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|
/* ---------------------------------------------------------------------
*
* -- PBLAS routine (version 2.0) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* April 1, 1998
*
* ---------------------------------------------------------------------
*/
/*
* Include files
*/
#include "pblas.h"
#include "PBpblas.h"
#include "PBtools.h"
#include "PBblacs.h"
#include "PBblas.h"
#ifdef __STDC__
void pdtrsm_( F_CHAR_T SIDE, F_CHAR_T UPLO, F_CHAR_T TRANS, F_CHAR_T DIAG,
Int * M, Int * N, double * ALPHA,
double * A, Int * IA, Int * JA, Int * DESCA,
double * B, Int * IB, Int * JB, Int * DESCB )
#else
void pdtrsm_( SIDE, UPLO, TRANS, DIAG, M, N, ALPHA,
A, IA, JA, DESCA, B, IB, JB, DESCB )
/*
* .. Scalar Arguments ..
*/
F_CHAR_T DIAG, SIDE, TRANS, UPLO;
Int * IA, * IB, * JA, * JB, * M, * N;
double * ALPHA;
/*
* .. Array Arguments ..
*/
Int * DESCA, * DESCB;
double * A, * B;
#endif
{
/*
* Purpose
* =======
*
* PDTRSM solves one of the matrix equations
*
* op( sub( A ) )*X = alpha*sub( B ), or
*
* X*op( sub( A ) ) = alpha*sub( B ),
*
* where
*
* sub( A ) denotes A(IA:IA+M-1,JA:JA+M-1) if SIDE = 'L',
* A(IA:IA+N-1,JA:JA+N-1) if SIDE = 'R', and,
*
* sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1).
*
* Alpha is a scalar, X and sub( B ) are m by n submatrices, sub( A ) is
* a unit, or non-unit, upper or lower triangular submatrix and op( Y )
* is one of
*
* op( Y ) = Y or op( Y ) = Y'.
*
* The submatrix X is overwritten on sub( B ).
*
* Notes
* =====
*
* A description vector is associated with each 2D block-cyclicly dis-
* tributed matrix. This vector stores the information required to
* establish the mapping between a matrix entry and its corresponding
* process and memory location.
*
* In the following comments, the character _ should be read as
* "of the distributed matrix". Let A be a generic term for any 2D
* block cyclicly distributed matrix. Its description vector is DESC_A:
*
* NOTATION STORED IN EXPLANATION
* ---------------- --------------- ------------------------------------
* DTYPE_A (global) DESCA[ DTYPE_ ] The descriptor type.
* CTXT_A (global) DESCA[ CTXT_ ] The BLACS context handle, indicating
* the NPROW x NPCOL BLACS process grid
* A is distributed over. The context
* itself is global, but the handle
* (the integer value) may vary.
* M_A (global) DESCA[ M_ ] The number of rows in the distribu-
* ted matrix A, M_A >= 0.
* N_A (global) DESCA[ N_ ] The number of columns in the distri-
* buted matrix A, N_A >= 0.
* IMB_A (global) DESCA[ IMB_ ] The number of rows of the upper left
* block of the matrix A, IMB_A > 0.
* INB_A (global) DESCA[ INB_ ] The number of columns of the upper
* left block of the matrix A,
* INB_A > 0.
* MB_A (global) DESCA[ MB_ ] The blocking factor used to distri-
* bute the last M_A-IMB_A rows of A,
* MB_A > 0.
* NB_A (global) DESCA[ NB_ ] The blocking factor used to distri-
* bute the last N_A-INB_A columns of
* A, NB_A > 0.
* RSRC_A (global) DESCA[ RSRC_ ] The process row over which the first
* row of the matrix A is distributed,
* NPROW > RSRC_A >= 0.
* CSRC_A (global) DESCA[ CSRC_ ] The process column over which the
* first column of A is distributed.
* NPCOL > CSRC_A >= 0.
* LLD_A (local) DESCA[ LLD_ ] The leading dimension of the local
* array storing the local blocks of
* the distributed matrix A,
* IF( Lc( 1, N_A ) > 0 )
* LLD_A >= MAX( 1, Lr( 1, M_A ) )
* ELSE
* LLD_A >= 1.
