SUBROUTINE PCPOSVX( FACT, UPLO, N, NRHS, A, IA, JA, DESCA, AF,
$ IAF, JAF, DESCAF, EQUED, SR, SC, B, IB, JB,
$ DESCB, X, IX, JX, DESCX, RCOND, FERR, BERR,
$ WORK, LWORK, RWORK, LRWORK, INFO )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* December 31, 1998
*
* .. Scalar Arguments ..
CHARACTER EQUED, FACT, UPLO
INTEGER IA, IAF, IB, INFO, IX, JA, JAF, JB, JX, LRWORK,
$ LWORK, N, NRHS
REAL RCOND
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCAF( * ), DESCB( * ), DESCX( * )
REAL BERR( * ), FERR( * ), SC( * ),
$ SR( * ), RWORK( * )
COMPLEX A( * ), AF( * ),
$ B( * ), WORK( * ), X( * )
* ..
*
* Purpose
* =======
*
* PCPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
* compute the solution to a complex system of linear equations
*
* A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1),
*
* where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and
* B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices.
*
* Error bounds on the solution and a condition estimate are also
* provided. In the following comments Y denotes Y(IY:IY+M-1,JY:JY+K-1)
* a M-by-K matrix where Y can be A, AF, B and X.
*
* 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
*
* Description
* ===========
*
* The following steps are performed:
*
* 1. If FACT = 'E', real scaling factors are computed to equilibrate
* the system:
* diag(SR) * A * diag(SC) * inv(diag(SC)) * X = diag(SR) * B
* Whether or not the system will be equilibrated depends on the
* scaling of the matrix A, but if equilibration is used, A is
* overwritten by diag(SR)*A*diag(SC) and B by diag(SR)*B.
*
* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
* factor the matrix A (after equilibration if FACT = 'E') as
* A = U**T* U, if UPLO = 'U', or
* A = L * L**T, if UPLO = 'L',
* where U is an upper triangular matrix and L is a lower triangular
* matrix.
*
* 3. The factored form of A is used to estimate the condition number
* of the matrix A. If the reciprocal of the condition number is
* less than machine precision, steps 4-6 are skipped.
*
* 4. The system of equations is solved for X using the factored form
* of A.
*
* 5. Iterative refinement is applied to improve the computed solution
* matrix and calculate error bounds and backward error estimates
* for it.
*
* 6. If equilibration was used, the matrix X is premultiplied by
* diag(SR) so that it solves the original system before
* equilibration.
*
* Arguments
* =========
*
* FACT (global input) CHARACTER
* Specifies whether or not the factored form of the matrix A is
* supplied on entry, and if not, whether the matrix A should be
* equilibrated before it is factored.
* = 'F': On entry, AF contains the factored form of A.
* If EQUED = 'Y', the matrix A has been equilibrated
* with scaling factors given by S. A and AF will not
* be modified.
* = 'N': The matrix A will be copied to AF and factored.
* = 'E': The matrix A will be equilibrated if necessary, then
* copied to AF and factored.
*
* UPLO (global input) CHARACTER
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of 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 A(IA:IA+N-1,JA:JA+N-1).
* N >= 0.
*
* NRHS (global input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the distributed submatrices B and X. NRHS >= 0.
*
* A (local input/local output) COMPLEX pointer into
* the local memory to an array of local dimension
* ( LLD_A, LOCc(JA+N-1) ).
* On entry, the Hermitian matrix A, except if FACT = 'F' and
* EQUED = 'Y', then A must contain the equilibrated matrix
* diag(SR)*A*diag(SC). If UPLO = 'U', the leading
* N-by-N upper triangular part of A contains the upper
* triangular part of the matrix A, and the strictly lower
* triangular part of A is not referenced. If UPLO = 'L', the
* leading N-by-N lower triangular part of A contains the lower
* triangular part of the matrix A, and the strictly upper
* triangular part of A is not referenced. A is not modified if
* FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit.
*
* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by
* diag(SR)*A*diag(SC).
*
* 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.
*
* AF (local input or local output) COMPLEX pointer
* into the local memory to an array of local dimension
* ( LLD_AF, LOCc(JA+N-1)).
* If FACT = 'F', then AF is an input argument and on entry
* contains the triangular factor U or L from the Cholesky
* factorization A = U**T*U or A = L*L**T, in the same storage
* format as A. If EQUED .ne. 'N', then AF is the factored form
* of the equilibrated matrix diag(SR)*A*diag(SC).
