{"action":"created","comment":{"url":"https://api.github.com/repos/sxs-collaboration/spectre/pulls/comments/241675231","pull_request_review_id":185006798,"id":241675231,"node_id":"MDI0OlB1bGxSZXF1ZXN0UmV2aWV3Q29tbWVudDI0MTY3NTIzMQ==","diff_hunk":"@@ -196,4 +200,154 @@ Scalar<DataType> time_deriv_of_lapse(\n     const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,\n     const tnsr::iaa<DataType, SpatialDim, Frame>& phi,\n     const tnsr::aa<DataType, SpatialDim, Frame>& pi) noexcept;\n+\n+/*!\n+ * \\ingroup GeneralRelativityGroup\n+ * \\brief Computes spatial derivatives of the shift vector from\n+ *        the generalized harmonic and geometric variables\n+ *\n+ * \\details Let the generalized harmonic spatial derivative variable be\n+ * \\f$\\Phi_{iab} = \\partial_i \\psi_{ab} \\f$. The spatial derivatives of the\n+ * shift vector \\f$N^i\\f$ are:\n+ * \\f{align*}\n+ *  \\psi^{ja} N t^b \\Phi_{iab} - 2 t^j \\partial_i N\n+ *  =& (g^{ja} - t^j t^a) N t^b \\Phi_{iab} - 2 t^j \\partial_i N \\\\\n+ *  =& N g^{ja} t^b \\partial_i \\psi_{ab}\n+ * \\f}\n+ * where we used the equation from above for \\f$\\partial_i N\\f$. Then\n+ * \\f{align*}\n+ * \\psi^{ja} N t^b \\Phi_{iab} - 2 t^j \\partial_i N\n+ *  =& g^{ja} (\\partial_i \\psi_{a0} - N^k \\partial _i \\psi_{ak}) \\\\\n+ *  =& g^{jl} (\\partial_i N_l - N^k \\partial_i g_{lk}) (\\because g^{j0} = 0) \\\\\n+ *  =& g^{jl} (N^k \\partial_i g_{lk}\n+ *             + g_{kl}\\partial_i N^k - N^k \\partial_i g_{kl}) \\\\\n+ *  =& g^{jl} g_{kl} \\partial_i N^k \\\\\n+ *  =& \\partial_i N^j\n+ * \\f}\n+ * I.E.\n+ * \\f{align*}\n+ *  \\partial_i N^j =& N\\psi^{ja} t^b \\Phi_{iab} - 2 t^j \\partial_i N \\\\\n+ *                 =& N (\\psi^{ja} + t^j t^a) t^b \\Phi_{iab}.\n+ * \\f}\n+ */\n+template <size_t SpatialDim, typename Frame, typename DataType>\n+void spatial_deriv_of_shift(\n+    gsl::not_null<tnsr::iJ<DataType, SpatialDim, Frame>*> deriv_shift,\n+    const Scalar<DataType>& lapse,\n+    const tnsr::AA<DataType, SpatialDim, Frame>& inverse_spacetime_metric,\n+    const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,\n+    const tnsr::iaa<DataType, SpatialDim, Frame>& phi) noexcept;\n+\n+template <size_t SpatialDim, typename Frame, typename DataType>\n+tnsr::iJ<DataType, SpatialDim, Frame> spatial_deriv_of_shift(\n+    const Scalar<DataType>& lapse,\n+    const tnsr::AA<DataType, SpatialDim, Frame>& inverse_spacetime_metric,\n+    const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,\n+    const tnsr::iaa<DataType, SpatialDim, Frame>& phi) noexcept;\n+\n+/*!\n+ * \\ingroup GeneralRelativityGroup\n+ * \\brief Computes time derivative of the shift vector from\n+ *        the generalized harmonic and geometric variables\n+ *\n+ * \\details Let the generalized harmonic spatial derivative variable be\n+ * \\f$\\Phi_{iab} = \\partial_i \\psi_{ab} \\f$. The time derivative of \\f$ N^i \\f$\n+ * is given by:\n+ * \\f{align*}\n+ *  -N^2 t^b \\Pi_{kb} g^{ik} + N N^j t^b \\Phi_{jkb} g^{ik}\n+ *  =& N g^{ik} t^b (\\partial_0 - N^j\\partial_j) \\psi_{kb}\n+ *                  + N g^{ik} t^b N^j\\partial_j \\psi_{kb} \\\\\n+ *  =& N g^{ik} t^b \\partial_0 \\psi_{kb} \\\\\n+ *  =& g^{ik} \\partial_0 (g_{kj} N^j) - N^j g^{ik} \\partial_0 g_{kj} \\\\\n+ *  =& \\partial_0 N^i\n+ * \\f}\n+ * where the second to last to last line used the same manipulations\n+ * as at the end of the spatial derivative calculation. Therefore:\n+ * \\f{align*}\n+ * \\partial_0 N^i =& -N^2 t^b\\Pi_{kb} g^{ik} + N N^j t^b\\Phi_{jkb} g^{ik} \\\\\n+ *                =& -N g^{ik} t^b (N \\Pi_{kb} - N^j \\Phi_{jkb})\n+ * \\f}\n+ */\n+template <size_t SpatialDim, typename Frame, typename DataType>\n+void time_deriv_of_shift(\n+    gsl::not_null<tnsr::I<DataType, SpatialDim, Frame>*> dt_shift,\n+    const Scalar<DataType>& lapse,\n+    const tnsr::I<DataType, SpatialDim, Frame>& shift,\n+    const tnsr::II<DataType, SpatialDim, Frame>& inverse_spatial_metric,\n+    const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,\n+    const tnsr::iaa<DataType, SpatialDim, Frame>& phi,\n+    const tnsr::aa<DataType, SpatialDim, Frame>& pi) noexcept;\n+\n+template <size_t SpatialDim, typename Frame, typename DataType>\n+tnsr::I<DataType, SpatialDim, Frame> time_deriv_of_shift(\n+    const Scalar<DataType>& lapse,\n+    const tnsr::I<DataType, SpatialDim, Frame>& shift,\n+    const tnsr::II<DataType, SpatialDim, Frame>& inverse_spatial_metric,\n+    const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,\n+    const tnsr::iaa<DataType, SpatialDim, Frame>& phi,\n+    const tnsr::aa<DataType, SpatialDim, Frame>& pi) noexcept;\n+\n+/*!\n+ * \\ingroup GeneralRelativityGroup\n+ * \\brief Computes time derivative of index lowered shift from generalized\n+ *        harmonic variables, spatial metric and its time derivative.\n+ *\n+ * \\details The time derivative of \\f$ N_i \\f$ is given by:\n+ * \\f{align*}\n+ *  \\partial_0 N_i = g_{ij} \\partial_0 N^j + N^j \\partial_0 g_{ij}\n+ * \\f}\n+ * where the first term is obtained from `time_deriv_of_shift`, and the latter","path":"src/PointwiseFunctions/GeneralRelativity/ComputeGhQuantities.hpp","position":null,"original_position":111,"commit_id":"1d66c25c3012b516eb4867059ec2e73b63737d7d","original_commit_id":"4ac7a0ed1d8aa0af4ac5191b7baad73cc7080fdd","user":{"login":"prayush","id":7142969,"node_id":"MDQ6VXNlcjcxNDI5Njk=","avatar_url":"https://avatars0.githubusercontent.com/u/7142969?v=4","gravatar_id":"","url":"https://api.github.com/users/prayush","html_url":"https://github.com/prayush","followers_url":"https://api.github.com/users/prayush/followers","following_url":"https://api.github.com/users/prayush/following{/other_user}","gists_url":"https://api.github.com/users/prayush/gists{/gist_id}","starred_url":"https://api.github.com/users/prayush/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/prayush/subscriptions","organizations_url":"https://api.github.com/users/prayush/orgs","repos_url":"https://api.github.com/users/prayush/repos","events_url":"https://api.github.com/users/prayush/events{/privacy}","received_events_url":"https://api.github.com/users/prayush/received_events","type":"User","site_admin":false},"body":"changed","created_at":"2018-12-14T08:30:32Z","updated_at":"2018-12-14T08:30:33Z","html_url":"https://github.com/sxs-collaboration/spectre/pull/1177#discussion_r241675231","pull_request_url":"https://api.github.com/repos/sxs-collaboration/spectre/pulls/1177","author_association":"CONTRIBUTOR","_links":{"self":{"href":"https://api.github.com/repos/sxs-collaboration/spectre/pulls/comments/241675231"},"html":{"href":"https://github.com/sxs-collaboration/spectre/pull/1177#discussion_r241675231"},"pull_request":{"href":"https://api.github.com/repos/sxs-collaboration/spectre/pulls/1177"}},"in_reply_to_id":240831105},"pull_request":{"url":"https://api.github.com/repos/sxs-collaboration/spectre/pulls/1177","id":231341070,"node_id":"MDExOlB1bGxSZXF1ZXN0MjMxMzQxMDcw","html_url":"https://github.com/sxs-collaboration/spectre/pull/1177","diff_url":"https://github.com/sxs-collaboration/spectre/pull/1177.diff","patch_url":"https://github.com/sxs-collaboration/spectre/pull/1177.patch","issue_url":"https://api.github.com/repos/sxs-collaboration/spectre/issues/1177","number":1177,"state":"open","locked":false,"title":"Get derivatives of shift from GH variables","user":{"login":"prayush","id":7142969,"node_id":"MDQ6VXNlcjcxNDI5Njk=","avatar_url":"https://avatars0.githubusercontent.com/u/7142969?v=4","gravatar_id":"","url":"https://api.github.com/users/prayush","html_url":"https://github.com/prayush","followers_url":"https://api.github.com/users/prayush/followers","following_url":"https://api.github.com/users/prayush/following{/other_user}","gists_url":"https://api.github.com/users/prayush/gists{/gist_id}","starred_url":"https://api.github.com/users/prayush/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/prayush/subscriptions","organizations_url":"https://api.github.com/users/prayush/orgs","repos_url":"https://api.github.com/users/prayush/repos","events_url":"https://api.github.com/users/prayush/events{/privacy}","received_events_url":"https://api.github.com/users/prayush/received_events","type":"User","site_admin":false},"body":"## Proposed changes\r\n\r\n- Adds functions that compute derivatives of shift from generalized harmonic variables.\r\n\r\n### Types of changes:\r\n\r\n- [ ] Bugfix\r\n- [x] New feature\r\n\r\n### Component:\r\n\r\n- [ ] Code\r\n- [ ] Documentation\r\n- [ ] Build system\r\n- [ ] Continuous integration\r\n\r\n### Code review checklist\r\n\r\n- [ ] The PR passes all checks, including unit tests, `clang-tidy` and `IWYU`. For\r\n  instructions on how to perform the CI checks locally refer to the [Dev guide\r\n  on the Travis CI](https://spectre-code.org/travis_guide.html).\r\n- [ ] The code is documented and the documentation renders correctly. Run `make doc`\r\n  to generate the documentation locally into `BUILD_DIR/docs/html`. Then open\r\n  `index.html`.\r\n- [ ] The code follows the stylistic and code quality guidelines listed in the\r\n  [code review guide](https://spectre-code.org/code_review_guide.html).\r\n\r\n### Further comments\r\n\r\n<!--\r\nIf this is a relatively large or complex change, kick off the discussion by\r\nexplaining why you chose the solution you did and what alternatives you\r\nconsidered, etc...\r\n-->\r\n","created_at":"2018-11-15T21:32:10Z","updated_at":"2018-12-14T08:30:33Z","closed_at":null,"merged_at":null,"merge_commit_sha":"cdcdbd662c178b622fd3ae8a3c87792e5944a4cb","assignee":null,"assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[{"id":1143754825,"node_id":"MDU6TGFiZWwxMTQzNzU0ODI1","url":"https://api.github.com/repos/sxs-collaboration/spectre/labels/review%20help%20wanted","name":"review help 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