How do I get the combination of cell array "wmn" and set up the preallocation of "wmn"

Below is my code.

In the last line of my code. Because "i" is variable, I would like to ask how to combine the wmn without using "Combine=wmn{1}+wmn{2}+wmn{3}+wmn{4}". So I can combine more term when "i" is a large number.

Also, about the second for loop, I would like to know how should I preallocate the "wmn array" with zero matrix, just as I did for the first for loop "amn=zeros(1,len)" so that I can do the calculation more efficiently.

Thank you very much!!

clc
clear
format long
E=209e+3; 
q=-1; 
h=15; 
D=6.459478021978022e+07; 
I=2.8125e+02; 
a=600;b=2400; 

% change the value of mn
n =7;
[T1, T2] = meshgrid(1:2:n);
mn = [T1(:), T2(:)]


syms x y

x_value=0:10:600;
y_value=0:10:2400;
[X,Y]=meshgrid(x_value,y_value)

% Fine the amn
len=length(mn);
amn=zeros(1,len);
for  i=1:len
    m=mn(i,1);
    n=mn(i,2);
    amn(i)=(16*q/(m*n*D*pi^6))*(1/((m/a)^2+(n/b)^2)^2); % amn(i) storage the array
end

% Fine the wmn
% How do I preallocate the wmn array?
for i=1:len
    m=mn(i,1);
    n=mn(i,2);
    wmn{i}=amn(i).*((sin(m.*pi.*X./a)).*(sin(n.*pi.*Y./b))); 
end
% How do I find the combination of wmn ?
 Combine=wmn{1}+wmn{2}+wmn{3}+wmn{4}

Answer 1

[KSSV]

clc; clear all ;
clc
clear
format long
E=209e+3; 
q=-1; 
h=15; 
D=6.459478021978022e+07; 
I=2.8125e+02; 
a=600;b=2400; 

% change the value of mn
n =7;
[T1, T2] = meshgrid(1:2:n);
mn = [T1(:), T2(:)]


syms x y

x_value=0:10:600;
y_value=0:10:2400;
[X,Y]=meshgrid(x_value,y_value) ; 

% Fine the amn
len=length(mn);
amn=zeros(1,len);
for  i=1:len
    m=mn(i,1);
    n=mn(i,2);
    amn(i)=(16*q/(m*n*D*pi^6))*(1/((m/a)^2+(n/b)^2)^2); % amn(i) storage the array
end

% Fine the wmn
wmn = zeros(size(X,1),size(X,2),len) ;    % preallocation 
for i=1:len
    m=mn(i,1);
    n=mn(i,2);
    wmn(:,:,i)=amn(i).*((sin(m.*pi.*X./a)).*(sin(n.*pi.*Y./b))); 
end
 Combine=sum(wmn(:,:,1:4),3) ;   % use the function sum 

[Mark]

Thanks for your explanation.

But it seems that "sum" can not do the cell calculation

Below is the error in my command window:

Error using sum

Invalid option. Option must be 'double', 'native', 'default', 'omitnan', or 'includenan'.

Error in Untitled7 (line 34)

Combine=sum(wmn(:,:,1:4),[],3) ; % use the function sum

[KSSV]

Type error:

Replace

 Combine=sum(wmn(:,:,1:4),[],3) ;  

with

  Combine=sum(wmn(:,:,1:4),3) ;   

Edited the answer.

[Mark]

It works! Thank you very much!