*
* If FACT = 'N', then AF is an output argument and on exit
* returns the triangular factor U or L from the Cholesky
* factorization A = U**T*U or A = L*L**T of the original
* matrix A.
*
* If FACT = 'E', then AF is an output argument and on exit
* returns the triangular factor U or L from the Cholesky
* factorization A = U**T*U or A = L*L**T of the equilibrated
* matrix A (see the description of A for the form of the
* equilibrated matrix).
*
* IAF (global input) INTEGER
* The row index in the global array AF indicating the first
* row of sub( AF ).
*
* JAF (global input) INTEGER
* The column index in the global array AF indicating the
* first column of sub( AF ).
*
* DESCAF (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix AF.
*
* EQUED (global input/global output) CHARACTER
* Specifies the form of equilibration that was done.
* = 'N': No equilibration (always true if FACT = 'N').
* = 'Y': Equilibration was done, i.e., A has been replaced by
* diag(SR) * A * diag(SC).
* EQUED is an input variable if FACT = 'F'; otherwise, it is an
* output variable.
*
* SR (local input/local output) COMPLEX array,
* dimension (LLD_A)
* The scale factors for A distributed across process rows;
* not accessed if EQUED = 'N'. SR is an input variable if
* FACT = 'F'; otherwise, SR is an output variable.
* If FACT = 'F' and EQUED = 'Y', each element of SR must be
* positive.
*
* SC (local input/local output) COMPLEX array,
* dimension (LOC(N_A))
* The scale factors for A distributed across
* process columns; not accessed if EQUED = 'N'. SC is an input
* variable if FACT = 'F'; otherwise, SC is an output variable.
* If FACT = 'F' and EQUED = 'Y', each element of SC must be
* positive.
*
* B (local input/local output) COMPLEX pointer into
* the local memory to an array of local dimension
* ( LLD_B, LOCc(JB+NRHS-1) ).
* On entry, the N-by-NRHS right-hand side matrix B.
* On exit, if EQUED = 'N', B is not modified; if TRANS = 'N'
* and EQUED = 'R' or 'B', B is overwritten by diag(R)*B; if
* TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is overwritten
* by diag(C)*B.
*
* 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.
*
* X (local input/local output) COMPLEX pointer into
* the local memory to an array of local dimension
* ( LLD_X, LOCc(JX+NRHS-1) ).
* If INFO = 0, the N-by-NRHS solution matrix X to the original
* system of equations. Note that A and B are modified on exit
* if EQUED .ne. 'N', and the solution to the equilibrated
* system is inv(diag(SC))*X if TRANS = 'N' and EQUED = 'C' or
* 'B', or inv(diag(SR))*X if TRANS = 'T' or 'C' and EQUED = 'R'
* or 'B'.
*
* IX (global input) INTEGER
* The row index in the global array X indicating the first
* row of sub( X ).
*
* JX (global input) INTEGER
* The column index in the global array X indicating the
* first column of sub( X ).
*
* DESCX (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix X.
*
* RCOND (global output) REAL
* The estimate of the reciprocal condition number of the matrix
* A after equilibration (if done). If RCOND is less than the
* machine precision (in particular, if RCOND = 0), the matrix
* is singular to working precision. This condition is
* indicated by a return code of INFO > 0, and the solution and
* error bounds are not computed.
*
* FERR (local output) REAL array, dimension (LOC(N_B))
* The estimated forward error bounds for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution, FERR(j) bounds the magnitude
* of the largest entry in (X(j) - XTRUE) divided by
* the magnitude of the largest entry in X(j). The quality of
* the error bound depends on the quality of the estimate of
* norm(inv(A)) computed in the code; if the estimate of
* norm(inv(A)) is accurate, the error bound is guaranteed.
*
* BERR (local output) REAL array, dimension (LOC(N_B))
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any entry of A or B that makes X(j) an exact solution).
*
* WORK (local workspace/local output) COMPLEX array,
* dimension (LWORK)
* On exit, WORK(1) returns the minimal and optimal LWORK.
*
* LWORK (local or global input) INTEGER
* The dimension of the array WORK.
* LWORK is local input and must be at least
* LWORK = MAX( PCPOCON( LWORK ), PCPORFS( LWORK ) )
* + LOCr( N_A ).
* LWORK = 3*DESCA( LLD_ )
*
* If LWORK = -1, then LWORK is global input and a workspace
* query is assumed; the routine only calculates the minimum
* and optimal size for all work arrays. Each of these
* values is returned in the first entry of the corresponding
* work array, and no error message is issued by PXERBLA.
