simple_linear_operators.py 13.1 KB
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# 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/>.
#
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# Copyright(C) 2013-2019 Max-Planck-Society
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#
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# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
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from ..domain_tuple import DomainTuple
from ..domains.unstructured_domain import UnstructuredDomain
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from ..field import Field
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from ..multi_domain import MultiDomain
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from ..multi_field import MultiField
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from .endomorphic_operator import EndomorphicOperator
from .linear_operator import LinearOperator
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import numpy as np
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class VdotOperator(LinearOperator):
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    """Operator computing the scalar product of its input with a given Field.

    Parameters
    ----------
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    field : Field or MultiField
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        The field used to build the scalar product with the operator input
    """
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    def __init__(self, field):
        self._field = field
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        self._domain = field.domain
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        self._target = DomainTuple.scalar_domain()
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        self._capability = self.TIMES | self.ADJOINT_TIMES
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    def apply(self, x, mode):
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        self._check_mode(mode)
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        if mode == self.TIMES:
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            return self._field.vdot(x)
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        return self._field*x.val[()]
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class ConjugationOperator(EndomorphicOperator):
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    """Operator computing the complex conjugate of its input.

    Parameters
    ----------
    domain: Domain, tuple of domains or DomainTuple
        domain of the input field

    """
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    def __init__(self, domain):
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        self._domain = DomainTuple.make(domain)
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        self._capability = self._all_ops
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    def apply(self, x, mode):
        self._check_input(x, mode)
        return x.conjugate()


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class WeightApplier(EndomorphicOperator):
    """Operator multiplying its input by a given power of dvol.

    Parameters
    ----------
    domain: Domain, tuple of domains or DomainTuple
        domain of the input field
    spaces: list or tuple of int
        indices of subdomains for which the weights shall be applied
    power: int
        the power of to be used for the volume factors

    """
    def __init__(self, domain, spaces, power):
        from .. import utilities
        self._domain = DomainTuple.make(domain)
        if spaces is None:
            self._spaces = None
        else:
            self._spaces = utilities.parse_spaces(spaces, len(self._domain))
        self._power = int(power)
        self._capability = self._all_ops

    def apply(self, x, mode):
        self._check_input(x, mode)
        power = self._power if (mode & 3) else -self._power
        return x.weight(power, spaces=self._spaces)


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class Realizer(EndomorphicOperator):
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    """Operator returning the real component of its input.

    Parameters
    ----------
    domain: Domain, tuple of domains or DomainTuple
        domain of the input field

    """
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    def __init__(self, domain):
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        self._domain = DomainTuple.make(domain)
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        self._capability = self.TIMES | self.ADJOINT_TIMES
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    def apply(self, x, mode):
        self._check_input(x, mode)
        return x.real
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class FieldAdapter(LinearOperator):
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    """Operator for conversion between Fields and MultiFields.
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    Parameters
    ----------
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    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.
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    name : String
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        The relevant key of the MultiDomain.
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    """

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    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]})
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        self._capability = self.TIMES | self.ADJOINT_TIMES
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    def apply(self, x, mode):
        self._check_input(x, mode)
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        if isinstance(x, MultiField):
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            return x.values()[0]
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        else:
            return MultiField(self._tgt(mode), (x,))

    def __repr__(self):
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        s = 'FieldAdapter'
        dom = isinstance(self._domain, MultiDomain)
        tgt = isinstance(self._target, MultiDomain)
        if dom and tgt:
            s += ' {} <- {}'.format(self._target.keys(), self._domain.keys())
        elif dom:
            s += ' <- {}'.format(self._domain.keys())
        elif tgt:
            s += ' {} <-'.format(self._target.keys())
        return s
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class _SlowFieldAdapter(LinearOperator):
    """Operator for conversion between Fields and MultiFields.
    The operator is built so that the MultiDomain is always the target.
    Its domain is `tgt[name]`

    Parameters
    ----------
    dom : dict or MultiDomain:
        the operator's dom

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

    def __init__(self, dom, name):
        from ..sugar import makeDomain
        tmp = makeDomain(dom)
        if not isinstance(tmp, MultiDomain):
            raise TypeError("MultiDomain expected")
        self._name = str(name)
        self._domain = tmp
        self._target = 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[self._name]
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        return MultiField.from_dict({self._name: x}, domain=self._tgt(mode))
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    def __repr__(self):
        return '_SlowFieldAdapter'
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def ducktape(left, right, name):
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    """Convenience function creating an operator that converts between a
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    DomainTuple and a MultiDomain.
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    Parameters
    ----------
    left : None, Operator, or Domainoid
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        Something describing the new operator's target domain.
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        If `left` is an `Operator`, its domain is used as `left`.

    right : None, Operator, or Domainoid
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        Something describing the new operator's input domain.
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        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.

