Operation
The xGEMM routine calculates the new value of matrix C based on the matrix-product of matrices A and B, and the old value of matrix C
where and values are scalar coefficients.
The Fortran interface for these procedures are:
SUBROUTINE xGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )where TRANSA and TRANSB determines if the matrices A and B are to be transposed. M is the number of rows in matrix C and, depending on TRANSA, the number of rows in the original matrix A or its transpose. N is the number of columns in matrix C and, depending on TRANSB, the number of columns in the matrix B or its transpose. K is the number of columns in matrix A (or its transpose) and rows in matrix B (or its transpose). LDA, LDB and LDC specifies the size of the first dimension of the matrices, as laid out in memory; meaning the memory distance between the start of each row/column, depending on the memory structure (Dongarra et al. 1990).
The C interface for these procedures are similar:
void cblas_xgemm ( const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const int M, const int N, const int K, const SCALAR alpha, const TYPE * A, const int lda, const TYPE * B, const int ldb, const SCALAR beta, TYPE * C, const int ldc)where 'x' in name is s,d,c, or z meaning single precision real, double precision real, single precision complex, or double precision complex, and other types have similar meanings as in Fortran interface.
For the C interface, a higher API also exists. For example, in the GNU Scientific Library, a corresponding interface is (take the double precision real case for instance):
int gsl_blas_dgemm( CBLAS_TRANSPOSE_t TransA, CBLAS_TRANSPOSE_t TransB, double alpha, const gsl_matrix * A, const gsl_matrix * B, double beta, gsl_matrix * C)where TransA is CblasNoTrans or CblasTrans for A or transposed A respectively, and TransB has similar choices (GSL Team 2007).
Read more about this topic: General Matrix Multiply
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