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Math Kernel Library (MKL)

Intel MKL (Math Kernel Library) is a library of optimized math routines for numerical computations such as linear algebra (using BLAS, LAPACK, ScaLAPACK) and discrete Fourier Transformation. With its standard interface in matrix computation and the interface of the popular fast Fourier transformation library fftw, MKL can be used to replace other libraries with minimal code changes. In fact a program which uses FFTW without MPI doesn't need to be changed at all. Just recompile it with the MKL linker flags.

Online documentation: http://software.intel.com/en-us/articles/intel-math-kernel-library-documentation

Local documentation: There is some information in the module help file accessible via

$ module help numlib/mkl

and after loading the module, the environment variable $MKL_DOC_DIR points to the local documentation folder. Various examples can be found in $MKLROOT/examples.

Compiling and linking: Compilation is possible with both GCC and Intel compilers but it is easier for Intel compilers, so this case is explained here. After loading the compiler and the library module with

$ module load compiler/intel
$ module load numlib/mkl

you can include the MKL header file in your program:

#include <mkl.h>

Compilation is simple:

$ icpc -c example_mkl.c

When linking the program you have to tell the compiler to link against the mkl library:

$ icpc example_mkl.o -mkl

With the -mkl switch the intel compiler automatically sets the correct linker flags but you can specify them explicitly for example to enable static linking or when non-intel compilers are used. Information about the different options can be found at http://software.intel.com/en-us/node/438568 and especially helpful is the MKL link line advisor at http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor. By default $MKL_NUM_THREADS is set to 1 and so only one thread will be created, but if you feel the need to run the computation on more cores (after benchmarking) you can set $MKL_NUM_THREADS to a higher number.

Examples: To help getting started we provide two C++ examples. The first one computes the square of a 2x2 matrix:

#include <iostream> #include <mkl.h> using namespace std; int main() { double m[2][2] = {{2,1}, {0,2}}; double c[2][2]; for(int i = 0; i < 2; ++i) { for(int j = 0; j < 2; ++j) cout << m[i][j] << " "; cout << endl; } cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, 2, 2, 2, 1.0, &m[0][0], 2, &m[0][0], 2, 0.0, &c[0][0], 2); cout << endl; for(int i = 0; i < 2; ++i) { for(int j = 0; j < 2; ++j) cout << c[i][j] << " "; cout << endl; } return 0; }

And the second one does a fast Fourier transformation using the Intel MKL interface (DFTI):

#include <iostream> #include <complex> #include <cmath> #include <mkl.h> using namespace std; int main() { const int N = 3; complex<double> x[N] = {2, -1, 0.5}; cout << "Input: " << endl; for(int i = 0; i < N; i++) cout << x[i] << endl; DFTI_DESCRIPTOR_HANDLE desc; DftiCreateDescriptor(&desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, N); DftiCommitDescriptor(desc); DftiComputeForward(desc, x); DftiFreeDescriptor(&desc); cout << "\nOutput: " << endl; for(int i = 0; i < N; i++) cout << x[i] << endl; cout << "\nTest the interpolation function f:" << endl; for(int i = 0; i < N; i++) { double t = i/(double)N; complex<double> u(0, 2*M_PI*t); complex<double> z = exp(u); complex<double> w = 1.0/N * (x[0] + x[1]*z + x[2]*z*z); cout << "f(" << t << ") = " << w << endl; } return 0; }