{"action":"created","comment":{"url":"https://api.github.com/repos/odlgroup/odl/pulls/comments/70037237","id":70037237,"diff_hunk":"@@ -0,0 +1,227 @@\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+\"\"\"Test for the forward-backward solver.\"\"\"\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+\n+# External\n+import pytest\n+import numpy as np\n+\n+# Internal\n+import odl\n+from odl.solvers import forward_backward_pd\n+from odl.util.testutils import all_almost_equal, almost_equal, example_element\n+\n+# Places for the accepted error when comparing results\n+HIGH_ACCURACY = 8\n+LOW_ACCURACY = 4\n+\n+\n+def test_forward_backward_input_handling():\n+    \"\"\"Test to see that input is handled correctly.\"\"\"\n+\n+    space1 = odl.uniform_discr(0, 1, 10)\n+\n+    lin_ops = [odl.ZeroOperator(space1), odl.ZeroOperator(space1)]\n+    prox_cc_g = [odl.solvers.proximal_zero(space1),  # Identity operator\n+                 odl.solvers.proximal_zero(space1)]  # Identity operator\n+    prox_f = odl.solvers.proximal_zero(space1)  # Identity operator\n+    grad_h = odl.ZeroOperator(space1)\n+\n+    # Check that the algorithm runs. With the above operators, the algorithm\n+    # returns the input.\n+    x0 = example_element(space1)\n+    x = x0.copy()\n+    niter = 3\n+\n+    forward_backward_pd(x, prox_f, prox_cc_g, lin_ops, grad_h, tau=1.0,\n+                        sigma=[1.0, 1.0], niter=niter)\n+\n+    assert x == x0\n+\n+    # Testing that sizes needs to agree:\n+    # Too few sigma_i:s\n+    with pytest.raises(ValueError):\n+        forward_backward_pd(x, prox_f, prox_cc_g, lin_ops, grad_h, tau=1.0,\n+                            sigma=[1.0], niter=niter)\n+\n+    # Too many operators\n+    prox_cc_g_too_many = [odl.solvers.proximal_zero(space1),\n+                          odl.solvers.proximal_zero(space1),\n+                          odl.solvers.proximal_zero(space1)]\n+    with pytest.raises(ValueError):\n+        forward_backward_pd(x, prox_f, prox_cc_g_too_many, lin_ops, grad_h,\n+                            tau=1.0, sigma=[1.0, 1.0], niter=niter)\n+\n+    # Test for correct space\n+    space2 = odl.uniform_discr(1, 2, 10)\n+    x = example_element(space2)\n+    with pytest.raises(ValueError):\n+        forward_backward_pd(x, prox_f, prox_cc_g, lin_ops, grad_h, tau=1.0,\n+                            sigma=[1.0, 1.0], niter=niter)\n+\n+\n+def test_forward_backward_basic():\n+    \"\"\"Test for the forward-backward solver by minimizing ||x||_2^2.\n+\n+    The general problem is of the form\n+\n+        ``min_x f(x) + sum_i g_i(L_i x) + h(x)``\n+\n+    and here we take f(x) = g(x) = 0, h(x) = ||x||_2^2 and L is the\n+    zero-operator.\n+    \"\"\"\n+\n+    space = odl.rn(10)\n+\n+    lin_ops = [odl.ZeroOperator(space)]\n+    prox_cc_g = [odl.solvers.proximal_cconj(odl.solvers.proximal_zero(space))]\n+    prox_f = odl.solvers.proximal_zero(space)\n+    grad_h = 2.0 * odl.IdentityOperator(space)  # Gradient of two-norm square\n+\n+    x = example_element(space)\n+    x_global_min = space.zero()\n+\n+    forward_backward_pd(x, prox_f, prox_cc_g, lin_ops, grad_h, tau=0.5,\n+                        sigma=[1.0], niter=10)\n+\n+    assert all_almost_equal(x, x_global_min, places=HIGH_ACCURACY)\n+\n+\n+def test_forward_backward_with_lin_ops():\n+    \"\"\"Test for the forward-backward solver with linear operatros.\n+\n+    The test is done by minimizing ||x - b||_2^2 + ||alpha * x||_2^2. The\n+    general problem is of the form\n+\n+        ``min_x f(x) + sum_i g_i(L_i x) + h(x)``\n+\n+    and here we take f = 0, g = ||.||_2^2, L = alpha * IndentityOperator,\n+    and h = ||. - b||_2^2.\n+    \"\"\"\n+\n+    space = odl.rn(10)\n+    scaling = 0.1\n+    b = example_element(space)\n+\n+    lin_op = scaling * odl.IdentityOperator(space)\n+    lin_ops = [lin_op]\n+    prox_cc_g = [odl.solvers.proximal_cconj_l2_squared(space)]\n+    prox_f = odl.solvers.proximal_zero(space)\n+    # Gradient of two-norm square\n+    grad_h = 2.0 * (odl.IdentityOperator(space) - odl.ConstantOperator(b))\n+\n+    x = example_element(space)\n+\n+    # Explicit solution: x_hat = (I^T * I + (alpha*I)^T * (alpha*I))^-1 * (I*b)\n+    op = odl.IdentityOperator(space) + lin_op.adjoint * lin_op\n+    x_global_min = space.zero()\n+    odl.solvers.conjugate_gradient(op, x_global_min, b, niter=10)\n+\n+    forward_backward_pd(x, prox_f, prox_cc_g, lin_ops, grad_h, tau=0.5,\n+                        sigma=[1.0], niter=20)\n+\n+    assert all_almost_equal(x, x_global_min, places=LOW_ACCURACY)\n+\n+\n+def test_forward_backward_with_li():\n+    \"\"\"Test for the forward-backward solver with infimal convolution.