SUBROUTINE PZPOSV( UPLO, N, NRHS, A, IA, JA, DESCA, B, IB, JB,
$ DESCB, INFO )
*
* -- ScaLAPACK routine (version 1.5) --
* 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