ZTRCON (3lapack)

estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

  SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, RWORK, INFO )

      CHARACTER      DIAG, NORM, UPLO

      INTEGER        INFO, LDA, N

      DOUBLE         PRECISION RCOND

      DOUBLE         PRECISION RWORK( * )

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

PURPOSE

  ZTRCON estimates the reciprocal of the condition number of a triangular
  matrix A, in either the 1-norm or the infinity-norm.

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

ARGUMENTS

  NORM    (input) CHARACTER*1
          Specifies whether the 1-norm condition number or the infinity-norm
          condition number is required:
          = '1' or 'O':  1-norm;
          = 'I':         Infinity-norm.

  UPLO    (input) CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular.

  DIAG    (input) CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular.

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

  A       (input) COMPLEX*16 array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading N-by-N upper
          triangular part of the array A contains the upper triangular
          matrix, and the strictly lower triangular part of A is not
          referenced.  If UPLO = 'L', the leading N-by-N lower triangular
          part of the array A contains the lower triangular matrix, and the
          strictly upper triangular part of A is not referenced.  If DIAG =
          'U', the diagonal elements of A are also not referenced and are
          assumed to be 1.

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

  RCOND   (output) DOUBLE PRECISION
          The reciprocal of the condition number of the matrix A, computed as
          RCOND = 1/(norm(A) * norm(inv(A))).

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

  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

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