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.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
# Copyright(C) 2013-2018 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
# and financially supported by the Studienstiftung des deutschen Volkes.

from __future__ import absolute_import, division, print_function

from ..compat import *
from ..domain_tuple import DomainTuple
from ..multi_field import MultiField
from ..multi_domain import MultiDomain
from ..operators.domain_distributor import DomainDistributor
from ..operators.harmonic_transform_operator import HarmonicTransformOperator
from ..operators.power_distributor import PowerDistributor
from ..operators.operator import Operator


class CorrelatedField(Operator):
    '''
    Class for construction of correlated fields

    Parameters
    ----------
    s_space : Field domain

    amplitude_model : model for correlation structure
    '''
    def __init__(self, s_space, amplitude_model):
        self._s_space = s_space
        self._amplitude_model = amplitude_model
        self._h_space = s_space.get_default_codomain()
        self._ht = HarmonicTransformOperator(self._h_space, s_space)
        self._p_space = amplitude_model.target[0]
        self._power_distributor = PowerDistributor(self._h_space,
                                                   self._p_space)
        self._domain = MultiDomain.union(
            (self._amplitude_model.domain,
             MultiDomain.make({"xi": self._h_space})))

    @property
    def domain(self):
        return self._domain

    @property
    def target(self):
        return self._ht.target

    def apply(self, x):
        A = self._power_distributor(self._amplitude_model(x))
        correlated_field_h = A * x["xi"]
        correlated_field = self._ht(correlated_field_h)
        return correlated_field


# def make_mf_correlated_field(s_space_spatial, s_space_energy,
#                              amplitude_model_spatial, amplitude_model_energy):
#     '''
#     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, space=0)
#     ht2 = HarmonicTransformOperator(ht1.target, space=1)
#     ht = ht2*ht1
#
#     p_space_spatial = amplitude_model_spatial.value.domain[0]
#     p_space_energy = amplitude_model_energy.value.domain[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 = DomainDistributor(pd.domain, 0)
#     dom_distr_energy = DomainDistributor(pd.domain, 1)
#
#     a_spatial = dom_distr_spatial(amplitude_model_spatial)
#     a_energy = dom_distr_energy(amplitude_model_energy)
#     a = a_spatial*a_energy
#     A = pd(a)
#
#     position = MultiField.from_dict(
#         {'xi': Field.from_random('normal', h_space)})
#     xi = Variable(position)['xi']
#     correlated_field_h = A*xi
#     correlated_field = ht(correlated_field_h)
#     return PointwiseExponential(correlated_field)