ZHESV 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.


 The diagonal pivoting method is used to factor A as


    A = U * D * U**H,  if UPLO = 'U', or


    A = L * D * L**H,  if UPLO = 'L',


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


 triangular matrices, and D is Hermitian and block diagonal with


 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the


          multipliers used to obtain the factor U or L from the


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


          ZHETRF.

LDA

          LDA is INTEGER


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

IPIV

          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D, as


          determined by ZHETRF.  If IPIV(k) > 0, then rows and columns


          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1


          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,


          then rows and columns k-1 and -IPIV(k) were interchanged and


          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and


          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and


          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2


          diagonal block.

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 >= 1, and for best performance


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


          ZHETRF.


          for LWORK < N, TRS will be done with Level BLAS 2


          for LWORK >= N, TRS will be done with Level BLAS 3


          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.

December 2016