spstrf.f (3) - Linux Manuals


spstrf.f -



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

Function/Subroutine Documentation

subroutine spstrf (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, integer, dimension( n )PIV, integerRANK, realTOL, real, dimension( 2*n )WORK, integerINFO)



 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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