{"action":"created","comment":{"url":"https://api.github.com/repos/odlgroup/odl/pulls/comments/77640187","id":77640187,"diff_hunk":"@@ -0,0 +1,731 @@\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+\"\"\"Default functionals defined on any (reasonable) space.\"\"\"\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+\n+from odl.solvers.functional.functional import Functional\n+from odl.operator.operator import Operator\n+from odl.solvers.advanced.proximal_operators import (\n+    proximal_l1, proximal_cconj_l1, proximal_l2, proximal_cconj_l2,\n+    proximal_l2_squared)\n+\n+from odl.operator.default_ops import (ZeroOperator, IdentityOperator)\n+\n+\n+__all__ = ('L1Norm', 'L2Norm', 'L2NormSquare', 'ZeroFunctional',\n+           'ConstantFunctional')\n+\n+\n+# TODO: Implement some of the missing gradients\n+\n+class L1Norm(Functional):\n+\n+    \"\"\"The functional corresponding to L1-norm.\n+\n+    The L1-norm, ``||x||_1``,  is defined as the integral/sum of ``|x|``.\n+\n+    References\n+    ----------\n+    Wikipedia article on `Norms\n+        <https://en.wikipedia.org/wiki/Norm_(mathematics)>`_.\n+    \"\"\"\n+\n+    def __init__(self, domain):\n+        \"\"\"Initialize a new instance.\n+\n+        Parameters\n+        ----------\n+        domain : `LinearSpace`\n+            Domain of the functional.\n+        \"\"\"\n+        super().__init__(domain=domain, linear=False, grad_lipschitz=np.inf)\n+\n+    def _call(self, x):\n+        \"\"\"Applies the functional to the given point.\n+\n+        Parameters\n+        ----------\n+        x : `LinearSpaceVector`\n+            Element in the domain of the functional.\n+\n+        Returns\n+        -------\n+        out : `field` element\n+            Result of the evaluation.\n+        \"\"\"\n+        return np.abs(x).inner(self.domain.one())\n+\n+    @property\n+    def gradient(x):\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+        # It does not exist on all of the space\n+        raise NotImplementedError('functional not differential.')\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+            Step size-like parameter\n+\n+        Returns\n+        -------\n+        out : Operator\n+            Domain and range equal to domain of functional\n+        \"\"\"\n+\n+        return proximal_l1(space=self.domain)(sigma)\n+\n+    @property\n+    def conjugate_functional(self):\n+        \"\"\"The convex conjugate functional of the L1-norm.\"\"\"\n+        return IndicatorLinftyUnitBall(self.domain)\n+\n+\n+class IndicatorLinftyUnitBall(Functional):\n+\n+    \"\"\"The indicator function on the unit ball, in the L-infinity norm.\n+\n+    This functional is defined as\n+\n+        ``f(x) = 0 if ||x||_infty <= 1, infty else,``\n+\n+    where ``||x||_infty`` is the infinity norm\n+\n+        ``||x||_infty = max(|x|)``.\n+\n+    Notes\n+    -----\n+    This functional is the convex conjugate functional of the L1-norm.\n+    \"\"\"\n+\n+    def __init__(self, domain):\n+        \"\"\"Initialize a new instance.\n+\n+        Parameters\n+        ----------\n+        domain : `LinearSpace`\n+            Domain of the functional.\n+        \"\"\"\n+        super().__init__(domain=domain, linear=False)\n+\n+    def _call(self, x):\n+        \"\"\"Applies the functional the given point.\n+\n+        Parameters\n+        ----------\n+        x : `LinearSpaceVector`\n+            Element in the domain of the functional.\n+\n+        Returns\n+        -------\n+        out : `field` element\n+            Result of the evaluation.\n+        \"\"\"\n+        if np.max(np.abs(x)) > 1:\n+            return np.inf\n+        else:\n+            return 0\n+\n+    @property\n+    def gradient(x):\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+        # It does not exist on all of the space, only for ||x|| < 1\n+        # where it is the ZeroOperator\n+        raise NotImplementedError('functional not differential.')\n+\n+    @property\n+    def conjugate_functional(self):\n+        \"\"\"The conjugate functional of IndicatorLinftyUnitBall.\n+\n+        Notes\n+        -----\n+        Since the functional is the conjugate functional of the L1-norm, and\n+        since the L1-norm is proper, convex and lower-semicontinuous,\n+        by the Fenchel-Moreau theorem the convex conjugate functional\n+        of the convex conjugate functional of IndicatorLinftyUnitBall, also\n+        known as the biconjugate of the L1-norm, is the L1-norm [BC2011]_.