{"action":"created","comment":{"url":"https://api.github.com/repos/odlgroup/odl/pulls/comments/78017149","id":78017149,"diff_hunk":"@@ -0,0 +1,1671 @@\n+# Copyright 2014-2016 The ODL development group\n+#\n+# This file is part of ODL.\n+#\n+# ODL is free software: you can redistribute it and/or modify\n+# it under the terms of the GNU General Public License as published by\n+# the Free Software Foundation, either version 3 of the License, or\n+# (at your option) any later version.\n+#\n+# ODL is distributed in the hope that it will be useful,\n+# but WITHOUT ANY WARRANTY; without even the implied warranty of\n+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n+# GNU General Public License for more details.\n+#\n+# You should have received a copy of the GNU General Public License\n+# along with ODL.  If not, see <http://www.gnu.org/licenses/>.\n+\n+# Imports for common Python 2/3 codebase\n+from __future__ import print_function, division, absolute_import\n+from future import standard_library\n+standard_library.install_aliases()\n+from builtins import super\n+\n+import numpy as np\n+from numbers import Number\n+\n+from odl.operator.operator import (\n+    Operator, OperatorComp, OperatorLeftScalarMult, OperatorRightScalarMult,\n+    OperatorRightVectorMult, OperatorSum)\n+from odl.operator.default_ops import (ResidualOperator, IdentityOperator,\n+                                      ConstantOperator, ScalingOperator)\n+from odl.set.space import LinearSpaceVector\n+from odl.solvers.advanced import (proximal_arg_scaling, proximal_translation,\n+                                  proximal_quadratic_perturbation)\n+\n+\n+__all__ = ('Functional', 'FunctionalLeftScalarMult',\n+           'FunctionalRightScalarMult', 'FunctionalComp',\n+           'FunctionalRightVectorMult', 'FunctionalSum', 'FunctionalScalarSum',\n+           'TranslatedFunctional', 'ConvexConjugateTranslation',\n+           'ConvexConjugateFuncScaling', 'ConvexConjugateArgScaling',\n+           'ConvexConjugateLinearPerturb')\n+\n+\n+class Functional(Operator):\n+\n+    \"\"\"Implementation of a functional class.\n+\n+    A functional is an operator ``f`` that maps from some domain ``X`` to the\n+    field of scalars ``F`` associated with the domain:\n+\n+        ``f : X -> F``.\n+\n+    Notes\n+    -----\n+    The implementation of the functional class assumes that the domain\n+    :math:`X` is a Hilbert space and that the field of scalars :math:`F` is a\n+    is the real numbers. It is possible to create functions that do not fulfil\n+    these assumptions, however some mathematical results might not be valide in\n+    this case. For more information, see\n+    http://odl.readthedocs.io/guide/in_depth/functional_guide.html.\n+    \"\"\"\n+\n+    def __init__(self, domain, linear=False, grad_lipschitz=np.inf):\n+        \"\"\"Initialize a new instance.\n+\n+        Parameters\n+        ----------\n+        domain : `Set`\n+            The domain of this functional, i.e., the set of elements to\n+            which this functional can be applied\n+        linear : `bool`\n+            If `True`, the functional is considered as linear. In this\n+            case, ``domain`` and ``range`` have to be instances of\n+            `LinearSpace`, or `Field`.\n+        grad_lipschitz : 'float', optional\n+            The Lipschitz constant of the gradient.\n+        \"\"\"\n+\n+        Operator.__init__(self, domain=domain,\n+                          range=domain.field, linear=linear)\n+        self._grad_lipschitz = float(grad_lipschitz)\n+\n+    @property\n+    def gradient(self):\n+        \"\"\"Gradient operator of the functional.\n+\n+        Notes\n+        -----\n+        The operator that corresponds to the mapping\n+\n+        .. math::\n+\n+            x \\\\to \\\\nabla f(x)\n+\n+        where :math:`\\\\nabla f(x)` is the element used to evaluate\n+        derivatives in a direction :math:`d` by\n+        :math:`\\\\langle \\\\nabla f(x), d \\\\rangle`.