ZHECON (3lapack)

estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF

SYNOPSIS

  SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO )

      CHARACTER      UPLO

      INTEGER        INFO, LDA, N

      DOUBLE         PRECISION ANORM, RCOND

      INTEGER        IPIV( * )

      COMPLEX*16     A( LDA, * ), WORK( * )

PURPOSE

  ZHECON estimates the reciprocal of the condition number of a complex
  Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
  computed by ZHETRF.

  An estimate is obtained for norm(inv(A)), and the reciprocal of the
  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS

  UPLO    (input) CHARACTER*1
          Specifies whether the details of the factorization are stored as an
          upper or lower triangular matrix.  = 'U':  Upper triangular, form
          is A = U*D*U**H;
          = 'L':  Lower triangular, form is A = L*D*L**H.

  N       (input) INTEGER
          The order of the matrix A.  N >= 0.

  A       (input) COMPLEX*16 array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to obtain the
          factor U or L as computed by ZHETRF.

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

  IPIV    (input) INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D as
          determined by ZHETRF.

  ANORM   (input) DOUBLE PRECISION
          The 1-norm of the original matrix A.

  RCOND   (output) DOUBLE PRECISION
          The reciprocal of the condition number of the matrix A, computed as
          RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-
          norm of inv(A) computed in this routine.

  WORK    (workspace) COMPLEX*16 array, dimension (2*N)

  INFO    (output) INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value