DSYTRF_AA_2STAGE 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 band matrix with the


 bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is 


 LU factorized with partial pivoting).


 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, L is stored below (or above) the subdiaonal blocks,


          when UPLO  is 'L' (or 'U').

LDA

          LDA is INTEGER


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

TB

          TB is DOUBLE PRECISION array, dimension (LTB)


          On exit, details of the LU factorization of the band matrix.

LTB

          The size of the array TB. LTB >= 4*N, internally


          used to select NB such that LTB >= (3*NB+1)*N.


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


          routine only calculates the optimal size of LTB, 


          returns this value as the first entry of TB, and


          no error message related to LTB is issued by XERBLA.

WORK

          WORK is DOUBLE PRECISION workspace of size LWORK

LWORK

          The size of WORK. LWORK >= N, internally used to select NB


          such that LWORK >= N*NB.


          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.

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).

IPIV2

          IPIV is INTEGER array, dimension (N)


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


          the row and column k of T were interchanged with the


          row and column IPIV(k).

INFO

          INFO is INTEGER


          = 0:  successful exit


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


          > 0:  if INFO = i, band LU factorization failed on i-th column

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2017