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

NAME
     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
     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
     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  /

									Page 2

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

						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

									Page 3

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

	     x.

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

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

									Page 4

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