How to make 2 for loops code to run faster?

Dear MATLAB Experts;

I want to make this part of code to run faster it takes hours to process. there are two for loops which take a lot of time to compile the code.

I need your guidance to make this code run faster.

Thank you so much.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x_vect = (-5:0.02:5);
y_vect = (-5:0.02:5);
z_vect = 0;
[x_mat,y_mat,z_mat] = meshgrid(x_vect,y_vect,z_vect);

img = zeros(size(x_mat));
tic;
for ii = 1:2:length(angle)
    dR = sqrt((R0*cos(alpha*pi/180).*cos(angle(ii)*pi/180) + x_mat).^2 ...
        + (R0*cos(alpha*pi/180).*sin(angle(ii)*pi/180) + y_mat).^2 +...
        (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
    for jj = 1:length(Fvec)
        img = img + data(ii,jj).*exp(1j*4*pi*Fvec(jj)/c0*dR);
    end
end
toc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Amjad Iqbal]

@Image Analyst

Please check this query. Thank you!

[Walter Roberson]

We need some additional information. In particular we need to know whether R0 and alpha and c0 are scalar.

[Amjad Iqbal]

@Walter Roberson

Data matrix is large size file to attach, however size is (83348*235) = angle * points.

additional parameters are:

c0 = 3e8;

R0 = 135.16;

Fc = 9.6e9;

Bchirp = 0.5e9;

Nrange = size(data);

Fvec = Fc + (-0.5:1/Nrange:0.5-1/Nrange)*Bchirp;

[Walter Roberson]

@Amjad Iqbal

I am left uncertain about the size of alpha ?

Also, you say Nrange = size(data) but size() with a single parameter returns a vector, and you then use the vector in a colon operation. Perhaps Nrange = size(data,1) ?

[Amjad Iqbal]

@Walter Roberson

These are the all required parameters for loop operation. I have organized the code. Please check with given parameters if it reduce run time.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

data = rand(83348, 235);

Nrange = size(data,2);

alpha = 3;

win_ham = repmat(hamming(size(data,2)).',size(data,1),1); %

data = data.*win_ham;

c0 = 3e8;

R0 = 135.16;

Fc = 9.6e9;

Bchirp = 0.5e9;

Fvec = Fc + (-0.5:1/Nrange:0.5-1/Nrange)*Bchirp;

x_vect = (-5:0.02:5);

y_vect = (-5:0.02:5);

z_vect = 0;

[x_mat,y_mat,z_mat] = meshgrid(x_vect,y_vect,z_vect);

img = zeros(size(x_mat));

angle = size(data,1);

tic;

for ii = 1:2:length(angle)

dR = sqrt((R0*cos(alpha*pi/180).*cos(angle(ii)*pi/180) + x_mat).^2 ...

+ (R0*cos(alpha*pi/180).*sin(angle(ii)*pi/180) + y_mat).^2 +...

(z_mat - R0*sin(alpha*pi/180)).^2) - R0;

for jj = 1:length(Fvec)

img = img + data(ii,jj).*exp(1j*4*pi*Fvec(jj)/c0*dR);

end

end

toc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[Bruno Luong]

angle = size(data,1);

I guess you really want is to generate a (random) vector of size(data,1) NOT a scalar of value size(data,1)

[Amjad Iqbal]

@Bruno Luong

its 2D data of size (83348, 235) which represents (angle, data_points)

Yes, I mentioned it in final version angle = size(data,1);

[Bruno Luong]

You don't understand: Angle is angle in degres NOT a size(data,1) as your code written. What you really mean is length(angle) is size(data,1), something like

angle = 2*pi*rand(1,size(data,1));

NOT obviously wrong statement

angle = size(data,1)

[Bruno Luong]

I'm affraid your code does a lot of calculations, very demending. One can reduce a little bit by matrix multiplication by it is very very expensive.

[Amjad Iqbal]

@Bruno Luong

Yes we can say like this, in my data number of angles are 83348 = 2π (0:360)

So yes, this is also right to say like this

angle = 2*pi*rand(1,size(data,1));

[Amjad Iqbal]

@Bruno Luong

Yes, its very time consuming to process the code, I tired with "bsxfun" may be it needs again loops. If you can suggest using filter2 to process 2D data simultaneously?

[Bruno Luong]

It is NOT 2D filter or convolution. Your "kernel" change form. It is NOT Fourier transform either. Tere is perhaps no fancy algorithms that can possiblyy reduces the flops of your calculation.