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| 2 | 1 | equemene | <HEAD>
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| 3 | 1 | equemene | <TITLE>HPL_pdfact HPL 2.0 Library Functions September 10, 2008</TITLE> |
| 4 | 1 | equemene | </HEAD>
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| 5 | 1 | equemene | |
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| 8 | 1 | equemene | |
| 9 | 1 | equemene | <H1>Name</H1> |
| 10 | 1 | equemene | <B>HPL_pdfact</B> recursive panel factorization. |
| 11 | 1 | equemene | |
| 12 | 1 | equemene | <H1>Synopsis</H1> |
| 13 | 1 | equemene | <CODE>#include "hpl.h"</CODE><BR><BR> |
| 14 | 1 | equemene | <CODE>void</CODE> |
| 15 | 1 | equemene | <CODE>HPL_pdfact(</CODE> |
| 16 | 1 | equemene | <CODE>HPL_T_panel *</CODE> |
| 17 | 1 | equemene | <CODE>PANEL</CODE> |
| 18 | 1 | equemene | <CODE>);</CODE> |
| 19 | 1 | equemene | |
| 20 | 1 | equemene | <H1>Description</H1> |
| 21 | 1 | equemene | <B>HPL_pdfact</B> |
| 22 | 1 | equemene | recursively factorizes a 1-dimensional panel of columns. |
| 23 | 1 | equemene | The RPFACT function pointer specifies the recursive algorithm to be |
| 24 | 1 | equemene | used, either Crout, Left- or Right looking. NBMIN allows to vary the |
| 25 | 1 | equemene | recursive stopping criterium in terms of the number of columns in the |
| 26 | 1 | equemene | panel, and NDIV allow to specify the number of subpanels each panel |
| 27 | 1 | equemene | should be divided into. Usuallly a value of 2 will be chosen. Finally |
| 28 | 1 | equemene | PFACT is a function pointer specifying the non-recursive algorithm to |
| 29 | 1 | equemene | to be used on at most NBMIN columns. One can also choose here between |
| 30 | 1 | equemene | Crout, Left- or Right looking. Empirical tests seem to indicate that |
| 31 | 1 | equemene | values of 4 or 8 for NBMIN give the best results. |
| 32 | 1 | equemene | |
| 33 | 1 | equemene | Bi-directional exchange is used to perform the swap::broadcast |
| 34 | 1 | equemene | operations at once for one column in the panel. This results in a |
| 35 | 1 | equemene | lower number of slightly larger messages than usual. On P processes |
| 36 | 1 | equemene | and assuming bi-directional links, the running time of this function |
| 37 | 1 | equemene | can be approximated by (when N is equal to N0): |
| 38 | 1 | equemene | |
| 39 | 1 | equemene | N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) + |
| 40 | 1 | equemene | N0^2 * ( M - N0/3 ) * gam2-3 |
| 41 | 1 | equemene | |
| 42 | 1 | equemene | where M is the local number of rows of the panel, lat and bdwth are |
| 43 | 1 | equemene | the latency and bandwidth of the network for double precision real |
| 44 | 1 | equemene | words, and gam2-3 is an estimate of the Level 2 and Level 3 BLAS |
| 45 | 1 | equemene | rate of execution. The recursive algorithm allows indeed to almost |
| 46 | 1 | equemene | achieve Level 3 BLAS performance in the panel factorization. On a |
| 47 | 1 | equemene | large number of modern machines, this operation is however latency |
| 48 | 1 | equemene | bound, meaning that its cost can be estimated by only the latency |
| 49 | 1 | equemene | portion N0 * log_2(P) * lat. Mono-directional links will double this |
| 50 | 1 | equemene | communication cost. |
| 51 | 1 | equemene | |
| 52 | 1 | equemene | <H1>Arguments</H1> |
| 53 | 1 | equemene | <PRE>
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| 54 | 1 | equemene | PANEL (local input/output) HPL_T_panel * |
| 55 | 1 | equemene | On entry, PANEL points to the data structure containing the |
| 56 | 1 | equemene | panel information. |
| 57 | 1 | equemene | </PRE>
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| 58 | 1 | equemene | |
| 59 | 1 | equemene | <H1>See Also</H1> |
| 60 | 1 | equemene | <A HREF="HPL_dlocmax.html">HPL_dlocmax</A>, |
| 61 | 1 | equemene | <A HREF="HPL_dlocswpN.html">HPL_dlocswpN</A>, |
| 62 | 1 | equemene | <A HREF="HPL_dlocswpT.html">HPL_dlocswpT</A>, |
| 63 | 1 | equemene | <A HREF="HPL_pdmxswp.html">HPL_pdmxswp</A>, |
| 64 | 1 | equemene | <A HREF="HPL_pdpancrN.html">HPL_pdpancrN</A>, |
| 65 | 1 | equemene | <A HREF="HPL_pdpancrT.html">HPL_pdpancrT</A>, |
| 66 | 1 | equemene | <A HREF="HPL_pdpanllN.html">HPL_pdpanllN</A>, |
| 67 | 1 | equemene | <A HREF="HPL_pdpanllT.html">HPL_pdpanllT</A>, |
| 68 | 1 | equemene | <A HREF="HPL_pdpanrlN.html">HPL_pdpanrlN</A>, |
| 69 | 1 | equemene | <A HREF="HPL_pdpanrlT.html">HPL_pdpanrlT</A>, |
| 70 | 1 | equemene | <A HREF="HPL_pdrpancrN.html">HPL_pdrpancrN</A>, |
| 71 | 1 | equemene | <A HREF="HPL_pdrpancrT.html">HPL_pdrpancrT</A>, |
| 72 | 1 | equemene | <A HREF="HPL_pdrpanllN.html">HPL_pdrpanllN</A>, |
| 73 | 1 | equemene | <A HREF="HPL_pdrpanllT.html">HPL_pdrpanllT</A>, |
| 74 | 1 | equemene | <A HREF="HPL_pdrpanrlN.html">HPL_pdrpanrlN</A>, |
| 75 | 1 | equemene | <A HREF="HPL_pdrpanrlT.html">HPL_pdrpanrlT</A>. |
| 76 | 1 | equemene | |
| 77 | 1 | equemene | </BODY>
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| 78 | 1 | equemene | </HTML> |