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svd-js

1.1.0 • Public • Published

SVD-JS

Build Status Coverage Status JavaScript Style Guide npm

A simple library to compute Singular Value Decomposition as explained in "Singular Value Decomposition and Least Squares Solutions. By G.H. Golub et al."

Usage

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 decomposed
  • withu (Optional default is true) {bool}: true if U is desired false otherwise
  • withv (Optional default is true) {bool}: true if V is desired false otherwise
  • eps (Optional) {Number}: A constant used in the test for convergence; should not be smaller than the machine precision
  • tol (Optional) {Number}: A machine dependent constant which should be set equal to B/eps where 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 sequence
  • u: Represents the matrix U with orthonormalized columns (if withu is true otherwise u is used as a working storage)
  • v: Represents the orthogonal matrix V (if withv is true, otherwise v is 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.

npm package

Golub and Reinsch first example

import { SVD } from 'svd-js'
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)
console.log(u)
console.log(v)
console.log(q)
umd package

Golub and Reinsch first example

<html>
 <script src="https://unpkg.com/svd-js" type="application/javascript"></script> 
 <script>
   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 } = SVDJS.SVD(a)
   console.log(u)
   console.log(v)
   console.log(q)
 </script> 
</html>

Install

npm i svd-js

DownloadsWeekly Downloads

35

Version

1.1.0

License

MIT

Unpacked Size

77.1 kB

Total Files

22

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