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<TITLE>HPL_pdfact HPL 2.0 Library Functions September 10, 2008</TITLE> |
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<BODY BGCOLOR="WHITE" TEXT = "#000000" LINK = "#0000ff" VLINK = "#000099" |
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ALINK = "#ffff00"> |
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<H1>Name</H1> |
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<B>HPL_pdfact</B> recursive panel factorization. |
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<H1>Synopsis</H1> |
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<CODE>#include "hpl.h"</CODE><BR><BR> |
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<CODE>void</CODE> |
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<CODE>HPL_pdfact(</CODE> |
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<CODE>HPL_T_panel *</CODE> |
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<CODE>PANEL</CODE> |
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<CODE>);</CODE> |
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<H1>Description</H1> |
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<B>HPL_pdfact</B> |
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recursively factorizes a 1-dimensional panel of columns. |
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The RPFACT function pointer specifies the recursive algorithm to be |
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used, either Crout, Left- or Right looking. NBMIN allows to vary the |
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recursive stopping criterium in terms of the number of columns in the |
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panel, and NDIV allow to specify the number of subpanels each panel |
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should be divided into. Usuallly a value of 2 will be chosen. Finally |
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PFACT is a function pointer specifying the non-recursive algorithm to |
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to be used on at most NBMIN columns. One can also choose here between |
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Crout, Left- or Right looking. Empirical tests seem to indicate that |
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values of 4 or 8 for NBMIN give the best results. |
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Bi-directional exchange is used to perform the swap::broadcast |
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operations at once for one column in the panel. This results in a |
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lower number of slightly larger messages than usual. On P processes |
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and assuming bi-directional links, the running time of this function |
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can be approximated by (when N is equal to N0): |
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N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) + |
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N0^2 * ( M - N0/3 ) * gam2-3 |
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where M is the local number of rows of the panel, lat and bdwth are |
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the latency and bandwidth of the network for double precision real |
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words, and gam2-3 is an estimate of the Level 2 and Level 3 BLAS |
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rate of execution. The recursive algorithm allows indeed to almost |
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achieve Level 3 BLAS performance in the panel factorization. On a |
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large number of modern machines, this operation is however latency |
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bound, meaning that its cost can be estimated by only the latency |
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portion N0 * log_2(P) * lat. Mono-directional links will double this |
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communication cost. |
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<H1>Arguments</H1> |
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<PRE>
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PANEL (local input/output) HPL_T_panel * |
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On entry, PANEL points to the data structure containing the |
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panel information. |
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</PRE>
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<H1>See Also</H1> |
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<A HREF="HPL_dlocmax.html">HPL_dlocmax</A>, |
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<A HREF="HPL_dlocswpN.html">HPL_dlocswpN</A>, |
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<A HREF="HPL_dlocswpT.html">HPL_dlocswpT</A>, |
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<A HREF="HPL_pdmxswp.html">HPL_pdmxswp</A>, |
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<A HREF="HPL_pdpancrN.html">HPL_pdpancrN</A>, |
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<A HREF="HPL_pdpancrT.html">HPL_pdpancrT</A>, |
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<A HREF="HPL_pdpanllN.html">HPL_pdpanllN</A>, |
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<A HREF="HPL_pdpanllT.html">HPL_pdpanllT</A>, |
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<A HREF="HPL_pdpanrlN.html">HPL_pdpanrlN</A>, |
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<A HREF="HPL_pdpanrlT.html">HPL_pdpanrlT</A>, |
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<A HREF="HPL_pdrpancrN.html">HPL_pdrpancrN</A>, |
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<A HREF="HPL_pdrpancrT.html">HPL_pdrpancrT</A>, |
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<A HREF="HPL_pdrpanllN.html">HPL_pdrpanllN</A>, |
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<A HREF="HPL_pdrpanllT.html">HPL_pdrpanllT</A>, |
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<A HREF="HPL_pdrpanrlN.html">HPL_pdrpanrlN</A>, |
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<A HREF="HPL_pdrpanrlT.html">HPL_pdrpanrlT</A>. |
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