*
* RWORK (local workspace/local output) REAL array,
* dimension (LRWORK)
* On exit, RWORK(1) returns the minimal and optimal LRWORK.
*
* LRWORK (local or global input) INTEGER
* The dimension of the array RWORK.
* LRWORK is local input and must be at least
* LRWORK = 2*LOCc(N_A).
*
* If LRWORK = -1, then LRWORK is global input and a workspace
* query is assumed; the routine only calculates the minimum
* and optimal size for all work arrays. Each of these
* values is returned in the first entry of the corresponding
* work array, and no error message is issued by PXERBLA.
*
*
* INFO (global output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, and i is
* <= N: if INFO = i, the leading minor of order i of A
* is not positive definite, so the factorization
* could not be completed, and the solution and error
* bounds could not be computed.
* = N+1: RCOND is less than machine precision. The
* factorization has been completed, but the matrix
* is singular to working precision, and the solution
* and error bounds 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 ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL EQUIL, LQUERY, NOFACT, RCEQU
INTEGER I, IACOL, IAROW, IAFROW, IBROW, IBCOL, ICOFF,
$ ICOFFA, ICTXT, IDUMM, IIA, IIB, IIX, INFEQU,
$ IROFF, IROFFA, IROFFAF, IROFFB, IROFFX, IXCOL,
$ IXROW, J, JJA, JJB, JJX, LDB, LDX, LRWMIN,
$ LWMIN, MYCOL, MYROW, NP, NPCOL, NPROW, NRHSQ,
$ NQ
REAL AMAX, ANORM, BIGNUM, SCOND, SMAX, SMIN, SMLNUM
* ..
* .. Local Arrays ..
INTEGER IDUM1( 5 ), IDUM2( 5 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, PCHK2MAT, INFOG2L,
$ PCPOCON, PCPOEQU,
$ PCPORFS, PCPOTRF, PCPOTRS,
$ PCLACPY, PCLAQSY, PXERBLA,
$ SGAMN2D, SGAMX2D
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER INDXG2P, NUMROC
REAL PCLANHE, PSLAMCH
EXTERNAL INDXG2P, LSAME, NUMROC, PCLANHE, PSLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ICHAR, MAX, MIN, 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 = -(800+CTXT_)
ELSE
CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 8, INFO )
IF( LSAME( FACT, 'F' ) )
$ CALL CHK1MAT( N, 3, N, 3, IAF, JAF, DESCAF, 12, INFO )
CALL CHK1MAT( N, 3, NRHS, 4, IB, JB, DESCB, 20, INFO )
IF( INFO.EQ.0 ) THEN
IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
$ NPROW )
IAFROW = INDXG2P( IAF, DESCAF( MB_ ), MYROW,
$ DESCAF( RSRC_ ), NPROW )
IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ),
$ NPROW )
IXROW = INDXG2P( IX, DESCX( MB_ ), MYROW, DESCX( RSRC_ ),
$ NPROW )
IROFFA = MOD( IA-1, DESCA( MB_ ) )
IROFFAF = MOD( IAF-1, DESCAF( MB_ ) )
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
IROFFB = MOD( IB-1, DESCB( MB_ ) )
IROFFX = MOD( IX-1, DESCX( MB_ ) )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IIA, JJA, IAROW, IACOL )
NP = NUMROC( N+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW )
IF( MYROW.EQ.IAROW )
$ NP = NP-IROFFA
NQ = NUMROC( N+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
IF( MYCOL.EQ.IACOL )
$ NQ = NQ-ICOFFA
LWMIN = 3*DESCA( LLD_ )
LRWMIN = MAX( 2*NQ, NP )
NOFACT = LSAME( FACT, 'N' )
EQUIL = LSAME( FACT, 'E' )
IF( NOFACT .OR. EQUIL ) THEN
EQUED = 'N'
RCEQU = .FALSE.
ELSE
RCEQU = LSAME( EQUED, 'Y' )
SMLNUM = PSLAMCH( ICTXT, 'Safe minimum' )
BIGNUM = ONE / SMLNUM
END IF
IF( .NOT.NOFACT .AND. .NOT.EQUIL .AND.
$ .NOT.LSAME( FACT, 'F' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( UPLO, 'U' ) .AND.
