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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 pztrsv_( F_CHAR_T UPLO, F_CHAR_T TRANS, F_CHAR_T DIAG, int * N,
double * A, int * IA, int * JA, int * DESCA,
double * X, int * IX, int * JX, int * DESCX,
int * INCX )
#else
void pztrsv_( UPLO, TRANS, DIAG, N, A, IA, JA, DESCA, X, IX, JX,
DESCX, INCX )
/*
* .. Scalar Arguments ..
*/
F_CHAR_T DIAG, TRANS, UPLO;
int * IA, * INCX, * IX, * JA, * JX, * N;
/*
* .. Array Arguments ..
*/
int * DESCA, * DESCX;
double * A, * X;
#endif
{
/*
* Purpose
* =======
*
* PZTRSV solves one of the systems of equations
*
* sub( A )*sub( X ) = b, or sub( A )'*sub( X ) = b, or
*
* conjg( sub( A )' )*sub( X ) = b,
*
* where
*
* sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1), and,
*
* sub( X ) denotes X(IX,JX:JX+N-1) if INCX = M_X,
* X(IX:IX+N-1,JX) if INCX = 1 and INCX <> M_X.
*
* b and sub( X ) are n element subvectors and sub( A ) is an n by n
* unit, or non-unit, upper or lower triangular submatrix.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* 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
* =========
*
* 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.
*
* TRANS (global input) CHARACTER*1
* On entry, TRANS specifies the operation to be performed as
* follows:
*
* TRANS = 'N' or 'n' sub( A ) * sub( X ) = b.
*
* TRANS = 'T' or 't' sub( A )' * sub( X ) = b.
*
* TRANS = 'C' or 'c' conjg( sub( A )' ) * sub( X ) = b.
*
* 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.
*
* N (global input) INTEGER
* On entry, N specifies the order of the submatrix sub( A ).
* N must be at least zero.
*
* A (local input) COMPLEX*16 array
* On entry, A is an array of dimension (LLD_A, Ka), where Ka is
* at least Lc( 1, JA+N-1 ). 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.
*
* X (local input/local output) COMPLEX*16 array
* On entry, X is an array of dimension (LLD_X, Kx), where LLD_X
* is at least MAX( 1, Lr( 1, IX ) ) when INCX = M_X and
* MAX( 1, Lr( 1, IX+N-1 ) ) otherwise, and, Kx is at least
* Lc( 1, JX+N-1 ) when INCX = M_X and Lc( 1, JX ) otherwise.
* Before entry, this array contains the local entries of the
* matrix X. On entry, sub( X ) is the n element right-hand side
* b. On exit, sub( X ) is overwritten with the solution subvec-
* tor.
*
* IX (global input) INTEGER
* On entry, IX specifies X's global row index, which points to
* the beginning of the submatrix sub( X ).
*
* JX (global input) INTEGER
* On entry, JX specifies X's global column index, which points
* to the beginning of the submatrix sub( X ).
*
* DESCX (global and local input) INTEGER array
* On entry, DESCX is an integer array of dimension DLEN_. This
* is the array descriptor for the matrix X.
*
* INCX (global input) INTEGER
* On entry, INCX specifies the global increment for the
* elements of X. Only two values of INCX are supported in
* this version, namely 1 and M_X. INCX must not be zero.
*
* -- Written on April 1, 1998 by
* Antoine Petitet, University of Tennessee, Knoxville 37996, USA.
*
* ---------------------------------------------------------------------
*/
/*
* .. Local Scalars ..
*/
char DiagA, TranOp, UploA, Xroc, btop, ctop, * negone, * one,
* zero;
int Acol, Ai, Aii, Aimb1, Ainb1, Aj, Ajj, Akp, Akq, Ald, Amb, Anb,
Anp, Anp0, Anq, Anq0, Arow, Asrc, XACapbX, XACfr, XACld,
XACsum, XARapbX, XARfr, XARld, XARsum, Xi, Xj, ctxt, info,
ione=1, k, kb, kbnext, kbprev, ktmp, mycol, myrow, nb, notran,
nounit, npcol, nprow, size, upper;
PBTYP_T * type;
/*
* .. Local Arrays ..
