DSYTRF_AA computes the factorization of a real symmetric matrix A


 using the Aasen's algorithm.  The form of the factorization is


    A = U*T*U**T  or  A = L*T*L**T


 where U (or L) is a product of permutation and unit upper (lower)


 triangular matrices, and T is a symmetric tridiagonal matrix.


 This is the blocked version of the algorithm, calling Level 3 BLAS.

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

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, the tridiagonal matrix is stored in the diagonals


          and the subdiagonals of A just below (or above) the diagonals,


          and L is stored below (or above) the subdiaonals, when UPLO


          is 'L' (or 'U').

LDA

          LDA is INTEGER


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

IPIV

          IPIV is INTEGER array, dimension (N)


          On exit, it contains the details of the interchanges, i.e.,


          the row and column k of A were interchanged with the


          row and column IPIV(k).

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER


          The length of WORK.  LWORK >= MAX(1,2*N). For optimum performance


          LWORK >= N*(1+NB), where NB is the optimal blocksize.


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal size of the WORK array, returns


          this value as the first entry of the WORK array, and no error


          message related to LWORK is issued by XERBLA.

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2017