Singular Value Decomposition

svds(A) Returns a vector containing the singular values of A, the positive square roots of the eigenvalues of the matrix A^T·A.

svd(A) Returns one matrix containing two stacked matrices U and V satisfying the equation A = U·diag(s)·V^T, where s is the vector returned by svds. The upper matrix, U, is the same size as A. The lower matrix, V, is a square matrix with the same number of columns as A. Use submatrix to extract these smaller matrices.

svd2(A) Returns a vector of 3 nested arrays. The first array contains the vector of singular values returned by svds. The next two arrays are the matrices U and V^T returned by svd, with the exception that V is already transposed. This function uses the BLAS/LAPACK libraries from Intel.

Arguments:

• A is an m × n array, where m ≥ n. For svds and svd, the array elements must be real numbers; for svd2, complex values are allowed.

Notes:

• Singular values are always real and positive. Very small values should be interpreted as 0.
• The svd function returns a singular value decomposition for A. The decomposition is not unique.
• The svd2 function is faster and more usable than svd and svds, and we recommend that you upgrade to the newer function.

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