How to find if a matrix is Singular in Matlab

Question

I use the function below to generate the betas for a given set of guess lambdas from my optimiser.

When running I often get the following warning message:

Answer 1

There are special tools designed for this problem, appropriately called "rank revealing matrix factorizations". To my best (albeit a little old) knowledge, a good enough way to decide whether a n x n matrix A is nonsingular is to go with

det(A) <> 0 <=> rank(A) = n

and use a rank-revealing QR factorization of A:

AP = QR

where Q is orthogonal, P is a permutation matrix and R is an upper triangular matrix with the property that the magnitude of the diagonal elements is decreased along the diagonal.