svd-finder

Singular Value Decomposition port to js

This procedure computes the singular values and complete orthogonal decomposition of a real rectangular matrix A:

A = U * diag(q) * V(t), U(t) * U = V(t) * V = I

where the arrays a, u, v, q represent A, U, V, q respectively. The actual parameters corresponding to a, u, v may all be identical unless withu = withv = true. In this case, the actual parameters corresponding to u and v must differ.

m >= n is assumed (with m = a.length and n = a[0].length)

Usage:

let a = [
  [22, 10, 2, 3, 7],
  [14, 7, 10, 0, 8],
  [-1, 13, -1, -11, 3],
  [-3, -2, 13, -2, 4],
  [9, 8, 1, -2, 4],
  [9, 1, -7, 5, -1],
  [2, -6, 6, 5, 1],
  [4, 5, 0, -2, 2]
];

let { u, v, q } = SVD(a);

SVD(a [options])

Parameters

// Represents the matrix A to be decomposed
a: number[][]

Options

{
  // if U is desired `false` otherwise
  u: boolean = true,

  // if V is desired `false` otherwise
  v: boolean = true,

  // A constant used in the test for convergence; should not be smaller than the machine precision
  eps: number = Math.pow(2, -52)
}

Result

{
  // Represents the matrix U with orthonormalized columns (`if withu is true` otherwise `u` is used as a working storage)
  u: number[][],

  //Represents the orthogonal matrix V (`if u === true`, otherwise `v` is not used)
  v: number[][],

  // A vector holding the singular values of `A`; they are non-negative but not necessarily ordered in decreasing sequence
  q: number[]
}