pstrtrs.f

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      SUBROUTINE pstrtrs( 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( * )
      REAL               A( * ), B( * )
*     ..
*
*  Purpose
*  =======
*
*  PSTRTRS solves a triangular system of the form
*
*     sub( A ) * X = sub( B )  or  sub( A )**T * 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 )**T * X = sub( B ) (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) REAL 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) REAL 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 )
      REAL               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, pstrsm, 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, 'PSTRTRS', -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  or  A' * x = b.
*
      CALL pstrsm( 'Left', uplo, trans, diag, n, nrhs, one, a, ia, ja,
     $             desca, b, ib, jb, descb )
*
      RETURN
*
*     End of PSTRTRS
*
      SUBROUTINE pstrtrs( UPLO, TRANS, DIAG, N, NRHS, A, IA, JA, DESCA, …
      END