_TPMV,_TPSV(3F)						       _TPMV,_TPSV(3F)

NAME    [Toc]    [Back]

     dtpmv, stpmv, ztpmv, ctpmv, dtpsv,	stpsv, ztpsv, ctpsv - BLAS Level Two
     Matrix-Vector Product  and	 Solution of System of Equations


FORTRAN	77 SYNOPSIS
     subroutine	dtpmv( uplo, trans, diag, n, ap, x, incx )
     subroutine	dtpsv( uplo, trans, diag, n, ap, x, incx )
	   character*1	      uplo, trans, diag
	   integer	      n, incx
	   double precision   ap(*), x(*)

     subroutine	stpmv( uplo, trans, diag, n, ap, x, incx )
     subroutine	stpsv( uplo, trans, diag, n, ap, x, incx )
	   character*1	      uplo, trans, diag
	   integer	      n, incx
	   real		      ap(*), x(*)

     subroutine	ztpmv( uplo, trans, diag, n, ap, x, incx )
     subroutine	ztpsv( uplo, trans, diag, n, ap, x, incx )
	   character*1	      uplo, trans, diag
	   integer	      n, incx
	   double complex     ap(*), x(*)

     subroutine	ctpmv( uplo, trans, diag, n, ap, x, incx )
     subroutine	ctpsv( uplo, trans, diag, n, ap, x, incx )
	   character*1	      uplo, trans, diag
	   integer	      n, incx
	   complex	      ap(*), x(*)


FORTRAN	77 SYNOPSIS
     void dtpmv( uplo, trans, diag, n, ap, x, incx )
     void dtpsv( uplo, trans, diag, n, ap, x, incx )
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 trans;
	   MatrixUnitTriangular	 diag;
	   Integer		 n, incx;
	   double		(*ap[ n	], (*x)[ n ];

     void stpmv( uplo, trans, diag, n, ap, x, incx )
     void stpsv( uplo, trans, diag, n, ap, x, incx )
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 trans;
	   MatrixUnitTriangular	 diag;
	   Integer		 n, incx;
	   float		(*ap[ n	], (*x)[ n ];

     void ztpmv( uplo, trans, diag, n, ap, x, incx )
     void ztpsv( uplo, trans, diag, n, ap, x, incx )
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 trans;



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_TPMV,_TPSV(3F)						       _TPMV,_TPSV(3F)



	   MatrixUnitTriangular	 diag;
	   Integer		 n, incx;
	   Zomplex		 (*ap[ n ], (*x)[ n ];

     void ctpmv( uplo, trans, diag, n, ap, x, incx )
     void ctpsv( uplo, trans, diag, n, ap, x, incx )
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 trans;
	   MatrixUnitTriangular	 diag;
	   Integer		 n, incx;
	   Complex		 (*ap[ n ], (*x)[ n ];

DESCRIPTION    [Toc]    [Back]

     dtpmv, stpmv, ztpmv and ctpmv perform one of the matrix-vector operations

	   x :=	A*x,   or   x := A'*x,	 or   x	:= conjg( A' )*x,

     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.

     dtpsv, stpsv, ztpsv and ctpsv solve one of	the systems of equations

	   A*x = b,   or   A'*x	= b,   or   conjg( A' )*x = b,

     where b and x are n element vectors and A is an n by n unit, or non-unit,
     upper or lower triangular matrix, supplied	in packed form.	No test	for
     singularity or near-singularity is	included in this routine. Such tests
     must be performed before calling this routine.

PARAMETERS    [Toc]    [Back]

     uplo    On	entry, uplo specifies whether the matrix is an upper or	lower
	     triangular	matrix as follows:

		  FORTRAN
		  uplo = 'U' or	'u'	   A is	an upper triangular matrix.
		  uplo = 'L' or	'l'	   A is	a lower	triangular matrix.

		  C
		  uplo = UpperTriangle	   A is	an upper triangular matrix.
		  uplo = LowerTriangle	   A is	a lower	triangular matrix.

	     Unchanged on exit.

     trans   On	entry, trans specifies the operation to	be

		  FORTRAN
		  trans	= 'N' or 'n'	   x :=	A*x /  A*x = b.
		  trans	= 'T' or 't'	   x :=	A'*x / A'*x = b.
		  trans	= 'C' or 'c'	   x :=	conjg( A' )*x  /



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						conjg( A' )*x =	b.

		  C
		  trans	= NoTranspose		x := A*x /  A*x	= b.
		  trans	= Transpose		x := A'*x / A'*x = b.
		  trans	= ConjugateTranspose	x := conjg( A' )*x
						conjg( A' )*x =	b.

	     For real value matrices, trans='C'	and trans='T' has the same
	     meaning.

	     Unchanged on exit.

     diag    On	entry, diag specifies whether or not A is unit triangular as
	     follows:

		  FORTRAN
		  diag = 'U' or	'u'   A	is assumed to be unit triangular.
		  diag = 'N' or	'n'   A	is not assumed to be unit triangular.

		  C
		  diag = UnitTriangular	   A is	assumed	to be unit
					   triangular.
		  diag = NotUnitTriangular A is	not assumed to be unit
					   triangular.

	     Unchanged on exit.

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

     ap	     Array of size at least ( (	n*( n +	1 ) )/2	).
	     Before entry with uplo = 'U' or 'u' or 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' or , 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' or , the elements	of a
	     corresponding to the diagonal elements of the matrix A are	not
	     referenced	either,	but are	assumed	to be unity.

	     Unchanged on exit.

     x	     Array of size 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 transformed/solution	vector



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	     x.

     incx    On	entry, incx specifies the increment for	the elements of	x.
	     incx must not be zero.
	     Unchanged on exit.

AUTHORS    [Toc]    [Back]

	  Jack Dongarra, Argonne National Laboratory.
	  Iain Duff, AERE Harwell.
	  Jeremy Du Croz, Numerical Algorithms Group Ltd.
	  Sven Hammarling, Numerical Algorithms	Group Ltd.


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