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DTPMV(1)			 BLAS routine			      DTPMV(1)

NAME
       DTPMV  -	 performs 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				     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.

ARGUMENTS
       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  fol‐
	      lows:

	      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  )  respec‐
	      tively,  and  so	on.   Before entry with UPLO = 'L' or 'l', the
	      array AP must contain the lower triangular matrix packed sequen‐
	      tially,  column  by  column, so that AP( 1 ) contains a( 1, 1 ),
	      AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and	 a(  3,	 1  )  respec‐
	      tively, and so on.  Note that when  DIAG = 'U' or 'u', the diag‐
	      onal 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 over‐
	      written 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.

FURTHER DETAILS
       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.

BLAS routine			 November 2008			      DTPMV(1)
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