\n+        \"\"\"\n+        raise NotImplementedError\n+\n+    def proximal(self, sigma=1.0):\n+        \"\"\"Return the proximal operator of the functional.\n+\n+        Parameters\n+        ----------\n+        sigma : positive float, optional\n+            Regularization parameter of the proximal operator.\n+\n+        Returns\n+        -------\n+        out : `Operator`\n+            Domain and range equal to domain of functional.\n+\n+        Notes\n+        -----\n+        The nonsmooth solvers that make use of proximal operators in order to\n+        solve a given optimization problem, see for example\n+        `forward_backward_pd`, take a `proximal factory` as input. Note that\n+        ``Functional.proximal`` is in fact a `proximal factory`.\n+        \"\"\"\n+        raise NotImplementedError\n+\n+    @property\n+    def conjugate_functional(self):\n+        \"\"\"Convex conjugate functional of the functional.\n+\n+        Notes\n+        -----\n+        The convex conjugate functional of a convex functional :math:`f(x)`,\n+        defined on a Hilber space, is defined as the functional\n+\n+        .. math::\n+\n+            f^*(x^*) = \\\\sup_{x} \\{ \\\\langle x^*,x \\\\rangle - f(x)  \\}.\n+\n+        The concept is also known as the Legendre transformation.\n+\n+        References\n+        ----------\n+        Wikipedia article on `Convex conjugate\n+        <https://en.wikipedia.org/wiki/Convex_conjugate>`_.\n+\n+        Wikipedia article on `Legendre transformation\n+        https://en.wikipedia.org/wiki/Legendre_transformation\n+\n+        For literature references see, e.g., [Lue1969]_, [Roc1970]_.\n+        \"\"\"\n+        raise NotImplementedError\n+\n+    def derivative(self, point):\n+        \"\"\"Return the derivative operator in the given point.\n+\n+        This function returns the linear operator\n+\n+            ``x --> <x, grad_f(point)>``,\n+\n+        where ``grad_f(point)`` is the gradient of the functional in the point\n+        ``point``.\n+\n+        Parameters\n+        ----------\n+        point : `LinearSpaceVector`\n+            The point in which the gradient is evaluated.\n+\n+        Returns\n+        -------\n+        out : `Operator`\n+            The linear operator that maps ``x --> <x, grad_f(point)>``.\n+        \"\"\"\n+        return self.gradient(point).T\n+\n+    def translate(self, shift):\n+        \"\"\"Return a translation of the functional.\n+\n+        For a given functional ``f`` and an element ``translation`` in the\n+        domain of ``f``, this operation creates the functional\n+        ``f(. - translation)``.\n+\n+        Parameters\n+        ----------\n+        translation : `LinearSpaceVector`\n+            Element in the domain of the functional\n+\n+        Returns\n+        -------\n+        out : `TranslatedFunctional`\n+            The functional ``f(. - translation)``\n+        \"\"\"\n+        if shift not in self.domain:\n+            raise TypeError('the translation {} is not in the domain of the'\n+                            'functional {!r}'.format(shift, self))\n+\n+        return TranslatedFunctional(self, shift)\n+\n+    def __mul__(self, other):\n+        \"\"\"Return ``self * other``.\n+\n+        If ``other`` is an operator, this corresponds to composition with the\n+        operator:\n+\n+            ``func * op <==> (x --> func(op(x)))``\n+\n+        If ``other`` is a scalar, this corresponds to right multiplication of\n+        scalars with functionals:\n+\n+            ``func * scalar <==> (x --> func(scalar * x))``\n+\n+        If ``other`` is a vector, this corresponds to right multiplication of\n+        vectors with functionals:\n+\n+            ``func * vector <==> (x --> func(vector * x))``\n+\n+        Note that left and right multiplications are generally different.