SRC/spstrf.f(3)

NAME
SRC/spstrf.f

SYNOPSIS

  Functions/Subroutines
subroutine spstrf (uplo, n, a, lda, piv, rank, tol, work, info)
SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

Function/Subroutine Documentation

  subroutine spstrf (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, real tol, real, dimension( 2*n ) work, integer info)

SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

Purpose:

    !>
    !> SPSTRF computes the Cholesky factorization with complete
    !> pivoting of a real symmetric positive semidefinite matrix A.
    !>
    !> The factorization has the form
    !>    P**T * A * P = U**T * U ,  if UPLO = 'U',
    !>    P**T * A * P = L  * L**T,  if UPLO = 'L',
    !> where U is an upper triangular matrix and L is lower triangular, and
    !> P is stored as vector PIV.
    !>
    !> This algorithm does not attempt to check that A is positive
    !> semidefinite. This version of the algorithm calls level 3 BLAS.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is stored.
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is REAL 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 INFO = 0, the factor U or L from the Cholesky
    !>          factorization as above.
    !>

    LDA

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

    PIV

    !>          PIV is INTEGER array, dimension (N)
    !>          PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
    !>

    RANK

    !>          RANK is INTEGER
    !>          The rank of A given by the number of steps the algorithm
    !>          completed.
    !>

    TOL

    !>          TOL is REAL
    !>          User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) )
    !>          will be used. The algorithm terminates at the (K-1)st step
    !>          if the pivot <= TOL.
    !>

    WORK

    !>          WORK is REAL array, dimension (2*N)
    !>          Work space.
    !>

    INFO

    !>          INFO is INTEGER
    !>          < 0: If INFO = -K, the K-th argument had an illegal value,
    !>          = 0: algorithm completed successfully, and
    !>          > 0: the matrix A is either rank deficient with computed rank
    !>               as returned in RANK, or is not positive semidefinite. See
    !>               Section 7 of LAPACK Working Note #161 for further
    !>               information.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 140 of file spstrf.f.

Author

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