root / src / pgesv / HPL_pdtrsv.c @ 9
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| 1 | 1 | equemene | /*
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| 2 | 1 | equemene | * -- High Performance Computing Linpack Benchmark (HPL)
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| 3 | 1 | equemene | * HPL - 2.0 - September 10, 2008
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| 4 | 1 | equemene | * Antoine P. Petitet
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| 5 | 1 | equemene | * University of Tennessee, Knoxville
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| 6 | 1 | equemene | * Innovative Computing Laboratory
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| 7 | 1 | equemene | * (C) Copyright 2000-2008 All Rights Reserved
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| 8 | 1 | equemene | *
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| 9 | 1 | equemene | * -- Copyright notice and Licensing terms:
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| 10 | 1 | equemene | *
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| 11 | 1 | equemene | * Redistribution and use in source and binary forms, with or without
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| 12 | 1 | equemene | * modification, are permitted provided that the following conditions
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| 13 | 1 | equemene | * are met:
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| 14 | 1 | equemene | *
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| 15 | 1 | equemene | * 1. Redistributions of source code must retain the above copyright
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| 16 | 1 | equemene | * notice, this list of conditions and the following disclaimer.
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| 17 | 1 | equemene | *
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| 18 | 1 | equemene | * 2. Redistributions in binary form must reproduce the above copyright
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| 19 | 1 | equemene | * notice, this list of conditions, and the following disclaimer in the
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| 20 | 1 | equemene | * documentation and/or other materials provided with the distribution.
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| 21 | 1 | equemene | *
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| 22 | 1 | equemene | * 3. All advertising materials mentioning features or use of this
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| 23 | 1 | equemene | * software must display the following acknowledgement:
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| 24 | 1 | equemene | * This product includes software developed at the University of
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| 25 | 1 | equemene | * Tennessee, Knoxville, Innovative Computing Laboratory.
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| 26 | 1 | equemene | *
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| 27 | 1 | equemene | * 4. The name of the University, the name of the Laboratory, or the
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| 28 | 1 | equemene | * names of its contributors may not be used to endorse or promote
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| 29 | 1 | equemene | * products derived from this software without specific written
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| 30 | 1 | equemene | * permission.
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| 31 | 1 | equemene | *
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| 32 | 1 | equemene | * -- Disclaimer:
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| 33 | 1 | equemene | *
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| 34 | 1 | equemene | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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| 35 | 1 | equemene | * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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| 36 | 1 | equemene | * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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| 37 | 1 | equemene | * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE UNIVERSITY
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| 38 | 1 | equemene | * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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| 39 | 1 | equemene | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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| 40 | 1 | equemene | * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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| 41 | 1 | equemene | * DATA OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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| 42 | 1 | equemene | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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| 43 | 1 | equemene | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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| 44 | 1 | equemene | * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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| 45 | 1 | equemene | * ---------------------------------------------------------------------
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| 46 | 1 | equemene | */
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| 47 | 1 | equemene | /*
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| 48 | 1 | equemene | * Include files
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| 49 | 1 | equemene | */
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| 50 | 1 | equemene | #include "hpl.h" |
| 51 | 1 | equemene | |
| 52 | 1 | equemene | #ifdef STDC_HEADERS
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| 53 | 1 | equemene | void HPL_pdtrsv
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| 54 | 1 | equemene | ( |
| 55 | 1 | equemene | HPL_T_grid * GRID, |
| 56 | 1 | equemene | HPL_T_pmat * AMAT |
| 57 | 1 | equemene | ) |
| 58 | 1 | equemene | #else
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| 59 | 1 | equemene | void HPL_pdtrsv
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| 60 | 1 | equemene | ( GRID, AMAT ) |
| 61 | 1 | equemene | HPL_T_grid * GRID; |
| 62 | 1 | equemene | HPL_T_pmat * AMAT; |
| 63 | 1 | equemene | #endif
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| 64 | 1 | equemene | {
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| 65 | 1 | equemene | /*
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| 66 | 1 | equemene | * Purpose
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| 67 | 1 | equemene | * =======
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| 68 | 1 | equemene | *
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| 69 | 1 | equemene | * HPL_pdtrsv solves an upper triangular system of linear equations.
