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

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WLL
WLL on 8 Jun 2021
Commented: WLL on 8 Jun 2021
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}

Accepted Answer

KSSV
KSSV on 8 Jun 2021
Edited: KSSV on 8 Jun 2021
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
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