{"id":364,"date":"2013-12-01T19:48:00","date_gmt":"2013-12-01T19:48:00","guid":{"rendered":"http:\/\/ahay.org\/blog\/?p=364"},"modified":"2015-08-30T15:17:46","modified_gmt":"2015-08-30T15:17:46","slug":"program-of-the-month-sfcausint","status":"publish","type":"post","link":"https:\/\/ahay.org\/blog\/2013\/12\/01\/program-of-the-month-sfcausint\/","title":{"rendered":"Program of the month: sfcausint"},"content":{"rendered":"<p><a href=\"\/RSF\/sfcausint.html\">sfcausint<\/a> implements an operation of causal numerical integration. This is a simple operation, which mathematically amounts to recursion<br \/>\n$$y<em>n = y<\/em>{n-1} + x_n$$<br \/>\nor to inversion of a simple bidiagonal matrix. See <a href=\"\/RSF\/book\/gee\/ajt\/paper_html\/node12.html\">Geophysical Image Estimation by Example<\/a> for more explanation. <\/p>\n<p>The only parameter in <strong>sfcausint<\/strong> is <strong>adj=<\/strong>, the flag for adjoint computation. The adjoint operation applies recursion backwards<br \/>\n$$x<em>{n-1} = x<\/em>n + y_{n-1}$$<\/p>\n<p>The following example from <a href=\"\/RSF\/book\/gee\/ajt\/causint.html\">gee\/ajt\/causint<\/a> illustrates forward and ajoint causal integration with <strong>sfcausint<\/strong>: <\/p>\n<p><img decoding=\"async\" src=\"\/RSF\/book\/gee\/ajt\/causint\/Fig\/causint.png\" alt=\"\" title=\"\" \/><\/p>\n<h3 id=\"10previousprogramsofthemonth\">10 previous programs of the month<\/h3>\n<ul>\n<li><a href=\"\/blog\/2013\/11\/03\/program-of-the-month-sfremap1\/\">sfremap1<\/a><\/li>\n<li><a href=\"\/blog\/2013\/10\/03\/program-of-the-month-sfunif2\/\">sfunif2<\/a><\/li>\n<li><a href=\"\/blog\/2013\/09\/14\/program-of-the-month-sfpatch\/\">sfpatch<\/a><\/li>\n<li><a href=\"\/blog\/2013\/08\/02\/program-of-the-month-sfai2refl\/\">sfai2refl<\/a><\/li>\n<li><a href=\"\/blog\/2013\/07\/01\/program-of-the-month-sftime2depth\/\">sftime2depth<\/a><\/li>\n<li><a href=\"\/blog\/2013\/06\/12\/program-of-the-month-sfwiggle\/\">sfwiggle<\/a><\/li>\n<li><a href=\"\/blog\/2013\/05\/04\/program-of-the-month-sfvscan\/\">sfvscan<\/a><\/li>\n<li><a href=\"\/blog\/2013\/04\/08\/program-of-the-month-sfnmo\/\">sfnmo<\/a><\/li>\n<li><a href=\"\/blog\/2013\/03\/10\/program-of-the-month-sfpow\/\">sfpow<\/a><\/li>\n<li><a href=\"\/blog\/2013\/02\/09\/program-of-the-month-sfpwd\/\">sfpwd<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>sfcausint implements an operation of causal numerical integration. This is a simple operation, which mathematically amounts to recursion $$yn = y{n-1} + x_n$$ or to inversion of a simple bidiagonal matrix. See Geophysical Image Estimation by Example for more explanation. The only parameter in sfcausint is adj=, the flag for adjoint computation. The adjoint operation [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","activitypub_content_warning":"","activitypub_content_visibility":"local","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-364","post","type-post","status-publish","format-standard","hentry","category-programs"],"_links":{"self":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/364","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/comments?post=364"}],"version-history":[{"count":3,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/364\/revisions"}],"predecessor-version":[{"id":15268,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/364\/revisions\/15268"}],"wp:attachment":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/media?parent=364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/categories?post=364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/tags?post=364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}