ZHESV_AA computes the solution to a complex system of linear equations


    A * X = B,


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


 matrices.


 Aasen's algorithm is used to factor A as


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


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


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


 triangular matrices, and T is Hermitian and tridiagonal. The factored form


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

UPLO

          UPLO is CHARACTER*1


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


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

N

          N is INTEGER


          The number of linear equations, i.e., 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 COMPLEX*16 array, dimension (LDA,N)


          On entry, the Hermitian 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 tridiagonal matrix T and the


          multipliers used to obtain the factor U or L from the


          factorization A = U*T*U**H or A = L*T*L**H as computed by


          ZHETRF_AA.

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).

B

          B is COMPLEX*16 array, dimension (LDB,NRHS)


          On entry, the N-by-NRHS right hand side matrix B.


          On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

          LDB is INTEGER


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

WORK

          WORK is COMPLEX*16 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,3*N-2), and for best 


          performance LWORK >= max(1,N*NB), where NB is the optimal


          blocksize for ZHETRF.


          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, D(i,i) is exactly zero.  The factorization


               has been completed, but the block diagonal matrix D is


               exactly singular, so the solution could not be computed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2017