Using Fminsearch to Minimize Data difference

I need to create a function that can be passed to fminsearch. I want to get argmink =||ak-d||^2, where a is a time series output ie x,y (amplitude/time) and d is another different time series output signal. I need to find the value of k that will cause convergence or give the minimum difference value between a and d. So I want to use fminsearch to do this. Some pointer will be very useful. Thanks.

Answer 1

[Star Strider]

If I understand correctly what you want to do, this works:

d = randi(9, 10, 1);                            % Create Data
a = randi(9, 10, 1);                            % Create Data

argmin_k = @(k) norm(a*k-d).^2;                 % ‘argmin’ Function

[k,normval] = fminsearch(argmin_k, 1);

[Suki Sule]

Splendid!Star Strider. What if k will have different values, k(1)...k(n). So say f(k) is such that k(1) = depth, k(2) = radius ...k(n)?

[Suki Sule]

Or do I have to run fminsearch separately for each parameter, f(k1) then f(k2)...f(kn)

[Star Strider]

Thank you!

I am not certain what you want to do. For ‘k’ to be a vector, ‘k’ would have to be the same length as ‘a’ and ‘d’, and you would then use element-wise multiplication (.*) in your ‘argmin_k’ function.

The code changes to:

d = randi(9, 10, 1);                            % Create Data
a = randi(9, 10, 1);                            % Create Data

argmin_k = @(k) norm(a.*k-d).^2;                % ‘argmin’ Function
K0 = ones(size(d));                             % Vector ‘k’ Is The Same Length As The Data Vectors
[k,normval] = fminsearch(argmin_k, K0);