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


SYNOPSIS

       SUBROUTINE DTRCON( NORM,  UPLO,  DIAG,  N,  A, LDA, RCOND,
                          WORK, IWORK, INFO )

           CHARACTER      DIAG, NORM, UPLO

           INTEGER        INFO, LDA, N

           DOUBLE         PRECISION RCOND

           INTEGER        IWORK( * )

           DOUBLE         PRECISION A( LDA, * ), WORK( * )


PURPOSE

       DTRCON estimates the reciprocal of the condition number of
       a  triangular matrix A, in either the 1-norm or the infin­
       ity-norm.  The norm of A is computed and  an  estimate  is
       obtained for norm(inv(A)), then the reciprocal of the con­
       dition 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) DOUBLE PRECISION array, dimension (LDA,N)
               The triangular matrix A.  If UPLO = 'U', the lead­
               ing 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  refer­
               enced.   If  UPLO  = 'L', the leading N-by-N lower
               triangular part of the array A contains the  lower
               triangular   matrix,   and   the   strictly  upper

               'U',  the diagonal elements of A are also not ref­
               erenced 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) DOUBLE PRECISION array, dimension
               (3*N)

       IWORK   (workspace) INTEGER array, dimension (N)

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


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