*/
int Ad[DLEN_], Ad0[DLEN_], XACd[DLEN_], XARd[DLEN_], Xd[DLEN_];
char * Aptr = NULL, * XAC = NULL, * XAR = NULL;
/* ..
* .. Executable Statements ..
*
*/
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( *IX, *JX, DESCX, &Xi, &Xj, Xd );
#ifndef NO_ARGCHK
/*
* Test the input parameters
*/
Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
if( !( info = ( ( nprow == -1 ) ? -( 801 + CTXT_ ) : 0 ) ) )
{
if( ( !upper ) && ( UploA != CLOWER ) )
{
PB_Cwarn( ctxt, __LINE__, "PZTRSV", "Illegal UPLO = %c\n", UploA );
info = -1;
}
else if( ( !notran ) && ( TranOp != CTRAN ) && ( TranOp != CCOTRAN ) )
{
PB_Cwarn( ctxt, __LINE__, "PZTRSV", "Illegal TRANS = %c\n", TranOp );
info = -2;
}
else if( ( !nounit ) && ( DiagA != CUNIT ) )
{
PB_Cwarn( ctxt, __LINE__, "PZTRSV", "Illegal DIAG = %c\n", DiagA );
info = -3;
}
PB_Cchkmat( ctxt, "PZTRSV", "A", *N, 4, *N, 4, Ai, Aj, Ad, 8, &info );
PB_Cchkvec( ctxt, "PZTRSV", "X", *N, 4, Xi, Xj, Xd, *INCX, 12, &info );
}
if( info ) { PB_Cabort( ctxt, "PZTRSV", info ); return; }
#endif
/*
* Quick return if possible
*/
if( *N == 0 ) return;
/*
* Retrieve process grid information
*/
#ifdef NO_ARGCHK
Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol );
#endif
/*
* Get type structure
*/
type = PB_Cztypeset();
size = type->size; one = type->one; zero = type->zero; negone = type->negone;
/*
* Compute descriptor Ad0 for sub( A )
*/
PB_Cdescribe( *N, *N, Ai, Aj, Ad, nprow, npcol, myrow, mycol, &Aii, &Ajj,
&Ald, &Aimb1, &Ainb1, &Amb, &Anb, &Arow, &Acol, Ad0 );
/*
* Computational partitioning size is computed as the product of the logical
* value returned by pilaenv_ and 2 * lcm( nprow, npcol )
*/
nb = 2 * pilaenv_( &ctxt, C2F_CHAR( &type->type ) ) *
PB_Clcm( ( Arow >= 0 ? nprow : 1 ), ( Acol >= 0 ? npcol : 1 ) );
Xroc = ( *INCX == Xd[M_] ? CROW : CCOLUMN );
if( notran )
{
if( upper )
{
/*
* Save current and enforce ring BLACS topologies
*/
btop = *PB_Ctop( &ctxt, BCAST, COLUMN, TOP_GET );
ctop = *PB_Ctop( &ctxt, COMBINE, ROW, TOP_GET );
(void) PB_Ctop( &ctxt, BCAST, COLUMN, TOP_DRING );
(void) PB_Ctop( &ctxt, COMBINE, ROW, TOP_DRING );
/*
* Remove next line when BLACS combine operations support ring topologies.
