Using ALS algorithm for writing a code

Is ALS algorithm supported by MATLAB R2019a. What is the best source of downloading the alogorithm and the reference to write the code for analysing spectral data?

Answer 1

[Star Strider]

See page 5 of Baseline Correction with Asymmetric Least Squares Smoothing (link).

I’ve not run this, so I have no experience with it. It’s the only MATLAB code for the algorithm that I could find.

The slightly corrected version of the function:

function z = baseline(y, lambda, p)
% Estimate baseline with asymmetric least squares
m = length(y);
D = diff(speye(m), 2);w = ones(m, 1);
for it = 1:10
    W = spdiags(w, 0, m, m);
    C = chol(W + lambda * D' * D);
    z = C \ (C' \ (w .* y));
    w = p * (y > z) + (1 - p) * (y < z);
end

Also consider:

function z = baseline(y, lambda, p)
% Estimate baseline with asymmetric least squares
m = length(y);
D = diff(speye(m), 2);w = ones(m, 1);
for it = 1:10
    W = spdiags(w, 0, m, m);
    C = chol(W + lambda * (D' * D));
    z = C \ (C' \ (w .* y));
    w = p * (y > z) + (1 - p) * (y < z);
end

The documentation for the function is in the paper.

Experiment to get the result you want.

[Csaba]

at the very beginning I would add:

if isrow(y)
    y=y';
end

[Timothy Loayza]

Thanks a lot, it works very well for Raman's spectras. (lambda = 100'000, p = 0.01)

BTW : I don't know who to cite for it as the link is not working anymore.

[Star Strider]

Timothy Loayza — I actually saved it. I am attaching it here. (It was apparently open-access at the time, so I doubt that I am violating any copyright by posting it here.)

Also, with respect to Csaba’s comment, if you want to force it to be a column vector, just do this:

y(:)

.