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
def power_backward_conversion_rg(k_space,p,mean=None,bare=True):
"""
This function is designed to convert a theoretical/statistical power
spectrum of a log-normal field to the theoretical power spectrum of
the underlying Gaussian 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 log-normal field.
Needs to have the same number of entries as
`k_space.get_power_indices()[0]`
mean : float, *optional*
specifies the mean of the log-normal field. If `mean` is not
specified the function will use the monopole of the power spectrum.
If it is specified the function will NOT use the monopole of the
spectrum (default: None).
WARNING: a mean that is too low can violate positive definiteness
of the log-normal field. In this case the function produces an
error.
bare : bool, *optional*
whether `p` is the bare power spectrum or not (default: True).
Returns
-------
mean : float,
the recovered mean of the underlying Gaussian distribution.
p1 : np.array,
the power spectrum of the underlying Gaussian field, where the
monopole has been set to zero. Eventual monopole power has been
shifted to the mean.
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]
V = k_space.vol.prod()**(-1)
mono_ind = np.where(pindex==0)
spec = power_operator(k_space,spec=p,bare=bare).get_power(bare=False)
if(mean is None):
mean = 0.
else:
spec[0] = 0.
pf = field(k_space,val=spec[pindex]).transform()+mean**2
if(np.any(pf.val<0.)):
raise ValueError(about._errors.cstring("ERROR: spectrum or mean incompatible with positive definiteness.\n Try increasing the mean."))
return None
p1 = sqrt(log(pf).power())
p1[0] = (log(pf)).transform()[mono_ind][0]
p2 = 0.5*V*log(k_space.calc_weight(spec[pindex],1).sum()+mean**2)
logmean = 1/V * (p1[0]-p2)
p1[0] = 0.
if(np.any(p1<0.)):
raise ValueError(about._errors.cstring("ERROR: spectrum or mean incompatible with positive definiteness.\n Try increasing the mean."))
return None
if(bare==True):
return logmean.real,power_operator(k_space,spec=p1,bare=False).get_power(bare=True).real
else:
return logmean.real,p1.real
def power_backward_conversion_lm(k_space, p, mean=None):
"""
This function is designed to convert a theoretical/statistical power
spectrum of a log-normal field to the theoretical power spectrum of
the underlying Gaussian 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 log-normal field.
Needs to have the same number of entries as
`k_space.get_power_indices()[0]`
mean : float, *optional*
specifies the mean of the log-normal field. If `mean` is not
specified the function will use the monopole of the power spectrum.
If it is specified the function will NOT use the monopole of the
spectrum. (default: None)
WARNING: a mean that is too low can violate positive definiteness
of the log-normal field. In this case the function produces an
error.
Returns
-------
mean : float,
the recovered mean of the underlying Gaussian distribution.
p1 : np.array,
the power spectrum of the underlying Gaussian field, where the
monopole has been set to zero. Eventual monopole power has been
shifted to the mean.
References
----------
.. [#] M. Greiner and T.A. Ensslin, "Log-transforming the matter power spectrum";
`arXiv:1312.1354 <http://arxiv.org/abs/1312.1354>`_
"""
p = np.copy(p)
if (mean is not None):
p[0] = 4 * pi * mean**2
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()
if (np.any(C_0_Omega.val < 0.)):
raise ValueError(
about._errors.cstring(
"ERROR: spectrum or mean incompatible with positive definiteness.\n Try increasing the mean."
))
return None
lC = log(C_0_Omega)
Z = lC.transform()
spec = Z.val[:len(klen)]
mean = (spec[0] - 0.5 * sqrt(4 * pi) * log(
(p * (2 * klen + 1) / (4 * pi)).sum())) / sqrt(4 * pi)
spec[0] = 0.
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 mean.real, spec
def power_backward_conversion_lm(k_space,p,mean=None):
"""
This function is designed to convert a theoretical/statistical power
spectrum of a log-normal field to the theoretical power spectrum of
the underlying Gaussian 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 log-normal field.
Needs to have the same number of entries as
`k_space.get_power_indices()[0]`
mean : float, *optional*
specifies the mean of the log-normal field. If `mean` is not
specified the function will use the monopole of the power spectrum.
If it is specified the function will NOT use the monopole of the
spectrum. (default: None)
WARNING: a mean that is too low can violate positive definiteness
of the log-normal field. In this case the function produces an
error.
Returns
-------
mean : float,
the recovered mean of the underlying Gaussian distribution.
p1 : np.array,
the power spectrum of the underlying Gaussian field, where the
monopole has been set to zero. Eventual monopole power has been
shifted to the mean.
References
----------
.. [#] M. Greiner and T.A. Ensslin, "Log-transforming the matter power spectrum";
`arXiv:1312.1354 <http://arxiv.org/abs/1312.1354>`_
"""
p = np.copy(p)
if(mean is not None):
p[0] = 4*pi*mean**2
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()
if(np.any(C_0_Omega.val<0.)):
raise ValueError(about._errors.cstring("ERROR: spectrum or mean incompatible with positive definiteness.\n Try increasing the mean."))
return None
lC = log(C_0_Omega)
Z = lC.transform()
spec = Z.val[:len(klen)]
mean = (spec[0]-0.5*sqrt(4*pi)*log((p*(2*klen+1)/(4*pi)).sum()))/sqrt(4*pi)
spec[0] = 0.
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 mean.real,spec
