2 Matrix Multiplications faster than one matrix Multiplication

Hello there,

im trying to optimize my program in reducing 2 matrix multiplcations into 1 multiplication like rewrite

for i = 1:10000
    filtSig = filtMat * Frame;
    recSig = recMat * filtSig:
end

into:

frMat = recMat * filtMat;
for i = 1:10000
    recSig = frMat * Frame;
end

Frame is a 128x1 Vector, filtMat is 13x128, recMat is 128x13 and thus frMat is 128x128

when i add tic,toc commands to measure the time, it says that the first version used 16.57ms while the last one uses 25.39ms

My question is, why dose the single Matrix multiplication version much slower than first one?

[dpb]

A)

 filtSig = [13x128] * [128,1]; ==> 13,128
 recSig = [128x13] * [13,128]; ==> 128,128

>> >> N1=10000*(13*128+128*13);
N1 =
  33280000

 B)
 frMat = [128x13] * [13,128]; ==> 128,128
 recSig = [128x128] * [128,1]; ==> 128,128

>> N2=128*13 + 128*128*10000
N2 =
 163841664
>> 

>> N2/N1
ans =
  4.9231
>>

It's testament to library optimization it's not worse than 2X you observed.

[Lewei He]

sry, i have not fully understood your answer, filtSig = [13x128]*[128x1] gaves 13x1 vector and need 13*128 multiplications,recSig produce a 128x1 vector... how do u get N1=13*128+10000*128*13 instead of (13*128+13*128)*10000?

[dpb]

Cut 'n paste error, sorry...only ~5X instead of 10.

Point is to minimize compute time it isn't the number of high-level language operations that necessarily matters but what those operations translate into. Or, stated another way, runtime isn't necessarily proportional to the quantity (number of lines of) the source code.

[Lewei He]

i know that when it gose with compiler languages, have thought matlab makes more optimaze with matrix xD thx for the explanation

[dpb]

Well, Matlab does wonders when you vectorize but even it can't do magic yet. The "Do What I Should Have Done Optimizer" toolbox is yet to be released.

Seriously, remember that there's really no difference between Matlab and any other language under the hood; it has to get translated to procedural code to be executed eventually. The benefit of Matlab syntax is you don't have to write the matrix multiply code loop constructs yourself or call the BLAS libraries directly as in C or Fortran but that's what Matlab is actually doing for you.