SRC/dsposv.f(3)

NAME
SRC/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 (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( n, * ) work, real, dimension( * ) swork, integer iter, integer info)

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 = 0 and ITER >= 0, see description below), then A is
    !>          unchanged, if double precision factorization has been used
    !>          (INFO = 0 and ITER < 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 successfully 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 principal minor of order i
    !>                of (DOUBLE PRECISION) A is not positive, 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.

Definition at line 197 of file dsposv.f.

Author

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