\n+\n+        Parameters\n+        ----------\n+        other : `Operator` or `LinearSpaceVector` or scalar\n+            `Operator`:\n+            The `Operator.range` of ``other`` must match this functionals\n+            `Functional.domain`.\n+\n+            `LinearSpaceVector`:\n+            ``other`` must be an element of this functionals's\n+            `Functional.domain`.\n+\n+            scalar:\n+            The `Functional.domain` of this functional must be a\n+            `LinearSpace` and ``other`` must be an element of the ``field``\n+            of this functional's `Functional.domain`. Note that this\n+            ``field`` is also this functional's `Functional.range`.\n+\n+        Returns\n+        -------\n+        mul : `Functional`\n+            Multiplication result\n+\n+            If ``other`` is an `Operator`, ``mul`` is a\n+            `FunctionalComp`.\n+\n+            If ``other`` is a scalar, ``mul`` is a\n+            `FunctionalRightScalarMult`.\n+\n+            If ``other`` is a vector, ``mul`` is a\n+            `FunctionalRightVectorMult`.\n+\n+        Notes\n+        -------\n+        See also `Operator.__mul__`.\n+        \"\"\"\n+        if isinstance(other, Operator):\n+            return FunctionalComp(self, other)\n+        elif isinstance(other, Number):\n+            # Left multiplication is more efficient, so we can use this in the\n+            # case of linear functional.\n+            if self.is_linear:\n+                return FunctionalLeftScalarMult(self, other)\n+            else:\n+                return FunctionalRightScalarMult(self, other)\n+        elif isinstance(other, LinearSpaceVector) and other in self.domain:\n+            return FunctionalRightVectorMult(self, other)\n+        else:\n+            return super().__mul__(other)\n+\n+    def __rmul__(self, other):\n+        \"\"\"Return ``other * self``.\n+\n+        If ``other`` is an operator, since a functional is also an operator\n+        this corresponds to operator composition:\n+\n+            ``op * func <==> (x --> op(func(x))``\n+\n+        If ``other`` is a scalar, this corresponds to left multiplication of\n+        scalars with functionals:\n+\n+            ``scalar * func <==> (x --> scalar * func(x))``\n+\n+        If ``other`` is a vector,  since a functional is also an operator this\n+        corresponds to left multiplication of vectors with operators:\n+\n+            ``vector * func <==> (x --> vector * func(x))``\n+\n+        Note that left and right multiplications are generally\n+        different.\n+\n+        Parameters\n+        ----------\n+        other : `Operator` or `LinearSpaceVector` or scalar\n+            `Operator`:\n+            The `Operator.domain` of ``other`` must match this functional's\n+            `Functional.range`.\n+\n+            `LinearSpaceVector`:\n+            ``other`` must be an element of this functionals's\n+            `Functional.range`.\n+\n+            scalar:\n+            The `Operator.domain` of this operator must be a\n+            `LinearSpace` and ``other`` must be an\n+            element of the ``field`` of this operator's\n+            `Operator.domain`.\n+\n+        Returns\n+        -------\n+        rmul : `Functional` or `Operator`\n+            Multiplication result\n+\n+            If ``other`` is an `Operator`, ``rmul`` is a `OperatorComp`.\n+\n+            If ``other`` is a scalar, ``rmul`` is a\n+            `FunctionalLeftScalarMult`.\n+\n+            If ``other`` is a vector, ``rmul`` is a\n+            `OperatorLeftVectorMult`.\n+        \"\"\"\n+        if other in self.domain.field:\n+            if other == 0:\n+                from odl.solvers.functional.default_functionals import (\n+                    ZeroFunctional)\n+                return ZeroFunctional(self.domain)\n+            else:\n+                return FunctionalLeftScalarMult(self, other)\n+        else:\n+            return super().