# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see .
#
# Copyright(C) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
from functools import reduce
from operator import mul
from ..domain_tuple import DomainTuple
from ..operators.contraction_operator import ContractionOperator
from ..operators.distributors import PowerDistributor
from ..operators.harmonic_operators import HarmonicTransformOperator
from ..operators.simple_linear_operators import ducktape
def CorrelatedField(target, amplitude_operator, name='xi'):
"""Constructs an operator which turns a white Gaussian excitation field
into a correlated field.
This function returns an operator which implements:
ht @ (vol * A * xi),
where `ht` is a harmonic transform operator, `A` is the square root of the
prior covariance and `xi` is the excitation field.
Parameters
----------
target : Domain, DomainTuple or tuple of Domain
Target of the operator. Must contain exactly one space.
amplitude_operator: Operator
name : string
:class:`MultiField` key for the xi-field.
Returns
-------
Correlated field : Operator
"""
tgt = DomainTuple.make(target)
if len(tgt) > 1:
raise ValueError
h_space = tgt[0].get_default_codomain()
ht = HarmonicTransformOperator(h_space, tgt[0])
p_space = amplitude_operator.target[0]
power_distributor = PowerDistributor(h_space, p_space)
A = power_distributor(amplitude_operator)
vol = h_space.scalar_dvol**-0.5
# When doubling the resolution of `tgt` the value of the highest k-mode
# will scale with a square root. `vol` cancels this effect such that the
# same power spectrum can be used for the spaces with the same volume,
# different resolutions and the same object in them.
return ht(vol*A*ducktape(h_space, None, name))
def MfCorrelatedField(target, amplitudes, name='xi'):
"""Constructs an operator which turns white Gaussian excitation fields
into a correlated field defined on a DomainTuple with two entries and two
separate correlation structures.
This operator may be used as a model for multi-frequency reconstructions
with a correlation structure in both spatial and energy direction.
Parameters
----------
target : Domain, DomainTuple or tuple of Domain
Target of the operator. Must contain exactly one space.
amplitudes: iterable of Operator
List of two amplitude operators.
name : string
:class:`MultiField` key for xi-field.
Returns
-------
Correlated field : Operator
"""
tgt = DomainTuple.make(target)
if len(tgt) != 2:
raise ValueError
if len(amplitudes) != 2:
raise ValueError
hsp = DomainTuple.make([tt.get_default_codomain() for tt in tgt])
ht1 = HarmonicTransformOperator(hsp, target=tgt[0], space=0)
ht2 = HarmonicTransformOperator(ht1.target, space=1)
ht = ht2 @ ht1
psp = [aa.target[0] for aa in amplitudes]
pd0 = PowerDistributor(hsp, psp[0], 0)
pd1 = PowerDistributor(pd0.domain, psp[1], 1)
pd = pd0 @ pd1
dd0 = ContractionOperator(pd.domain, 1).adjoint
dd1 = ContractionOperator(pd.domain, 0).adjoint
d = [dd0, dd1]
a = [dd @ amplitudes[ii] for ii, dd in enumerate(d)]
a = reduce(mul, a)
A = pd @ a
# For `vol` see comment in `CorrelatedField`
vol = reduce(mul, [sp.scalar_dvol**-0.5 for sp in hsp])
return ht(vol*A*ducktape(hsp, None, name))