operator.py 18.8 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) 2013-2021 Max-Planck-Society
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#
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
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import numpy as np
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from .. import pointwise
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from ..logger import logger
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from ..multi_domain import MultiDomain
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from ..utilities import NiftyMeta, indent, myassert
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class Operator(metaclass=NiftyMeta):
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    """Transforms values defined on one domain into values defined on another
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    domain, and can also provide the Jacobian.
    """

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    @property
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    def domain(self):
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        """The domain on which the Operator's input Field is defined.
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        Returns
        -------
        domain : DomainTuple or MultiDomain
        """
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        return self._domain
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    @property
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    def target(self):
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        """The domain on which the Operator's output Field is defined.

        Returns
        -------
        target : DomainTuple or MultiDomain
        """
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        return self._target
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    @property
    def val(self):
        """The numerical value associated with this object
        For "pure" operators this is `None`. For Field-like objects this
        is a `numpy.ndarray` or a dictionary of `numpy.ndarray`s mathcing the
        object's `target`.

        Returns
        -------
        None or numpy.ndarray or dictionary of np.ndarrays : the numerical value
        """
        return None

    @property
    def jac(self):
        """The Jacobian associated with this object
        For "pure" operators this is `None`. For Field-like objects this
        can be `None` (in which case the object is a constant), or it can be a
        `LinearOperator` with `domain` and `target` matching the object's.

        Returns
        -------
        None or LinearOperator : the Jacobian

        Notes
        -----
        if `value` is None, this must be `None` as well!
        """
        return None

    @property
    def want_metric(self):
        """Whether a metric should be computed for the full expression.
        This is `False` whenever `jac` is `None`. In other cases it signals
        that operators processing this object should compute the metric.

        Returns
        -------
        bool : whether the metric should be computed
        """
        return False

    @property
    def metric(self):
        """The metric associated with the object.
        This is `None`, except when all the following conditions hold:
        - `want_metric` is `True`
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        - `target` is the scalar domain
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        - the operator chain contained an operator which could compute the
          metric

        Returns
        -------
        None or LinearOperator : the metric
        """
        return None

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    def get_transformation(self):
        """The coordinate transformation that maps into a coordinate system
        where the metric of a likelihood is the Euclidean metric.
        This is `None`, except when the object is considered a likelihood i.E. 
        for an instance of `EnergyOperator` with its metric being a proper
        Fisher information metric, or a sum or nested sum thereof.
        
        Retruns
        -------
        np.dtype, or dict of np.dtype : The dtype(s) of the target space of the
        transformation.
        
        Operator : The transformation that maps from `domain` into the
        Euclidean target space.
        """
        return None

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    @staticmethod
    def _check_domain_equality(dom_op, dom_field):
        if dom_op != dom_field:
            s = "The operator's and field's domains don't match."
            from ..domain_tuple import DomainTuple
            from ..multi_domain import MultiDomain
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            if not isinstance(dom_op, (DomainTuple, MultiDomain,)):
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                s += " Your operator's domain is neither a `DomainTuple`" \
                     " nor a `MultiDomain`."
            raise ValueError(s)

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    def scale(self, factor):
        if factor == 1:
            return self
        from .scaling_operator import ScalingOperator
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        return ScalingOperator(self.target, factor)(self)
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    def conjugate(self):
        from .simple_linear_operators import ConjugationOperator
        return ConjugationOperator(self.target)(self)

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    def sum(self, spaces=None):
        from .contraction_operator import ContractionOperator
        return ContractionOperator(self.target, spaces)(self)

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    def integrate(self, spaces=None):
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        from .contraction_operator import IntegrationOperator
        return IntegrationOperator(self.target, spaces)(self)

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    def vdot(self, other):
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        from ..sugar import makeOp
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        if not isinstance(other, Operator):
            raise TypeError
        if other.jac is None:
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            res = self.conjugate()*other
        else:
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            res = makeOp(other) @ self.conjugate()
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        return res.sum()
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    @property
    def real(self):
        from .simple_linear_operators import Realizer
        return Realizer(self.target)(self)

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    @property
    def imag(self):
        from .simple_linear_operators import Imaginizer
        return Imaginizer(self.target)(self)

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    def __neg__(self):
        return self.scale(-1)

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    def __matmul__(self, x):
        if not isinstance(x, Operator):
            return NotImplemented
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        return _OpChain.make((self, x))
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    def __rmatmul__(self, x):
        if not isinstance(x, Operator):
            return NotImplemented
        return _OpChain.make((x, self))

