ZHESV (3lapack)

compute the solution to a complex system of linear equations A * X = B,

SYNOPSIS

  SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO )

      CHARACTER     UPLO

      INTEGER       INFO, LDA, LDB, LWORK, N, NRHS

      INTEGER       IPIV( * )

      COMPLEX*16    A( LDA, * ), B( LDB, * ), WORK( LWORK )

PURPOSE

  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.

ARGUMENTS

  UPLO    (input) CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.

  N       (input) INTEGER
          The number of linear equations, i.e., the order of the matrix A.  N
          >= 0.

  NRHS    (input) INTEGER
          The number of right hand sides, i.e., the number of columns of the
          matrix B.  NRHS >= 0.

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

  IPIV    (output) 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       (input/output) 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     (input) INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

  WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK   (input) INTEGER
          The length of WORK.  LWORK >= 1, and for best performance LWORK >=
          N*NB, where NB is the optimal blocksize for ZHETRF.

  INFO    (output) 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.