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| 70 | 1 | equemene | *
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| 71 | 1 | equemene | * The rhs is the last column of the N by N+1 matrix A. The solve starts
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| 72 | 1 | equemene | * in the process column owning the Nth column of A, so the rhs b may
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| 73 | 1 | equemene | * need to be moved one process column to the left at the beginning. The
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| 74 | 1 | equemene | * routine therefore needs a column vector in every process column but
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| 75 | 1 | equemene | * the one owning b. The result is replicated in all process rows, and
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| 76 | 1 | equemene | * returned in XR, i.e. XR is of size nq = LOCq( N ) in all processes.
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| 77 | 1 | equemene | *
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| 78 | 1 | equemene | * The algorithm uses decreasing one-ring broadcast in process rows and
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| 79 | 1 | equemene | * columns implemented in terms of synchronous communication point to
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| 80 | 1 | equemene | * point primitives. The lookahead of depth 1 is used to minimize the
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| 81 | 1 | equemene | * critical path. This entire operation is essentially ``latency'' bound
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| 82 | 1 | equemene | * and an estimate of its running time is given by:
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| 83 | 1 | equemene | *
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| 84 | 1 | equemene | * (move rhs) lat + N / ( P bdwth ) +
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| 85 | 1 | equemene | * (solve) ((N / NB)-1) 2 (lat + NB / bdwth) +
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| 86 | 1 | equemene | * gam2 N^2 / ( P Q ),
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| 87 | 1 | equemene | *
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| 88 | 1 | equemene | * where gam2 is an estimate of the Level 2 BLAS rate of execution.
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| 89 | 1 | equemene | * There are N / NB diagonal blocks. One must exchange 2 messages of
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| 90 | 1 | equemene | * length NB to compute the next NB entries of the vector solution, as
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| 91 | 1 | equemene | * well as performing a total of N^2 floating point operations.
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| 92 | 1 | equemene | *
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| 93 | 1 | equemene | * Arguments
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| 94 | 1 | equemene | * =========
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| 95 | 1 | equemene | *
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| 96 | 1 | equemene | * GRID (local input) HPL_T_grid *
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| 97 | 1 | equemene | * On entry, GRID points to the data structure containing the
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| 98 | 1 | equemene | * process grid information.
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| 99 | 1 | equemene | *
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| 100 | 1 | equemene | * AMAT (local input/output) HPL_T_pmat *
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| 101 | 1 | equemene | * On entry, AMAT points to the data structure containing the
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| 102 | 1 | equemene | * local array information.
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| 103 | 1 | equemene | *
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| 104 | 1 | equemene | * ---------------------------------------------------------------------
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| 105 | 1 | equemene | */
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| 106 | 1 | equemene | /*
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| 107 | 1 | equemene | * .. Local Variables ..
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| 108 | 1 | equemene | */
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| 109 | 1 | equemene | MPI_Comm Ccomm, Rcomm; |
| 110 | 1 | equemene | double * A=NULL, * Aprev=NULL, * Aptr, * XC=NULL, |
| 111 | 1 | equemene | * XR=NULL, * Xd=NULL, * Xdprev=NULL, |
| 112 | 1 | equemene | * W=NULL;
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| 113 | 1 | equemene | int Alcol, Alrow, Anpprev, Anp, Anq, Bcol,
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| 114 | 1 | equemene | Cmsgid, GridIsNotPx1, GridIsNot1xQ, Rmsgid, |
| 115 | 1 | equemene | Wfr=0, colprev, kb, kbprev, lda, mycol,
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| 116 | 1 | equemene | myrow, n, n1, n1p, n1pprev=0, nb, npcol,
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| 117 | 1 | equemene | nprow, rowprev, tmp1, tmp2; |
| 118 | 1 | equemene | /* ..
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| 119 | 1 | equemene | * .. Executable Statements ..
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| 120 | 1 | equemene | */
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| 121 | 1 | equemene | #ifdef HPL_DETAILED_TIMING
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| 122 | 1 | equemene | HPL_ptimer( HPL_TIMING_PTRSV ); |
| 123 | 1 | equemene | #endif
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| 124 | 1 | equemene | if( ( n = AMAT->n ) <= 0 ) return; |
| 125 | 1 | equemene | nb = AMAT->nb; lda = AMAT->ld; A = AMAT->A; XR = AMAT->X; |
| 126 | 1 | equemene | |
| 127 | 1 | equemene | (void) HPL_grid_info( GRID, &nprow, &npcol, &myrow, &mycol );
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| 128 | 1 | equemene | Rcomm = GRID->row_comm; Rmsgid = MSGID_BEGIN_PTRSV; |
| 129 | 1 | equemene | Ccomm = GRID->col_comm; Cmsgid = MSGID_BEGIN_PTRSV + 1;
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| 130 | 1 | equemene | GridIsNot1xQ = ( nprow > 1 ); GridIsNotPx1 = ( npcol > 1 ); |
| 131 | 1 | equemene | /*
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| 132 | 1 | equemene | * Move the rhs in the process column owning the last column of A.
