How to fix the error :Index exceeds matrix dimensions

clear all; clc; close all

rho_sea=1027;
rho_air=1225;  
g=9.8; 
k=0.4; 
alpha=0.008;
gamma=3.3;
delta_1=0.07; 
delta_2=0.09; 
Tp=[2 10 16];   
fp=1./Tp;  
T=2:1:70;
f_T=1./T;
u= [1.192 1.194 1.120];  
z=[0.0021 0.0029  0.0033];  
sigma= 2*pi*f_T; 
k_nw=sigma.^2./g; 

i_freq=1:69;
f1=0.03093;  
c=1.1;
for i = 1:length(i_freq)
fi=f1.*c.^(i_freq-1);
end
 
%%%  Dir(teta)

i_teta=1:36;
teta_i=10.*i_teta;
teta_i_cos=cos(2*teta_i);

for i = 1:length(teta_i_cos)
 if teta_i_cos>0
    dir_teta=0;
else
    dir_teta= (2/pi())*(1/2)*(1+teta_i_cos);%cos^2(x) = (1+cos2x)/2
end 
end

dir_teta;

%% T=2s

%mi
mi_2 = zeros(numel(teta_i),numel(sigma));
for i=1:length(sigma)
        
    for j=1:length(teta_i)
        mi_2(i,j)=(((g*z(1,1).*(k_nw(i).^2))./sigma(i).^2).*exp((k*sigma(i))./(k_nw(i).*u(1,1)).*cos(teta_i(j))));
    end
   
end

mi_2;

mi_2(:,[37:69])=[]; 

% mp
mp_2=(1.2./k).*mi_2.*log(mi_2).*log(mi_2).*log(mi_2).*log(mi_2);


%%%%%%%%%%%%%%%%%%%%%%%%%%%% My  problem below  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%beta
beta_2= zeros(numel(sigma),numel(teta_i));

Cf=(g.*T)./(2.*pi);

for i=1:length(sigma)
    for j=1:length(teta_i)
        beta_2(i,j)=(rho_air./rho_sea).*mp_2(i,j).*((u(1,1))./(Cf(i))).^2.*(1+cos(teta_i(i).*2)./2);
    end
end

My mistake is on this line (third line from the bottom of the code):

 beta_2(i,j)=(rho_air./rho_sea).*mp_2(i,j).*((u(1,1))./(Cf(i))).^2.*(1+cos(teta_i(i).*2)./2);
 

Thank you for your help

[Walter Roberson]

you loop j to length of teta_i but you index teta_i by i which is up to length of sigma

[Jacqueline Rigatto]

Sorry, I did not understand the last part of your explanation :

Is the lenght of witch loop wrong?

[Walter Roberson]

i_teta=1:36;
teta_i=10.*i_teta;

so teta_i is length 36.

T=2:1:70;

That is length 69

f_T=1./T;

so that is length 69

  sigma= 2*pi*f_T; 

and so is sigma.

  for i=1:length(sigma)
    for j=1:length(teta_i)

so i ranges from 1 to 69 and j ranges from 1 to 36

beta_2(i,j)=(rho_air./rho_sea).*mp_2(i,j).*((u(1,1))./(Cf(i))).^2.*(1+cos(teta_i(i).*2)./2);
                                                                          ^^^^^^^^^

i is at most 69. Consider in particular when i becomes 37. teta_i(i) would be teta_i(37) . But teta_i only has 36 elements.

Cf=(g.*T)./(2.*pi);

with T being length 69, Cf has 69 elements, so indexing Cf(i) with i to 69 is correct.

mi_2 = zeros(numel(teta_i),numel(sigma));

mi_2 is going to be initialized as 36 by 69.

for i=1:length(sigma)

i is going to be 1 to 69

    for j=1:length(teta_i)

j is going to be 1 to 36

        mi_2(i,j)=(((g*z(1,1).*(k_nw(i).^2))./sigma(i).^2).*exp((k*sigma(i))./(k_nw(i).*u(1,1)).*cos(teta_i(j))));

so you are going to assign up to mi_2(69, 36) when m_2 was initialized to 36 by 69. When you assign explicitly to a row or column that is larger than the existing size of the matrix, then the matrix is automatically expanded, so with the row index being up to 69, m_2 is going to expand up to 69 rows, giving you an m_2 that is 69 by 69 with the columns 37 and beyond left at their initial values of 0.

  for i=1:length(sigma)
    for j=1:length(teta_i)

so i ranges from 1 to 69 and j ranges from 1 to 36

beta_2(i,j)=(rho_air./rho_sea).*mp_2(i,j).*((u(1,1))./(Cf(i))).^2.*(1+cos(teta_i(i).*2)./2);
                                ^^^^^^^^^

so you are going to access up to mp_2(69, 36) which is the part of mp_2 that had data written into it. That will be okay, but it does lead to the question of why you set up mp_2 to be 69 x 69 when you never use columns 37 to 69 from it.

=====

My recommendation would be that you rewrite your code to not use the variable names i or j as you are obviously losing track of what they mean. I suggest that you consider using names such as sigmaidx and thetaidx which would make it much clearer which variable has which role.

[Jacqueline Rigatto]

Thanks for the clue, Walter Roberson! I'll remake!