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Inner matrix dimensions must agree error message,

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Noob
Noob on 22 Sep 2020
Edited: Adam Danz on 22 Sep 2020
Hi,
I'm getting an error message that says inner matrix dimensions must agree, but I checked both matrices and they seem fine -- it's just a 2x2 matrix left-multiplying with a 2x1 matrix.
Here's the error message:
Error using *
Inner matrix dimensions must agree.
Error in Root_finding_practice (line 78)
x(:,i+1) = x(:,i) - ( inv( H( x(:, i) ) ) * J( x(:,i) ) ); % Newton's method in 2 variables
And here's the piece of the code:
J = @(x) [ cos( x(2) ), -x(1) * sin( x(2) ) ]; % Jacobian of f
H = @(x) [ 0, -sin( x(2) ); % Hessian matrix of 2nd derivatives
-sin( x(2) ), -cos( x(2) ) * x(1) ];
% An initial guess at a multivariable root:
x = [1; 1];
for i = 1:100 % The for-loop should stop when the function tolerance is satisfied
x(:,i+1) = x(:,i) - ( inv( H( x(:, i) ) ) * J( x(:,i) ) ); % Newton's method in 2 variables
What am I missing?
Thanks,

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Accepted Answer

Adam Danz
Adam Danz on 22 Sep 2020
Edited: Adam Danz on 22 Sep 2020
You can either perform element-wise multiplication with implicit expansion
x(:,i) - inv(H(x(:, i)) .* J(x(:,i)))
% add this ^
however that will produce a 2x2 output which will cause an error when you index it into
x(:,i+1) =
or you can perform matrix multiplication
H(x(:, i)) is a 2x2 matrix, J(x(:,i)) is a 1x2 matrix. If you multiply these matricies, you either need to transpose the J term or switch the two terms
H(x(:, i)) * J(x(:,i)).' % result is 2x1 matrix
% or
J(x(:,i)) * H(x(:, i)) % result is a 1x2 matrix
but matrix inversion using inv() requires the use of a square matrix and neither of those fulfill that requirement.
So, you've got some thinking to do regarding what the output should be and how you'll store it.

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Adam Danz
Adam Danz on 22 Sep 2020
Ahhh, right. All of those spaces between the brackets threw me off.
Noob
Noob on 22 Sep 2020
haha, yeah, I like those spaces. it's kinda weird but it makes it more readable to me.
Have a great night / day, Adam!
Adam Danz
Adam Danz on 22 Sep 2020
Thanks; and no problem with the spaces! You'll see lots of style manuals out there suggesting best practices when writing code that will be used by more than 1 person but it's fine to come up with a style that makes sense to you. Just today I was told by a friend that I write too many comments in my code 🙄.

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