Using Numpy (np.linalg.svd) for Singular Value Decomposition

Question

Im reading Abdi & Williams (2010) \"Principal Component Analysis\", and I\'m trying to redo the SVD to attain values for further PCA.

The article states that followi

Answer 1

From the scipy.linalg.svd docstring, where (M,N) is the shape of the input matrix, and K is the lesser of the two:

Returns
-------
U : ndarray
    Unitary matrix having left singular vectors as columns.
    Of shape ``(M,M)`` or ``(M,K)``, depending on `full_matrices`.
s : ndarray
    The singular values, sorted in non-increasing order.
    Of shape (K,), with ``K = min(M, N)``.
Vh : ndarray
    Unitary matrix having right singular vectors as rows.
    Of shape ``(N,N)`` or ``(K,N)`` depending on `full_matrices`.

Vh, as described, is the transpose of the Q used in the Abdi and Williams paper. So just

X_a = P.dot(D).dot(Q)

should give you your answer.