__rmul__(other)\n+\n+    def __add__(self, other):\n+        \"\"\"Return ``self + other``.\n+\n+        Parameters\n+        ----------\n+        other : `Functional` or scalar\n+            `Functional`:\n+            The `Functional.domain` and `Functional.range` of ``other``\n+            must match this functional's  `Functional.domain` and\n+            `Functional.range`.\n+\n+            scalar:\n+            The scalar needs to be in this functional's `Functional.range`.\n+\n+        Returns\n+        -------\n+        add : `Functional`\n+            Addition result\n+\n+            If ``other`` is in ``Functional.range``, ``add`` is a\n+            `FunctionalScalarSum`.\n+\n+            If ``other`` is a `Functional`, ``add`` is a `FunctionalSum`.\n+        \"\"\"\n+        if other in self.domain.field:\n+            return FunctionalScalarSum(self, other)\n+        elif isinstance(other, Functional):\n+            return FunctionalSum(self, other)\n+        else:\n+            return NotImplemented\n+\n+    def __radd__(self, other):\n+        \"\"\"Return ``other + self``.\n+\n+        Since addition is commutative, also for functionals, this is similar\n+        to `Functional.__add__`.\n+        \"\"\"\n+        if other in self.domain.field:\n+            return FunctionalScalarSum(self, other)\n+        elif isinstance(other, Functional):\n+            return FunctionalSum(self, other)\n+        else:\n+            return NotImplemented\n+\n+    def __sub__(self, other):\n+        \"\"\"Return ``self - other``.\"\"\"\n+        return self.__add__(-1 * other)\n+","path":"odl/solvers/functional/functional.py","position":373,"original_position":373,"commit_id":"0ff83b452bbf60b9b4e7f1e85d1c14610262479e","original_commit_id":"0ff83b452bbf60b9b4e7f1e85d1c14610262479e","user":{"login":"adler-j","id":2202312,"avatar_url":"https://avatars.githubusercontent.com/u/2202312?v=3","gravatar_id":"","url":"https://api.github.com/users/adler-j","html_url":"https://github.com/adler-j","followers_url":"https://api.github.com/users/adler-j/followers","following_url":"https://api.github.com/users/adler-j/following{/other_user}","gists_url":"https://api.github.com/users/adler-j/gists{/gist_id}","starred_url":"https://api.github.com/users/adler-j/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/adler-j/subscriptions","organizations_url":"https://api.github.com/users/adler-j/orgs","repos_url":"https://api.github.com/users/adler-j/repos","events_url":"https://api.github.com/users/adler-j/events{/privacy}","received_events_url":"https://api.github.com/users/adler-j/received_events","type":"User","site_admin":false},"body":"Well for operators we only have scalar division, since `*` means composition, one would expect `/` to mean composition with the inverse, e.g. ` ((f * g) / g)(x) == f(x)`. Since we don't provide an inverse I say we skip this (we have not added it for operators so far).","created_at":"2016-09-08T14:30:09Z","updated_at":"2016-09-08T14:30:09Z","html_url":"https://github.com/odlgroup/odl/pull/498#discussion_r78017149","pull_request_url":"https://api.github.com/repos/odlgroup/odl/pulls/498","_links":{"self":{"href":"https://api.github.com/repos/odlgroup/odl/pulls/comments/78017149"},"html":{"href":"https://github.com/odlgroup/odl/pull/498#discussion_r78017149"},"pull_request":{"href":"https://api.github.com/repos/odlgroup/odl/pulls/498"}}},"pull_request":{"url":"https://api.github.com/repos/odlgroup/odl/pulls/498","id":77972925,"html_url":"https://github.com/odlgroup/odl/pull/498","diff_url":"https://github.com/odlgroup/odl/pull/498.diff","patch_url":"https://github.com/odlgroup/odl/pull/498.patch","issue_url":"https://api.github.com/repos/odlgroup/odl/issues/498","number":498,"state":"open","locked":false,"title":"Issue 