src/det.js

//	Determinant
import dim from './dim'
import clone from './clone'

/**
 * Determinant of matix
 * 
 * @export
 * @param {Array} x
 * @returns {Number}
 * @example
 * 
 * det([[1, 2], [1, 2]])
 * // 0
 */
export default function det (x) {
  // TODO
  var s = dim(x)
  if (s.length !== 2 || s[0] !== s[1]) { throw new Error('det() only works on square matrices'); }
  var n = s[0], ret = 1,i,j,k,A = clone(x),Aj,Ai,alpha,temp,k1,k2,k3
  for (j = 0;j < n - 1;j++) {
    k = j
    for (i = j + 1;i < n;i++) { if (Math.abs(A[i][j]) > Math.abs(A[k][j])) { k = i; } }
    if (k !== j) {
      temp = A[k]; A[k] = A[j]; A[j] = temp
      ret *= -1
    }
    Aj = A[j]
    for (i = j + 1;i < n;i++) {
      Ai = A[i]
      alpha = Ai[j] / Aj[j]
      for (k = j + 1;k < n - 1;k += 2) {
        k1 = k + 1
        Ai[k] -= Aj[k] * alpha
        Ai[k1] -= Aj[k1] * alpha
      }
      if (k !== n) { Ai[k] -= Aj[k] * alpha; }
    }
    if (Aj[j] === 0) { return 0; }
    ret *= Aj[j]
  }
  return ret * A[j][j]
}