NAME

       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 triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit 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
              contain 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
              contain 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 elements 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.