246  functional","user":{"login":"aringh","id":15774494,"avatar_url":"https://avatars.githubusercontent.com/u/15774494?v=3","gravatar_id":"","url":"https://api.github.com/users/aringh","html_url":"https://github.com/aringh","followers_url":"https://api.github.com/users/aringh/followers","following_url":"https://api.github.com/users/aringh/following{/other_user}","gists_url":"https://api.github.com/users/aringh/gists{/gist_id}","starred_url":"https://api.github.com/users/aringh/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/aringh/subscriptions","organizations_url":"https://api.github.com/users/aringh/orgs","repos_url":"https://api.github.com/users/aringh/repos","events_url":"https://api.github.com/users/aringh/events{/privacy}","received_events_url":"https://api.github.com/users/aringh/received_events","type":"User","site_admin":false},"body":"This adds `functional`'s to `odl.solvers`.\r\n\r\nThe branch is not complete yet, but review of parts of it can start (especially the basic functionality in the functional-file).\r\n\r\nMoreover, the commit history is not very nice, but I will update this before merge.\r\n\r\n","created_at":"2016-07-19T13:11:21Z","updated_at":"2016-09-08T14:30:09Z","closed_at":null,"merged_at":null,"merge_commit_sha":"51a7c44dbf975b27fc1ee1330d330789817b9668","assignee":null,"assignees":[],"milestone":null,"commits_url":"https://api.github.com/repos/odlgroup/odl/pulls/498/commits","review_comments_url":"https://api.github.com/repos/odlgroup/odl/pulls/498/comments","review_comment_url":"https://api.github.com/repos/odlgroup/odl/pulls/comments{/number}","comments_url":"https://api.github.com/repos/odlgroup/odl/issues/498/comments","statuses_url":"https://api.github.com/repos/odlgroup/odl/statuses/0ff83b452bbf60b9b4e7f1e85d1c14610262479e","head":{"label":"odlgroup:issue-246__functional","ref":"issue-246__functional","sha":"0ff83b452bbf60b9b4e7f1e85d1c14610262479e","user":{"login":"odlgroup","id":15667171,"avatar_url":"https://avatars.githubusercontent.com/u/15667171?v=3","gravatar_id":"","url":"https://api.github.com/users/odlgroup","html_url":"https://github.com/odlgroup","followers_url":"https://api.github.com/users/odlgroup/followers","following_url":"https://api.github.com/users/odlgroup/following{/other_user}","gists_url":"https://api.github.com/users/odlgroup/gists{/gist_id}","starred_url":"https://api.github.com/users/odlgroup/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/odlgroup/subscriptions","organizations_url":"https://api.github.com/users/odlgroup/orgs","repos_url":"https://api.github.com/users/odlgroup/repos","events_url":"https://api.github.com/users/odlgroup/events{/privacy}","received_events_url":"https://api.github.com/users/odlgroup/received_events","type":"Organization","site_admin":false},"repo":{"id":45596393,"name":"odl","full_name":"odlgroup/odl","owner":{"login":"odlgroup","id":15667171,"avatar_url":"https://avatars.githubusercontent.com/u/15667171?v=3","gravatar_id":"","url":"https://api.github.com/users/odlgroup","html_url":"https://github.com/odlgroup","followers_url":"https://api.github.com/users/odlgroup/followers","following_url":"https://api.github.com/users/odlgroup/following{/other_user}","gists_url":"https://api.github.com/users/odlgroup/gists{/gist_id}","starred_url":"https://api.github.com/users/odlgroup/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/odlgroup/subscriptions","organizations_url":"https://api.github.com/users/odlgroup/orgs","repos_url":"https://api.github.com/users/odlgroup/repos","events_url":"https://api.github.com/users/odlgroup/events{/privacy}","received_events_url":"https://api.github.com/users/odlgroup/received_events","type":"Organization","site_admin":false},"private":false,"html_url":"https://github.com/odlgroup/odl","description":"Operator 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