SUBROUTINE PCTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, IA, JA, DESCA,
$ B, IB, JB, DESCB, INFO )
*
* -- ScaLAPACK auxiliary routine (version 1.5) --
* 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 A( * ), B( * )
* ..
*
* Purpose
* =======
*
* PCTRTRS 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 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 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 ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+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, PCTRSM, PXERBLA
* ..
* .. 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, 'PCTRTRS', -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 PCTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, IA, JA,
$ DESCA, B, IB, JB, DESCB )
*
RETURN
*
* End of PCTRTRS
*
END