DPSTF2 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 2 BLAS.

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 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 INFO = 0, the factor U or L from the Cholesky


          factorization as above.

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 DOUBLE PRECISION


          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.

LDA

          LDA is INTEGER


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

WORK

          WORK is DOUBLE PRECISION 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.

Univ. of Tennessee

Univ. of California Berkeley

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NAG Ltd.

December 2016