src/inv.js

import dim from './dim'
import identity from './identity'
import clone from './clone'

/**
 * Inverse of an matrix
 * 
 * @export
 * @param {Array} x
 * @returns {Array}
 * @example 
 * 
 * inv([[1,2],[3,4]])
 * // [[   -2,    1],
 * //  [  1.5, -0.5]]
 */
export default function inv (x) {
  var s = dim(x), abs = Math.abs, m = s[0], n = s[1]
  var A = clone(x), Ai, Aj
  var I = identity(m), Ii, Ij
  var i,j,k,x
  for (j = 0;j < n;++j) {
    var i0 = -1
    var v0 = -1
    for (i = j;i !== m;++i) { k = abs(A[i][j]); if (k > v0) { i0 = i; v0 = k; } }
    Aj = A[i0]; A[i0] = A[j]; A[j] = Aj
    Ij = I[i0]; I[i0] = I[j]; I[j] = Ij
    x = Aj[j]
    for (k = j;k !== n;++k)    Aj[k] /= x
    for (k = n - 1;k !== -1;--k) Ij[k] /= x
    for (i = m - 1;i !== -1;--i) {
      if (i !== j) {
        Ai = A[i]
        Ii = I[i]
        x = Ai[j]
        for (k = j + 1;k !== n;++k)  Ai[k] -= Aj[k] * x
        for (k = n - 1;k > 0;--k) { Ii[k] -= Ij[k] * x; --k; Ii[k] -= Ij[k] * x; }
        if (k === 0) Ii[0] -= Ij[0] * x
      }
    }
  }
  return I
}