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    def partial_insert(self, x):
        from ..multi_domain import MultiDomain
        if not isinstance(x, Operator):
            raise TypeError
        if not isinstance(self.domain, MultiDomain):
            raise TypeError
        if not isinstance(x.target, MultiDomain):
            raise TypeError
        bigdom = MultiDomain.union([self.domain, x.target])
        k1, k2 = set(self.domain.keys()), set(x.target.keys())
        le, ri = k2 - k1, k1 - k2
        leop, riop = self, x
        if len(ri) > 0:
            riop = riop + self.identity_operator(
                MultiDomain.make({kk: bigdom[kk]
                                  for kk in ri}))
        if len(le) > 0:
            leop = leop + self.identity_operator(
                MultiDomain.make({kk: bigdom[kk]
                                  for kk in le}))
        return leop @ riop

    @staticmethod
    def identity_operator(dom):
        from .block_diagonal_operator import BlockDiagonalOperator
        from .scaling_operator import ScalingOperator
        idops = {kk: ScalingOperator(dd, 1.) for kk, dd in dom.items()}
        return BlockDiagonalOperator(dom, idops)

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    def __mul__(self, x):
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        if isinstance(x, Operator):
            return _OpProd(self, x)
        if np.isscalar(x):
            return self.scale(x)
        return NotImplemented
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    def __rmul__(self, x):
        return self.__mul__(x)

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    def __add__(self, x):
        if not isinstance(x, Operator):
            return NotImplemented
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        return _OpSum(self, x)
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    def __sub__(self, x):
        if not isinstance(x, Operator):
            return NotImplemented
        return _OpSum(self, -x)

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    def __abs__(self):
        return self.ptw("abs")

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    def __pow__(self, power):
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        if not (np.isscalar(power) or power.jac is None):
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            return NotImplemented
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        return self.ptw("power", power)
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    def apply(self, x):
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        """Applies the operator to a Field or MultiField.
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        Parameters
        ----------
        x : Field or MultiField
            Input on which the operator shall act. Needs to be defined on
            :attr:`domain`.
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        """
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        raise NotImplementedError
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    def force(self, x):
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        """Extract subset of domain of x according to `self.domain` and apply
        operator."""
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        return self.apply(x.extract(self.domain))
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    def _check_input(self, x):
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        from .scaling_operator import ScalingOperator
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        if not (isinstance(x, Operator) and x.val is not None):
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            raise TypeError
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        if x.jac is not None:
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            if not isinstance(x.jac, ScalingOperator):
                raise ValueError
            if x.jac._factor != 1:
                raise ValueError
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        self._check_domain_equality(self._domain, x.domain)
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    def __call__(self, x):
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        if not isinstance(x, Operator):
            raise TypeError
        if x.jac is not None:
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            return self.apply(x.trivial_jac()).prepend_jac(x.jac)
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        elif x.val is not None:
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            return self.apply(x)
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        return self @ x
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    def ducktape(self, name):
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        from ..sugar import is_operator
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        from .simple_linear_operators import ducktape
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        if not is_operator(self):
            raise RuntimeError("ducktape works only on operators")
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        return self @ ducktape(self, None, name)
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    def ducktape_left(self, name):
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        from ..sugar import is_fieldlike, is_linearization, is_operator
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        from .simple_linear_operators import ducktape
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        if is_operator(self):
            return ducktape(None, self, name) @ self
        if is_fieldlike(self) or is_linearization(self):
            return ducktape(None, self.domain, name)(self)
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    def __repr__(self):
        return self.__class__.__name__

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    def simplify_for_constant_input(self, c_inp):
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        from ..domain_tuple import DomainTuple
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        from ..multi_field import MultiField
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        from ..sugar import makeDomain
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        from .energy_operators import EnergyOperator
        from .simplify_for_const import (ConstantEnergyOperator,
                                         ConstantOperator)
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        if c_inp is None or (isinstance(c_inp, MultiField) and len(c_inp.keys()) == 0):
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            return None, self
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        dom = c_inp.domain
        if isinstance(dom, MultiDomain) and len(dom) == 0:
            return None, self
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        # Convention: If c_inp is MultiField, it needs to be defined on a
        # subdomain of self._domain
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        if isinstance(self.domain, MultiDomain):
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            myassert(isinstance(dom, MultiDomain))
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            if not set(c_inp.keys()) <= set(self.domain.keys()):
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                raise ValueError

