Inner matrix dimensions must agree error message,

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,

Answer 1

[Adam Danz]

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.

[Noob]

Ah, yes, J was of size 1x2, so I just transposed it.

I'm just inverting the 2x2 Hessian matrix, so it's fine.

Thanks!

[Adam Danz]

Ahhh, right. All of those spaces between the brackets threw me off.

[Noob]

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]

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 🙄.