*/
(void) PB_Ctop( &ctxt, COMBINE, ROW, TOP_DEFAULT );
/*
* Reuse sub( X ) and/or create vector XAC in process column owning the last
* column of sub( A )
*/
PB_CInOutV2( type, NOCONJG, COLUMN, *N, *N, *N-1, Ad0, 1,
((char *) X), Xi, Xj, Xd, &Xroc, &XAC, XACd,
&XACfr, &XACsum, &XACapbX );
/*
* Create vector XAR in process rows spanned by sub( A )
*/
PB_COutV( type, ROW, INIT, *N, *N, Ad0, 1, &XAR, XARd, &XARfr,
&XARsum );
/*
* Retrieve local quantities related to Ad0 -> sub( A )
*/
Aimb1 = Ad0[IMB_ ]; Ainb1 = Ad0[INB_ ];
Amb = Ad0[MB_ ]; Anb = Ad0[NB_ ];
Arow = Ad0[RSRC_]; Acol = Ad0[CSRC_]; Ald = Ad0[LLD_];
Anp = PB_Cnumroc( *N, 0, Aimb1, Amb, myrow, Arow, nprow );
Anq = PB_Cnumroc( *N, 0, Ainb1, Anb, mycol, Acol, npcol );
if( ( Anp > 0 ) && ( Anq > 0 ) )
Aptr = Mptr( ((char *) A), Aii, Ajj, Ald, size );
XACld = XACd[LLD_]; XARld = XARd[LLD_];
for( k = ( ( *N - 1 ) / nb ) * nb; k >= 0; k -= nb )
{
ktmp = *N - k; kb = MIN( ktmp, nb );
/*
* Solve logical diagonal block, XAC contains the solution scattered in multiple
* process columns and XAR contains the solution replicated in the process rows.
*/
Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow );
Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol );
PB_Cptrsv( type, XARsum, &UploA, &TranOp, &DiagA, kb, Aptr, k, k,
Ad0, Mptr( XAC, Akp, 0, XACld, size ), 1, Mptr( XAR, 0,
Akq, XARld, size ), XARld );
/*
* Update: only the part of sub( X ) to be solved at the next step is locally
* updated and combined, the remaining part of the vector to be solved later is
* only locally updated.
*/
if( Akp > 0 )
{
Anq0 = PB_Cnumroc( kb, k, Ainb1, Anb, mycol, Acol, npcol );
if( XACsum )
{
kbprev = MIN( k, nb );
ktmp = PB_Cnumroc( kbprev, k-kbprev, Aimb1, Amb, myrow,
Arow, nprow );
Akp -= ktmp;
if( ktmp > 0 )
{
if( Anq0 > 0 )
zgemv_( TRANS, &ktmp, &Anq0, negone,
Mptr( Aptr, Akp, Akq, Ald, size ), &Ald,
Mptr( XAR, 0, Akq, XARld, size ), &XARld, one,
Mptr( XAC, Akp, 0, XACld, size ), &ione );
Asrc = PB_Cindxg2p( k-1, Ainb1, Anb, Acol, Acol, npcol );
Czgsum2d( ctxt, ROW, &ctop, ktmp, 1, Mptr( XAC, Akp,
0, XACld, size ), XACld, myrow, Asrc );
if( mycol != Asrc )
zset_( &ktmp, zero, Mptr( XAC, Akp, 0, XACld,
size ), &ione );
}
if( Akp > 0 && Anq0 > 0 )
zgemv_( TRANS, &Akp, &Anq0, negone,
Mptr( Aptr, 0, Akq, Ald, size ), &Ald,
Mptr( XAR, 0, Akq, XARld, size ), &XARld, one,
XAC, &ione );
}
else
{
if( Anq0 > 0 )
zgemv_( TRANS, &Akp, &Anq0, negone,
Mptr( Aptr, 0, Akq, Ald, size ), &Ald,
Mptr( XAR, 0, Akq, XARld, size ), &XARld, one,
XAC, &ione );
}
}
}
/*
* Combine the scattered resulting vector XAC
*/
if( XACsum && ( Anp > 0 ) )
{
Czgsum2d( ctxt, ROW, &ctop, Anp, 1, XAC, XACld, myrow,
XACd[CSRC_] );
}
/*
* sub( X ) := XAC (if necessary)
*/
if( XACapbX )
{
PB_Cpaxpby( type, NOCONJG, *N, 1, one, XAC, 0, 0, XACd, COLUMN,
zero, ((char *) X), Xi, Xj, Xd, &Xroc );
}
/*
* Restore BLACS topologies
*/
(void) PB_Ctop( &ctxt, BCAST, COLUMN, &btop );
(void) PB_Ctop( &ctxt, COMBINE, ROW, &ctop );
}
else
{
/*
* Save current and enforce ring BLACS topologies
*/
btop = *PB_Ctop( &ctxt, BCAST, COLUMN, TOP_GET );
ctop = *PB_Ctop( &ctxt, COMBINE, ROW, TOP_GET );
(void) PB_Ctop( &ctxt, BCAST, COLUMN, TOP_IRING );
(void) PB_Ctop( &ctxt, COMBINE, ROW, TOP_IRING );
/*
* Remove next line when BLACS combine operations support ring topologies.
