{"action":"created","comment":{"url":"https://api.github.com/repos/odlgroup/odl/pulls/comments/78141720","id":78141720,"diff_hunk":"@@ -0,0 +1,189 @@\n+.. _functional_in_depth:\n+\n+#####################\n+Functional\n+#####################\n+\n+A *functional* is an operator :math:`S: X \\to \\mathbb{F}` that maps that maps from some vector space :math:`X` to the field of scalars :math:`F`.\n+\n+In the ODL `solvers` package, functionals are implemented in the `Functional` class, a subclass to `Operator`.\n+\n+From a mathematical perspective, the above is a valid definition of a functional.\n+However, since these functionals are primarily to be used for solving optimization problems, the following assumptions are made:\n+\n+ * the vector space :math:`X` is a Hilbert space.\n+ * the field of scalars :math:`F` are the real numbers.\n+\n+The first assumption is made in order to simplify the concept of *convex conjugate functional*, see ``convex_conj`` under :ref:`implementation` for more details, or the Wikipedia articles on `convex conjugate`_ and `Legendre transformation`_.\n+\n+The second assumption is made in order to guarantee that we use a well-ordered set (in contrast to e.g. the complex numbers) over which optimization problems can be meaningfully defined, and that optimal solutions are in fact obtained.\n+See, for example, the Wikipedia articles on `field`_, `ordered field`_ and `least-upper-bound property`_.\n+\n+Note that these conditions are not explicitly checked.\n+However, using the class in violation to the above assumptions might lead to unknown behavior since some of the mathematical results might not hold.\n+Also note that most of the theory, and most solvers, requires the functional to be convex.\n+However this property is not stored or checked anywhere in the class.\n+It is therefore the users responsibility to ensure that a functional has the properties required for a given optimization method.\n+\n+The intended use of the `Functional` class is, as mentioned above, to be used when formulating and solving optimization problems.\n+One main difference with the `Operator` class is thus that it contains notions specially intended for optimization, such as *convex conjugate functional* and *proximal operator*.\n+For more information on these concepts, see ``convex_conj`` and ``proximal`` under :ref:`implementation`.\n+There is also a certain type of arithmetics associated with functionals, for more on this see :ref:`arithmetic`.\n+\n+\n+.. _convex conjugate: https://en.wikipedia.org/wiki/Convex_conjugate\n+.. _Legendre transformation: https://en.wikipedia.org/wiki/Legendre_transformation\n+\n+.. _field: https://en.wikipedia.org/wiki/Field_(mathematics)\n+.. _ordered field: https://en.wikipedia.org/wiki/Ordered_field\n+.. _least-upper-bound property: https://en.wikipedia.org/wiki/Least-upper-bound_property\n+\n+.. _implementation:\n+\n+Implementation of functionals\n+=============================\n+\n+To define your own functional, start by writing::\n+\n+    class MyFunctional(odl.solvers.Functional):\n+\n+        \"\"\"Docstring goes here.\"\"\"\n+    \n+        def __init__(self, space):\n+            # Sets `Operator.domain` to `space` and `Operator.range` to `space.field`\n+            odl.solvers.Functional.__init__(self, space)\n+\n+        ...\n+\n+`Functional` needs to be provided with a domain, from which it infers the range.\n+\n+.. automethod:: Functional.domain","path":"doc/source/guide/in_depth/functional_guide.rst","position":60,"original_position":60,"commit_id":"4ec350f0ab8f4d5d0fe9b11b67a271f88a7afdd2","original_commit_id":"4ec350f0ab8f4d5d0fe9b11b67a271f88a7afdd2","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":"My local build does not seem to import correctly.... it does nothing on the corresponding line. I will just copy-past from description in `Functional` for now.","created_at":"2016-09-09T07:56:15Z","updated_at":"2016-09-09T07:56:15Z","html_url":"https://github.com/odlgroup/odl/pull/498#discussion_r78141720","pull_request_url":"https://api.github.com/repos/odlgroup/odl/pulls/498","_links":{"self":{"href":"https://api.github.com/repos/odlgroup/odl/pulls/comments/78141720"},"html":{"href":"https://github.com/odlgroup/odl/pull/498#discussion_r78141720"},"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":"2016-09-09T07:56:15Z","closed_at":null,"merged_at":null,"merge_commit_sha":"76955499373ab5f620fdd84ddf58256b74245eb2","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/4ec350f0ab8f4d5d0fe9b11b67a271f88a7afdd2","head":{"label":"odlgroup:issue-246__functional","ref":"issue-246__functional","sha":"4ec350f0ab8f4d5d0fe9b11b67a271f88a7afdd2","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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