https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Is-it-possible-to-update-Schur-complement-quickly-with-MKL/m-p/1026044#M19890 <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">I have a matrix</P> <PRE class="lang-cpp prettyprint prettyprinted" style="margin-top: 0px; margin-bottom: 10px; padding: 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; overflow: auto; width: auto; max-height: 600px; word-wrap: normal; color: rgb(0, 0, 0); line-height: 17.804800033569336px; background: rgb(238, 238, 238);"><CODE style="margin: 0px; padding: 0px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: inherit; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">A </SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">=</SPAN><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;"> </SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">[</SPAN><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">A11 A12</SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">;</SPAN><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">A21 A22</SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">];</SPAN></CODE></PRE> <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">and I'd like to compute the Schur complement of A11 in A using pardiso:&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">S = A22 - A21 * A11^-1 * A12</CODE>. This seems well supported by the PARDISO-SCHUR routine&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">IPARM(38)</CODE>.</P> <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">However, I'm wondering if I can do some prefactorization on&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">A11</CODE>&nbsp;so that if I change only&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">A12,A21,A22</CODE>&nbsp;then I could compute&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">S</CODE>&nbsp;quickly (quicker than just recomputing everything).</P> <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">Is there an interface to alter part of&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">A</CODE>?</P> Wed, 28 May 2014 21:25:19 GMT Alec_J_ 2014-05-28T21:25:19Z https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Is-it-possible-to-update-Schur-complement-quickly-with-MKL/m-p/1026044#M19890 <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">I have a matrix</P> <PRE class="lang-cpp prettyprint prettyprinted" style="margin-top: 0px; margin-bottom: 10px; padding: 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; overflow: auto; width: auto; max-height: 600px; word-wrap: normal; color: rgb(0, 0, 0); line-height: 17.804800033569336px; background: rgb(238, 238, 238);"><CODE style="margin: 0px; padding: 0px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: inherit; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;"><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">A </SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">=</SPAN><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;"> </SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">[</SPAN><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">A11 A12</SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">;</SPAN><SPAN class="pln" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">A21 A22</SPAN><SPAN class="pun" style="margin: 0px; padding: 0px; border: 0px; vertical-align: baseline; background: transparent;">];</SPAN></CODE></PRE> <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">and I'd like to compute the Schur complement of A11 in A using pardiso:&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">S = A22 - A21 * A11^-1 * A12</CODE>. This seems well supported by the PARDISO-SCHUR routine&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">IPARM(38)</CODE>.</P> <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">However, I'm wondering if I can do some prefactorization on&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">A11</CODE>&nbsp;so that if I change only&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">A12,A21,A22</CODE>&nbsp;then I could compute&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">S</CODE>&nbsp;quickly (quicker than just recomputing everything).</P> <P style="margin-bottom: 1em; border: 0px; font-size: 14px; vertical-align: baseline; clear: both; color: rgb(0, 0, 0); font-family: Arial, 'Liberation Sans', 'DejaVu Sans', sans-serif; line-height: 17.804800033569336px; background-image: initial; background-attachment: initial; background-size: initial; background-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">Is there an interface to alter part of&nbsp;<CODE style="margin: 0px; padding: 1px 5px; border: 0px; font-size: 14px; vertical-align: baseline; font-family: Consolas, Menlo, Monaco, 'Lucida Console', 'Liberation Mono', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', 'Courier New', monospace, serif; white-space: pre-wrap; background: rgb(238, 238, 238);">A</CODE>?</P> Wed, 28 May 2014 21:25:19 GMT https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Is-it-possible-to-update-Schur-complement-quickly-with-MKL/m-p/1026044#M19890 Alec_J_ 2014-05-28T21:25:19Z