*/
(void) PB_Ctop( &ctxt, COMBINE, ROW, TOP_DEFAULT );
/*
* Reuse sub( X ) and/or create vector XAC in process column owning the first
* column of sub( A )
*/
PB_CInOutV2( type, NOCONJG, COLUMN, *N, *N, 0, Ad0, 1,
((char *) X), Xi, Xj, Xd, &Xroc, &XAC, XACd,
&XACfr, &XACsum, &XACapbX );
/*
* Create vector XAR in process rows spanned by sub( A )
*/
PB_COutV( type, ROW, INIT, *N, *N, Ad0, 1, &XAR, XARd, &XARfr,
&XARsum );
/*
* Retrieve local quantities related to Ad0 -> sub( A )
*/
Aimb1 = Ad0[IMB_ ]; Ainb1 = Ad0[INB_ ];
Amb = Ad0[MB_ ]; Anb = Ad0[NB_ ];
Arow = Ad0[RSRC_]; Acol = Ad0[CSRC_]; Ald = Ad0[LLD_];
Anp = PB_Cnumroc( *N, 0, Aimb1, Amb, myrow, Arow, nprow );
Anq = PB_Cnumroc( *N, 0, Ainb1, Anb, mycol, Acol, npcol );
if( ( Anp > 0 ) && ( Anq > 0 ) )
Aptr = Mptr( ((char *) A), Aii, Ajj, Ald, size );
XACld = XACd[LLD_]; XARld = XARd[LLD_];
for( k = 0; k < *N; k += nb )
{
ktmp = *N - k; kb = MIN( ktmp, nb );
/*
* Solve logical diagonal block, XAC contains the solution scattered in multiple
* process columns and XAR contains the solution replicated in the process rows.
*/
Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow );
Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol );
PB_Cptrsv( type, XARsum, &UploA, &TranOp, &DiagA, kb, Aptr, k, k,
Ad0, Mptr( XAC, Akp, 0, XACld, size ), 1, Mptr( XAR, 0,
Akq, XARld, size ), XARld );
/*
* Update: only the part of sub( X ) to be solved at the next step is locally
* updated and combined, the remaining part of the vector to be solved later is
* only locally updated.
*/
Akp = PB_Cnumroc( k+kb, 0, Aimb1, Amb, myrow, Arow, nprow );
if( ( Anp0 = Anp - Akp ) > 0 )
{
Anq0 = PB_Cnumroc( kb, k, Ainb1, Anb, mycol, Acol, npcol );
if( XACsum )
{
kbnext = ktmp - kb; kbnext = MIN( kbnext, nb );
ktmp = PB_Cnumroc( kbnext, k+kb, Aimb1, Amb, myrow, Arow,
nprow );
Anp0 -= ktmp;
if( ktmp > 0 )
{
if( Anq0 > 0 )
zgemv_( TRANS, &ktmp, &Anq0, negone,
Mptr( Aptr, Akp, Akq, Ald, size ), &Ald,
Mptr( XAR, 0, Akq, XARld, size ), &XARld, one,
Mptr( XAC, Akp, 0, XACld, size ), &ione );
Asrc = PB_Cindxg2p( k+kb, Ainb1, Anb, Acol, Acol, npcol );
Czgsum2d( ctxt, ROW, &ctop, ktmp, 1, Mptr( XAC, Akp,
0, XACld, size ), XACld, myrow, Asrc );
if( mycol != Asrc )
zset_( &ktmp, zero, Mptr( XAC, Akp, 0, XACld,
size ), &ione );
}
if( Anp0 > 0 && Anq0 > 0 )
zgemv_( TRANS, &Anp0, &Anq0, negone,
Mptr( Aptr, Akp+ktmp, Akq, Ald, size ), &Ald,
Mptr( XAR, 0, Akq, XARld, size ), &XARld,
one,
Mptr( XAC, Akp+ktmp, 0, XACld, size ), &ione );
}
else
{
if( Anq0 > 0 )
