simple_linear_operators.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/>.
#
# Copyright(C) 2013-2019 Max-Planck-Society
#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.

from ..domain_tuple import DomainTuple
from ..domains.unstructured_domain import UnstructuredDomain
from ..field import Field
from ..multi_domain import MultiDomain
from ..multi_field import MultiField
from .endomorphic_operator import EndomorphicOperator
from .linear_operator import LinearOperator


class VdotOperator(LinearOperator):
    """Operator computing the scalar product of its input with a given Field.

    Parameters
    ----------
    field : Field/MultiField
        The field used to build the scalar product with the operator input
    """
    def __init__(self, field):
        self._field = field
        self._domain = field.domain
        self._target = DomainTuple.scalar_domain()
        self._capability = self.TIMES | self.ADJOINT_TIMES

    def apply(self, x, mode):
        self._check_mode(mode)
        if mode == self.TIMES:
            return Field.scalar(self._field.vdot(x))
        return self._field*x.local_data[()]


class ConjugationOperator(EndomorphicOperator):
    """Operator computing the complex conjugate of its input."""
    def __init__(self, domain):
        self._domain = DomainTuple.make(domain)
        self._capability = self._all_ops

    def apply(self, x, mode):
        self._check_input(x, mode)
        return x.conjugate()


class Realizer(EndomorphicOperator):
    """Operator returning the real component of its input."""
    def __init__(self, domain):
        self._domain = DomainTuple.make(domain)
        self._capability = self.TIMES | self.ADJOINT_TIMES

    def apply(self, x, mode):
        self._check_input(x, mode)
        return x.real


class FieldAdapter(LinearOperator):
    """Operator for conversion between Fields and MultiFields.

    Parameters
    ----------
    tgt : Domain, tuple of Domain, DomainTuple, dict or MultiDomain:
        If this is a Domain, tuple of Domain or DomainTuple, this will be the
        operator's target, and its domain will be a MultiDomain consisting of
        its domain with the supplied `name`
        If this is a dict or MultiDomain, everything except for `name` will
        be stripped out of it, and the result will be the operator's target.
        Its domain will then be the DomainTuple corresponding to the single
        entry in the operator's domain.

    name : String
        The relevant key of the MultiDomain.
    """

    def __init__(self, tgt, name):
        from ..sugar import makeDomain
        tmp = makeDomain(tgt)
        if isinstance(tmp, DomainTuple):
            self._target = tmp
            self._domain = MultiDomain.make({name: tmp})
        else:
            self._domain = tmp[name]
            self._target = MultiDomain.make({name: tmp[name]})
        self._capability = self.TIMES | self.ADJOINT_TIMES

    def apply(self, x, mode):
        self._check_input(x, mode)
        if isinstance(x, MultiField):
            return x.values()[0]
        else:
            return MultiField(self._tgt(mode), (x,))

    def __repr__(self):
        key = self.domain.keys()[0]
        return 'FieldAdapter: {}'.format(key)


def ducktape(left, right, name):
    """Convenience function creating an operator that converts between a
    DomainTuple and a single-entry MultiDomain.

    Parameters
    ----------
    left : None, Operator, or Domainoid
        Something describing the new operator's target domain.
        If `left` is an `Operator`, its domain is used as `left`.

    right : None, Operator, or Domainoid
        Something describing the new operator's input domain.
        If `right` is an `Operator`, its target is used as `right`.

    name : string
        The component of the `MultiDomain` that will be extracted/inserted

    Notes
    -----
    - one of the involved domains must be a `DomainTuple`, the other a
      `MultiDomain`.
    - `left` and `right` must not be both `None`, but one of them can (and
      probably should) be `None`. In this case, the missing information is
      inferred.
    - the returned operator's domains are
        - a `DomainTuple` and
        - a `MultiDomain` with exactly one entry called `name` and the same
          `DomainTuple`

      Which of these is the domain and which is the target depends on the
      input.

    Returns
    -------
    FieldAdapter : an adapter operator converting between the two (possibly
                   partially inferred) domains.
    """
    from ..sugar import makeDomain
    from .operator import Operator
    if left is None:  # need to infer left from right
        if isinstance(right, Operator):
            right = right.target
        elif right is not None:
            right = makeDomain(right)
        if isinstance(right, MultiDomain):
            left = right[name]
        else:
            left = MultiDomain.make({name: right})
    else:
        if isinstance(left, Operator):
            left = left.domain
        else:
            left = makeDomain(left)
    return FieldAdapter(left, name)


class GeometryRemover(LinearOperator):
    """Operator which transforms between a structured and an unstructured
    domain.

    Parameters
    ----------
    domain: Domain, tuple of Domain, or DomainTuple:
        the full input domain of the operator.
    space: int, optional
        The index of the subdomain on which the operator should act
        If None, it acts on all spaces

    Notes
    -----
    The operator will convert every sub-domain of its input domain to an
    UnstructuredDomain with the same shape. No weighting by volume factors
    is carried out.
    """

    def __init__(self, domain, space=None):
        self._domain = DomainTuple.make(domain)
        if space is not None:
            tgt = [dom for dom in self._domain]
            tgt[space] = UnstructuredDomain(self._domain[space].shape)
        else:
            tgt = [UnstructuredDomain(dom.shape) for dom in self._domain]
        self._target = DomainTuple.make(tgt)
        self._capability = self.TIMES | self.ADJOINT_TIMES

    def apply(self, x, mode):
        self._check_input(x, mode)
        return x.cast_domain(self._tgt(mode))


class NullOperator(LinearOperator):
    """Operator corresponding to a matrix of all zeros.

    Parameters
    ----------
    domain : DomainTuple or MultiDomain
        input domain
    target : DomainTuple or MultiDomain
        output domain
    """

    def __init__(self, domain, target):
        from ..sugar import makeDomain
        self._domain = makeDomain(domain)
        self._target = makeDomain(target)
        self._capability = self.TIMES | self.ADJOINT_TIMES

    @staticmethod
    def _nullfield(dom):
        if isinstance(dom, DomainTuple):
            return Field(dom, 0)
        else:
            return MultiField.full(dom, 0)

    def apply(self, x, mode):
        self._check_input(x, mode)
        return self._nullfield(self._tgt(mode))