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_TRMV,_TRSV(3F)						       _TRMV,_TRSV(3F)


NAME    [Toc]    [Back]

     dtrmv, strmv, ztrmv, ctrmv, dtrsv,	strsv, ztrsv, ctrsv - BLAS Level Two
     Matrix-Vector Product and Solution	of system of equations.


FORTRAN	77 SYNOPSIS
     subroutine	dtrmv( uplo, trans, diag, n, a,	lda, x,	incx )
     subroutine	dtrsv( uplo, trans, diag, n, a,	lda, x,	incx )
	   character*1	      uplo, trans, diag
	   integer	      n, lda, incx
	   double precision   a( lda,*), x(*)

     subroutine	strmv( uplo, trans, diag, n, a,	lda, x,	incx )
     subroutine	strsv( uplo, trans, diag, n, a,	lda, x,	incx )
	   character*1	      uplo, trans, diag
	   integer	      n, lda, incx
	   real		      a( lda,*), x(*)

     subroutine	ztrmv( uplo, trans, diag, n, a,	lda, x,	incx )
     subroutine	ztrsv( uplo, trans, diag, n, a,	lda, x,	incx )
	   character*1	      uplo, trans, diag
	   integer	      n, lda, incx
	   double complex     a( lda,*), x(*)

     subroutine	ctrmv( uplo, trans, diag, n, a,	lda, x,	incx )
     subroutine	ctrsv( uplo, trans, diag, n, a,	lda, x,	incx )
	   character*1	      uplo, trans, diag
	   integer	      n, lda, incx
	   complex	      a( lda,*), x(*)


C SYNOPSIS    [Toc]    [Back]

     void dtrmv( uplo, trans, diag, n, a, lda, x, incx )
     void dtrsv( uplo, trans, diag, n, a, lda, x, incx )
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 trans;
	   MatrixUnitTriangular	 diag;
	   Integer		 n, lda, incx;
	   double		 (*a)[lda*n], (*x)[ n ];

     void strmv( uplo, trans, diag, n, a, lda, x, incx )
     void strsv( uplo, trans, diag, n, a, lda, x, incx )
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 trans;
	   MatrixUnitTriangular	 diag;
	   Integer		 n, lda, incx;
	   float		 (*a)[lda*n], (*x)[ n ];

     void ztrmv( uplo, trans, diag, n, a, lda, x, incx )
     void ztrsv( uplo, trans, diag, n, a, lda, x, incx )
	   MatrixTriangle	 uplo;



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_TRMV,_TRSV(3F)						       _TRMV,_TRSV(3F)



	   MatrixTranspose	 trans;
	   MatrixUnitTriangular	 diag;
	   Integer		 n, lda, incx;
	   Zomplex		 (*a)[lda*n], (*x)[ n ];

     void ctrmv( uplo, trans, diag, n, a, lda, x, incx )
     void ctrsv( uplo, trans, diag, n, a, lda, x, incx )
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 trans;
	   MatrixUnitTriangular	 diag;
	   Integer		 n, lda, incx;

	   Complex		 (*a)[lda*n], (*x)[ n ];


DESCRIPTION    [Toc]    [Back]

     dtrmv, strmv, ztrmv and ctrmv 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.

     dtrsv, strsv, ztrsv and ctrsv 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.	No test	for singularity	or nearsingularity
 is included in	these routines.	Such tests must	be performed
     before calling these routines.

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.



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_TRMV,_TRSV(3F)						       _TRMV,_TRSV(3F)



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

     a	     An	array containing the matrix A.

	     FORTRAN
	     Array of dimension	(lda, n).

	     C
	     A pointer to an array of size lda*n.
	     See note below about array	storage	convention for C.

	     Before entry with uplo = 'U' or 'u' or , the elements of the
	     array a corresponding to the leading n by n upper triangular part
	     of	the matrix A must contain the upper triangular matrix and the
	     elements corresponding to the strictly lower triangular part of A
	     are not referenced.

	     Before entry with uplo = 'L' or 'l' or , the elements
	     corresponding to the leading n by n lower triangular elements of
	     the matrix	A  must	contain	the lower triangular matrix and	the



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_TRMV,_TRSV(3F)						       _TRMV,_TRSV(3F)



	     corresponding strictly upper triangular part of the matrix	A is
	     not referenced.

	     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.

     lda     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	     Array of size at least ( 1	+ ( n -	1 )*abs( incx )	). Before
	     entry, the	incremented array x must contain the vector x. On
	     exit, x is	overwritten with the transformed/solution vector x.

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

       The matrices  are assumed  to be	stored in a  one dimensional C array
       in an analogous fashion as a Fortran array (column major). Therefore,
       the element  A(i+1,j)  of matrix	A  is stored  immediately  after the
       element	A(i,j),	while  A(i,j+1)	is lda	elements apart from  A(i,j).
       The element A(i,j) of the matrix	can be accessed	directly by reference
       to  a[ (j-1)*lda	+ (i-1)	].

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.


									PPPPaaaaggggeeee 4444
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