SUBROUTINE PZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, IA, JA, DESCA, $ B, IB, JB, DESCB, INFO ) * * -- ScaLAPACK auxiliary routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER DIAG, TRANS, UPLO INTEGER IA, IB, INFO, JA, JB, N, NRHS * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ) COMPLEX*16 A( * ), B( * ) * .. * * Purpose * ======= * * PZTRTRS solves a triangular system of the form * * sub( A ) * X = sub( B ) or sub( A )**T * X = sub( B ) or * * sub( A )**H * X = sub( B ), * * where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is a triangular * distributed matrix of order N, and B(IB:IB+N-1,JB:JB+NRHS-1) is an * N-by-NRHS distributed matrix denoted by sub( B ). A check is made * to verify that sub( A ) is nonsingular. * * 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 * * Arguments * ========= * * UPLO (global input) CHARACTER * = 'U': sub( A ) is upper triangular; * = 'L': sub( A ) is lower triangular. * * TRANS (global input) CHARACTER * Specifies the form of the system of equations: * = 'N': Solve sub( A ) * X = sub( B ) (No transpose) * = 'T': Solve sub( A )**T * X = sub( B ) (Transpose) * = 'C': Solve sub( A )**H * X = sub( B ) (Conjugate transpose) * * DIAG (global input) CHARACTER * = 'N': sub( A ) is non-unit triangular; * = 'U': sub( A ) is unit triangular. * * 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 matrix sub( B ). NRHS >= 0. * * A (local input) COMPLEX*16 pointer into the local memory * to an array of dimension (LLD_A,LOCc(JA+N-1) ). This array * contains the local pieces of the distributed triangular * matrix sub( A ). If UPLO = 'U', the leading N-by-N upper * triangular part of sub( A ) contains the upper triangular * matrix, and the strictly lower triangular part of sub( A ) * is not referenced. If UPLO = 'L', the leading N-by-N lower * triangular part of sub( A ) contains the lower triangular * matrix, and the strictly upper triangular part of sub( A ) * is not referenced. If DIAG = 'U', the diagonal elements of * sub( A ) are also not referenced and are assumed to be 1. * * 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) COMPLEX*16 pointer into the * local memory to an array of dimension * (LLD_B,LOCc(JB+NRHS-1)). On entry, this array contains the * local pieces of the right hand side distributed matrix * sub( B ). On exit, if INFO = 0, sub( B ) is overwritten by * the solution 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 (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. * > 0: If INFO = i, the i-th diagonal element of sub( A ) is * zero, indicating that the submatrix is singular and the * solutions X have not been computed. * * ===================================================================== * * .. 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 ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOTRAN, NOUNIT, UPPER INTEGER I, IAROW, IBROW, ICOFFA, ICTXT, ICURCOL, $ ICURROW, IROFFA, IROFFB, IDUM, II, IOFFA, J, $ JBLK, JJ, JN, LDA, LL, MYCOL, MYROW, NPCOL, $ NPROW * .. * .. Local Arrays .. INTEGER IDUM1( 3 ), IDUM2( 3 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, CHK1MAT, IGAMX2D, INFOG2L, $ PCHK2MAT, PXERBLA, PZTRSM * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL, INDXG2P EXTERNAL ICEIL, INDXG2P, LSAME * .. * .. Intrinsic Functions .. INTRINSIC ICHAR, MIN, MOD * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * * Test input parameters * INFO = 0 IF( NPROW.EQ.-1 ) THEN INFO = -907 ELSE UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) NOTRAN = LSAME( TRANS, 'N' ) * CALL CHK1MAT( N, 4, N, 4, IA, JA, DESCA, 9, INFO ) CALL CHK1MAT( N, 4, NRHS, 5, IB, JB, DESCB, 13, INFO ) IF( INFO.EQ.0 ) THEN IROFFA = MOD( IA-1, DESCA( MB_ ) ) ICOFFA = MOD( JA-1, DESCA( NB_ ) ) IROFFB = MOD( IB-1, DESCB( MB_ ) ) IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), $ NPROW ) IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ), $ NPROW ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. $ .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -3 ELSE IF( IROFFA.NE.ICOFFA .OR. IROFFA.NE.0 ) THEN INFO = -8 ELSE IF( IROFFA.NE.IROFFB .OR. IAROW.NE.IBROW ) THEN INFO = -11 ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -904 ELSE IF( DESCB( MB_ ).NE.DESCA( NB_ ) ) THEN INFO = -1304 END IF END IF * IF( UPPER ) THEN IDUM1( 1 ) = ICHAR( 'U' ) ELSE IDUM1( 1 ) = ICHAR( 'L' ) END IF IDUM2( 1 ) = 1 IF( NOTRAN ) THEN IDUM1( 2 ) = ICHAR( 'N' ) ELSE IF( LSAME( TRANS, 'T' ) ) THEN IDUM1( 2 ) = ICHAR( 'T' ) ELSE IF( LSAME( TRANS, 'C' ) ) THEN IDUM1( 2 ) = ICHAR( 'C' ) END IF IDUM2( 2 ) = 2 IF( NOUNIT ) THEN IDUM1( 3 ) = ICHAR( 'N' ) ELSE IDUM1( 3 ) = ICHAR( 'D' ) END IF IDUM2( 3 ) = 3 CALL PCHK2MAT( N, 4, N, 4, IA, JA, DESCA, 9, N, 4, NRHS, 5, $ IB, JB, DESCB, 13, 3, IDUM1, IDUM2, INFO ) END IF * IF( INFO.NE.0 ) THEN CALL PXERBLA( ICTXT, 'PZTRTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * * Check for singularity if non-unit. * IF( NOUNIT ) THEN CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, $ II, JJ, ICURROW, ICURCOL ) JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) LDA = DESCA( LLD_ ) IOFFA = II + ( JJ - 1 ) * LDA * * Handle first block separately * JBLK = JN-JA+1 IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN LL = IOFFA DO 10 I = 0, JBLK-1 IF( A( LL ).EQ.ZERO .AND. INFO.EQ.0 ) $ INFO = I + 1 LL = IOFFA + LDA + 1 10 CONTINUE END IF IF( MYROW.EQ.ICURROW ) $ IOFFA = IOFFA + JBLK IF( MYCOL.EQ.ICURCOL ) $ IOFFA = IOFFA + JBLK*LDA ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) * * Loop over remaining blocks of columns * DO 30 J = JN+1, JA+N-1, DESCA( NB_ ) JBLK = MIN( JA+N-J, DESCA( NB_ ) ) IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN LL = IOFFA DO 20 I = 0, JBLK-1 IF( A( LL ).EQ.ZERO .AND. INFO.EQ.0 ) $ INFO = J + I - JA + 1 LL = IOFFA + LDA + 1 20 CONTINUE END IF IF( MYROW.EQ.ICURROW ) $ IOFFA = IOFFA + JBLK IF( MYCOL.EQ.ICURCOL ) $ IOFFA = IOFFA + JBLK*LDA ICURROW = MOD( ICURROW+1, NPROW ) ICURCOL = MOD( ICURCOL+1, NPCOL ) 30 CONTINUE CALL IGAMX2D( ICTXT, 'All', ' ', 1, 1, INFO, 1, IDUM, IDUM, $ -1, -1, MYCOL ) IF( INFO.NE.0 ) $ RETURN END IF * * Solve A * x = b, A**T * x = b, or A**H * x = b. * CALL PZTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, IA, JA, $ DESCA, B, IB, JB, DESCB ) * RETURN * * End of PZTRTRS * END