## MATLAB mex functions using the NAG C Library in Windows

The NAG C Library is one of the largest commercial collections of numerical software currently available and I often find it very useful when writing MATLAB mex files. “*Why is that?*” I hear you ask.

One of the main reasons for writing a mex file is to gain more speed over native MATLAB. However, one of the main problems with writing mex files is that you have to do it in a low level language such as Fortran or C and so you lose much of the ease of use of MATLAB.

In particular, you lose straightforward access to most of the massive collections of MATLAB routines that you take for granted. Technically speaking that’s a lie because you could use the mex function **mexCallMATLAB** to call a MATLAB routine from within your mex file but then you’ll be paying a time overhead every time you go in and out of the mex interface. Since you are going down the mex route in order to gain speed, this doesn’t seem like the best idea in the world. This is also the reason why you’d use the NAG C Library and not the NAG Toolbox for MATLAB when writing mex functions.

One way out that I use often is to take advantage of the NAG C library and it turns out that it is extremely easy to add the NAG C library to your mex projects on Windows. Let’s look at a trivial example. The following code, nag_normcdf.c, uses the NAG function **nag_cumul_normal **to produce a simplified version of MATLAB’s normcdf function (laziness is all that prevented me from implementing a full replacement).

/* A simplified version of normcdf that uses the NAG C library * Written to demonstrate how to compile MATLAB mex files that use the NAG C Library * Only returns a normcdf where mu=0 and sigma=1 * October 2011 Michael Croucher * www.walkingrandomly.com */ #include <math.h> #include "mex.h" #include "nag.h" #include "nags.h" void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] ) { double *in,*out; int rows,cols,num_elements,i; if(nrhs>1) { mexErrMsgIdAndTxt("NAG:BadArgs","This simplified version of normcdf only takes 1 input argument"); } /*Get pointers to input matrix*/ in = mxGetPr(prhs[0]); /*Get rows and columns of input matrix*/ rows = mxGetM(prhs[0]); cols = mxGetN(prhs[0]); num_elements = rows*cols; /* Create output matrix */ plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL); /* Assign pointer to the output */ out = mxGetPr(plhs[0]); for(i=0; i<num_elements; i++){ out[i] = nag_cumul_normal(in[i]); } }

To compile this in MATLAB, just use the following command

mex nag_normcdf.c CLW6I09DA_nag.lib

If your system is set up the same as mine then the above should ‘just work’ (see **System Information** at the bottom of this post). The new function works just as you would expect it to

>> format long >> format compact >> nag_normcdf(1) ans = 0.841344746068543

Compare the result to normcdf from the statistics toolbox

>> normcdf(1) ans = 0.841344746068543

So far so good. I could stop the post here since all I really wanted to do was say **‘The NAG C library is useful for MATLAB mex functions and it’s a doddle to use – here’s a toy example and here’s the mex command to compile it’**

However, out of curiosity, I looked to see if my toy version of normcdf was any faster than The Mathworks’ version. Let there be 10 million numbers:

>> x=rand(1,10000000);

Let’s time how long it takes MATLAB to take the normcdf of those numbers

>> tic;y=normcdf(x);toc Elapsed time is 0.445883 seconds. >> tic;y=normcdf(x);toc Elapsed time is 0.405764 seconds. >> tic;y=normcdf(x);toc Elapsed time is 0.366708 seconds. >> tic;y=normcdf(x);toc Elapsed time is 0.409375 seconds.

Now let’s look at my toy-version that uses NAG.

>> tic;y=nag_normcdf(x);toc Elapsed time is 0.544642 seconds. >> tic;y=nag_normcdf(x);toc Elapsed time is 0.556883 seconds. >> tic;y=nag_normcdf(x);toc Elapsed time is 0.553920 seconds. >> tic;y=nag_normcdf(x);toc Elapsed time is 0.540510 seconds.

So my version is slower! Never mind, I’ll just make my version parallel using OpenMP – Here is the code: nag_normcdf_openmp.c

/* A simplified version of normcdf that uses the NAG C library * Written to demonstrate how to compile MATLAB mex files that use the NAG C Library * Only returns a normcdf where mu=0 and sigma=1 * October 2011 Michael Croucher * www.walkingrandomly.com */ #include <math.h> #include "mex.h" #include "nag.h" #include "nags.h" #include <omp.h> void do_calculation(double in[],double out[],int num_elements) { int i,tid; #pragma omp parallel for shared(in,out,num_elements) private(i,tid) for(i=0; i<num_elements; i++){ out[i] = nag_cumul_normal(in[i]); } } void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] ) { double *in,*out; int rows,cols,num_elements; if(nrhs>1) { mexErrMsgIdAndTxt("NAG_NORMCDF:BadArgs","This simplified version of normcdf only takes 1 input argument"); } /*Get pointers to input matrix*/ in = mxGetPr(prhs[0]); /*Get rows and columns of input matrix*/ rows = mxGetM(prhs[0]); cols = mxGetN(prhs[0]); num_elements = rows*cols; /* Create output matrix */ plhs[0] = mxCreateDoubleMatrix(rows, cols, mxREAL); /* Assign pointer to the output */ out = mxGetPr(plhs[0]); do_calculation(in,out,num_elements); }

Compile that with

mex COMPFLAGS="$COMPFLAGS /openmp" nag_normcdf_openmp.c CLW6I09DA_nag.lib

and on my quad-core machine I get the following timings

>> tic;y=nag_normcdf_openmp(x);toc Elapsed time is 0.237925 seconds. >> tic;y=nag_normcdf_openmp(x);toc Elapsed time is 0.197531 seconds. >> tic;y=nag_normcdf_openmp(x);toc Elapsed time is 0.206511 seconds. >> tic;y=nag_normcdf_openmp(x);toc Elapsed time is 0.211416 seconds.

This is faster than MATLAB and so normal service is resumed :)

**System Information**

- 64bit Windows 7
- MATLAB 2011b
- NAG C Library Mark 9 – CLW6I09DAL
- Visual Studio 2008
- Intel Core i7-2630QM processor

Hi,

Have you compared your NAG/OpenMP version with the native Matlab Parallel Computing Toolbox version?

Hi Robert

The MATLAB Parallel Computing Toolbox does nothing to speed up normcdf (as of 2011b at least). normcdf.m uses a MATLAB mex file, erfc to do the majority of the computation and the PCT doesn’t affect the speed of mex functions at all.

With all of that said, however, I note that the single threaded version of MATLAB’s function is faster than the one I wrote using NAG. So, if The Mathworks used OpenMP on their erfc function then I fully expect MATLAB to take the lead again. This new function wouldn’t need the PCT.

Cheers,

Mike