{"action":"created","issue":{"url":"https://api.github.com/repos/stan-dev/stan/issues/680","labels_url":"https://api.github.com/repos/stan-dev/stan/issues/680/labels{/name}","comments_url":"https://api.github.com/repos/stan-dev/stan/issues/680/comments","events_url":"https://api.github.com/repos/stan-dev/stan/issues/680/events","html_url":"https://github.com/stan-dev/stan/issues/680","id":35236957,"number":680,"title":"Matrix exponential","user":{"login":"chjackson","id":7807096,"avatar_url":"https://avatars.githubusercontent.com/u/7807096?v=3","gravatar_id":"","url":"https://api.github.com/users/chjackson","html_url":"https://github.com/chjackson","followers_url":"https://api.github.com/users/chjackson/followers","following_url":"https://api.github.com/users/chjackson/following{/other_user}","gists_url":"https://api.github.com/users/chjackson/gists{/gist_id}","starred_url":"https://api.github.com/users/chjackson/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chjackson/subscriptions","organizations_url":"https://api.github.com/users/chjackson/orgs","repos_url":"https://api.github.com/users/chjackson/repos","events_url":"https://api.github.com/users/chjackson/events{/privacy}","received_events_url":"https://api.github.com/users/chjackson/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/stan-dev/stan/labels/Feature","name":"Feature","color":"84b6eb"},{"url":"https://api.github.com/repos/stan-dev/stan/labels/new%20function","name":"new function","color":"bfe5bf"}],"state":"open","locked":false,"assignee":null,"milestone":{"url":"https://api.github.com/repos/stan-dev/stan/milestones/2","html_url":"https://github.com/stan-dev/stan/milestones/Future","labels_url":"https://api.github.com/repos/stan-dev/stan/milestones/2/labels","id":341383,"number":2,"title":"Future","description":"For tasks and features not scheduled for the next release.","creator":{"login":"bob-carpenter","id":3383807,"avatar_url":"https://avatars.githubusercontent.com/u/3383807?v=3","gravatar_id":"","url":"https://api.github.com/users/bob-carpenter","html_url":"https://github.com/bob-carpenter","followers_url":"https://api.github.com/users/bob-carpenter/followers","following_url":"https://api.github.com/users/bob-carpenter/following{/other_user}","gists_url":"https://api.github.com/users/bob-carpenter/gists{/gist_id}","starred_url":"https://api.github.com/users/bob-carpenter/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/bob-carpenter/subscriptions","organizations_url":"https://api.github.com/users/bob-carpenter/orgs","repos_url":"https://api.github.com/users/bob-carpenter/repos","events_url":"https://api.github.com/users/bob-carpenter/events{/privacy}","received_events_url":"https://api.github.com/users/bob-carpenter/received_events","type":"User","site_admin":false},"open_issues":164,"closed_issues":2,"state":"open","created_at":"2013-05-24T19:02:14Z","updated_at":"2015-05-26T20:01:35Z","due_on":null,"closed_at":null},"comments":6,"created_at":"2014-06-08T13:47:22Z","updated_at":"2015-05-27T11:16:24Z","closed_at":null,"body":"Feature request for a matrix exponential function, as raised recently on the stan-users list."},"comment":{"url":"https://api.github.com/repos/stan-dev/stan/issues/comments/105874066","html_url":"https://github.com/stan-dev/stan/issues/680#issuecomment-105874066","issue_url":"https://api.github.com/repos/stan-dev/stan/issues/680","id":105874066,"user":{"login":"wds15","id":12070126,"avatar_url":"https://avatars.githubusercontent.com/u/12070126?v=3","gravatar_id":"","url":"https://api.github.com/users/wds15","html_url":"https://github.com/wds15","followers_url":"https://api.github.com/users/wds15/followers","following_url":"https://api.github.com/users/wds15/following{/other_user}","gists_url":"https://api.github.com/users/wds15/gists{/gist_id}","starred_url":"https://api.github.com/users/wds15/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/wds15/subscriptions","organizations_url":"https://api.github.com/users/wds15/orgs","repos_url":"https://api.github.com/users/wds15/repos","events_url":"https://api.github.com/users/wds15/events{/privacy}","received_events_url":"https://api.github.com/users/wds15/received_events","type":"User","site_admin":false},"created_at":"2015-05-27T11:16:24Z","updated_at":"2015-05-27T11:16:24Z","body":"The matrix exponential would be extremely relevant for analytic solvable ODE systems when the solution is then exp(A*t). Here A is the coefficient matrix of the ODE system at hand. The catch is that the matrix must be evaluated repeatedly. The ODE systems which matter for PK systems fall into the class of \"almost non-negative\", i.e. only the diagonal entries are negative and all others are positive. These matrices apparently have some nice properties with respect to the solution of exp(At) which are documented here:\r\n\r\nhttp://www.mscf.uky.edu/~qye/reports/expENM.pdf\r\n\r\nI hope this helps for an implementation in Stan."}}