\n+        \"\"\"\n+        return L1Norm(domain=self.domain)\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+            Step size-like parameter\n+\n+        Returns\n+        -------\n+        out : Operator\n+            Domain and range equal to domain of functional\n+        \"\"\"\n+\n+        return proximal_cconj_l1(space=self.domain)(sigma)\n+\n+\n+class L2Norm(Functional):\n+\n+    \"\"\"The functional corresponding to the L2-norm.\n+\n+    The L2-norm, ``||x||_2``,  is defined as the square-root out of the\n+    integral/sum of ``x^2``.\n+\n+    References\n+    ----------\n+    Wikipedia article on `Norms\n+        <https://en.wikipedia.org/wiki/Norm_(mathematics)>`_.\n+        \"\"\"\n+\n+    def __init__(self, domain):\n+        \"\"\"Initialize a new instance.\n+\n+        Parameters\n+        ----------\n+        domain : `LinearSpace`\n+            Domain of the functional.\n+        \"\"\"\n+        super().__init__(domain=domain, linear=False, grad_lipschitz=np.inf)\n+\n+    def _call(self, x):\n+        \"\"\"Applies the functional to the given point.\n+\n+        Parameters\n+        ----------\n+        x : `LinearSpaceVector`\n+            Element in the domain of the functional.\n+\n+        Returns\n+        -------\n+        out : `field` element\n+            Result of the evaluation.\n+        \"\"\"\n+        return np.sqrt(x.inner(x))\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+        functional = self\n+\n+        class L2Gradient(Operator):\n+\n+            \"\"\"The gradient operator of this functional.\"\"\"\n+\n+            def __init__(self):\n+                \"\"\"Initialize a new instance.\"\"\"\n+                super().__init__(functional.domain, functional.domain,\n+                                 linear=False)\n+\n+            def _call(self, x):\n+                \"\"\"Applies the gradient operator to the given point.\n+\n+                Parameters\n+                ----------\n+                x : `LinearSpaceVector`\n+                    Element in the domain of the functional to which the\n+                    gradient operator is applied. The element must have a\n+                    non-zero norm\n+\n+                Returns\n+                -------\n+                out : `LinearSpaceVector`\n+                    Result of the evaluation of the gradient operator. An\n+                    element in the domain of the functional.\n+                \"\"\"\n+                norm_of_x = x.norm()\n+                if norm_of_x == 0:\n+                    # The derivative is not defined for such a point.","path":"odl/solvers/functional/default_functionals.py","position":300,"original_position":300,"commit_id":"0ff83b452bbf60b9b4e7f1e85d1c14610262479e","original_commit_id":"0ff83b452bbf60b9b4e7f1e85d1c14610262479e","user":{"login":"kohr-h","id":5030250,"avatar_url":"https://avatars.githubusercontent.com/u/5030250?v=3","gravatar_id":"","url":"https://api.github.com/users/kohr-h","html_url":"https://github.com/kohr-h","followers_url":"https://api.github.com/users/kohr-h/followers","following_url":"https://api.github.com/users/kohr-h/following{/other_user}","gists_url":"https://api.github.com/users/kohr-h/gists{/gist_id}","starred_url":"https://api.github.com/users/kohr-h/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/kohr-h/subscriptions","organizations_url":"https://api.github.com/users/kohr-h/orgs","repos_url":"https://api.github.com/users/kohr-h/repos","events_url":"https://api.github.com/users/kohr-h/events{/privacy}","received_events_url":"https://api.github.com/users/kohr-h/received_events","type":"User","site_admin":false},"body":"\"such a point\" is the point 0","created_at":"2016-09-06T14:02:47Z","updated_at":"2016-09-06T14:02:48Z","html_url":"https://github.com/odlgroup/odl/pull/498#discussion_r77640187","pull_request_url":"https://api.github.com/repos/odlgroup/odl/pulls/498","_links":{"self":{"href":"https://api.github.com/repos/odlgroup/odl/pulls/comments/77640187"},"html":{"href":"https://github.com/odlgroup/odl/pull/498#discussion_r77640187"},"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":"2016-09-06T14:02:48Z","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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