operator.py 5.02 KB
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from __future__ import absolute_import, division, print_function

from ..compat import *
from ..utilities import NiftyMetaBase


class Operator(NiftyMetaBase()):
    """Transforms values living on one domain into values living on another
    domain, and can also provide the Jacobian.
    """

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    @property
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    def domain(self):
        """DomainTuple or MultiDomain : the operator's input domain

            The domain on which the Operator's input Field lives."""
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        raise NotImplementedError
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    @property
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    def target(self):
        """DomainTuple or MultiDomain : the operator's output domain

            The domain on which the Operator's output Field lives."""
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        raise NotImplementedError
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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 __mul__(self, x):
        if not isinstance(x, Operator):
            return NotImplemented
        return _OpProd.make((self, x))

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    def chain(self, x):
        res = self.__matmul__(x)
        if res == NotImplemented:
            raise TypeError("operator expected")
        return res

    def __call__(self, x):
        """Returns transformed x

        Parameters
        ----------
        x : Linearization
            input

        Returns
        -------
        Linearization
            output
        """
        raise NotImplementedError


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for f in ["sqrt", "exp", "log", "tanh", "positive_tanh"]:
    def func(f):
        def func2(self):
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            fa = _FunctionApplier(self.target, f)
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            return _OpChain.make((fa, self))
        return func2
    setattr(Operator, f, func(f))


class _FunctionApplier(Operator):
    def __init__(self, domain, funcname):
        from ..sugar import makeDomain
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        self._domain = makeDomain(domain)
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        self._funcname = funcname

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

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

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    def __call__(self, x):
        return getattr(x, 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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    @property
    def domain(self):
        return self._ops[-1].domain

    @property
    def target(self):
        return self._ops[0].target
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    def __call__(self, x):
        for op in reversed(self._ops):
            x = op(x)
        return x


class _OpProd(_CombinedOperator):
    def __init__(self, ops, _callingfrommake=False):
        super(_OpProd, self).__init__(ops, _callingfrommake)
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    @property
    def domain(self):
        return self._ops[0].domain

    @property
    def target(self):
        return self._ops[0].target
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    def __call__(self, x):
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        from ..utilities import my_product
        return my_product(map(lambda op: op(x), self._ops))
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class _OpSum(_CombinedOperator):
    def __init__(self, ops, _callingfrommake=False):
        super(_OpSum, self).__init__(ops, _callingfrommake)
        self._domain = domain_union([op.domain for op in self._ops])
        self._target = domain_union([op.target for op in self._ops])

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

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

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    def __call__(self, x):
        raise NotImplementedError
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class SquaredNormOperator(Operator):
    def __init__(self, domain):
        super(SquaredNormOperator, self).__init__()
        self._domain = domain
        self._target = DomainTuple.scalar_domain()

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

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

    def __call__(self, x):
        return Field(self._target, x.vdot(x))


class QuadraticFormOperator(Operator):
    def __init__(self, op):
        from .endomorphic_operator import EndomorphicOperator
        super(QuadraticFormOperator, self).__init__()
        if not isinstance(op, EndomorphicOperator):
            raise TypeError("op must be an EndomorphicOperator")
        self._op = op
        self._target = DomainTuple.scalar_domain()

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

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

    def __call__(self, x):
        if isinstance(x, Linearization):
            jac = self._op(x)
            val = Field(self._target, 0.5 * x.vdot(jac))
            return Linearization(val, jac)
        return Field(self._target, 0.5 * x.vdot(self._op(x)))