    Returns
    -------
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    FieldAdapter or _SlowFieldAdapter
        an adapter operator converting between the two (possibly
        partially inferred) domains.
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    """
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    from ..sugar import makeDomain
    from .operator import Operator
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    if isinstance(right, Operator):
        right = right.target
    elif right is not None:
        right = makeDomain(right)
    if isinstance(left, Operator):
        left = left.domain
    elif left is not None:
        left = makeDomain(left)
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    if left is None:  # need to infer left from right
        if isinstance(right, MultiDomain):
            left = right[name]
        else:
            left = MultiDomain.make({name: right})
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    elif right is None:  # need to infer right from left
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        if isinstance(left, MultiDomain):
            right = left[name]
        else:
            right = MultiDomain.make({name: left})
    lmulti = isinstance(left, MultiDomain)
    rmulti = isinstance(right, MultiDomain)
    if lmulti+rmulti != 1:
        raise ValueError("need exactly one MultiDomain")
    if lmulti:
        if len(left) == 1:
            return FieldAdapter(left, name)
        else:
            return _SlowFieldAdapter(left, name).adjoint
    if rmulti:
        if len(right) == 1:
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            return FieldAdapter(left, name)
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        else:
            return _SlowFieldAdapter(right, name)
    raise ValueError("must not arrive here")
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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.
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    space: int, optional
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        The index of the subdomain on which the operator should act.
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        If None, it acts on all spaces.
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    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.
    """

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    def __init__(self, domain, space=None):
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        self._domain = DomainTuple.make(domain)
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        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)
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        self._capability = self.TIMES | self.ADJOINT_TIMES
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    def apply(self, x, mode):
        self._check_input(x, mode)
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        return x.cast_domain(self._tgt(mode))
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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)
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        self._capability = self.TIMES | self.ADJOINT_TIMES
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    @staticmethod
    def _nullfield(dom):
        if isinstance(dom, DomainTuple):
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            return Field(dom, 0)
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        else:
            return MultiField.full(dom, 0)

    def apply(self, x, mode):
        self._check_input(x, mode)
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        return self._nullfield(self._tgt(mode))
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class PartialExtractor(LinearOperator):
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    def __init__(self, domain, target):
        if not isinstance(domain, MultiDomain):
            raise TypeError("MultiDomain expected")
        if not isinstance(target, MultiDomain):
            raise TypeError("MultiDomain expected")
        self._domain = domain
        self._target = target
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        for key in self._target.keys():
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            if self._domain[key] is not self._target[key]:
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                raise ValueError("domain mismatch")
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        self._capability = self.TIMES | self.ADJOINT_TIMES
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        self._compldomain = MultiDomain.make({kk: self._domain[kk]
                                              for kk in self._domain.keys()
                                              if kk not in self._target.keys()})
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    def apply(self, x, mode):
        self._check_input(x, mode)
        if mode == self.TIMES:
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            return x.extract(self._target)
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        res0 = MultiField.from_dict({key: x[key] for key in x.domain.keys()})
        res1 = MultiField.full(self._compldomain, 0.)
        return res0.unite(res1)
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class MatrixProductOperator(EndomorphicOperator):
    """Endomorphic matrix multiplication with input field.

    Parameters
    ----------
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    domain: :class:`Domain` or :class:`DomainTuple`
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        Domain of the operator.
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        If :class:`DomainTuple` it is assumed to have only one entry.
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    matrix: scipy.sparse matrix or numpy array
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        Matrix of shape `(domain.shape, domain.shape)`. Needs to support
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        `dot()` and `transpose()` in the style of numpy arrays.
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    axis: integer or None
        in case of multi-dim input fields (N > 1), along which axis
        of the input field to apply the matrix
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    """
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    def __init__(self, domain, matrix, axis=None):
        self._capability = self.TIMES | self.ADJOINT_TIMES
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        self._domain = DomainTuple.make(domain)
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        shp = self._domain.shape
        if len(shp) > 1:
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            if axis is None:
                raise ValueError(
                    "For multi-dim inputs an axis needs to be specified.")
            ref_shp = (shp[axis], shp[axis])
        else:
            if not (axis is None or axis == 0):
                raise ValueError(
                    "For one-dim inputs axis must be None or zero")
            ref_shp = (shp[0], shp[0])
            axis = None

        if matrix.shape != ref_shp:
            raise ValueError(
                "Domain/domain on axis and matrix shape do not match.")

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        self._mat = matrix
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        self._mat_tr = matrix.transpose().conjugate()
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        self._axis = axis
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    def apply(self, x, mode):
        self._check_input(x, mode)
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        m = self._mat if mode == self.TIMES else self._mat_tr
        if self._axis is None:
            res = m.dot(x.val)
        else:
            res = np.tensordot(m, x.val, axes=(-1, self._axis))
            res = np.moveaxis(res, 0, self._axis)
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        return Field(self._domain, res)