*
* Let K be the number of rows of a matrix A starting at the global in-
* dex IA,i.e, A( IA:IA+K-1, : ). Lr( IA, K ) denotes the number of rows
* that the process of row coordinate MYROW ( 0 <= MYROW < NPROW ) would
* receive if these K rows were distributed over NPROW processes. If K
* is the number of columns of a matrix A starting at the global index
* JA, i.e, A( :, JA:JA+K-1, : ), Lc( JA, K ) denotes the number of co-
* lumns that the process MYCOL ( 0 <= MYCOL < NPCOL ) would receive if
* these K columns were distributed over NPCOL processes.
*
* The values of Lr() and Lc() may be determined via a call to the func-
* tion PB_Cnumroc:
* Lr( IA, K ) = PB_Cnumroc( K, IA, IMB_A, MB_A, MYROW, RSRC_A, NPROW )
* Lc( JA, K ) = PB_Cnumroc( K, JA, INB_A, NB_A, MYCOL, CSRC_A, NPCOL )
*
* Arguments
* =========
*
* SIDE (global input) CHARACTER*1
* On entry, SIDE specifies whether op( sub( A ) ) appears on
* the left or right of X as follows:
*
* SIDE = 'L' or 'l' op( sub( A ) )*X = alpha*sub( B ),
*
* SIDE = 'R' or 'r' X*op( sub( A ) ) = alpha*sub( B ).
*
* UPLO (global input) CHARACTER*1
* On entry, UPLO specifies whether the submatrix sub( A ) is
* an upper or lower triangular submatrix as follows:
*
* UPLO = 'U' or 'u' sub( A ) is an upper triangular
* submatrix,
*
* UPLO = 'L' or 'l' sub( A ) is a lower triangular
* submatrix.
*
* TRANSA (global input) CHARACTER*1
* On entry, TRANSA specifies the form of op( sub( A ) ) to be
* used in the matrix multiplication as follows:
*
* TRANSA = 'N' or 'n' op( sub( A ) ) = sub( A ),
*
* TRANSA = 'T' or 't' op( sub( A ) ) = sub( A )',
*
* TRANSA = 'C' or 'c' op( sub( A ) ) = sub( A )'.
*
* DIAG (global input) CHARACTER*1
* On entry, DIAG specifies whether or not sub( A ) is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' sub( A ) is assumed to be unit trian-
* gular,
*
* DIAG = 'N' or 'n' sub( A ) is not assumed to be unit tri-
* angular.
*
* M (global input) INTEGER
* On entry, M specifies the number of rows of the submatrix
* sub( B ). M must be at least zero.
*
* N (global input) INTEGER
* On entry, N specifies the number of columns of the submatrix
* sub( B ). N must be at least zero.
*
* ALPHA (global input) DOUBLE PRECISION
* On entry, ALPHA specifies the scalar alpha. When ALPHA is
* supplied as zero then the local entries of the array B
* corresponding to the entries of the submatrix sub( B ) need
* not be set on input.
*
* A (local input) DOUBLE PRECISION array
* On entry, A is an array of dimension (LLD_A, Ka), where Ka is
* at least Lc( 1, JA+M-1 ) when SIDE = 'L' or 'l' and is at
* least Lc( 1, JA+N-1 ) otherwise. Before entry, this array
* contains the local entries of the matrix A.
* Before entry with UPLO = 'U' or 'u', this array contains the
* local entries corresponding to the entries of the upper tri-
* angular submatrix sub( A ), and the local entries correspon-
* ding to the entries of the strictly lower triangular part of
* the submatrix sub( A ) are not referenced.
* Before entry with UPLO = 'L' or 'l', this array contains the
* local entries corresponding to the entries of the lower tri-
* angular submatrix sub( A ), and the local entries correspon-
* ding to the entries of the strictly upper triangular part of
* the submatrix sub( A ) are not referenced.
* Note that when DIAG = 'U' or 'u', the local entries corres-
* ponding to the diagonal elements of the submatrix sub( A )
* are not referenced either, but are assumed to be unity.
*
* IA (global input) INTEGER
* On entry, IA specifies A's global row index, which points to
* the beginning of the submatrix sub( A ).
*
* JA (global input) INTEGER
* On entry, JA specifies A's global column index, which points
* to the beginning of the submatrix sub( A ).
*
* DESCA (global and local input) INTEGER array
* On entry, DESCA is an integer array of dimension DLEN_. This
* is the array descriptor for the matrix A.
