DTRSV  -  solve one of the systems of equations   A*x = b,
       or A'*x = b,


SYNOPSIS

       SUBROUTINE DTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )

           INTEGER      INCX, LDA, N

           CHARACTER*1  DIAG, TRANS, UPLO

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


PURPOSE

       DTRSV  solves one of the systems of equations

       where  b  and  x  are n element vectors and A is an n by n
       unit, or non-unit, upper or lower triangular matrix.

       No test for singularity or near-singularity is included in
       this  routine. Such tests must be performed before calling
       this routine.


PARAMETERS

       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the matrix  is  an
              upper or lower triangular matrix as follows:

              UPLO  =  'U'  or  'u'    A  is  an upper triangular
              matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

              Unchanged on exit.

       TRANS  - CHARACTER*1.
              On  entry,  TRANS  specifies  the  equations  to be
              solved as follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   A'*x = b.

              Unchanged on exit.

       DIAG   - CHARACTER*1.
              On entry, DIAG specifies whether or not A  is  unit
              triangular as follows:

              DIAG  = 'U' or 'u'   A is assumed to be unit trian­
              gular.

              triangular.

              Unchanged on exit.

       N      - INTEGER.
              On entry, N specifies the order of the matrix A.  N
              must be at least zero.  Unchanged on exit.

       A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
              Before entry with  UPLO = 'U' or 'u', the leading n
              by n upper triangular part of the array A must con­
              tain the upper triangular matrix and  the  strictly
              lower  triangular  part  of  A  is  not referenced.
              Before entry with UPLO = 'L' or 'l', the leading  n
              by n lower triangular part of the array A must con­
              tain the lower triangular matrix and  the  strictly
              upper triangular part of A is not referenced.  Note
              that when  DIAG = 'U' or 'u', the diagonal elements
              of  A are not referenced either, but are assumed to
              be unity.  Unchanged on exit.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as
              declared  in the calling (sub) program. LDA must be
              at least max( 1, n ).  Unchanged on exit.

       X      - DOUBLE PRECISION array of dimension at least
              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the
              incremented  array  X  must  contain  the n element
              right-hand side vector b. On exit, X is overwritten
              with the solution vector x.

       INCX   - INTEGER.
              On entry, INCX specifies the increment for the ele­
              ments of X. INCX must not be  zero.   Unchanged  on
              exit.

              Level 2 Blas routine.

              --  Written  on  22-October-1986.   Jack  Dongarra,
              Argonne National Lab.  Jeremy Du Croz, Nag  Central
              Office.    Sven  Hammarling,  Nag  Central  Office.
              Richard Hanson, Sandia National Labs.


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