Hi, I'm new to Matlab. I keep getting Index exceeds matrix dimensions error. Maybe someone can help me with this.

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Muhamad Mohd-Adly
Muhamad Mohd-Adly 2017-12-13
评论： Muhamad Mohd-Adly 2017-12-14
function [ J ] = J_springs( x )
%Jacobian Matrix Jf
%df/dx(i) df/dx(i-1) df/dx(i+1)
%Initialization
x=1:20
N=20
K=zeros(N,1);
b=zeros(N,1);
J=zeros(N,1);
for i = 1:N
K(i) = (100+i-N/2); %N/cm
b(i) = (-10+0.1*(i-N/2)); %N/cm^3
end
for i = 2:N-2
J(i,i) = -(K(i,i)+K(i+1,i))+3*b(i,i)*(x(i,i)-x(i-1,i))^2+3*b(i+1,i)*(x(i+1,i)-x(i,i))^2;
end
%
for i = 2:N-1
J(i,i-1) = K(i,i-1)-3*b(i,i-1)*(x(i,i-1)-x(i-1,i-1))^2;
end
%
for i = 1:N-2
J(i,i+1) = K(i+1,i+1)-3*b(i+1,i+1)*(x(i+1,i+1)-x(i,i+1))^2;
end
%
end

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Walter Roberson
Walter Roberson 2017-12-13
K=zeros(N,1);
So K is a column vector with N rows.
for i = 1:N
K(i) = (100+i-N/2); %N/cm
b(i) = (-10+0.1*(i-N/2)); %N/cm^3
end
so the first N entries in K are initialized (that is, all of it.)
for i = 2:N-2
J(i,i) = -(K(i,i)+K(i+1,i))+3*b(i,i)*(x(i,i)-x(i-1,i))^2+3*b(i+1,i)*(x(i+1,i)-x(i,i))^2;
end
So i starts from 2, so the right hand side immediate starts trying to evaluate K(i,i) which is K(2,2) but K only has one column.
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Walter Roberson
Walter Roberson 2017-12-13
Most of your code does not make sense unless you are using 2D arrays instead of column vectors. However, I would then expect you to be doing nested loops instead of single loops.
If I were writing the code, I would vectorize. For example instead of
for i = 2:N-2
J(i,i) = -(K(i,i)+K(i+1,i))+3*b(i,i)*(x(i,i)-x(i-1,i))^2+3*b(i+1,i)*(x(i+1,i)-x(i,i))^2;
end
I would look at
J(2:N-1, 2:N-1) = -K(2:N-1,2:N-1)+K(3:N,2:N-1)) + 3 * b(2:N-1,2:N-1) * (x(2:N-1, 2:N-1) - X(1:N-2, 2:N-1)).^2 + 3 * b(3:N, 2:N-1) * (x(3:N, 2:N-1) - x(2:N-1, 2:N-1)).^2;

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