*
* B (local input/local output) DOUBLE PRECISION array
* On entry, B is an array of dimension (LLD_B, Kb), where Kb is
* at least Lc( 1, JB+N-1 ). Before entry, this array contains
* the local entries of the matrix B.
* On exit, the local entries of this array corresponding to the
* to the entries of the submatrix sub( B ) are overwritten by
* the local entries of the m by n solution submatrix.
*
* IB (global input) INTEGER
* On entry, IB specifies B's global row index, which points to
* the beginning of the submatrix sub( B ).
*
* JB (global input) INTEGER
* On entry, JB specifies B's global column index, which points
* to the beginning of the submatrix sub( B ).
*
* DESCB (global and local input) INTEGER array
* On entry, DESCB is an integer array of dimension DLEN_. This
* is the array descriptor for the matrix B.
*
* -- Written on April 1, 1998 by
* Antoine Petitet, University of Tennessee, Knoxville 37996, USA.
*
* ---------------------------------------------------------------------
*/
/*
* .. Local Scalars ..
*/
char DiagA, DirB, OpC, OpR, SideOp, TopC, TopR, TranOp, UploA,
Var, ctop, ctopsave, rtop, rtopsave;
Int Ai, Aj, Bi, Bj, ChooseAB, ForceTop, ctxt, info, itmp, lside,
mycol, myrow, nb, notran, nounit, npcol, nprow, upper;
double ABestL, ABestR, Best, tmp1, tmp2, tmp3, tmp4;
PBTYP_T * type;
/*
* .. Local Arrays ..
*/
Int Ad[DLEN_], Bd[DLEN_];
/* ..
* .. Executable Statements ..
*
*/
lside = ( ( SideOp = Mupcase( F2C_CHAR( SIDE )[0] ) ) == CLEFT );
upper = ( ( UploA = Mupcase( F2C_CHAR( UPLO )[0] ) ) == CUPPER );
notran = ( ( TranOp = Mupcase( F2C_CHAR( TRANS )[0] ) ) == CNOTRAN );
nounit = ( ( DiagA = Mupcase( F2C_CHAR( DIAG )[0] ) ) == CNOUNIT );
PB_CargFtoC( *IA, *JA, DESCA, &Ai, &Aj, Ad );
PB_CargFtoC( *IB, *JB, DESCB, &Bi, &Bj, Bd );
#ifndef NO_ARGCHK
/*
* Test the input parameters
*/
Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
if( !( info = ( ( nprow == -1 ) ? -( 1101 + CTXT_ ) : 0 ) ) )
{
if( ( !lside ) && ( SideOp != CRIGHT ) )
{
PB_Cwarn( ctxt, __LINE__, "PDTRSM", "Illegal SIDE = %c\n", SideOp );
info = -1;
}
else if( ( !upper ) && ( UploA != CLOWER ) )
{
PB_Cwarn( ctxt, __LINE__, "PDTRSM", "Illegal UPLO = %c\n", UploA );
info = -2;
}
else if( ( !notran ) && ( TranOp != CTRAN ) && ( TranOp != CCOTRAN ) )
{
PB_Cwarn( ctxt, __LINE__, "PDTRSM", "Illegal TRANS = %c\n", TranOp );
info = -3;
}
else if( ( !nounit ) && ( DiagA != CUNIT ) )
{
PB_Cwarn( ctxt, __LINE__, "PDTRSM", "Illegal DIAG = %c\n", DiagA );
info = -4;
}
if( lside )
PB_Cchkmat( ctxt, "PDTRSM", "A", *M, 5, *M, 5, Ai, Aj, Ad, 11,
&info );
else
PB_Cchkmat( ctxt, "PDTRSM", "A", *N, 6, *N, 6, Ai, Aj, Ad, 11,
&info );
PB_Cchkmat( ctxt, "PDTRSM", "B", *M, 5, *N, 6, Bi, Bj, Bd, 15,
&info );
}
if( info ) { PB_Cabort( ctxt, "PDTRSM", info ); return; }
#endif
/*
* Quick return if possible
*/
if( *M == 0 || *N == 0 ) return;
/*
* Get type structure
*/
type = PB_Cdtypeset();
/*
* And when alpha is zero
*/
if( ALPHA[REAL_PART] == ZERO )
{
PB_Cplapad( type, ALL, NOCONJG, *M, *N, type->zero, type->zero,
((char *) B), Bi, Bj, Bd );
return;
}
/*
* Start the operations
*/
#ifdef NO_ARGCHK
Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
#endif
/*
* Algorithm selection is based on approximation of the communication volume
* for distributed and aligned operands.
