# mgs_ortho¶

Modified Gram-Schmidt Orthogonalisation

Orthogonalises input matrix $$\mathbf{X}$$ column by column.

param X

Input matrix of dimensions $$n$$ by $$m$$.

type X

np.ndarray

returns

Orthogonalised matrix of dimensions $$n$$ by $$m$$.

rtype

np.ndarray

Notes

This method is faster than scipy’s scipy.linalg.qr() method that returns an orthogonal matrix as part of the QR decomposition, albeit at a higher number of function calls.