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_TRMM(3F)							     _TRMM(3F)

NAME
     dtrmm, strmm, ztrmm, ctrmm - BLAS level three Matrix Product

FORTRAN 77 SYNOPSIS
     subroutine dtrmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   character*1	      side,uplo,transa,diag
	   integer	      m, n, lda, ldb
	   double precision   alpha
	   double precision   a( lda,*), b(ldb,*)

     subroutine strmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   character*1	      side,uplo,transa,diag
	   integer	      m, n, lda, ldb
	   real		      alpha
	   real		      a( lda,*), b(ldb,*)

     subroutine ztrmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   character*1	      side,uplo,transa,diag
	   integer	      m, n, lda, ldb
	   double complex     alpha
	   double complex     a( lda,*), b(ldb,*)

     subroutine ctrmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   character*1	      side,uplo,transa,diag
	   integer	      m, n, lda, ldb
	   complex	      alpha
	   complex	      a( lda,*), b(ldb,*)

C SYNOPSIS
     void dtrmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 transa;
	   MatrixUnitTriangular	 diag;
	   Integer		 m, n, lda, ldb;
	   double		 alpha;
	   double		 (*a)[lda*k], (*b)[lda*n];

     void strmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 transa;
	   MatrixUnitTriangular	 diag;
	   Integer		 m, n, lda, ldb;
	   float		 alpha;
	   float		 (*a)[lda*k], (*b)[lda*n];

     void ztrmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;

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_TRMM(3F)							     _TRMM(3F)

	   MatrixTranspose	 transa;
	   MatrixUnitTriangular	 diag;
	   Integer		 m, n, lda, ldb;
	   Zomplex		 alpha;
	   Zomplex		 (*a)[lda*k], (*b)[lda*n];

     void ctrmm( side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb )
	   OperationSide	 side;
	   MatrixTriangle	 uplo;
	   MatrixTranspose	 transa;
	   MatrixUnitTriangular	 diag;
	   Integer		 m, n, lda, ldb;
	   Complex		 alpha;
	   Complex		 (*a)[lda*k], (*b)[lda*n];

DESCRIPTION
     dtrmm, strmm, ztrmm and ctrmm perform one of the matrix-matrix operations

	  B := alpha*op( A )*B,	  or   B := alpha*B*op( A )

     where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit,
     upper or lower triangular matrix and op( A ) is one of

	  op( A ) = A	or   op( A ) = A'   or	 op( A ) = conjg( A' ).

PARAMETERS
     side    On entry, side specifies whether op( A ) multiplies B from the
	     left or right as follows:

		  FORTRAN
		  side = 'L' or 'l'   B := alpha*op( A )*B.
		  side = 'R' or 'r'   B := alpha*B*op( A ).

		  C
		  side = LeftSide     B := alpha*op( A )*B.
		  side = RightSide    B := alpha*B*op( A ).

	     Unchanged on exit.

     uplo    On entry, uplo specifies whether the matrix A 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

									Page 2

_TRMM(3F)							     _TRMM(3F)

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

	     Unchanged on exit.

     transa  On entry, transa specifies the form of op( A ) to be used in the
	     matrix multiplication as follows:

		  FORTRAN
		  transa = 'N' or 'n'		op( A ) = A.
		  transa = 'T' or 't'		op( A ) = A'.
		  transa = 'C' or 'c'		op( A ) = conjg( A' ).

		  C
		  transa = NoTranspose		op( A ) = A.
		  transa = Transpose		op( A ) = A'.
		  transa = ConjugateTranspose	op( A ) = conjg( A' ).

	     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.

     m	     On entry, m specifies the number of rows of B. m must be at least
	     zero.
	     Unchanged on exit.

     n	     On entry, n specifies the number of columns of B.	n must be at
	     least zero.
	     Unchanged on exit.

     alpha   On entry, alpha specifies the scalar alpha. When alpha is zero
	     then a is not referenced and b need not be set before entry.

									Page 3

_TRMM(3F)							     _TRMM(3F)

	     Unchanged on exit.

     a	     An array containing the matrix A.

	     FORTRAN
	     Array of dimension (lda, k).

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

	     k is m when side = 'L' or 'l' or LeftSide and is n when  side =
	     'R' or 'r' or RightSide.

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

	     Before entry with uplo = 'L' or 'l' or , the elements
	     corresponding to the leading k by k lower triangular elements of
	     the matrix A  must contain the lower triangular matrix and the
	     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. When side = 'L' or 'l' or LeftSide,
	     then lda must be at least max( 1, m ). When side = 'R' or 'r' or
	     RightSide, then lda must be at least max( 1, n ).
	     Unchanged on exit.

     B	     An array containing the matrix B.

	     FORTRAN
	     An array of dimension ( ldb, n ).

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

	     Before entry, the leading m by n part of the array b should
	     contain the elements corresponding to the m by n matrix B. On
	     exit it is overwritten by the transformed matrix.

									Page 4

_TRMM(3F)							     _TRMM(3F)

     ldb     On entry, ldb specifies the first dimension of B as declared in
	     the calling (sub)program. ldb  must be at least max( 1, m ).
	     Unchanged on exit.

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

TUNING
	  Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.

									Page 5

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