DTRTRI - compute the inverse of a real upper or lower tri­
       angular matrix A


SYNOPSIS

       SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )

           CHARACTER      DIAG, UPLO

           INTEGER        INFO, LDA, N

           DOUBLE         PRECISION A( LDA, * )


PURPOSE

       DTRTRI computes the inverse of a real upper or lower  tri­
       angular matrix A.  This is the Level 3 BLAS version of the
       algorithm.


ARGUMENTS

       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/output) DOUBLE PRECISION array, dimension
               (LDA,N)
               On entry, 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 ref­
               erenced and are assumed to be  1.   On  exit,  the
               (triangular)  inverse  of  the original matrix, in
               the same storage format.

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

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

               triangular  matrix is singular and its inverse can
               not be computed.


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