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Householder matrices

Category: misc
#linear algebra #householder #QR

Householder matrices are square matrices of the form

$$ P = I - \beta v v^T$$

where $\beta$ is a scalar and $v$ is …

Ridge regression path

Category: misc
#scikit-learn #scipy #linear algebra

Ridge coefficients for multiple values of the regularization parameter can be elegantly computed by updating the thin SVD decomposition of the design matrix:

import numpy as np
from scipy import linalg
def ridge(A, b, alphas):
    """
    Return coefficients for regularized least squares

         min ||A x - b||^2 + alpha ||x||^2 …

Computing the vector norm

Category: misc
#linear algebra #norm #scipy

Update: a fast and stable norm was added to scipy.linalg in August 2011 and will be available in scipy 0.10 Last week I discussed with Gael how we should compute the euclidean norm of a vector a using SciPy. Two approaches suggest themselves, either calling scipy.linalg.norm …