Multiplying Matrices Using dgemm
Intel MKL provides several routines for multiplying matrices. The most widely used is the
routine, which calculates the product of double precision matrices:
dgemm
The
routine can perform several calculations. For example, you can perform this operation with the transpose or conjugate transpose of
routine and all of its arguments can be found in the
topic in the
dgemm
A
and
B
. The complete details of capabilities of the
dgemm
cblas_?gemm
Intel Math Kernel Library Developer Reference
.
Use dgemm to Multiply Matrices
This exercise demonstrates declaring variables, storing matrix values in the arrays, and calling
to compute the product of the matrices. The arrays are used to store these matrices:
dgemm
The onedimensional arrays in the exercises store the matrices by placing the elements of each column in successive cells of the arrays.
The C source code for the exercises in this tutorial
can be downloaded from
https://software.intel.com/enus/productcodesamples
.
/* C source code is found in dgemm_example.c */ #define min(x,y) (((x) < (y)) ? (x) : (y)) #include <stdio.h> #include <stdlib.h> #include "mkl.h" int main() { double *A, *B, *C; int m, n, k, i, j; double alpha, beta; printf ("\n This example computes real matrix C=alpha*A*B+beta*C using \n" " Intel(R) MKL function dgemm, where A, B, and C are matrices and \n" " alpha and beta are double precision scalars\n\n"); m = 2000, k = 200, n = 1000; printf (" Initializing data for matrix multiplication C=A*B for matrix \n" " A(%ix%i) and matrix B(%ix%i)\n\n", m, k, k, n); alpha = 1.0; beta = 0.0; printf (" Allocating memory for matrices aligned on 64byte boundary for better \n" " performance \n\n"); A = (double *)mkl_malloc( m*k*sizeof( double ), 64 ); B = (double *)mkl_malloc( k*n*sizeof( double ), 64 ); C = (double *)mkl_malloc( m*n*sizeof( double ), 64 ); if (A == NULL  B == NULL  C == NULL) { printf( "\n ERROR: Can't allocate memory for matrices. Aborting... \n\n"); mkl_free(A); mkl_free(B); mkl_free(C); return 1; } printf (" Intializing matrix data \n\n"); for (i = 0; i < (m*k); i++) { A[i] = (double)(i+1); } for (i = 0; i < (k*n); i++) { B[i] = (double)(i1); } for (i = 0; i < (m*n); i++) { C[i] = 0.0; } printf (" Computing matrix product using Intel(R) MKL dgemm function via CBLAS interface \n\n"); cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, m, n, k, alpha, A, k, B, n, beta, C, n); printf ("\n Computations completed.\n\n"); printf (" Top left corner of matrix A: \n"); for (i=0; i<min(m,6); i++) { for (j=0; j<min(k,6); j++) { printf ("%12.0f", A[j+i*k]); } printf ("\n"); } printf ("\n Top left corner of matrix B: \n"); for (i=0; i<min(k,6); i++) { for (j=0; j<min(n,6); j++) { printf ("%12.0f", B[j+i*n]); } printf ("\n"); } printf ("\n Top left corner of matrix C: \n"); for (i=0; i<min(m,6); i++) { for (j=0; j<min(n,6); j++) { printf ("%12.5G", C[j+i*n]); } printf ("\n"); } printf ("\n Deallocating memory \n\n"); mkl_free(A); mkl_free(B); mkl_free(C); printf (" Example completed. \n\n"); return 0; }
This exercise illustrates how to call the
routine. An actual application would make use of the result of the matrix multiplication.
dgemm
This call to the
dgemm
routine multiplies the matrices:
cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, m, n, k, alpha, A, k, B, n, beta, C, n);
The arguments provide options for how Intel MKL performs the operation. In this case:
 CblasRowMajor
 Indicates that the matrices are stored in row major order, with the elements of each row of the matrix stored contiguously as shown in the figure above.
 CblasNoTrans
 Enumeration typeindicating that the matricesAandBshould not be transposed or conjugate transposed before multiplication.
 m, n, k
 Integers indicating the size of the matrices:
 A:mrows bykcolumns
 B:krows byncolumns
 C:mrows byncolumns
 alpha
 Real value used to scale the product of matricesAandB.
 A
 Array used to store matrixA.
 k
 Leading dimension of arrayA, or the number of elements between successiverows (for row major storage)in memory. In the case of this exercise the leading dimension is the same as the number ofcolumns.
 B
 Array used to store matrixB.
 n
 Leading dimension of arrayB, or the number of elements between successiverows (for row major storage)in memory. In the case of this exercise the leading dimension is the same as the number ofcolumns.
 beta
 Real value used to scale matrixC.
 C
 Array used to store matrixC.
 n
 Leading dimension of arrayC, or the number of elements between successiverows (for row major storage)in memory. In the case of this exercise the leading dimension is the same as the number ofcolumns.
Compile and Link Your Code
Intel MKL provides many options for creating code for multiple processors and operating systems, compatible with different compilers and thirdparty libraries, and with different interfaces. To compile and link the exercises in this tutorial with Intel® Parallel Studio XE Composer Edition, type
 Windows* OS:icl /Qmkl src\dgemm_example.c
 Linux* OS, macOS*:icc mkl src/dgemm_example.c
Alternatively, you can use the supplied build scripts to build and run the executables.
 Windows* OS:build build run_dgemm_example
 Linux* OS, macOS*:make make run_dgemm_example
For the executables in this tutorial, the build scripts are named:
Example
 Executable


dgemm_example .c  run_dgemm_example 
dgemm_with_timing .c  run_dgemm_with_timing 
matrix_multiplication .c  run_matrix_multiplication 
dgemm_threading_effect_example .c  run_dgemm_threading_effect_example 
This assumes that you have installed Intel MKL and set environment variables as described in
https://software.intel.com/enus/articles/intelmathkernellibraryintelmkl2019gettingstarted.
For other compilers, use the Intel MKL Link Line Advisor to generate a command line to compile and link the exercises in this tutorial:
http://software.intel.com/enus/articles/intelmkllinklineadvisor/.
After compiling and linking, execute the resulting executable file, named
dgemm_example.exe
on Windows* OS or
a.out
on Linux* OS and macOS*.
Optimization Notice


Intel's compilers may or may not optimize to the same degree
for nonIntel microprocessors for optimizations that are not unique to Intel
microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction
sets and other optimizations. Intel does not guarantee the availability,
functionality, or effectiveness of any optimization on microprocessors not
manufactured by Intel. Microprocessordependent optimizations in this product
are intended for use with Intel microprocessors. Certain optimizations not
specific to Intel microarchitecture are reserved for Intel microprocessors.
Please refer to the applicable product User and Reference Guides for more
information regarding the specific instruction sets covered by this notice.
Notice revision #20110804