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        if dom is self.domain:
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            if isinstance(self, DomainTuple):
                raise RuntimeError
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            if isinstance(self, EnergyOperator):
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                op = ConstantEnergyOperator(self(c_inp))
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            else:
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                op = ConstantOperator(self(c_inp))
            return None, op
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        if not isinstance(dom, MultiDomain):
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            raise RuntimeError
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        c_out, op = self._simplify_for_constant_input_nontrivial(c_inp)
        vardom = makeDomain({kk: vv for kk, vv in self.domain.items()
                             if kk not in c_inp.keys()})
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        myassert(op.domain is vardom)
        myassert(op.target is self.target)
        myassert(isinstance(op, Operator))
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        if c_out is not None:
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            myassert(isinstance(c_out, MultiField))
            myassert(len(set(c_out.keys()) & self.domain.keys()) == 0)
            myassert(set(c_out.keys()) <= set(c_inp.keys()))
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        return c_out, op
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    def _simplify_for_constant_input_nontrivial(self, c_inp):
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        from .simplify_for_const import InsertionOperator
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        logger.warning('SlowPartialConstantOperator used for:')
        logger.warning(self.__repr__())
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        return None, self @ InsertionOperator(self.domain, c_inp)
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    def ptw(self, op, *args, **kwargs):
        return _OpChain.make((_FunctionApplier(self.target, op, *args, **kwargs), self))
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    def ptw_pre(self, op, *args, **kwargs):
        return _OpChain.make((self, _FunctionApplier(self.domain, op, *args, **kwargs)))

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for f in pointwise.ptw_dict.keys():
    def func(f):
        def func2(self, *args, **kwargs):
            return self.ptw(f, *args, **kwargs)
        return func2
    setattr(Operator, f, func(f))
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    def func(f):
        def func2(self, *args, **kwargs):
            return self.ptw_pre(f, *args, **kwargs)
        return func2
    setattr(Operator, f + "_pre", func(f))
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class _FunctionApplier(Operator):
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    def __init__(self, domain, funcname, *args, **kwargs):
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        from ..sugar import makeDomain
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        self._domain = self._target = makeDomain(domain)
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        self._funcname = funcname
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        self._args = args
        self._kwargs = kwargs
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    def apply(self, x):
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        self._check_input(x)
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        return x.ptw(self._funcname, *self._args, **self._kwargs)
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    def __repr__(self):
        return f"_FunctionApplier ('{self._funcname}')"

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class _CombinedOperator(Operator):
    def __init__(self, ops, _callingfrommake=False):
        if not _callingfrommake:
            raise NotImplementedError
        self._ops = tuple(ops)

    @classmethod
    def unpack(cls, ops, res):
        for op in ops:
            if isinstance(op, cls):
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                res = cls.unpack(op._ops, res)
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            else:
                res = res + [op]
        return res

    @classmethod
    def make(cls, ops):
        res = cls.unpack(ops, [])
        if len(res) == 1:
            return res[0]
        return cls(res, _callingfrommake=True)


class _OpChain(_CombinedOperator):
    def __init__(self, ops, _callingfrommake=False):
        super(_OpChain, self).__init__(ops, _callingfrommake)
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        self._domain = self._ops[-1].domain
        self._target = self._ops[0].target
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        for i in range(1, len(self._ops)):
            if self._ops[i-1].domain != self._ops[i].target:
                raise ValueError("domain mismatch")
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    def apply(self, x):
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        self._check_input(x)
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        for op in reversed(self._ops):
            x = op(x)
        return x

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    def get_transformation(self):
        tr = self._ops[0].get_transformation()
        if tr is None:
            return tr
        return tr[0], _OpChain.make((tr[1],)+self._ops[1:])

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    def _simplify_for_constant_input_nontrivial(self, c_inp):
        from ..multi_domain import MultiDomain
        if not isinstance(self._domain, MultiDomain):
            return None, self
        newop = None
        for op in reversed(self._ops):
            c_inp, t_op = op.simplify_for_constant_input(c_inp)
            newop = t_op if newop is None else op(newop)
        return c_inp, newop
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    def __repr__(self):
        subs = "\n".join(sub.__repr__() for sub in self._ops)
        return "_OpChain:\n" + indent(subs)


