SUBROUTINE PSPOTRS( UPLO, N, NRHS, A, IA, JA, DESCA, B, IB, JB, $ DESCB, INFO ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER IA, IB, INFO, JA, JB, N, NRHS * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ) REAL A( * ), B( * ) * .. * * Purpose * ======= * * PSPOTRS solves a system of linear equations * * sub( A ) * X = sub( B ) * A(IA:IA+N-1,JA:JA+N-1)*X = B(IB:IB+N-1,JB:JB+NRHS-1) * * where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is a N-by-N * symmetric positive definite distributed matrix using the Cholesky * factorization sub( A ) = U**T*U or L*L**T computed by PSPOTRF. * sub( B ) denotes the distributed matrix B(IB:IB+N-1,JB:JB+NRHS-1). * * Notes * ===== * * Each global data object is described by an associated description * vector. This vector stores the information required to establish * the mapping between an object element and its corresponding process * and memory location. * * Let A be a generic term for any 2D block cyclicly distributed array. * Such a global array has an associated description vector DESCA. * In the following comments, the character _ should be read as * "of the global array". * * NOTATION STORED IN EXPLANATION * --------------- -------------- -------------------------------------- * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, * DTYPE_A = 1. * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating * the BLACS process grid A is distribu- * ted over. The context itself is glo- * bal, but the handle (the integer * value) may vary. * M_A (global) DESCA( M_ ) The number of rows in the global * array A. * N_A (global) DESCA( N_ ) The number of columns in the global * array A. * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute * the rows of the array. * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute * the columns of the array. * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first * row of the array A is distributed. * CSRC_A (global) DESCA( CSRC_ ) The process column over which the * first column of the array A is * distributed. * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local * array. LLD_A >= MAX(1,LOCr(M_A)). * * Let K be the number of rows or columns of a distributed matrix, * and assume that its process grid has dimension p x q. * LOCr( K ) denotes the number of elements of K that a process * would receive if K were distributed over the p processes of its * process column. * Similarly, LOCc( K ) denotes the number of elements of K that a * process would receive if K were distributed over the q processes of * its process row. * The values of LOCr() and LOCc() may be determined via a call to the * ScaLAPACK tool function, NUMROC: * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). * An upper bound for these quantities may be computed by: * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A * * This routine requires square block decomposition ( MB_A = NB_A ). * * Arguments * ========= * * UPLO (global input) CHARACTER * = 'U': Upper triangle of sub( A ) is stored; * = 'L': Lower triangle of sub( A ) is stored. * * N (global input) INTEGER * The number of rows and columns to be operated on, i.e. the * order of the distributed submatrix sub( A ). N >= 0. * * NRHS (global input) INTEGER * The number of right hand sides, i.e., the number of columns * of the distributed submatrix sub( B ). NRHS >= 0. * * A (local input) REAL pointer into local memory to * an array of dimension (LLD_A, LOCc(JA+N-1)). On entry, this * array contains the factors L or U from the Cholesky facto- * rization sub( A ) = L*L**T or U**T*U, as computed by PSPOTRF. * * IA (global input) INTEGER * The row index in the global array A indicating the first * row of sub( A ). * * JA (global input) INTEGER * The column index in the global array A indicating the * first column of sub( A ). * * DESCA (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix A. * * B (local input/local output) REAL pointer into the * local memory to an array of local dimension * (LLD_B,LOCc(JB+NRHS-1)). On entry, this array contains the * the local pieces of the right hand sides sub( B ). * On exit, this array contains the local pieces of the solution * distributed matrix X. * * IB (global input) INTEGER * The row index in the global array B indicating the first * row of sub( B ). * * JB (global input) INTEGER * The column index in the global array B indicating the * first column of sub( B ). * * DESCB (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix B. * * INFO (global output) INTEGER * = 0: successful exit * < 0: If the i-th argument is an array and the j-entry had * an illegal value, then INFO = -(i*100+j), if the i-th * argument is a scalar and had an illegal value, then * INFO = -i. * * ===================================================================== * * .. Parameters .. INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, $ LLD_, MB_, M_, NB_, N_, RSRC_ PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER IAROW, IBROW, ICTXT, IROFFA, IROFFB, ICOFFA, $ MYCOL, MYROW, NPCOL, NPROW * .. * .. Local Arrays .. INTEGER IDUM1( 1 ), IDUM2( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, PSTRSM, $ PXERBLA * .. * .. External Functions .. LOGICAL LSAME INTEGER INDXG2P EXTERNAL INDXG2P, LSAME * .. * .. Intrinsic Functions .. INTRINSIC ICHAR, MOD * .. * .. Executable Statements .. * * Get grid parameters. * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Test the input parameters. * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -(700+CTXT_) ELSE CALL CHK1MAT( N, 2, N, 2, IA, JA, DESCA, 7, INFO ) CALL CHK1MAT( N, 2, NRHS, 3, IB, JB, DESCB, 11, INFO ) UPPER = LSAME( UPLO, 'U' ) IF( INFO.EQ.0 ) THEN IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ), $ NPROW ) IROFFA = MOD( IA-1, DESCA( MB_ ) ) IROFFB = MOD( IB-1, DESCB( MB_ ) ) ICOFFA = MOD( JA-1, DESCA( NB_ ) ) IF ( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( IROFFA.NE.0 ) THEN INFO = -5 ELSE IF( ICOFFA.NE.0 ) THEN INFO = -6 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(700+NB_) ELSE IF( IROFFB.NE.0 .OR. IBROW.NE.IAROW ) THEN INFO = -9 ELSE IF( DESCB( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -(1100+NB_) END IF END IF IF( UPPER ) THEN IDUM1( 1 ) = ICHAR( 'U' ) ELSE IDUM1( 1 ) = ICHAR( 'L' ) END IF IDUM2( 1 ) = 1 CALL PCHK2MAT( N, 2, N, 2, IA, JA, DESCA, 7, N, 2, NRHS, $ 3, IB, JB, DESCB, 11, 1, IDUM1, IDUM2, INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PSPOTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Solve sub( A ) * X = sub( B ) where sub( A ) = U'*U. * * Solve U'*X = sub( B ), overwriting sub( B ) with X. * CALL PSTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS, $ ONE, A, IA, JA, DESCA, B, IB, JB, DESCB ) * * Solve U*X = sub( B ), overwriting sub( B ) with X. * CALL PSTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, $ NRHS, ONE, A, IA, JA, DESCA, B, IB, JB, DESCB ) ELSE * * Solve sub( A ) *X = sub( B ) where sub( A ) = L*L'. * * Solve L*X = sub( B ), overwriting sub( B ) with X. * CALL PSTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N, $ NRHS, ONE, A, IA, JA, DESCA, B, IB, JB, DESCB ) * * Solve L'*X = sub( B ), overwriting sub( B ) with X. * CALL PSTRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', N, NRHS, $ ONE, A, IA, JA, DESCA, B, IB, JB, DESCB ) END IF * RETURN * * End of PSPOTRS * END