I can not figure out how to express this equation in Matlab

I have tried in two methods as follows:

if true
clear;
clc;
a=8.1*10^(-3);
b=0.74;
U=10;
g=9.8;
M=500;
N=500;
w_max=1.5;
w_min=0.5;
del_w=(w_max-w_min)/(M-1);
del_Q=pi/(N-1);
phase=2*pi*rand(M,N);% generate random initial phase
i=1:1:M;
j=1:1:N;
w_i=w_min+(i-1)*del_w;
Q_j=-pi/2+(j-1)*del_Q;
[w_i,Q_j]=meshgrid(w_i,Q_j);
W=a.*g^2.*exp(-b*g^4./(U^4.*w_i.^4))./w_i.^5.*(cos(Q_j./2)).^4;%wave spectrum
%amp=sqrt(2*W*del_w*del_Q);
amp=sqrt(2.*W.*del_w.*del_Q);
Ki=w_i.^2./g;
x=1:1:M;
y=1:1:N;
[X,Y]=meshgrid(x,y);
S=0;
for t=1
 figure(t)
 for a=1:M
     for b=1:N
  S=amp.*cos(w_i(a,b).*t-Ki(a,b).*(X.*cos(Q_j(a,b))+Y.*sin(Q_j(a,b)))+phase(a,b))+S;
     end
 end
  mesh(X,Y,S);
  view(60,60);
  xlabel('x(m)');
  ylabel('y(m)');
  shading interp;
end
end

and also in this way

if true
clear;
clc;
%%constant numbers
a=8.1*10^(-3);
b=0.74;
U=10;
g=9.8;
M=100;%length
N=100;% length
w_max=1.5;
w_min=0.5;
del_w=(w_max-w_min)/(M-1);
del_Q=pi/(N-1);
phase=2*pi*rand(M,N);%generate random initial phase
x=1:1:M;
y=1:1:N;
[X,Y]=meshgrid(x,y);
S=0; %initialize the wave height 
wave=zeros(M,N);% construct wave height matrix
for t=1%time
 figure(t)
 for x=1:1:M;
     for y=1:1:N;
 for i=1:M
     for j=1:N
        w(i)=w_min+(i-1)*del_w;%frequency
       Q(j)=-pi/2+(j-1)*del_Q;% angle
       W=a.*g^2.*exp(-b*g^4./(U^4.*w(i).^4))./w(i).^5.*(cos(Q(j)./2)).^4;%wave spectrum
       amp=sqrt(2.*W.*del_w.*del_Q);%amplitude
        K(i)=w(i).^2./g;%dispersion relation
       S=amp.*cos(w(i).*t-K(i).*(X(x,y).*cos(Q(j))+Y(x,y).*sin(Q(j)))+phase(i,j))+S;
     end
 end
     wave(x,y)=S;%record the calculated wave height in the matrix
     end 
     x
 end
  mesh(X,Y,wave);%draw
  %view(60,60);
  xlabel('x(m)');
  ylabel('y(m)');
  shading interp;
end
end

but I can not figure it out if this is right, the first code gave out a good image but do not make sense for the code. The second code do not give good results but the code seem to be right. I do not what is wrong. maybe someone can help me. thanks

[arun]

Ur second code looks correct, but in ur first code u r treating "amp" as a scalar throughout the code but that supposed to be a tensor, in ur second code u have treated that as a temporary variable inside the 2 loop so that is fine. please note that i didn't check any index mismatch error or syntax error according to the formula u provided

Answer 1

[Zhang Xudong]

http://www.mathworks.com/matlabcentral/answers/223977#comment_292356

thanks, but the second code will take a long time to get the result. this is an easy question, it should not be that complicated. I just can not figure it out..thanks any way

[arun]

Loops are relatively very slow in matlab. U can consider parallelizing the code. I have no idea about parallel computing . I'm sorry to say that in this blog that if u use high level programming languages like C, C++, FORTRAN, python etc that can build those nested loop within one second!