zgemv_( TRANS, &Anp0, &Anq0, negone,
Mptr( Aptr, Akp, Akq, Ald, size ), &Ald,
Mptr( XAR, 0, Akq, XARld, size ), &XARld,
one,
Mptr( XAC, Akp, 0, XACld, size ), &ione );
}
}
}
/*
* Combine the scattered resulting vector XAC
*/
if( XACsum && ( Anp > 0 ) )
{
Czgsum2d( ctxt, ROW, &ctop, Anp, 1, XAC, XACld, myrow,
XACd[CSRC_] );
}
/*
* sub( X ) := XAC (if necessary)
*/
if( XACapbX )
{
PB_Cpaxpby( type, NOCONJG, *N, 1, one, XAC, 0, 0, XACd,
COLUMN, zero, ((char *) X), Xi, Xj, Xd, &Xroc );
}
/*
* Restore BLACS topologies
*/
(void) PB_Ctop( &ctxt, BCAST, COLUMN, &btop );
(void) PB_Ctop( &ctxt, COMBINE, ROW, &ctop );
}
}
else
{
if( upper )
{
/*
* Save current and enforce ring BLACS topologies
*/
btop = *PB_Ctop( &ctxt, BCAST, ROW, TOP_GET );
ctop = *PB_Ctop( &ctxt, COMBINE, COLUMN, TOP_GET );
(void) PB_Ctop( &ctxt, BCAST, ROW, TOP_IRING );
(void) PB_Ctop( &ctxt, COMBINE, COLUMN, TOP_IRING );
/*
* Remove next line when BLACS combine operations support ring topologies.
*/
(void) PB_Ctop( &ctxt, COMBINE, COLUMN, TOP_DEFAULT );
/*
* Reuse sub( X ) and/or create vector XAR in process row owning the first row
* of sub( A )
*/
PB_CInOutV2( type, NOCONJG, ROW, *N, *N, 0, Ad0, 1,
((char *) X), Xi, Xj, Xd, &Xroc, &XAR, XARd,
&XARfr, &XARsum, &XARapbX );
/*
* Create vector XAC in process columns spanned by sub( A )
*/
PB_COutV( type, COLUMN, INIT, *N, *N, Ad0, 1, &XAC, XACd, &XACfr,
&XACsum );
/*
* Retrieve local quantities related to Ad0 -> sub( A )
*/
Aimb1 = Ad0[IMB_ ]; Ainb1 = Ad0[INB_ ];
Amb = Ad0[MB_ ]; Anb = Ad0[NB_ ];
Arow = Ad0[RSRC_]; Acol = Ad0[CSRC_]; Ald = Ad0[LLD_];
Anp = PB_Cnumroc( *N, 0, Aimb1, Amb, myrow, Arow, nprow );
Anq = PB_Cnumroc( *N, 0, Ainb1, Anb, mycol, Acol, npcol );
if( ( Anp > 0 ) && ( Anq > 0 ) )
Aptr = Mptr( ((char *) A), Aii, Ajj, Ald, size );
XACld = XACd[LLD_]; XARld = XARd[LLD_];
for( k = 0; k < *N; k += nb )
{
ktmp = *N - k; kb = MIN( ktmp, nb );
/*
* Solve logical diagonal block, XAR contains the solution scattered in multiple
* process rows and XAC contains the solution replicated in the process columns.
*/
Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow );
Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol );
PB_Cptrsv( type, XACsum, &UploA, &TranOp, &DiagA, kb, Aptr, k, k,
Ad0, Mptr( XAC, Akp, 0, XACld, size ), 1, Mptr( XAR, 0,
Akq, XARld, size ), XARld );
/*
* Update: only the part of sub( X ) to be solved at the next step is locally
* updated and combined, the remaining part of the vector to be solved later is
* only locally updated.
