DGEMMS man page on IRIX

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DGEMMS(3S)							    DGEMMS(3S)

NAME
     DGEMMS - Multiplies a real general matrix by a real general matrix, using
     Strassen's algorithm

SYNOPSIS
     Fortran:

	  CALL DGEMMS (transa, transb, m, n, k, alpha, a, lda, b, ldb, beta,
	  c, ldc)

     C/C++:
	  #include <scsl_blas.h>
	  void dgemms (char *transa, char *transb, int m, int n, int k, double
	  alpha, double *a, int lda, double *b, int ldb, double beta, double
	  *c, int ldc);

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

     The C and C++ prototypes shown above are appropriate for the 4-byte
     integer version of SCSL. When using the 8-byte integer version, the
     variables of type int become long long and the <scsl_blas_i8.h> header
     file should be included.

DESCRIPTION
     DGEMMS multiplies a double precision general matrix by a double precision
     general matrix.

     This routine is an implementation of the Winograd's variation of
     Strassen's algorithm for matrix multiplication.  Because of a very
     different order of operations performed by the Strassen's algorithm,
     numerical results from DGEMMS may differ slightly from those of DGEMM.

     DGEMMS is functionally equivalent to DGEMM, but it does require temporary
     space which it allocates and manages automatically.

     This routine performs one of the matrix-matrix operations:

	  C  <- alpha op(A) op(B) + beta C

									Page 1

DGEMMS(3S)							    DGEMMS(3S)

     where op(X) is one of the following:

	  op(X) = X

	  op(X) = XT

     where

     *	 alpha and beta are scalars

     *	 A, B, and C are matrices

     *	 op(A) is an m-by-k matrix

     *	 op(B) is a k-by-n matrix

     *	 C is an m-by-n matrix

     *	 XT is the transpose of X

     See the NOTES section of this man page for information about the
     interpretation of the data types described in the following arguments.

     This routine has the following arguments:

     transa    Character.  (input)
	       Specifies the form of op(A) to be used in the matrix
	       multiplication, as follows:

	       transa = 'N' or 'n':  op(A) = A

	       transa = 'T' or 't':  op(A) = AT

	       transa = 'C' or 'c':  op(A) = AT

	       For C/C++, a pointer to this character is passed.

     transb    Character.  (input)
	       Specifies the form of op(B) to be used in the matrix
	       multiplication, as follows:

	       transb = 'N' or 'n':  op(B) = B

	       transb = 'T' or 't':  op(B) = BT

	       transb = 'C' or 'c':  op(B) = BT

	       For C/C++, a pointer to this character is passed.

     m	       Integer.	 (input)
	       Specifies the number of rows in matrix op(A) and in matrix C.
	       m must be >= 0.

									Page 2

DGEMMS(3S)							    DGEMMS(3S)

     n	       Integer.	 (input)
	       Specifies the number of columns in matrix op(B) and in matrix
	       C.  n must be >= 0.

     k	       Integer.	 (input)
	       Specifies the number of columns of matrix op(A) and the number
	       of rows of matrix op(B).	 k must be >= 0.

     alpha     Double precision.  (input)
	       Scalar factor.

     a	       Double precision array of dimension (lda,ka).  (input)
	       When transa = 'N' or 'n', ka is k; otherwise, it is m.
	       Contains the matrix A.

	       Before entry with transa = 'N' or 'n', the leading m-by-k part
	       of array a must contain matrix A; otherwise, the leading k-by-m
	       part of array a must contain matrix A.

     lda       Integer.	 (input)
	       Specifies the first dimension of a as declared in the calling
	       (sub)program.  When transa = 'N' or 'n', lda >= MAX(1,m);
	       otherwise, lda >= MAX(1,k).

     b	       Double precision array of dimension (ldb,kb).  (input)
	       When transb = 'N' or 'n', kb is n; otherwise, it is k.
	       Contains the matrix B.

	       Before entry with transb = 'N' or 'n', the leading k-by-n part
	       of array b must contain matrix B; otherwise, the leading n-by-k
	       part of array b must contain matrix B.

     ldb       Integer.	 (input)
	       Specifies the first dimension of b as declared in the calling
	       (sub)program.
	       When transb = 'N' or 'n', ldb >= MAX(1,k); otherwise, ldb >=
	       MAX(1,n).

     beta      Double precision.  (input)
	       Scalar factor.  When beta is supplied as 0, c need not be set
	       on input.

     c	       Double precision array of dimension (ldc,n).  (input and
	       output)
	       Contains the matrix C.

	       Before entry, the leading m-by-n part of array c must contain
	       matrix C, except when beta is 0; in which case, c need not be
	       set.  On exit, the m-by-n result matrix overwrites array c.

									Page 3

DGEMMS(3S)							    DGEMMS(3S)

     ldc       Integer.	 (input)
	       Specifies the first dimension of c as declared in the calling
	       (sub)program.  ldc >= MAX(1,m).

NOTES
     This routine is an extension to the Level 3 BLAS.

     This routine is a modified version of the package developed through the
     PRISM project for multiplying matrices using Strassen's algorithm.
     Please see http://www.mcs.anl.gov/Projects/PRISM for more details.

   Data Types
     The following data types are described in this documentation:

	  Term Used			     Data type

     Fortran:

	  Array of dimensions (m,n)	x(m,n)

	  Character			CHARACTER

	  Integer			INTEGER (INTEGER*8 for -lscs_i8[_mp])

	  Double precision		DOUBLE PRECISION

     C/C++:

	  Array of dimensions (m, n)	x[m*n]

	  Character			char

	  Integer			int (long long for -lscs_i8[_mp])

	  Double precision		double

     Note that you can explicitly declare multidimensional C/C++ arrays
     provided that the array dimensions are swapped with respect to the
     Fortran declaration (e.g., x[n][m] in C/C++ versus x(m,n) in Fortran).
     To avoid a compiler type mismatch error in C++ (or a compiler warning
     message in C), however, the array should be cast to a pointer of the
     appropriate type when passed as an argument to a SCSL routine.

SEE ALSO
     INTRO_SCSL(3S), INTRO_BLAS3(3S)

     INTRO_CBLAS(3S) for information about using the C interface to Fortran 77
     Basic Linear Algebra Subprograms (legacy BLAS) set forth by the Basic
     Linear Algebra Subprograms Technical Forum.

									Page 4

DGEMMS(3S)							    DGEMMS(3S)

     DGEMM(3S), SGEMM(3S) to multiply general matrices by using the more
     standard inner product algorithm

									Page 5

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