$ .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -2
ELSE IF( IROFFA.NE.0 ) THEN
INFO = -6
ELSE IF( ICOFFA.NE.0 .OR. IROFFA.NE.ICOFFA ) THEN
INFO = -7
ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -(800+NB_)
ELSE IF( IAFROW.NE.IAROW ) THEN
INFO = -10
ELSE IF( IROFFAF.NE.0 ) THEN
INFO = -10
ELSE IF( ICTXT.NE.DESCAF( CTXT_ ) ) THEN
INFO = -(1200+CTXT_)
ELSE IF( LSAME( FACT, 'F' ) .AND. .NOT.
$ ( RCEQU .OR. LSAME( EQUED, 'N' ) ) ) THEN
INFO = -13
ELSE
IF( RCEQU ) THEN
*
SMIN = BIGNUM
SMAX = ZERO
DO 10 J = IIA, IIA + NP - 1
SMIN = MIN( SMIN, SR( J ) )
SMAX = MAX( SMAX, SR( J ) )
10 CONTINUE
CALL SGAMN2D( ICTXT, 'Columnwise', ' ', 1, 1, SMIN,
$ 1, IDUMM, IDUMM, -1, -1, MYCOL )
CALL SGAMX2D( ICTXT, 'Columnwise', ' ', 1, 1, SMAX,
$ 1, IDUMM, IDUMM, -1, -1, MYCOL )
IF( SMIN.LE.ZERO ) THEN
INFO = -14
ELSE IF( N.GT.0 ) THEN
SCOND = MAX( SMIN, SMLNUM ) / MIN( SMAX, BIGNUM )
ELSE
SCOND = ONE
END IF
END IF
END IF
END IF
*
WORK( 1 ) = REAL( LWMIN )
RWORK( 1 ) = REAL( LRWMIN )
LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 )
IF( INFO.EQ.0 ) THEN
IF( IBROW.NE.IAROW ) THEN
INFO = -18
ELSE IF( IXROW.NE.IBROW ) THEN
INFO = -22
ELSE IF( DESCB( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -(2000+NB_)
ELSE IF( ICTXT.NE.DESCB( CTXT_ ) ) THEN
INFO = -(2000+CTXT_)
ELSE IF( ICTXT.NE.DESCX( CTXT_ ) ) THEN
INFO = -(2400+CTXT_)
ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -28
ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
INFO = -30
END IF
IDUM1( 1 ) = ICHAR( FACT )
IDUM2( 1 ) = 1
IDUM1( 2 ) = ICHAR( UPLO )
IDUM2( 2 ) = 2
IF( LSAME( FACT, 'F' ) ) THEN
IDUM1( 3 ) = ICHAR( EQUED )
IDUM2( 3 ) = 13
IF( LWORK.EQ.-1 ) THEN
IDUM1( 4 ) = -1
ELSE
IDUM1( 4 ) = 1
END IF
IDUM2( 4 ) = 28
IF( LRWORK.EQ.-1 ) THEN
IDUM1( 5 ) = -1
ELSE
IDUM1( 5 ) = 1
END IF
IDUM2( 5 ) = 30
CALL PCHK2MAT( N, 3, N, 3, IA, JA, DESCA, 8, N, 3, NRHS,
$ 4, IB, JB, DESCB, 19, 5, IDUM1, IDUM2,
$ INFO )
ELSE
IF( LWORK.EQ.-1 ) THEN
IDUM1( 3 ) = -1
ELSE
IDUM1( 3 ) = 1
END IF
IDUM2( 3 ) = 28
IF( LRWORK.EQ.-1 ) THEN
IDUM1( 4 ) = -1
ELSE
IDUM1( 4 ) = 1
END IF
IDUM2( 4 ) = 30
CALL PCHK2MAT( N, 3, N, 3, IA, JA, DESCA, 8, N, 3, NRHS,
$ 4, IB, JB, DESCB, 19, 4, IDUM1, IDUM2,
$ INFO )
END IF
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PCPOSVX', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
IF( EQUIL ) THEN
*
* Compute row and column scalings to equilibrate the matrix A.
*
CALL PCPOEQU( N, A, IA, JA, DESCA, SR, SC, SCOND, AMAX,
$ INFEQU )
*
IF( INFEQU.EQ.0 ) THEN
*
* Equilibrate the matrix.
*
CALL PCLAQSY( UPLO, N, A, IA, JA, DESCA, SR, SC, SCOND,
$ AMAX, EQUED )
RCEQU = LSAME( EQUED, 'Y' )
END IF
END IF
*
* Scale the right-hand side.
