A simple library to compute Singular Value Decomposition as explained in "Singular Value Decomposition and Least Squares Solutions. By G.H. Golub et al."
SVD(a, withu, withv, eps, tol) => { u, v, q }
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
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).
The following is the description of all parameters:
a{Array}: Represents the matrix A to be decomposedwithu(Optional default is true) {bool | 'f'}:trueif U is desiredfalseotherwise. It can also be 'f' (see below)withv(Optional default is true) {bool}:trueif V is desiredfalseotherwiseeps(Optional) {Number}: A constant used in the test for convergence; should not be smaller than the machine precisiontol(Optional) {Number}: A machine dependent constant which should be set equal toB/epswhere B is the smallest positive number representable in the computer
The function returns an object with the following values:
q: A vector holding the singular values of A; they are non-negative but not necessarily ordered in decreasing sequenceu: Represents the matrix U with orthonormalized columns (ifwithuistrueotherwiseuis used as a working storage)v: Represents the orthogonal matrix V (ifwithvistrue, otherwisevis not used)
If 'f' is given to withu, it computes 'full' U with m*m dimension.
It is an extension in (i) of '5. Organization and Notation Details' in Golub et al."
The extension part of U (u[n] to u[m-1]) are orthonormal bases of A that correspond to null singular values, or the nullspace of A^T.
Golub and Reinsch first example
import { SVD } from 'svd-js'
const 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]
]
const { u, v, q } = SVD(a)
console.log(u)
console.log(v)
console.log(q)Golub and Reinsch first example
<html>
<script src="https://unpkg.com/svd-js" type="application/javascript"></script>
<script>
const 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]
]
const { u, v, q } = SVDJS.SVD(a)
console.log(u)
console.log(v)
console.log(q)
</script>
</html>