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| 133 | 1 | equemene | */
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| 134 | 1 | equemene | Mnumroc( Anp, n, nb, nb, myrow, 0, nprow );
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| 135 | 1 | equemene | Mnumroc( Anq, n, nb, nb, mycol, 0, npcol );
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| 136 | 1 | equemene | |
| 137 | 1 | equemene | tmp1 = ( n - 1 ) / nb;
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| 138 | 1 | equemene | Alrow = tmp1 - ( tmp1 / nprow ) * nprow; |
| 139 | 1 | equemene | Alcol = tmp1 - ( tmp1 / npcol ) * npcol; |
| 140 | 1 | equemene | kb = n - tmp1 * nb; |
| 141 | 1 | equemene | |
| 142 | 1 | equemene | Aptr = (double *)(A); XC = Mptr( Aptr, 0, Anq, lda ); |
| 143 | 1 | equemene | Mindxg2p( n, nb, nb, Bcol, 0, npcol );
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| 144 | 1 | equemene | |
| 145 | 1 | equemene | if( ( Anp > 0 ) && ( Alcol != Bcol ) ) |
| 146 | 1 | equemene | {
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| 147 | 1 | equemene | if( mycol == Bcol )
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| 148 | 1 | equemene | { (void) HPL_send( XC, Anp, Alcol, Rmsgid, Rcomm ); }
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| 149 | 1 | equemene | else if( mycol == Alcol ) |
| 150 | 1 | equemene | { (void) HPL_recv( XC, Anp, Bcol, Rmsgid, Rcomm ); }
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| 151 | 1 | equemene | } |
| 152 | 1 | equemene | Rmsgid = ( Rmsgid + 2 >
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| 153 | 1 | equemene | MSGID_END_PTRSV ? MSGID_BEGIN_PTRSV : Rmsgid + 2 );
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| 154 | 1 | equemene | if( mycol != Alcol )
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| 155 | 1 | equemene | { for( tmp1=0; tmp1 < Anp; tmp1++ ) XC[tmp1] = HPL_rzero; }
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| 156 | 1 | equemene | /*
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| 157 | 1 | equemene | * Set up lookahead
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| 158 | 1 | equemene | */
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| 159 | 1 | equemene | n1 = ( npcol - 1 ) * nb; n1 = Mmax( n1, nb );
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| 160 | 1 | equemene | if( Anp > 0 ) |
| 161 | 1 | equemene | {
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| 162 | 1 | equemene | W = (double*)malloc( (size_t)(Mmin( n1, Anp )) * sizeof( double ) ); |
| 163 | 1 | equemene | if( W == NULL ) |
| 164 | 1 | equemene | { HPL_pabort( __LINE__, "HPL_pdtrsv", "Memory allocation failed" ); }
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| 165 | 1 | equemene | Wfr = 1;
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| 166 | 1 | equemene | } |
| 167 | 1 | equemene | |
| 168 | 1 | equemene | Anpprev = Anp; Xdprev = XR; Aprev = Aptr = Mptr( Aptr, 0, Anq, lda );
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| 169 | 1 | equemene | tmp1 = n - kb; tmp1 -= ( tmp2 = Mmin( tmp1, n1 ) ); |
| 170 | 1 | equemene | MnumrocI( n1pprev, tmp2, Mmax( 0, tmp1 ), nb, nb, myrow, 0, nprow ); |
| 171 | 1 | equemene | |
| 172 | 1 | equemene | if( myrow == Alrow ) { Anpprev = ( Anp -= kb ); }
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| 173 | 1 | equemene | if( mycol == Alcol )
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| 174 | 1 | equemene | {
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| 175 | 1 | equemene | Aprev = ( Aptr -= lda * kb ); Anq -= kb; Xdprev = ( Xd = XR + Anq ); |
| 176 | 1 | equemene | if( myrow == Alrow )
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| 177 | 1 | equemene | {
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| 178 | 1 | equemene | HPL_dtrsv( HplColumnMajor, HplUpper, HplNoTrans, HplNonUnit, |
| 179 | 1 | equemene | kb, Aptr+Anp, lda, XC+Anp, 1 );
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| 180 | 1 | equemene | HPL_dcopy( kb, XC+Anp, 1, Xd, 1 ); |
| 181 | 1 | equemene | } |
| 182 | 1 | equemene | } |
| 183 | 1 | equemene | |
| 184 | 1 | equemene | rowprev = Alrow; Alrow = MModSub1( Alrow, nprow ); |
| 185 | 1 | equemene | colprev = Alcol; Alcol = MModSub1( Alcol, npcol ); |
| 186 | 1 | equemene | kbprev = kb; n -= kb; |
| 187 | 1 | equemene | tmp1 = n - ( kb = nb ); tmp1 -= ( tmp2 = Mmin( tmp1, n1 ) ); |
| 188 | 1 | equemene | MnumrocI( n1p, tmp2, Mmax( 0, tmp1 ), nb, nb, myrow, 0, nprow ); |
| 189 | 1 | equemene | /*
