dsposv.f(3)

NAME
dsposv.f -

SYNOPSIS

  Functions/Subroutines

subroutine dsposv (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, ITER, INFO)
DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

Function/Subroutine Documentation

  subroutine dsposv (characterUPLO, integerN, integerNRHS, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( n, * )WORK, real, dimension( * )SWORK, integerITER, integerINFO)

DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

Purpose:

     DSPOSV computes the solution to a real system of linear equations
        A * X = B,
     where A is an N-by-N symmetric positive definite matrix and X and B
     are N-by-NRHS matrices.

     DSPOSV first attempts to factorize the matrix in SINGLE PRECISION
     and use this factorization within an iterative refinement procedure
     to produce a solution with DOUBLE PRECISION normwise backward error
     quality (see below). If the approach fails the method switches to a
     DOUBLE PRECISION factorization and solve.

     The iterative refinement is not going to be a winning strategy if
     the ratio SINGLE PRECISION performance over DOUBLE PRECISION
     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.

Parameters:
    UPLO

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

    N

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

    NRHS

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

    A

              A is DOUBLE PRECISION array,
              dimension (LDA,N)
              On entry, the symmetric 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.
              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**T*U or A = L*L**T.

    LDA

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

    B

              B is DOUBLE PRECISION array, dimension (LDB,NRHS)
              The N-by-NRHS right hand side matrix B.

    LDB

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

    X

              X is DOUBLE PRECISION array, dimension (LDX,NRHS)
              If INFO = 0, the N-by-NRHS solution matrix X.

    LDX

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

    WORK

              WORK is DOUBLE PRECISION array, dimension (N,NRHS)
              This array is used to hold the residual vectors.

    SWORK

              SWORK is REAL 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.

    ITER

              ITER is INTEGER
              < 0: iterative refinement has failed, double precision
                   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 SPOTRF
                   -31: stop the iterative refinement after the 30th
                        iterations
              > 0: iterative refinement has been sucessfully used.
                   Returns the number of iterations

    INFO

              INFO is 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 (DOUBLE
                    PRECISION) A is not positive definite, so the
                    factorization could not be completed, and the solution
                    has not been computed.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 199 of file dsposv.f.

Author

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