spstrf.f - Man Page

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.

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.