Info Catalog octave: Function Support octave: Diagonal and Permutation Matrices octave: Zeros Treatment

octave: Example Code

 
 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);
 
 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;
 

Info Catalog octave: Function Support octave: Diagonal and Permutation Matrices octave: Zeros Treatment