'P4' in output:
multipoles['P4'][i] = np.sum(ps[idx]*P4[idx])/np.sum(P4[idx]**2)
multipoles['nmodes'] = nmodes
return multipoles, kbins[:-1]+dk
def power_spectrum_multipoles(input_array, kbins = 10, box_dims = None,\
los_axis = 0):
'''
Calculate the power spectrum of an array and
expand it in the first three Legendre polynomials.
Parameters:
* input_array (numpy array): the array to calculate the
power spectrum of. Can be of any dimensions.
* kbins = 10 (integer or array-like): The number of bins,
or a list containing the bin edges. If an integer is given, the bins
are logarithmically spaced.
* box_dims = None (float or array-like): the dimensions of the
box. If this is None, the current box volume is used along all
dimensions. If it is a float, this is taken as the box length
along all dimensions. If it is an array-like, the elements are
taken as the box length along each axis.
* los_axis = 0 (integer): the line-of-sight axis
Returns:
A tuple with (P0, P2, P4, k) where P0, P2 and P4
are the multipole moments as a function of k and
k contains the midpoints of the k bins.
All four arrays have the same length
'''
assert(los_axis >= 0 and los_axis <= len(input_array.shape))
#First calculate the power spectrum
box_dims = _get_dims(box_dims, input_array.shape)
ps = power_spectrum_nd(input_array, box_dims)
#Get k values and bins
k_comp, k = _get_k(input_array, box_dims)
kbins = _get_kbins(kbins, box_dims, k)
dk = (kbins[1:]-kbins[:-1])/2.
mu = _get_mu(k_comp, k, los_axis)
#Legendre polynomials
P0 = np.ones_like(mu)
P2 = 0.5*(3.*mu**2 - 1.)
P4 = 4.375*(mu**2-0.115587)*(mu**2-0.741556)
#Bin data
n_kbins = len(kbins)-1
outdata_P0 = np.zeros(n_kbins)
outdata_P2 = np.zeros_like(outdata_P0)
outdata_P4 = np.zeros_like(outdata_P0)
for i in range(n_kbins):
idx = (k > kbins[i]) * (k <= kbins[i+1])
outdata_P0[i] = np.sum(ps[idx]*P0[idx])/np.sum(P0[idx]**2)
outdata_P2[i] = np.sum(ps[idx]*P2[idx])/np.sum(P2[idx]**2)
outdata_P4[i] = np.sum(ps[idx]*P4[idx])/np.sum(P4[idx]**2)
return outdata_P0, outdata_P2, outdata_P4, kbins[:-1]+dk