pzposv.f

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      SUBROUTINE pzposv( 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( * )
      COMPLEX*16         A( * ), B( * )
*     ..
*
*  Purpose
*  =======
*
*  PZPOSV computes the solution to a complex system of linear equations
*
*                        sub( A ) * X = sub( B ),
*
*  where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is an N-by-N
*  hermitian distributed positive definite matrix and X and sub( B )
*  denoting B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed
*  matrices.
*
*  The Cholesky decomposition is used to factor sub( A ) as
*
*                     sub( A ) = U**H * U,  if UPLO = 'U', or
*
*                     sub( A ) = L * L**H,  if UPLO = 'L',
*
*  where U is an upper triangular matrix and L is a lower triangular
*  matrix.  The factored form of sub( A ) is then used to solve the
*  system of equations.
*
*  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/local output) COMPLEX*16 pointer into the
*          local memory to an array of dimension (LLD_A, LOCc(JA+N-1)).
*          On entry, this array contains the local pieces of the
*          N-by-N symmetric distributed matrix sub( A ) to be factored.
*          If UPLO = 'U', the leading N-by-N upper triangular part of
*          sub( A ) contains the upper triangular part of the matrix,
*          and its strictly lower triangular part is not referenced.
*          If UPLO = 'L', the leading N-by-N lower triangular part of
*          sub( A ) contains the lower triangular part of the distribu-
*          ted matrix, and its strictly upper triangular part is not
*          referenced. On exit, if INFO = 0, this array contains the
*          local pieces of the factor U or L from the Cholesky factori-
*          zation sub( A ) = U**H*U or L*L**H.
*
*  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,LOC(JB+NRHS-1)).
*          On entry, the local pieces of the right hand sides distribu-
*          ted matrix sub( B ). On exit, if INFO = 0, sub( B ) is over-
*          written with 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.
*          > 0:  If INFO = K, the leading minor of order K,
*                A(IA:IA+K-1,JA:JA+K-1) is not positive definite, and
*                the factorization could not be completed, and the
*                solution has 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 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            IAROW, IBROW, ICOFFA, ICTXT, IROFFA, IROFFB,
     $                   mycol, myrow, npcol, nprow
*     ..
*     .. Local Arrays ..
      INTEGER            IDUM1( 1 ), IDUM2( 1 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           blacs_gridinfo, chk1mat, pchk2mat, pxerbla,
     $                   pzpotrf, pzpotrs
*     ..
*     .. 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
         upper = lsame( uplo, 'U' )
         CALL chk1mat( n, 2, n, 2, ia, ja, desca, 7, info )
         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 = -(1000+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, 'PZPOSV', -info )
         RETURN
      END IF
*
*     Compute the Cholesky factorization sub( A ) = U'*U or L*L'.
*
      CALL pzpotrf( uplo, n, a, ia, ja, desca, info )
*
      IF( info.EQ.0 ) THEN
*
*        Solve the system sub( A ) * X = sub( B ) overwriting sub( B )
*        with X.
*
         CALL pzpotrs( uplo, n, nrhs, a, ia, ja, desca, b, ib, jb,
     $                 descb, info )
*
      END IF
*
      RETURN
*
*     End of PZPOSV
*
      END