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| 2 | 1 | equemene | <HEAD>
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| 3 | 1 | equemene | <TITLE>HPL_pdpanrlN HPL 2.0 Library Functions September 10, 2008</TITLE> |
| 4 | 1 | equemene | </HEAD>
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| 5 | 1 | equemene | |
| 6 | 1 | equemene | <BODY BGCOLOR="WHITE" TEXT = "#000000" LINK = "#0000ff" VLINK = "#000099" |
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| 8 | 1 | equemene | |
| 9 | 1 | equemene | <H1>Name</H1> |
| 10 | 1 | equemene | <B>HPL_pdpanrlN</B> Right-looking 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_pdpanrlN(</CODE> |
| 16 | 1 | equemene | <CODE>HPL_T_panel *</CODE> |
| 17 | 1 | equemene | <CODE>PANEL</CODE>, |
| 18 | 1 | equemene | <CODE>const int</CODE> |
| 19 | 1 | equemene | <CODE>M</CODE>, |
| 20 | 1 | equemene | <CODE>const int</CODE> |
| 21 | 1 | equemene | <CODE>N</CODE>, |
| 22 | 1 | equemene | <CODE>const int</CODE> |
| 23 | 1 | equemene | <CODE>ICOFF</CODE>, |
| 24 | 1 | equemene | <CODE>double *</CODE> |
| 25 | 1 | equemene | <CODE>WORK</CODE> |
| 26 | 1 | equemene | <CODE>);</CODE> |
| 27 | 1 | equemene | |
| 28 | 1 | equemene | <H1>Description</H1> |
| 29 | 1 | equemene | <B>HPL_pdpanrlN</B> |
| 30 | 1 | equemene | factorizes a panel of columns that is a sub-array of a |
| 31 | 1 | equemene | larger one-dimensional panel A using the Right-looking variant of the |
| 32 | 1 | equemene | usual one-dimensional algorithm. The lower triangular N0-by-N0 upper |
| 33 | 1 | equemene | block of the panel is stored in no-transpose form (i.e. just like the |
| 34 | 1 | equemene | input matrix itself). |
| 35 | 1 | equemene | |
| 36 | 1 | equemene | Bi-directional exchange is used to perform the swap::broadcast |
| 37 | 1 | equemene | operations at once for one column in the panel. This results in a |
| 38 | 1 | equemene | lower number of slightly larger messages than usual. On P processes |
| 39 | 1 | equemene | and assuming bi-directional links, the running time of this function |
| 40 | 1 | equemene | can be approximated by (when N is equal to N0): |
| 41 | 1 | equemene | |
| 42 | 1 | equemene | N0 * log_2( P ) * ( lat + ( 2*N0 + 4 ) / bdwth ) + |
| 43 | 1 | equemene | N0^2 * ( M - N0/3 ) * gam2-3 |
| 44 | 1 | equemene | |
| 45 | 1 | equemene | where M is the local number of rows of the panel, lat and bdwth are |
| 46 | 1 | equemene | the latency and bandwidth of the network for double precision real |
| 47 | 1 | equemene | words, and gam2-3 is an estimate of the Level 2 and Level 3 BLAS |
| 48 | 1 | equemene | rate of execution. The recursive algorithm allows indeed to almost |
| 49 | 1 | equemene | achieve Level 3 BLAS performance in the panel factorization. On a |
| 50 | 1 | equemene | large number of modern machines, this operation is however latency |
| 51 | 1 | equemene | bound, meaning that its cost can be estimated by only the latency |
| 52 | 1 | equemene | portion N0 * log_2(P) * lat. Mono-directional links will double this |
| 53 | 1 | equemene | communication cost. |
| 54 | 1 | equemene | |
| 55 | 1 | equemene | Note that one iteration of the the main loop is unrolled. The local |
| 56 | 1 | equemene | computation of the absolute value max of the next column is performed |
| 57 | 1 | equemene | just after its update by the current column. This allows to bring the |
| 58 | 1 | equemene | current column only once through cache at each step. The current |
| 59 | 1 | equemene | implementation does not perform any blocking for this sequence of |
| 60 | 1 | equemene | BLAS operations, however the design allows for plugging in an optimal |
| 61 | 1 | equemene | (machine-specific) specialized BLAS-like kernel. This idea has been |
| 62 | 1 | equemene | suggested to us by Fred Gustavson, IBM T.J. Watson Research Center. |
| 63 | 1 | equemene | |
| 64 | 1 | equemene | <H1>Arguments</H1> |
| 65 | 1 | equemene | <PRE>
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| 66 | 1 | equemene | PANEL (local input/output) HPL_T_panel * |
| 67 | 1 | equemene | On entry, PANEL points to the data structure containing the |
| 68 | 1 | equemene | panel information. |
| 69 | 1 | equemene | </PRE>
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| 70 | 1 | equemene | <PRE>
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| 71 | 1 | equemene | M (local input) const int |
| 72 | 1 | equemene | On entry, M specifies the local number of rows of sub(A). |
| 73 | 1 | equemene | </PRE>
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| 74 | 1 | equemene | <PRE>
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| 75 | 1 | equemene | N (local input) const int |
| 76 | 1 | equemene | On entry, N specifies the local number of columns of sub(A). |
| 77 | 1 | equemene | </PRE>
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| 78 | 1 | equemene | <PRE>
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| 79 | 1 | equemene | ICOFF (global input) const int |
| 80 | 1 | equemene | On entry, ICOFF specifies the row and column offset of sub(A) |
| 81 | 1 | equemene | in A. |
| 82 | 1 | equemene | </PRE>
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| 83 | 1 | equemene | <PRE>
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| 84 | 1 | equemene | WORK (local workspace) double * |
| 85 | 1 | equemene | On entry, WORK is a workarray of size at least 2*(4+2*N0). |
| 86 | 1 | equemene | </PRE>
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| 87 | 1 | equemene | |
| 88 | 1 | equemene | <H1>See Also</H1> |
| 89 | 1 | equemene | <A HREF="HPL_dlocmax.html">HPL_dlocmax</A>, |
| 90 | 1 | equemene | <A HREF="HPL_dlocswpN.html">HPL_dlocswpN</A>, |
| 91 | 1 | equemene | <A HREF="HPL_dlocswpT.html">HPL_dlocswpT</A>, |
| 92 | 1 | equemene | <A HREF="HPL_pdmxswp.html">HPL_pdmxswp</A>, |
| 93 | 1 | equemene | <A HREF="HPL_pdpancrN.html">HPL_pdpancrN</A>, |
| 94 | 1 | equemene | <A HREF="HPL_pdpancrT.html">HPL_pdpancrT</A>, |
| 95 | 1 | equemene | <A HREF="HPL_pdpanllN.html">HPL_pdpanllN</A>, |
| 96 | 1 | equemene | <A HREF="HPL_pdpanllT.html">HPL_pdpanllT</A>, |
| 97 | 1 | equemene | <A HREF="HPL_pdpanrlT.html">HPL_pdpanrlT</A>. |
| 98 | 1 | equemene | |
| 99 | 1 | equemene | </BODY>
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| 100 | 1 | equemene | </HTML> |