NAME

       DTPMV - perform one of the matrix-vector operations   x := A*x, or x := A'*x,

SYNOPSIS

       SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )

           INTEGER      INCX, N

           CHARACTER*1  DIAG, TRANS, UPLO

           DOUBLE       PRECISION AP( * ), X( * )

PURPOSE

       DTPMV  performs one of the matrix-vector operations

       where  x  is an n element vector and  A is an n by n unit, or non-unit, upper or lower triangular matrix,
       supplied in packed form.

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 operation to be performed as follows:

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

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

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

              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.

       AP     - DOUBLE PRECISION array of DIMENSION at least
              ( ( n*( n + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u', the array AP must contain the  upper
              triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2
              ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on.  Before entry with  UPLO  =
              'L'  or  'l', the array AP must contain the lower triangular matrix packed sequentially, column by
              column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a(  3,  1  )
              respectively,  and  so  on.  Note that when  DIAG = 'U' or 'u', the diagonal elements of A are not
              referenced, but are assumed to be unity.  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
              vector x. On exit, X is overwritten with the tranformed 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.