How to speed up the following Matlab script? Can anyone suggest me to speed up the process?

In the following scripts, I get expected result but the process is very slow. Is there any other way to make the execution faster/fastest ?

clc; close all; clear all;
load Array.mat; % B is the name
per_group = 1000;
[row,col]=size(B); % val would be a matrix of size (C*C)
limit=row/per_group;
value=cell(1,limit);
count=0;
val = zeros(col); % Memory Pre-allocation
for kk = 1:per_group:row
  count=count+1; 
  group_end = min(row, kk+per_group-1);
  for jj= 1:col
    f1 = A(kk:group_end,jj);
    for i=(jj+1):col
      f2= A(kk:group_end,i);
      [Pyy,freq]=cpsd(f2,f2,hanning(512),[],512,500);
      [Pxy,freq]=cpsd(f1,f2,hanning(512),[],512,500);
      [Pxx,freq]=cpsd(f1,f1,hanning(512),[],512,500);
      coh=(Pxy)./sqrt(Pxx.*Pyy);
      realCoh=real(coh(42));
      val(jj,i)=realCoh;
    end      
  end
  value{count}=val+val'+eye(col)
end

Answer 1

[dpb]

Since you're doing all the work only to return coherence, look at

doc mscohere

to return the coherence directly with all the intermediares buried in the call instead of separate.

Alternatively, you could use the array syntax of cpsd and pass arrays instead of three calls with vectors--

...
[P,freq]=cpsd([f1 f2 f1],[f1 f2 f2],hanning(512),[],512,500);
coh=P(:,3)./sqrt(P(:,1).*P(:,2));
realCoh=real(coh(42));

The burying of "magic numbers" in code makes things hard to change/debug; if that number would change, you have to change the code and find all occurrences to ensure everything changes together. If it were a variable, then only change data value and (hopefully) the variable is used everywhere.

Of course, this value and the inevitable comparison to Deep Thought and The Hitchhiker's Guide to the Galaxy, is purely coincidental, I'm sure.

[SA]

Thank you. I'm worried about this line

coh=P(:,3)./sqrt(P(:,1).*P(:,1));
                             ^

Do you think, this line is correct or

coh=P(:,3)./sqrt(P(:,1).*P(:,2));

later line is correct? As I've a very BIG data array (execution time takes some hours!), so I look for if any vectorization/other possibility could possible.

[dpb]

You caught the typo I had just corrected from the cut'n paste. The Answer is fixed now.

"As I've a very BIG data array (execution time takes some hours!)..."

I'd strongly suggest to then take a small section of the file and test the alternatives and time them rather than only working with the one huge dataset.

Make sure you get the right answer with the revised code compared to the original (again, just use one or a very few sections) first and you can also do the timing comparisons at the same time to see which option(s) hold out the most hope for improvement in speed.

I'd guess mscohere probably would still win, but the array input form should be able to run it a closer second, anyways, I'd think.

I'd intended to comment but forgot -- I'd also make my block size a power of 2 so is multiple of the fft blocksize.

You might also consider the overlap amount and whether you could use larger FFT size and still get required information. 512/1024 is awful short segment from an extremely long time record; is there a real reason for that?

We "know nuthink!" about the application so no idea about what might/might not make sense.

[SA]

In matlab "mscohere" & "cpsd" they perform same task but in different way, the output is slight fluctuated from expectation. So, I prefer 'cpsd' rather than 'mscohere'. Segment size could be a possible option to option, but I choose short segment to limit the spectral leakage!! For faster calculation, I can use larger size of the segment.

Thank you & best regards.

SA

[SA]

@dpb, is it possible to replace the for ...loop operation by vectorization. Can you help me to do that? Thanks and regards/SA

[dpb]

1. Not the outer loop if you must have the values as you've defined over pieces of the time series(*)
2. Probably the inner loop could be replaced with the full array and the 'mimo' option, but if col is sizable, it might end up taking as long as it does all combinations of input columns and returns result in 3D array.

[SA]

@dpb

I have a cell array of N*N size, each cell is a vector of 10 elements.

{0×0 double} {10×1 double} {10×1 double} {10×1 double}

{0×0 double} {0×0 double} {10×1 double} {10×1 double}

{0×0 double} {0×0 double} {0×0 double} {10×1 double}

{0×0 double} {0×0 double} {0×0 double} {0×0 double}

I want to extract individual elements of the cell sequentially and form a matrix like in the following. How can I form the matrix, A_1? Can you help me? @dpb

A_1 is a matrix consist of first element of each cell (as follows)=

0 x1 x2 x3

0 0 y1 y2

0 0 0 z3

0 0 0 0 ]; then the 2nd element of of every cell will form another 4*4 matrix=A_2,

3rd element of every cell will form 4*4 matrix=A_3,.....and so on up to A_10. With these A_1, A_2,...,A_10 matrices, I want to add its transpose+ Identity matrix(i.e. eye(4)). Finally, it should be like this

FullMatrix(1) = A_1+A_1’+eye(4)= 1 x1 x2 x3

X1 1 y1 y2

X2 y1 1 z3

X3 y2 z3 1;

FullMatrix(2), FullMatrix(3),......,FullMatrix(10). I've tried but failed to do it. Your support is highly appriciated @dpb. Thanks & Regards

[SA]

I can extract the cell element by “Cell{1,2}(1)” but how to form the matrix. Your help is highly appreciated.

[dpb]

Are the Xi the 10-element vectors so in your example A is 4x31 or what?

[SA]

Xi will be the 10 individual square matrix of size 4*4 (as for example if there is a 4*4 cell array & each cell has 10 vectors, I want to form the 10 matrices of size 4*4).

[dpb]

I don't follow that at all -- in the 4x4 cell array there is only one 10x1 vector, not 10 vectors.

Cut the size down to something manageable to write out by hand to illustrate because I have no idea what you're tyring to describe verbally, sorry.

You might want to look at cell2mat and kron in conjunction with cellfun in order to write something, I don't know....

[SA]

Ohh, I got the solution from the following link https://www.mathworks.com/matlabcentral/answers/829123-extract-elements-of-each-cell-to-form-a-matrix-and-store-it-can-anyone-give-me-suggestions?s_tid=mlc_ans_email_view#comment_1518608. Thank you very much.