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<TITLE>HPL_pdpancrN HPL 2.0 Library Functions September 10, 2008</TITLE> |
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<H1>Name</H1> |
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<B>HPL_pdpancrN</B> Crout 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_pdpancrN(</CODE> |
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<CODE>HPL_T_panel *</CODE> |
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<CODE>PANEL</CODE>, |
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<CODE>const int</CODE> |
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<CODE>M</CODE>, |
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<CODE>const int</CODE> |
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<CODE>N</CODE>, |
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<CODE>const int</CODE> |
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<CODE>ICOFF</CODE>, |
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<CODE>double *</CODE> |
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<CODE>WORK</CODE> |
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<CODE>);</CODE> |
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<H1>Description</H1> |
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<B>HPL_pdpancrN</B> |
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factorizes a panel of columns that is a sub-array of a |
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larger one-dimensional panel A using the Crout variant of the usual |
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one-dimensional algorithm. The lower triangular N0-by-N0 upper block |
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of the panel is stored in no-transpose form (i.e. just like the input |
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matrix itself). |
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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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Note that one iteration of the the main loop is unrolled. The local |
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computation of the absolute value max of the next column is performed |
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just after its update by the current column. This allows to bring the |
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current column only once through cache at each step. The current |
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implementation does not perform any blocking for this sequence of |
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BLAS operations, however the design allows for plugging in an optimal |
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(machine-specific) specialized BLAS-like kernel. This idea has been |
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suggested to us by Fred Gustavson, IBM T.J. Watson Research Center. |
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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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<PRE>
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M (local input) const int |
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On entry, M specifies the local number of rows of sub(A). |
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</PRE>
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<PRE>
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N (local input) const int |
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On entry, N specifies the local number of columns of sub(A). |
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</PRE>
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<PRE>
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ICOFF (global input) const int |
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On entry, ICOFF specifies the row and column offset of sub(A) |
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in A. |
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</PRE>
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<PRE>
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WORK (local workspace) double * |
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On entry, WORK is a workarray of size at least 2*(4+2*N0). |
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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_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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