LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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spstrf.f File Reference

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subroutine spstrf (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)

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 


Download SPSTRF + dependencies [TGZ] [ZIP] [TXT]
 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.
          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 is INTEGER
          The order of the matrix A.  N >= 0.
          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 is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
          PIV is INTEGER array, dimension (N)
          PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
          RANK is INTEGER
          The rank of A given by the number of steps the algorithm
          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 is REAL array, dimension (2*N)
          Work space.
          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 indefinite.  See Section 7 of
               LAPACK Working Note #161 for further information.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
November 2011

Definition at line 141 of file spstrf.f.

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