*
CALL INFOG2L( IB, JB, DESCB, NPROW, NPCOL, MYROW, MYCOL, IIB,
$ JJB, IBROW, IBCOL )
LDB = DESCB( LLD_ )
IROFF = MOD( IB-1, DESCB( MB_ ) )
ICOFF = MOD( JB-1, DESCB( NB_ ) )
NP = NUMROC( N+IROFF, DESCB( MB_ ), MYROW, IBROW, NPROW )
NRHSQ = NUMROC( NRHS+ICOFF, DESCB( NB_ ), MYCOL, IBCOL, NPCOL )
IF( MYROW.EQ.IBROW ) NP = NP-IROFF
IF( MYCOL.EQ.IBCOL ) NRHSQ = NRHSQ-ICOFF
*
IF( RCEQU ) THEN
DO 30 J = JJB, JJB+NRHSQ-1
DO 20 I = IIB, IIB+NP-1
B( I + ( J-1 )*LDB ) = SR( I )*B( I + ( J-1 )*LDB )
20 CONTINUE
30 CONTINUE
END IF
*
IF( NOFACT .OR. EQUIL ) THEN
*
* Compute the Cholesky factorization A = U'*U or A = L*L'.
*
CALL PCLACPY( 'Full', N, N, A, IA, JA, DESCA, AF, IAF, JAF,
$ DESCAF )
CALL PCPOTRF( UPLO, N, AF, IAF, JAF, DESCAF, INFO )
*
* Return if INFO is non-zero.
*
IF( INFO.NE.0 ) THEN
IF( INFO.GT.0 )
$ RCOND = ZERO
RETURN
END IF
END IF
*
* Compute the norm of the matrix A.
*
ANORM = PCLANHE( '1', UPLO, N, A, IA, JA, DESCA, RWORK )
*
* Compute the reciprocal of the condition number of A.
*
CALL PCPOCON( UPLO, N, AF, IAF, JAF, DESCAF, ANORM, RCOND, WORK,
$ LWORK, RWORK, LRWORK, INFO )
*
* Return if the matrix is singular to working precision.
*
IF( RCOND.LT.PSLAMCH( ICTXT, 'Epsilon' ) ) THEN
INFO = IA + N
RETURN
END IF
*
* Compute the solution matrix X.
*
CALL PCLACPY( 'Full', N, NRHS, B, IB, JB, DESCB, X, IX, JX,
$ DESCX )
CALL PCPOTRS( UPLO, N, NRHS, AF, IAF, JAF, DESCAF, X, IX, JX,
$ DESCX, INFO )
*
* Use iterative refinement to improve the computed solution and
* compute error bounds and backward error estimates for it.
*
CALL PCPORFS( UPLO, N, NRHS, A, IA, JA, DESCA, AF, IAF, JAF,
$ DESCAF, B, IB, JB, DESCB, X, IX, JX, DESCX, FERR,
$ BERR, WORK, LWORK, RWORK, LRWORK, INFO )
*
* Transform the solution matrix X to a solution of the original
* system.
*
CALL INFOG2L( IX, JX, DESCX, NPROW, NPCOL, MYROW, MYCOL, IIX,
$ JJX, IXROW, IXCOL )
LDX = DESCX( LLD_ )
IROFF = MOD( IX-1, DESCX( MB_ ) )
ICOFF = MOD( JX-1, DESCX( NB_ ) )
NP = NUMROC( N+IROFF, DESCX( MB_ ), MYROW, IXROW, NPROW )
NRHSQ = NUMROC( NRHS+ICOFF, DESCX( NB_ ), MYCOL, IXCOL, NPCOL )
IF( MYROW.EQ.IBROW ) NP = NP-IROFF
IF( MYCOL.EQ.IBCOL ) NRHSQ = NRHSQ-ICOFF
*
IF( RCEQU ) THEN
DO 50 J = JJX, JJX+NRHSQ-1
DO 40 I = IIX, IIX+NP-1
X( I + ( J-1 )*LDX ) = SR( I )*X( I + ( J-1 )*LDX )
40 CONTINUE
50 CONTINUE
DO 60 J = JJX, JJX+NRHSQ-1
FERR( J ) = FERR( J ) / SCOND
60 CONTINUE
END IF
*
WORK( 1 ) = REAL( LWMIN )
RWORK( 1 ) = REAL( LRWMIN )
RETURN
*
* End of PCPOSVX
*
END