*/
Akq = PB_Cnumroc( k+kb, 0, Ainb1, Anb, mycol, Acol, npcol );
if( ( Anq0 = Anq - Akq ) > 0 )
{
Anp0 = PB_Cnumroc( kb, k, Aimb1, Amb, myrow, Arow, nprow );
if( XARsum )
{
kbnext = ktmp - kb; kbnext = MIN( kbnext, nb );
ktmp = PB_Cnumroc( kbnext, k+kb, Ainb1, Anb, mycol, Acol,
npcol );
Anq0 -= ktmp;
if( ktmp > 0 )
{
if( Anp0 > 0 )
zgemv_( TRANS, &Anp0, &ktmp, negone,
Mptr( Aptr, Akp, Akq, Ald, size ), &Ald,
Mptr( XAC, Akp, 0, XACld, size ), &ione, one,
Mptr( XAR, 0, Akq, XARld, size ), &XARld );
Asrc = PB_Cindxg2p( k+kb, Aimb1, Amb, Arow, Arow, nprow );
Czgsum2d( ctxt, COLUMN, &ctop, 1, ktmp, Mptr( XAR, 0,
Akq, XARld, size ), XARld, Asrc, mycol );
if( myrow != Asrc )
zset_( &ktmp, zero, Mptr( XAR, 0, Akq, XARld,
size ), &XARld );
}
if( Anp0 > 0 && Anq0 > 0 )
zgemv_( TRANS, &Anp0, &Anq0, negone,
Mptr( Aptr, Akp, Akq+ktmp, Ald, size ), &Ald,
Mptr( XAC, Akp, 0, XACld, size ), &ione, one,
Mptr( XAR, 0, Akq+ktmp, XARld, size ), &XARld );
}
else
{
if( Anp0 > 0 )
zgemv_( TRANS, &Anp0, &Anq0, negone,
Mptr( Aptr, Akp, Akq, Ald, size ), &Ald,
Mptr( XAC, Akp, 0, XACld, size ), &ione, one,
Mptr( XAR, 0, Akq, XARld, size ), &XARld );
}
}
}
/*
* Combine the scattered resulting vector XAR
*/
if( XARsum && ( Anq > 0 ) )
{
Czgsum2d( ctxt, COLUMN, &ctop, 1, Anq, XAR, XARld, XARd[RSRC_],
mycol );
}
/*
* sub( X ) := XAR (if necessary)
*/
if( XARapbX )
{
PB_Cpaxpby( type, NOCONJG, 1, *N, one, XAR, 0, 0, XARd, ROW, zero,
((char *) X), Xi, Xj, Xd, &Xroc );
}
/*
* Restore BLACS topologies
*/
(void) PB_Ctop( &ctxt, BCAST, ROW, &btop );
(void) PB_Ctop( &ctxt, COMBINE, COLUMN, &ctop );
}
else
{
/*
* Save current and enforce ring BLACS topologies
*/
btop = *PB_Ctop( &ctxt, BCAST, ROW, TOP_GET );
ctop = *PB_Ctop( &ctxt, COMBINE, COLUMN, TOP_GET );
(void) PB_Ctop( &ctxt, BCAST, ROW, TOP_DRING );
(void) PB_Ctop( &ctxt, COMBINE, COLUMN, TOP_DRING );
/*
* Remove next line when BLACS combine operations support ring topologies.