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| 190 | 1 | equemene | * Start the operations
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| 191 | 1 | equemene | */
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| 192 | 1 | equemene | while( n > 0 ) |
| 193 | 1 | equemene | {
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| 194 | 1 | equemene | if( mycol == Alcol ) { Aptr -= lda * kb; Anq -= kb; Xd = XR + Anq; }
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| 195 | 1 | equemene | if( myrow == Alrow ) { Anp -= kb; }
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| 196 | 1 | equemene | /*
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| 197 | 1 | equemene | * Broadcast (decreasing-ring) of previous solution block in previous
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| 198 | 1 | equemene | * process column, compute partial update of current block and send it
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| 199 | 1 | equemene | * to current process column.
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| 200 | 1 | equemene | */
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| 201 | 1 | equemene | if( mycol == colprev )
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| 202 | 1 | equemene | {
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| 203 | 1 | equemene | /*
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| 204 | 1 | equemene | * Send previous solution block in process row above
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| 205 | 1 | equemene | */
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| 206 | 1 | equemene | if( myrow == rowprev )
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| 207 | 1 | equemene | {
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| 208 | 1 | equemene | if( GridIsNot1xQ )
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| 209 | 1 | equemene | (void) HPL_send( Xdprev, kbprev, MModSub1( myrow, nprow ),
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| 210 | 1 | equemene | Cmsgid, Ccomm ); |
| 211 | 1 | equemene | } |
| 212 | 1 | equemene | else
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| 213 | 1 | equemene | {
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| 214 | 1 | equemene | (void) HPL_recv( Xdprev, kbprev, MModAdd1( myrow, nprow ),
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| 215 | 1 | equemene | Cmsgid, Ccomm ); |
| 216 | 1 | equemene | } |
| 217 | 1 | equemene | /*
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| 218 | 1 | equemene | * Compute partial update of previous solution block and send it to cur-
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| 219 | 1 | equemene | * rent column
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| 220 | 1 | equemene | */
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| 221 | 1 | equemene | if( n1pprev > 0 ) |
| 222 | 1 | equemene | {
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| 223 | 1 | equemene | tmp1 = Anpprev - n1pprev; |
| 224 | 1 | equemene | HPL_dgemv( HplColumnMajor, HplNoTrans, n1pprev, kbprev, |
| 225 | 1 | equemene | -HPL_rone, Aprev+tmp1, lda, Xdprev, 1, HPL_rone,
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| 226 | 1 | equemene | XC+tmp1, 1 );
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| 227 | 1 | equemene | if( GridIsNotPx1 )
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| 228 | 1 | equemene | (void) HPL_send( XC+tmp1, n1pprev, Alcol, Rmsgid, Rcomm );
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| 229 | 1 | equemene | } |
| 230 | 1 | equemene | /*
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| 231 | 1 | equemene | * Finish the (decreasing-ring) broadcast of the solution block in pre-
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| 232 | 1 | equemene | * vious process column
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| 233 | 1 | equemene | */
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| 234 | 1 | equemene | if( ( myrow != rowprev ) &&
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| 235 | 1 | equemene | ( myrow != MModAdd1( rowprev, nprow ) ) ) |
| 236 | 1 | equemene | (void) HPL_send( Xdprev, kbprev, MModSub1( myrow, nprow ),
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| 237 | 1 | equemene | Cmsgid, Ccomm ); |
| 238 | 1 | equemene | } |
| 239 | 1 | equemene | else if( mycol == Alcol ) |
| 240 | 1 | equemene | {
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| 241 | 1 | equemene | /*
