def power_forward_conversion_lm(k_space, p, mean=0):
"""
This function is designed to convert a theoretical/statistical power
spectrum of a Gaussian field to the theoretical power spectrum of
the exponentiated field.
The function only works for power spectra defined for lm_spaces
Parameters
----------
k_space : nifty.rg_space,
a regular grid space with the attribute `Fourier = True`
p : np.array,
the power spectrum of the Gaussian field.
Needs to have the same number of entries as
`k_space.get_power_indices()[0]`
m : float, *optional*
specifies the mean of the Gaussian field (default: 0).
Returns
-------
p1 : np.array,
the power spectrum of the exponentiated Gaussian field.
References
----------
.. [#] M. Greiner and T.A. Ensslin, "Log-transforming the matter power spectrum";
`arXiv:1312.1354 <http://arxiv.org/abs/1312.1354>`_
"""
m = mean
klen = k_space.get_power_indices()[0]
C_0_Omega = field(k_space, val=0)
C_0_Omega.val[:len(klen)] = p * sqrt(2 * klen + 1) / sqrt(4 * pi)
C_0_Omega = C_0_Omega.transform()
C_0_0 = (p * (2 * klen + 1) / (4 * pi)).sum()
exC = exp(C_0_Omega + C_0_0 + 2 * m)
Z = exC.transform()
spec = Z.val[:len(klen)]
spec = spec * sqrt(4 * pi) / sqrt(2 * klen + 1)
spec = np.real(spec)
if (np.any(spec < 0.)):
spec = spec * (spec > 0.)
about.warnings.cprint("WARNING: negative modes set to zero.")
return spec
def power_forward_conversion_lm(k_space,p,mean=0):
"""
This function is designed to convert a theoretical/statistical power
spectrum of a Gaussian field to the theoretical power spectrum of
the exponentiated field.
The function only works for power spectra defined for lm_spaces
Parameters
----------
k_space : nifty.rg_space,
a regular grid space with the attribute `Fourier = True`
p : np.array,
the power spectrum of the Gaussian field.
Needs to have the same number of entries as
`k_space.get_power_indices()[0]`
m : float, *optional*
specifies the mean of the Gaussian field (default: 0).
Returns
-------
p1 : np.array,
the power spectrum of the exponentiated Gaussian field.
References
----------
.. [#] M. Greiner and T.A. Ensslin, "Log-transforming the matter power spectrum";
`arXiv:1312.1354 <http://arxiv.org/abs/1312.1354>`_
"""
m = mean
klen = k_space.get_power_indices()[0]
C_0_Omega = field(k_space,val=0)
C_0_Omega.val[:len(klen)] = p*sqrt(2*klen+1)/sqrt(4*pi)
C_0_Omega = C_0_Omega.transform()
C_0_0 = (p*(2*klen+1)/(4*pi)).sum()
exC = exp(C_0_Omega+C_0_0+2*m)
Z = exC.transform()
spec = Z.val[:len(klen)]
spec = spec*sqrt(4*pi)/sqrt(2*klen+1)
spec = np.real(spec)
if(np.any(spec<0.)):
spec = spec*(spec>0.)
about.warnings.cprint("WARNING: negative modes set to zero.")
return spec
def power_forward_conversion_rg(k_space,p,mean=0,bare=True):
"""
This function is designed to convert a theoretical/statistical power
spectrum of a Gaussian field to the theoretical power spectrum of
the exponentiated field.
The function only works for power spectra defined for rg_spaces
Parameters
----------
k_space : nifty.rg_space,
a regular grid space with the attribute `Fourier = True`
p : np.array,
the power spectrum of the Gaussian field.
Needs to have the same number of entries as
`k_space.get_power_indices()[0]`
mean : float, *optional*
specifies the mean of the Gaussian field (default: 0).
bare : bool, *optional*
whether `p` is the bare power spectrum or not (default: True).
Returns
-------
p1 : np.array,
the power spectrum of the exponentiated Gaussian field.
References
----------
.. [#] M. Greiner and T.A. Ensslin, "Log-transforming the matter power spectrum";
`arXiv:1312.1354 <http://arxiv.org/abs/1312.1354>`_
"""
pindex = k_space.get_power_indices()[2]
spec = power_operator(k_space,spec=p,bare=bare).get_power(bare=False)
S_x = field(k_space,val=spec[pindex]).transform()
S_0 = k_space.calc_weight(spec[pindex],1).sum()
pf = exp(S_x+S_0+2*mean)
p1 = sqrt(pf.power())
if(bare==True):
return power_operator(k_space,spec=p1,bare=False).get_power(bare=True).real
else:
return p1.real