fminsearch with matrices help

I'm attempting to use fminsearch to optimise the components of a matrix to fit some data.

The equation I am looking to fit to the data is:

(y - A*x)^2

where y and x are 150x3 matrices of data, and A is a 3x3 matrix where A(i,j) are the parameters I'm looking to optimise.

The code I have so far is:

type sseval
function sse = sseval(p,x,y)
    A1 = p(1);
    A2 = p(2);
    A3 = p(3);
    A4 = p(4);
    A5 = p(5);
    A6 = p(6);
    A7 = p(7);
    A8 = p(8);
    A9 = p(9);
    M = [A1 A2 A3; A4 A5 A6; A7 A8 A9];
    sse = sum((y - M*x)^2);
end

And then seperately:

fun = @(p)sseval(p,x,y)
p0 = rand(9,1)
bestp = fminsearch(fun,p0)

When i try this the error i recieve is:

Error using @(p)sseval(p,x,y)

'sseval' is used in Curve Fitting via Optimization.

Error in fminsearch (line 200)

fv(:,1) = funfcn(x,varargin{:});

Answer 1

[Ameer Hamza]

x and y should be 3x150 to match the dimensions of matrix A. Following shows the correct code with fminsearch

x = rand(3, 150);
y = rand(3, 150);

fun = @(p) sseval(p, x,y)
p0 = rand(9,1)
bestp = fminsearch(fun,p0)

function sse = sseval(p,x,y)
    M = reshape(p, [3 3]);
    sse = sum((y - M*x).^2, 'all');
end

But note that you don't need fminsearch for this. You can directly use mrdivide / operator

x = rand(3, 150);
y = rand(3, 150);

A = y/x

This will likely be much more efficient than fminsearch.

Answer 2

[Star Strider]

This might do what you want:

x = rand(150,3);                                % Create Data
y = rand(150,3);                                % Create Data

A = x \ y;

Note that ‘A’ is the (3x3) matrix that appears to be the desired result.

Answer 3

[Bruno Luong]

Sort out the dimensions of the matrix before doing anything on paper, programming, etc...

>> x=rand(150,3);
>> A=rand(3,3)

A =

    0.3181    0.6456    0.5447
    0.1192    0.4795    0.6473
    0.9398    0.6393    0.5439

>> y=x*A; % A*x does not make sense

>> Areconstruct = x\y

Areconstruct =

    0.3181    0.6456    0.5447
    0.1192    0.4795    0.6473
    0.9398    0.6393    0.5439