FFTW vs Matlab FFT

Question

I posted this on matlab central but didn\'t get any responses so I figured I\'d repost here.

I recently wrote a simple routine in Matlab that uses an FFT in a for-l

Answer 1

EDIT: @wakjah 's reply to this answer is accurate: FFTW does support split real and imaginary memory storage via its Guru interface. My claim about hacking is thus not accurate but can very well apply if FFTW's Guru interface is not used - which is the case by default, so beware still!

First, sorry for being a year late. I'm not convinced that the speed increase you see comes from MKL or other optimizations. There is something quite fundamentally different between FFTW and Matlab, and that is how complex data is stored in memory.

In Matlab, the real and imaginary parts of a complex vector X are separate arrays Xre[i] and Xim[i] (linear in memory, efficient when operating on either of them separately).

In FFTW, the real and imaginary parts are interlaced as double[2] by default, i.e. X[i][0] is the real part, and X[i][1] is the imaginary part.

Thus, to use the FFTW library in mex files one cannot use the Matlab array directly, but must allocate new memory first, then pack the input from Matlab into FFTW format, and then unpack the output from FFTW into Matlab format. i.e.

X = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
Y = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);

then

for (size_t i=0; i

then

for (size_t i=0; i

Hence, this requires 2x memory allocations + 4x reads + 4x writes -- all of size N. This does take a toll speed-wise on large problems.

I have a hunch that Mathworks may have hacked the FFTW3 code to allow it to read input vectors directly in the Matlab format, which avoids all of the above.

In this scenario, one can only allocate X and use X for Y to run FFTW in-place (as fftw_plan_*(N, X, X, ...) instead of fftw_plan_*(N, X, Y, ...)), since it'll be copied to the Yre and Yim Matlab vector, unless the application requires/benefits from keeping X and Y separate.

EDIT: Looking at the memory consumption in real-time when running Matlab's fft2() and my code based on the fftw3 library, it shows that Matlab only allocates only one additional complex array (the output), whereas my code needs two such arrays (the *fftw_complex buffer plus the Matlab output). An in-place conversion between the Matlab and fftw formats is not possible because the Matlab's real and imaginary arrays are not consecutive in memory. This suggests that Mathworks hacked the fftw3 library to read/write the data using the Matlab format.

One other optimization for multiple calls, is to allocate persistently (using mexMakeMemoryPersistent()). I'm not sure if the Matlab implementation does this as well.

Cheers.

p.s. As a side note, the Matlab complex data storage format is more efficient for operating on the real or imaginary vectors separately. On FFTW's format you'd have to do ++2 memory reads.