(octave.info)Example Code

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21.4 Examples of Usage
======================

The following can be used to solve a linear system ‘A*x = b’ using the
pivoted LU factorization:

       [L, U, P] = lu (A); ## now L*U = P*A
       x = U \ (L \ P) * b;

This is one way to normalize columns of a matrix X to unit norm:

       s = norm (X, "columns");
       X /= diag (s);

The same can also be accomplished with broadcasting (Note:
Broadcasting):

       s = norm (X, "columns");
       X ./= s;

The following expression is a way to efficiently calculate the sign of a
permutation, given by a permutation vector P.  It will also work in
earlier versions of Octave, but slowly.

       det (eye (length (p))(p, :))

Finally, here’s how to solve a linear system ‘A*x = b’ with Tikhonov
regularization (ridge regression) using SVD (a skeleton only):

       m = rows (A); n = columns (A);
       [U, S, V] = svd (A);
       ## determine the regularization factor alpha
       ## alpha = ...
       ## transform to orthogonal basis
       b = U'*b;
       ## Use the standard formula, replacing A with S.
       ## S is diagonal, so the following will be very fast and accurate.
       x = (S'*S + alpha^2 * eye (n)) \ (S' * b);
       ## transform to solution basis
       x = V*x;