DLATRF_AA factorizes a panel of a real symmetric matrix A using


 the Aasen's algorithm. The panel consists of a set of NB rows of A


 when UPLO is U, or a set of NB columns when UPLO is L.


 In order to factorize the panel, the Aasen's algorithm requires the


 last row, or column, of the previous panel. The first row, or column,


 of A is set to be the first row, or column, of an identity matrix,


 which is used to factorize the first panel.


 The resulting J-th row of U, or J-th column of L, is stored in the


 (J-1)-th row, or column, of A (without the unit diagonals), while


 the diagonal and subdiagonal of A are overwritten by those of T.

UPLO

          UPLO is CHARACTER*1


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


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

J1

          J1 is INTEGER


          The location of the first row, or column, of the panel


          within the submatrix of A, passed to this routine, e.g.,


          when called by SSYTRF_AA, for the first panel, J1 is 1,


          while for the remaining panels, J1 is 2.

M

          M is INTEGER


          The dimension of the submatrix. M >= 0.

NB

          NB is INTEGER


          The dimension of the panel to be facotorized.

A

          A is REAL array, dimension (LDA,M) for


          the first panel, while dimension (LDA,M+1) for the


          remaining panels.


          On entry, A contains the last row, or column, of


          the previous panel, and the trailing submatrix of A


          to be factorized, except for the first panel, only


          the panel is passed.


          On exit, the leading panel is factorized.

LDA

          LDA is INTEGER


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

IPIV

          IPIV is INTEGER array, dimension (M)


          Details of the row and column interchanges,


          the row and column k were interchanged with the row and


          column IPIV(k).

H

          H is REAL workspace, dimension (LDH,NB).

LDH

          LDH is INTEGER


          The leading dimension of the workspace H. LDH >= max(1,M).

WORK

          WORK is REAL workspace, dimension (M).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2017