*/
nb = pilaenv_( &ctxt, C2F_CHAR( &type->type ) );
/*
* ABestR, ABestL : both operands sub( A ) and sub( B ) are communicated
* ( N >> M when SIDE is left and M >> N otherwise )
* Best : only sub( B ) is communicated
* ( M >> N when SIDE is left and N >> M otherwise )
*/
if( lside )
{
if( notran )
{
tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp4 = DNROC( *N, Bd[NB_], npcol );
ABestR = (double)(*M) *
( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 / TWO ) +
( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp4 ) );
itmp = MIN( Ad[MB_], Ad[NB_] );
Best = (double)(*N) *
( (double)(CEIL( *M, itmp )) * (double)(itmp) *
( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : ONE ) +
( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : ONE ) );
ChooseAB = ( ABestR <= ( 2.0 * Best ) );
}
else
{
tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp2 = DNROC( *M, Ad[NB_], npcol );
tmp4 = DNROC( *N, Bd[NB_], npcol );
ABestL = (double)(*M) *
( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 / TWO ) +
CBRATIO *
( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp4 ) );
ABestR = (double)(*M) *
( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 / TWO ) +
( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp4 ) +
MAX( tmp2, tmp1 ) / TWO );
itmp = MIN( Ad[MB_], Ad[NB_] );
tmp2 = DNROC( *M, Ad[NB_], npcol ); tmp3 = DNROC( *M, Bd[MB_], nprow );
Best = (double)(*N) *
( (double)(CEIL( *M, itmp )) * (double)(itmp) *
( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : ONE ) +
( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : ONE ) ) +
MAX( tmp2, tmp3 ) );
ChooseAB = ( ( ABestL <= ( 2.0 * Best ) ) ||
( ABestR <= ( 2.0 * Best ) ) );
}
}
else
{
if( notran )
{
tmp2 = DNROC( *N, Ad[NB_], npcol ); tmp3 = DNROC( *M, Bd[MB_], nprow );
ABestR = (double)(*N) *
( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 / TWO ) +
( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp3 ) );
itmp = MIN( Ad[MB_], Ad[NB_] );
Best = (double)(*M) *
( (double)(CEIL( *N, itmp )) * (double)(itmp) *
( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : ONE ) +
( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : ONE ) );
ChooseAB = ( ABestR <= ( 2.0 * Best ) );
}
else
{
tmp1 = DNROC( *N, Ad[MB_], nprow ); tmp2 = DNROC( *N, Ad[NB_], npcol );
tmp3 = DNROC( *M, Bd[MB_], nprow );
ABestL = (double)(*N) *
( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 / TWO ) +
CBRATIO *
( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp3 ) );
ABestR = (double)(*N) *
( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 / TWO ) +
( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp3 ) +
MAX( tmp2, tmp1 ) / TWO );
itmp = MIN( Ad[MB_], Ad[NB_] );
tmp1 = DNROC( *N, Ad[MB_], nprow ); tmp4 = DNROC( *N, Bd[NB_], npcol );
Best = (double)(*M) *
( (double)(CEIL( *N, itmp )) * (double)(itmp) *
( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : ONE ) +
( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : ONE ) ) +
MAX( tmp1, tmp4 ) );
ChooseAB = ( ( ABestL <= ( 2.0 * Best ) ) ||
( ABestR <= ( 2.0 * Best ) ) );
}
}
/*
* Var can remain uninitialized but is nevertheless used in PB_CptrsmAB.c
* provide a default here. TODO: does this make sense ?
*==19891== at 0x44F81B: PB_CptrsmAB (PB_CptrsmAB.c:538)
*==19891== by 0x427BE7: pdtrsm_ (pdtrsm_.c:488)
*==19891== by 0x405E46: MAIN_ (pdblas3tim.f:727)
*/
Var = CRIGHT;
if( ChooseAB )
{
/*
* BLACS topologies are enforced iff M and N are strictly greater than the
* logical block size returned by pilaenv_. Otherwise, it is assumed that the
* routine calling this routine has already selected an adequate topology.