\n+\n+    The test is done by minimizing the functional ``(g @ l)(x)``, where\n+\n+        ``(g @ l)(x) = inf_y { g(y) + l(x-y) }``,\n+\n+    g is the indicator function on [-3, -1], and l(x) = 1/2||x||_2^2.\n+    The optimal solution to this problem is given by x in [-3, -1].\n+    \"\"\"\n+    # Parameter values for the box constraint\n+    upper_lim = -1\n+    lower_lim = -3\n+\n+    space = odl.rn(1)\n+\n+    lin_op = odl.IdentityOperator(space)\n+    lin_ops = [lin_op]\n+    prox_cc_g = [odl.solvers.proximal_cconj(\n+                 odl.solvers.proximal_box_constraint(space,\n+                                                     lower=lower_lim,\n+                                                     upper=upper_lim))]\n+    prox_f = odl.solvers.proximal_zero(space)\n+    grad_h = odl.ZeroOperator(space)\n+\n+    grad_cc_ls = [odl.IdentityOperator(space)]\n+\n+    # Centering around a point further away from [-3,-1].\n+    x = example_element(space) + space.element(3)\n+    print(x)\n+\n+    forward_backward_pd(x, prox_f, prox_cc_g, lin_ops, grad_h, tau=0.5,\n+                        sigma=[1.0], niter=20, grad_cc_l=grad_cc_ls)\n+\n+    solution_interv = odl.Interval(lower_lim - LOW_ACCURACY,\n+                                   upper_lim + LOW_ACCURACY)\n+    print(x)\n+\n+    assert x in solution_interv\n+\n+\n+def test_forward_backward_with_li_and_h():\n+    \"\"\"Test for the forward-backward solver with infimal convolution.\n+\n+    The test is done by minimizing the functional ``(g @ l)(x) + h(x)``, where\n+\n+        ``(g @ l)(x) = inf_y { g(y) + l(x-y) }``,\n+\n+    g is the indicator function on [-3, -1], and l(x) = h(x) = 1/2||x||_2^2.\n+    The optimal solution to this problem is given by x = 0.5.\n+    \"\"\"\n+\n+    # Parameter values for the box constraint\n+    upper_lim = -1\n+    lower_lim = -3\n+\n+    space = odl.rn(1)\n+\n+    lin_op = odl.IdentityOperator(space)\n+    lin_ops = [lin_op]\n+    prox_cc_g = [odl.solvers.proximal_cconj(\n+                 odl.solvers.proximal_box_constraint(space,\n+                                                     lower=lower_lim,\n+                                                     upper=upper_lim))]\n+    prox_f = odl.solvers.proximal_zero(space)\n+    grad_h = odl.IdentityOperator(space)\n+\n+    grad_cc_ls = [odl.IdentityOperator(space)]\n+\n+    # Centering the initial guess around the optimal solution, to reduce the\n+    # number of iterations needed.\n+    x = example_element(space)","path":"test/solvers/advanced/forward_backward_test.py","position":217,"original_position":217,"commit_id":"6d994764ffa31388bab3d42332e21132432059db","original_commit_id":"6d994764ffa31388bab3d42332e21132432059db","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":"x = 10 is fine","created_at":"2016-07-08T07:47:04Z","updated_at":"2016-07-08T07:47:04Z","html_url":"https://github.com/odlgroup/odl/pull/480#discussion_r70037237","pull_request_url":"https://api.github.com/repos/odlgroup/odl/pulls/480","_links":{"self":{"href":"https://api.github.com/repos/odlgroup/odl/pulls/comments/70037237"},"html":{"href":"https://github.com/odlgroup/odl/pull/480#discussion_r70037237"},"pull_request":{"href":"https://api.github.com/repos/odlgroup/odl/pulls/480"}}},"pull_request":{"url":"https://api.github.com/repos/odlgroup/odl/pulls/480","id":76295704,"html_url":"https://github.com/odlgroup/odl/pull/480","diff_url":"https://github.com/odlgroup/odl/pull/480.diff","patch_url":"https://github.com/odlgroup/odl/pull/480.patch","issue_url":"https://api.github.com/repos/odlgroup/odl/issues/480","number":480,"state":"open","locked":false,"title":"Forward backward primal dual","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":"Adds the forward-backward primal-dual solver. Reference article is found [here](http://www.mat.univie.ac.at/~rabot/publications/jour15-01.pdf) (algorithm is found in Theorem 2).","created_at":"2016-07-05T15:37:53Z","updated_at":"2016-07-08T07:47:04Z","closed_at":null,"merged_at":null,"merge_commit_sha":"0ab73e918f0ad5526b7862a0e6b7efbcf1f6a432","assignee":null,"assignees":[],"milestone":null,"commits_url":"https://api.github.com/repos/odlgroup/odl/pulls/480/commits","review_comments_url":"https://api.github.com/repos/odlgroup/odl/pulls/480/comments","review_comment_url":"https://api.github.com/repos/odlgroup/odl/pulls/comments{/number}","comments_url":"https://api.github.com/repos/odlgroup/odl/issues/480/comments","statuses_url":"https://api.github.com/repos/odlgroup/odl/statuses/6d994764ffa31388bab3d42332e21132432059db","head":{"label":"odlgroup:forward_backward_primal_dual","ref":"forward_backward_primal_dual","sha":"6d994764ffa31388bab3d42332e21132432059db","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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