Matlab runs very slower (almost stucks) after some iteration in for loop

Dear All,

In my program I have a for loop which has to run 5823x8153 times. The for loop runs quite faster until i= 3944 and j = 8153. However, after this iteration the for loop is running very slowly almost it stucks at this point. I tried some acceleration methods like pre allocation and computing some variables before the for loop but it did not work. The problematic for loop is given as below. Could you please help me about this problem? By the way, it works good for small portions(1000x1000 or 3000x3000) of the same data and I run this program using a workstation with 64GB RAM. I am looking forward to hearing from you

ro1 = (180*3600)/pi;
ro = ro1^2;  
sigma_h = horizontal_prec_secs;
sigma_v = vertical_prec_secs;
error_ellip_dim = nan(5823,8153,3);
for i = 1:5823
    for j = 1:8153
        sigma_r = range_precision(i,j);
        h = horizontal_angle(i,j);
        v = vertical_angle(i,j);
        r = range(i,j)*1000;
        if (isnan(h))||(isnan(sigma_r))
           error_ellip_dim(i,j,:) = NaN;
        else
            EXX(1,1) = sigma_r^2*COSDH(i,j)^2*COSDV(i,j)^2 + (r^2*sigma_h^2*COSDV(i,j)^2*SINDH(i,j)^2)/ro + (r^2*sigma_v^2*COSDH(i,j)^2*SINDV(i,j)^2)/ro;
            EXX(1,2) = sigma_r^2*COSDH(i,j)*COSDV(i,j)^2*SINDH(i,j) - (r^2*sigma_h^2*COSDH(i,j)*COSDV(i,j)^2*SINDH(i,j))/ro + (r^2*sigma_v^2*COSDH(i,j)*SINDH(i,j)*SINDV(i,j)^2)/ro;
            EXX(1,3) = COSDH(i,j)*COSDV(i,j)*SINDV(i,j)*sigma_r^2 - (r^2*sigma_v^2*COSDH(i,j)*COSDV(i,j)*SINDV(i,j))/ro;
            EXX(2,1) = EXX(1,2); 
            EXX(2,2) = sigma_r^2*COSDV(i,j)^2*SINDH(i,j)^2 + (r^2*sigma_h^2*COSDH(i,j)^2*COSDV(i,j)^2)/ro + (r^2*sigma_v^2*SINDH(i,j)^2*SINDV(i,j)^2)/ro;
            EXX(2,3) = COSDV(i,j)*SINDH(i,j)*SINDV(i,j)*sigma_r^2 - (r^2*sigma_v^2*COSDV(i,j)*SINDH(i,j)*SINDV(i,j))/ro;
            EXX(3,1) = EXX(1,3);
            EXX(3,2) = EXX(2,3);
            EXX(3,3) = sigma_r^2*SINDV(i,j)^2 + (r^2*sigma_v^2*COSDV(i,j)^2)/ro;
            [eig_vec_mat,eig_val_mat] = eig(EXX);
            ellip_params = sqrt(diag(eig_val_mat));
            error_ellip_dim(i,j,:) = ellip_params';            
        end
    end
    i
    j
end

[the cyclist]

Can you upload values (e.g. in a MAT file) for all the variables that are not defined here, so that we can run your code?

[mustafa ozendi]

Dear Cylist, I tried to upload MAT files but it allows files smaller than 5mb. My MAT files are larger than 5mb. Is there a way of uploading such data?

Answer 1

[Jan]

You can accelerate the code - although this was not your question:

ro1 = (180*3600)/pi;
ro = ro1^2;  
sigma_h = horizontal_prec_secs;
sigma_v = vertical_prec_secs;
error_ellip_dim = nan(5823,8153,3);
for i = 1:5823
   for j = 1:8153
      sigma_r = range_precision(i,j);
      h = horizontal_angle(i,j);
      if ~isnan(h) && ~isnan(sigma_r)  % No need to set other elements to NaN
         v = vertical_angle(i,j);
         r = range(i,j)*1000;

           sigma_r2 = sigma_r^2;  % Constants to avoid repeated calculations
           COSDV2   = COSDV(i,j)^2;
           SINDV2   = SINDV(i,j)^2;
           r2       = r^2;
           SINDH2   = SINDH(i,j)^2;
           COSDH2   = COSDH(i,j)^2;
           r2sigma_h2 = r2*sigma_h^2;
           r2sigma_v2 = r2*sigma_v^2;

           EXX(1,1) = sigma_r2 * COSDH2*COSDV2 + (r2sigma_h2*COSDV2*SINDH2)/ro + (r2sigma_v2*COSDH2*SINDV2)/ro;
           EXX(1,2) = sigma_r2*COSDH(i,j)*COSDV2*SINDH(i,j) - (r2sigma_h2*COSDH(i,j)*COSDV2*SINDH(i,j))/ro + (r2sigma_v2*COSDH(i,j)*SINDH(i,j)*SINDV2)/ro;
           EXX(1,3) = COSDH(i,j)*COSDV(i,j)*SINDV(i,j)*sigma_r2 - (r2sigma_v2*COSDH(i,j)*COSDV(i,j)*SINDV(i,j))/ro;
           EXX(2,1) = EXX(1,2); 
           EXX(2,2) = sigma_r2*COSDV2*SINDH2 + (r2sigma_h2*COSDH2*COSDV2)/ro + (r2sigma_v2*SINDH2*SINDV2)/ro;
           EXX(2,3) = COSDV(i,j)*SINDH(i,j)*SINDV(i,j)*sigma_r2 - (r2sigma_v2*COSDV(i,j)*SINDH(i,j)*SINDV(i,j))/ro;
           EXX(3,1) = EXX(1,3);
           EXX(3,2) = EXX(2,3);
           EXX(3,3) = sigma_r2*SINDV2 + (r2sigma_v2*COSDV2)/ro;
           [eig_vec_mat,eig_val_mat] = eig(EXX);
           error_ellip_dim(i,j,:) = sqrt(diag(eig_val_mat)).';  % ' or .' ?!
       end
    end
    % Output to command window might be time consuming - removed: "i j"
  end

I curious: Does avoiding the bunch of square operations speed up the code measurably? Most likely the eig() will be the bottleneck, so perhaps this suggestion is not important. I don't know if Matlab calculates the eigenvectors of 3x3 matrices efficiently. See: https://www.geometrictools.com/Documentation/RobustEigenSymmetric3x3.pdf and https://en.wikipedia.org/wiki/Eigenvalue_algorithm#3.C3.973_matrices .

[mustafa ozendi]

Dear Jan Simon, Thank you for answer. I avoided to compute square root of negative numbers and it works now. By the way, I will definitely take into consideration your suggestions about accelerating the code.

Answer 2

[mustafa ozendi]

Thank you very much for helps. I figured out the problem. At the point where it stucks, MAtlab is trying to compute square root of a negative number and getting complex number. And it is spending great effort for this job. I avoided from these numbers by a simple codification and it is running quite rapidly.