*/
ForceTop = ( ( *M > nb ) && ( *N > nb ) );
if( ForceTop )
{
if( lside )
{
if( notran )
{
OpR = CBCAST; OpC = CBCAST; Var = CRIGHT;
if( upper ) { TopR = TopC = CTOP_DRING; }
else { TopR = TopC = CTOP_IRING; }
}
else
{
if( ABestL <= ABestR )
{
OpR = CBCAST; OpC = CCOMBINE; Var = CLEFT;
if( upper ) { TopR = TopC = CTOP_IRING; }
else { TopR = TopC = CTOP_DRING; }
}
else
{
OpR = CBCAST; OpC = CBCAST; Var = CRIGHT;
if( upper ) { TopR = TopC = CTOP_IRING; }
else { TopR = TopC = CTOP_DRING; }
}
}
}
else
{
if( notran )
{
OpR = CBCAST; OpC = CBCAST; Var = CRIGHT;
if( upper ) { TopR = TopC = CTOP_IRING; }
else { TopR = TopC = CTOP_DRING; }
}
else
{
if( ABestL <= ABestR )
{
OpR = CCOMBINE; OpC = CBCAST; Var = CLEFT;
if( upper ) { TopR = TopC = CTOP_DRING; }
else { TopR = TopC = CTOP_IRING; }
}
else
{
OpR = CBCAST; OpC = CBCAST; Var = CRIGHT;
if( upper ) { TopR = TopC = CTOP_DRING; }
else { TopR = TopC = CTOP_IRING; }
}
}
}
rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET );
ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET );
if( ( rtopsave = rtop ) != TopR )
rtop = *PB_Ctop( &ctxt, &OpR, ROW, &TopR );
if( ( ctopsave = ctop ) != TopC )
ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, &TopC );
/*
* Remove the next 4 lines when the BLACS combine operations support ring
* topologies
*/
if( OpR == CCOMBINE )
rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_DEFAULT );
if( OpC == CCOMBINE )
ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_DEFAULT );
}
PB_CptrsmAB( type, &Var, &SideOp, &UploA, ( notran ? NOTRAN : TRAN ),
&DiagA, *M, *N, ((char *)ALPHA), ((char *)A), Ai, Aj, Ad,
((char *)B), Bi, Bj, Bd );
/*
* Restore the BLACS topologies when necessary.
*/
if( ForceTop )
{
rtopsave = *PB_Ctop( &ctxt, &OpR, ROW, &rtopsave );
ctopsave = *PB_Ctop( &ctxt, &OpC, COLUMN, &ctopsave );
}
}
else
{
/*
* BLACS topologies are always enforced.
*/
if( ( lside && notran ) || ( !lside && !notran ) )
{
OpR = CCOMBINE; OpC = CBCAST;
if( upper ) { TopR = TopC = CTOP_DRING; }
else { TopR = TopC = CTOP_IRING; }
/*
* Remove the next line when the BLACS combine operations support ring
* topologies
*/
TopR = CTOP_DEFAULT;
}
else
{
OpR = CBCAST; OpC = CCOMBINE;
if( upper ) { TopR = TopC = CTOP_IRING; }
else { TopR = TopC = CTOP_DRING; }
/*
* Remove the next line when the BLACS combine operations support ring
* topologies
*/
TopC = CTOP_DEFAULT;
}
rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET );
ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET );
if( ( rtopsave = rtop ) != TopR )
rtop = *PB_Ctop( &ctxt, &OpR, ROW, &TopR );
if( ( ctopsave = ctop ) != TopC )
ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, &TopC );
if( lside ) DirB = ( rtop == CTOP_DRING ? CBACKWARD : CFORWARD );
else DirB = ( ctop == CTOP_DRING ? CBACKWARD : CFORWARD );
PB_CptrsmB( type, &DirB, &SideOp, &UploA, ( notran ? NOTRAN : TRAN ),
&DiagA, *M, *N, ((char *)ALPHA), ((char *)A), Ai, Aj, Ad,
((char *)B), Bi, Bj, Bd );
/*
* Restore the BLACS topologies.
*/
rtopsave = *PB_Ctop( &ctxt, &OpR, ROW, &rtopsave );
ctopsave = *PB_Ctop( &ctxt, &OpC, COLUMN, &ctopsave );
}
/*
* End of PDTRSM
*/
}
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