SSYSV_AA_2STAGE computes the solution to a real system of


 linear equations


    A * X = B,


 where A is an N-by-N symmetric matrix and X and B are N-by-NRHS


 matrices.


 Aasen's 2-stage algorithm is used to factor A as


    A = U * T * U**T,  if UPLO = 'U', or


    A = L * T * L**T,  if UPLO = 'L',


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


 triangular matrices, and T is symmetric and band. The matrix T is


 then LU-factored with partial pivoting. The factored form of A


 is then used to solve the system of equations A * X = B.


 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.

NRHS

          NRHS is INTEGER


          The number of right hand sides, i.e., the number of columns


          of the matrix B.  NRHS >= 0.

A

          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, 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 REAL 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.

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).

B

          B is REAL array, dimension (LDB,NRHS)


          On entry, the right hand side matrix B.


          On exit, the solution matrix X.

LDB

          LDB is INTEGER


          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is REAL 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.

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