# Introduction

MKL (Math Kernel Library) is a library of math procedures from Intel, which includes BLAS, LAPACK, and ScaLAPACK. On this page, we will show how to start using MKL with the Intel compiler on maya. Before you begin, make sure to read the tutorial for compiling C programs. Extensive documentation about programming with MKL can be found in Intel’s reference manual.

# BLAS Example: Matrix Multiply

Consider three matrices: the m×k matrix A, the k×n matrix B, and the m×n matrix C, where all are represented as double precision floating point numbers. We will demonstrate the use of the “dgemm” function which computes

C=αAB+βC.

We will take α=1 and β=0 to compute the simple matrix multiplication C=AB. MKL has several versions of this function; we will use “cblas_dgemm”, which has bit friendlier “C-style” interface than other variants.

The most important line in the code is

cblas_dgemm(CblasColMajor, CblasNoTrans, CblasNoTrans,
m, n, k, 1.0, A, m, B, k, 0.0, C, m);


Also notice in the Makefile that the option “-mkl” is given in CFLAGS, which enables the use of MKL. Next we compile and run the code.

[araim1@maya-usr1 matrix-multply]$make clean rm -f *.o matrix-multiply [araim1@maya-usr1 matrix-multply]$ make
icc -O3 -std=c99 -mkl   -c matrix-multiply.c -o matrix-multiply.o
icc -O3 -std=c99 -mkl   matrix-multiply.o -o matrix-multiply
[araim1@maya-usr1 matrix-multply]$./matrix-multiply Matrix A (3 x 5) is: 1.0000 0.7290 0.5314 0.3874 0.2824 0.9000 0.6561 0.4783 0.3487 0.2542 0.8100 0.5905 0.4305 0.3138 0.2288 Matrix B (5 x 4) is: 1.0000 0.5905 0.3487 0.2059 0.9000 0.5314 0.3138 0.1853 0.8100 0.4783 0.2824 0.1668 0.7290 0.4305 0.2542 0.1501 0.6561 0.3874 0.2288 0.1351 Matrix C (3 x 4) = AB is: 2.5543 1.5083 0.8906 0.5259 2.2989 1.3575 0.8016 0.4733 2.0690 1.2217 0.7214 0.4260 [araim1@maya-usr1 matrix-multply]$


# LAPACK Example: Singular Value Decomposition

Given an m×n matrix A, we will demonstrate the LAPACK “dgesvd” function for computing the singular value decomposition (SVD)

A=USVT,

where S is an m×n diagonal matrix of singular values, U is m×m, and VT is n×n. The MKL function call we will use is “LAPACKE_dgesvd”.

The most important line in the code, where the SVD is being computed, is

int info = LAPACKE_dgesvd(CblasColMajor, 'A', 'A', m, n, A, m, S, U, m,
VT, n, superb);


Next we compile and run the code.

[araim1@maya-usr1 svd]$make clean rm -f *.o matrix-multiply [araim1@maya-usr1 svd]$ make
icc -O3 -std=c99 -mkl   -c -o matrix-svd.o matrix-svd.c
icc -O3 -std=c99 -mkl   matrix-svd.o -o matrix-svd
[araim1@maya-usr1 svd]$./matrix-svd Matrix A (3 x 4) is: 1.0000 0.5000 0.3333 0.2500 0.5000 0.3333 0.2500 0.2000 0.3333 0.2500 0.2000 0.1667 Matrix U (3 x 3) is: -0.8199 0.5563 0.1349 -0.4662 -0.5123 -0.7213 -0.3322 -0.6543 0.6794 Vector S (3 x 1) is: 1.4519 0.1433 0.0042 Matrix VT (4 x 4) is: -0.8015 -0.4466 -0.3143 -0.2435 0.5729 -0.3919 -0.5127 -0.5053 0.1692 -0.7398 0.1245 0.6392 -0.0263 0.3157 -0.7892 0.5261 [araim1@maya-usr1 svd]$