Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - computes the solution to a complex system of linear equations  A * X = B,

SYNOPSIS

       SUBROUTINE ZCPOSV( UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, ITER, LDA, LDB, LDX, N, NRHS

           DOUBLE         PRECISION RWORK( * )

           COMPLEX        SWORK( * )

           COMPLEX*16     A( LDA, * ), B( LDB, * ), WORK( N, * ), X( LDX, * )

PURPOSE

       ZCPOSV computes the solution to a complex system of linear equations
          A * X = B,
        where A is an N-by-N Hermitian positive definite matrix and X and B
        are N-by-NRHS matrices.
        ZCPOSV first attempts to factorize the matrix in COMPLEX and use this
        factorization within an iterative refinement procedure to produce a
        solution with COMPLEX*16 normwise backward error quality (see below).
        If the approach fails the method switches to a COMPLEX*16
        factorization and solve.
        The iterative refinement is not going to be a winning strategy if
        the ratio COMPLEX performance over COMPLEX*16 performance is too
        small. A reasonable strategy should take the number of right-hand
        sides and the size of the matrix into account. This might be done
        with a call to ILAENV in the future. Up to now, we always try
        iterative refinement.
        The iterative refinement process is stopped if
            ITER > ITERMAX
        or for all the RHS we have:
            RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
        where
            o ITER is the number of the current iteration in the iterative
              refinement process
            o RNRM is the infinity-norm of the residual
            o XNRM is the infinity-norm of the solution
            o ANRM is the infinity-operator-norm of the matrix A
            o EPS is the machine epsilon returned by DLAMCH('Epsilon')
        The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
        respectively.

ARGUMENTS

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

        N       (input) INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

        NRHS    (input) INTEGER
                The number of right hand sides, i.e., the number of columns
                of the matrix B.  NRHS >= 0.

        A       (input/output) COMPLEX*16 array,
                dimension (LDA,N)
                On entry, the Hermitian matrix A. 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.
                Note that the imaginary parts of the diagonal
                elements need not be set and are assumed to be zero.
                On exit, if iterative refinement has been successfully used
                (INFO.EQ.0 and ITER.GE.0, see description below), then A is
                unchanged, if double precision factorization has been used
                (INFO.EQ.0 and ITER.LT.0, see description below), then the
                array A contains the factor U or L from the Cholesky
                factorization A = U**H*U or A = L*L**H.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

        B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
                The N-by-NRHS right hand side matrix B.

        LDB     (input) INTEGER
                The leading dimension of the array B.  LDB >= max(1,N).

        X       (output) COMPLEX*16 array, dimension (LDX,NRHS)
                If INFO = 0, the N-by-NRHS solution matrix X.

        LDX     (input) INTEGER
                The leading dimension of the array X.  LDX >= max(1,N).

        WORK    (workspace) COMPLEX*16 array, dimension (N*NRHS)
                This array is used to hold the residual vectors.

        SWORK   (workspace) COMPLEX array, dimension (N*(N+NRHS))
                This array is used to use the single precision matrix and the
                right-hand sides or solutions in single precision.

        RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

        ITER    (output) INTEGER
                < 0: iterative refinement has failed, COMPLEX*16
                factorization has been performed
                -1 : the routine fell back to full precision for
                implementation- or machine-specific reasons
                -2 : narrowing the precision induced an overflow,
                the routine fell back to full precision
                -3 : failure of CPOTRF
                -31: stop the iterative refinement after the 30th
                iterations
                > 0: iterative refinement has been sucessfully used.
                Returns the number of iterations

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  if INFO = i, the leading minor of order i of
                (COMPLEX*16) A is not positive definite, so the
                factorization could not be completed, and the solution
                has not been computed.

 LAPACK PROTOTYPE driver routine (version 3.April 2011                            ZCPOSV(3lapack)