correlated_fields.py

# 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.
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# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
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# Copyright(C) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.

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
from ..operators.scaling_operator import ScalingOperator


def CorrelatedField(s_space, amplitude_operator, name='xi'):
    '''
    Function for construction of correlated fields

    Parameters
    ----------
    s_space : Domain
        Field domain
    amplitude_operator: Operator
        operator for correlation structure
    name : string
        MultiField component name
    '''
    h_space = s_space.get_default_codomain()
    ht = HarmonicTransformOperator(h_space, s_space)
    p_space = amplitude_operator.target[0]
    power_distributor = PowerDistributor(h_space, p_space)
    A = power_distributor(amplitude_operator)
    vol = h_space.scalar_dvol
    vol = ScalingOperator(vol**(-0.5), h_space)
    return ht(vol(A)*ducktape(h_space, None, name))


def MfCorrelatedField(s_space_spatial,
                      s_space_energy,
                      amplitude_operator_spatial,
                      amplitude_operator_energy,
                      name="xi"):
    '''
    Method for construction of correlated multi-frequency fields
    '''
    h_space_spatial = s_space_spatial.get_default_codomain()
    h_space_energy = s_space_energy.get_default_codomain()
    h_space = DomainTuple.make((h_space_spatial, h_space_energy))
    ht1 = HarmonicTransformOperator(h_space, target=s_space_spatial, space=0)
    ht2 = HarmonicTransformOperator(ht1.target, space=1)
    ht = ht2(ht1)

    p_space_spatial = amplitude_operator_spatial.target[0]
    p_space_energy = amplitude_operator_energy.target[0]

    pd_spatial = PowerDistributor(h_space, p_space_spatial, 0)
    pd_energy = PowerDistributor(pd_spatial.domain, p_space_energy, 1)
    pd = pd_spatial(pd_energy)

    dom_distr_spatial = ContractionOperator(pd.domain, 1).adjoint
    dom_distr_energy = ContractionOperator(pd.domain, 0).adjoint

    a_spatial = dom_distr_spatial(amplitude_operator_spatial)
    a_energy = dom_distr_energy(amplitude_operator_energy)
    a = a_spatial*a_energy
    A = pd(a)
    return ht(A*ducktape(h_space, None, name))