An easy? Matlab Problem involving matrices

[alba_ei]

Homework Statement

The Attempt at a Solution

%2.11
x=1:0.5:5; a=sqrt(2.8);
n=[1:1:100];
Sn=prod(1-(x.^2)./(n.^2-a^2));
S_inf=(a/sqrt(a^2+x.^2)).*sin(pi*sqrt(a^2+x.^2))/sin(pi*a);
e_n=100*(Sn-S_inf)./S_inf

I know I can't use ./ if the two matrices are different, meaning x./n.
How do I use the prod function without going through this issue?

 

[jimep]

Your best bet is to iterate through the Sn with x.

I've written a bit of code here, its the worst code possible, a programmer might murder me if they would get a look at this but it solves the problem.

Now go and write clean code;


%2.11
clear all;
clc;
a=sqrt(2.8);
n=1:1:100;
X=1:0.5:5;
i=1;

for x=1:0.5:5
Sn(i) = prod(1-(x^2./(n.^2-a^2)));
i=i+1;
end

S_inf=(a./sqrt(a^2+X.^2)).*(sin(pi*sqrt(a^2+X.^2))./sin(pi*a));

e_n=((Sn-S_inf)./S_inf)*100

 

[RoshanBBQ]

Your best bet is to use matrices instead of a for loop.

% define input
N = 100;
x = 1:0.5:5;
a = sqrt(2.8);

% Create big matrices
X = repmat(x, [N,1]);
n = repmat( (1:N).' ,[1,length(x)]);

% Calculate Sn
SN = prod(1-X.^2./(n.^2-a^2));

% Calculate inf values
Sinf = a./sqrt(a^2+x.^2).*sin(pi()*sqrt(a^2+x.^2))/sin(pi()*a);

% Caclulate eN
eN = 100*(SN-Sinf)./Sinf

 

[jimep]

Your best bet is to use matrices instead of a for loop.

% define input
N = 100;
x = 1:0.5:5;
a = sqrt(2.8);

% Create big matrices
X = repmat(x, [N,1]);
n = repmat( (1:N).' ,[1,length(x)]);

% Calculate Sn
SN = prod(1-X.^2./(n.^2-a^2));

% Calculate inf values
Sinf = a./sqrt(a^2+x.^2).*sin(pi()*sqrt(a^2+x.^2))/sin(pi()*a);

% Caclulate eN
eN = 100*(SN-Sinf)./Sinf

Yess! This is much nicer. I also feel that I have to apologize for my 'best bet' part.
I just thought that less computation time would be more efficient.

 

[DeeNos]

I would suggest using the dot product function (.*), which performs element-wise multiplication on two matrices of the same size. This would allow you to use the prod function without encountering any issues with different matrix sizes. Additionally, you can also use the colon operator to create a vector of values for n, rather than specifying it as a matrix. This would also ensure that the dimensions of the matrices are compatible for the dot product function.