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class _OpProd(Operator):
    def __init__(self, op1, op2):
        from ..sugar import domain_union
        self._domain = domain_union((op1.domain, op2.domain))
        self._target = op1.target
        if op1.target != op2.target:
            raise ValueError("target mismatch")
        self._op1 = op1
        self._op2 = op2
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    def apply(self, x):
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        from ..linearization import Linearization
        from ..sugar import makeOp
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        self._check_input(x)
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        lin = x.jac is not None
        wm = x.want_metric if lin else False
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        x = x.val if lin else x
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        v1 = x.extract(self._op1.domain)
        v2 = x.extract(self._op2.domain)
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        if not lin:
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            return self._op1(v1) * self._op2(v2)
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        lin1 = self._op1(Linearization.make_var(v1, wm))
        lin2 = self._op2(Linearization.make_var(v2, wm))
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        jac = (makeOp(lin1._val)(lin2._jac))._myadd(makeOp(lin2._val)(lin1._jac), False)
        return lin1.new(lin1._val*lin2._val, jac)
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    def _simplify_for_constant_input_nontrivial(self, c_inp):
        from ..multi_domain import MultiDomain
        from .simplify_for_const import ConstCollector
        f1, o1 = self._op1.simplify_for_constant_input(
            c_inp.extract_part(self._op1.domain))
        f2, o2 = self._op2.simplify_for_constant_input(
            c_inp.extract_part(self._op2.domain))
        if not isinstance(self._target, MultiDomain):
            return None, _OpProd(o1, o2)
        cc = ConstCollector()
        cc.mult(f1, o1.target)
        cc.mult(f2, o2.target)
        return cc.constfield, _OpProd(o1, o2)
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    def __repr__(self):
        subs = "\n".join(sub.__repr__() for sub in (self._op1, self._op2))
        return "_OpProd:\n"+indent(subs)


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class _OpSum(Operator):
    def __init__(self, op1, op2):
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        from ..sugar import domain_union
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        self._domain = domain_union((op1.domain, op2.domain))
        self._target = domain_union((op1.target, op2.target))
        self._op1 = op1
        self._op2 = op2
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    def apply(self, x):
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        from ..linearization import Linearization
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        self._check_input(x)
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        if x.jac is None:
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            v1 = x.extract(self._op1.domain)
            v2 = x.extract(self._op2.domain)
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            return self._op1(v1).unite(self._op2(v2))
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        v1 = x.val.extract(self._op1.domain)
        v2 = x.val.extract(self._op2.domain)
        wm = x.want_metric
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        lin1 = self._op1(Linearization.make_var(v1, wm))
        lin2 = self._op2(Linearization.make_var(v2, wm))
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        op = lin1._jac._myadd(lin2._jac, False)
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        res = lin1.new(lin1._val.unite(lin2._val), op)
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        if lin1._metric is not None and lin2._metric is not None:
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            res = res.add_metric(lin1._metric._myadd(lin2._metric, False))
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        return res
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    def get_transformation(self):
        tr1 = self._op1.get_transformation()
        tr2 = self._op2.get_transformation()
        if tr1 is None or tr2 is None:
            return None
        from ..extra import _KeyModifier
        dtype, trafo = {}, None
        for i, lh in enumerate([self._op1, self._op2]):
            dtp, tr = lh.get_transformation()
            if isinstance(tr.target, MultiDomain):
                dtype.update({str(i)+d:dtp[d] for d in dtp.keys()})
                tr = _KeyModifier(tr.target, str(i)) @ tr
                trafo = tr if trafo is None else trafo+tr
            else:
                dtype[str(i)] = dtp
                tr = tr.ducktape_left(str(i))
                trafo = tr if trafo is None else trafo + tr
        return dtype, trafo

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    def _simplify_for_constant_input_nontrivial(self, c_inp):
        from ..multi_domain import MultiDomain
        from .simplify_for_const import ConstCollector
        f1, o1 = self._op1.simplify_for_constant_input(
            c_inp.extract_part(self._op1.domain))
        f2, o2 = self._op2.simplify_for_constant_input(
            c_inp.extract_part(self._op2.domain))
        if not isinstance(self._target, MultiDomain):
            return None, _OpSum(o1, o2)
        cc = ConstCollector()
        cc.add(f1, o1.target)
        cc.add(f2, o2.target)
        return cc.constfield, _OpSum(o1, o2)
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    def __repr__(self):
        subs = "\n".join(sub.__repr__() for sub in (self._op1, self._op2))
        return "_OpSum:\n"+indent(subs)