*/
(void) PB_Ctop( &ctxt, COMBINE, COLUMN, TOP_DEFAULT );
/*
* Reuse sub( X ) and/or create vector XAC in process row owning the last row
* of sub( A )
*/
PB_CInOutV2( type, NOCONJG, ROW, *N, *N, *N-1, Ad0, 1,
((char *) X), Xi, Xj, Xd, &Xroc, &XAR, XARd,
&XARfr, &XARsum, &XARapbX );
/*
* Create vector XAC in process columns spanned by sub( A )
*/
PB_COutV( type, COLUMN, INIT, *N, *N, Ad0, 1, &XAC, XACd, &XACfr,
&XACsum );
/*
* Retrieve local quantities related to Ad0 -> sub( A )
*/
Aimb1 = Ad0[IMB_ ]; Ainb1 = Ad0[INB_ ];
Amb = Ad0[MB_ ]; Anb = Ad0[NB_ ];
Arow = Ad0[RSRC_]; Acol = Ad0[CSRC_]; Ald = Ad0[LLD_];
Anp = PB_Cnumroc( *N, 0, Aimb1, Amb, myrow, Arow, nprow );
Anq = PB_Cnumroc( *N, 0, Ainb1, Anb, mycol, Acol, npcol );
if( ( Anp > 0 ) && ( Anq > 0 ) )
Aptr = Mptr( ((char *) A), Aii, Ajj, Ald, size );
XACld = XACd[LLD_]; XARld = XARd[LLD_];
for( k = ( ( *N - 1 ) / nb ) * nb; k >= 0; k -= nb )
{
ktmp = *N - k; kb = MIN( ktmp, nb );
/*
* Solve logical diagonal block, XAR contains the solution scattered in multiple
* process rows and XAC contains the solution replicated in the process columns.
*/
Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow );
Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol );
PB_Cptrsv( type, XACsum, &UploA, &TranOp, &DiagA, kb, Aptr, k, k,
Ad0, Mptr( XAC, Akp, 0, XACld, size ), 1, Mptr( XAR, 0,
Akq, XARld, size ), XARld );
/*
* Update: only the part of sub( X ) to be solved at the next step is locally
* updated and combined, the remaining part of the vector to be solved later
* is only locally updated.
*/
if( Akq > 0 )
{
Anp0 = PB_Cnumroc( kb, k, Aimb1, Amb, myrow, Arow, nprow );
if( XARsum )
{
kbprev = MIN( k, nb );
ktmp = PB_Cnumroc( kbprev, k-kbprev, Ainb1, Anb, mycol,
Acol, npcol );
Akq -= ktmp;
if( ktmp > 0 )
{
if( Anp0 > 0 )
zgemv_( TRANS, &Anp0, &ktmp, negone,
Mptr( Aptr, Akp, Akq, Ald, size ), &Ald,
Mptr( XAC, Akp, 0, XACld, size ), &ione, one,
Mptr( XAR, 0, Akq, XARld, size ), &XARld );
Asrc = PB_Cindxg2p( k-1, Aimb1, Amb, Arow, Arow, nprow );
Czgsum2d( ctxt, COLUMN, &ctop, 1, ktmp, Mptr( XAR, 0,
Akq, XARld, size ), XARld, Asrc, mycol );
if( myrow != Asrc )
zset_( &ktmp, zero, Mptr( XAR, 0, Akq, XARld,
size ), &XARld );
}
if( Anp0 > 0 && Akq > 0 )
zgemv_( TRANS, &Anp0, &Akq, negone,
Mptr( Aptr, Akp, 0, Ald, size ), &Ald,
Mptr( XAC, Akp, 0, XACld, size ), &ione,
one, XAR, &XARld );
}
else
{
if( Anp0 > 0 )
zgemv_( TRANS, &Anp0, &Akq, negone,
Mptr( Aptr, Akp, 0, Ald, size ), &Ald,
Mptr( XAC, Akp, 0, XACld, size ), &ione,
one, XAR, &XARld );
}
}
}
/*
* Combine the scattered resulting vector XAR
*/
if( XARsum && ( Anq > 0 ) )
{
Czgsum2d( ctxt, COLUMN, &ctop, 1, Anq, XAR, XARld, XARd[RSRC_],
mycol );
}
/*
* sub( X ) := XAR (if necessary)
*/
if( XARapbX )
{
PB_Cpaxpby( type, NOCONJG, 1, *N, one, XAR, 0, 0, XARd, ROW, zero,
((char *) X), Xi, Xj, Xd, &Xroc );
}
/*
* Restore BLACS topologies
*/
(void) PB_Ctop( &ctxt, BCAST, ROW, &btop );
(void) PB_Ctop( &ctxt, COMBINE, COLUMN, &ctop );
}
}
if( XACfr ) free( XAC );
if( XARfr ) free( XAR );
/*
* End of PZTRSV
*/
}
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