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| 242 | 1 | equemene | * Current column receives and accumulates partial update of previous
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| 243 | 1 | equemene | * solution block
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| 244 | 1 | equemene | */
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| 245 | 1 | equemene | if( n1pprev > 0 ) |
| 246 | 1 | equemene | {
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| 247 | 1 | equemene | (void) HPL_recv( W, n1pprev, colprev, Rmsgid, Rcomm );
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| 248 | 1 | equemene | HPL_daxpy( n1pprev, HPL_rone, W, 1, XC+Anpprev-n1pprev, 1 ); |
| 249 | 1 | equemene | } |
| 250 | 1 | equemene | } |
| 251 | 1 | equemene | /*
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| 252 | 1 | equemene | * Solve current diagonal block
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| 253 | 1 | equemene | */
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| 254 | 1 | equemene | if( ( mycol == Alcol ) && ( myrow == Alrow ) )
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| 255 | 1 | equemene | {
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| 256 | 1 | equemene | HPL_dtrsv( HplColumnMajor, HplUpper, HplNoTrans, HplNonUnit, |
| 257 | 1 | equemene | kb, Aptr+Anp, lda, XC+Anp, 1 );
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| 258 | 1 | equemene | HPL_dcopy( kb, XC+Anp, 1, XR+Anq, 1 ); |
| 259 | 1 | equemene | } |
| 260 | 1 | equemene | /*
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| 261 | 1 | equemene | * Finish previous update
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| 262 | 1 | equemene | */
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| 263 | 1 | equemene | if( ( mycol == colprev ) && ( ( tmp1 = Anpprev - n1pprev ) > 0 ) ) |
| 264 | 1 | equemene | HPL_dgemv( HplColumnMajor, HplNoTrans, tmp1, kbprev, -HPL_rone, |
| 265 | 1 | equemene | Aprev, lda, Xdprev, 1, HPL_rone, XC, 1 ); |
| 266 | 1 | equemene | /*
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| 267 | 1 | equemene | * Save info of current step and update info for the next step
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| 268 | 1 | equemene | */
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| 269 | 1 | equemene | if( mycol == Alcol ) { Xdprev = Xd; Aprev = Aptr; }
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| 270 | 1 | equemene | if( myrow == Alrow ) { Anpprev -= kb; }
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| 271 | 1 | equemene | rowprev = Alrow; colprev = Alcol; |
| 272 | 1 | equemene | n1pprev = n1p; kbprev = kb; n -= kb; |
| 273 | 1 | equemene | Alrow = MModSub1( Alrow, nprow ); Alcol = MModSub1( Alcol, npcol ); |
| 274 | 1 | equemene | tmp1 = n - ( kb = nb ); tmp1 -= ( tmp2 = Mmin( tmp1, n1 ) ); |
| 275 | 1 | equemene | MnumrocI( n1p, tmp2, Mmax( 0, tmp1 ), nb, nb, myrow, 0, nprow ); |
| 276 | 1 | equemene | |
| 277 | 1 | equemene | Rmsgid = ( Rmsgid+2 > MSGID_END_PTRSV ?
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| 278 | 1 | equemene | MSGID_BEGIN_PTRSV : Rmsgid+2 );
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| 279 | 1 | equemene | Cmsgid = ( Cmsgid+2 > MSGID_END_PTRSV ?
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| 280 | 1 | equemene | MSGID_BEGIN_PTRSV+1 : Cmsgid+2 ); |
| 281 | 1 | equemene | } |
| 282 | 1 | equemene | /*
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| 283 | 1 | equemene | * Replicate last solution block
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| 284 | 1 | equemene | */
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| 285 | 1 | equemene | if( mycol == colprev )
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| 286 | 1 | equemene | (void) HPL_broadcast( (void *)(XR), kbprev, HPL_DOUBLE, rowprev, |
| 287 | 1 | equemene | Ccomm ); |
| 288 | 1 | equemene | |
| 289 | 1 | equemene | if( Wfr ) free( W );
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| 290 | 1 | equemene | #ifdef HPL_DETAILED_TIMING
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| 291 | 1 | equemene | HPL_ptimer( HPL_TIMING_PTRSV ); |
| 292 | 1 | equemene | #endif
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| 293 | 1 | equemene | /*
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| 294 | 1 | equemene | * End of HPL_pdtrsv
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| 295 | 1 | equemene | */
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| 296 | 1 | equemene | } |