@rayyamhk/matrix/lib/core/properties/det.js

A professional, comprehensive and high-performance library for you to manipulate matrices.

"use strict";

function _slicedToArray(arr, i) { return _arrayWithHoles(arr) || _iterableToArrayLimit(arr, i) || _unsupportedIterableToArray(arr, i) || _nonIterableRest(); }

function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); }

function _unsupportedIterableToArray(o, minLen) { if (!o) return; if (typeof o === "string") return _arrayLikeToArray(o, minLen); var n = Object.prototype.toString.call(o).slice(8, -1); if (n === "Object" && o.constructor) n = o.constructor.name; if (n === "Map" || n === "Set") return Array.from(o); if (n === "Arguments" || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(n)) return _arrayLikeToArray(o, minLen); }

function _arrayLikeToArray(arr, len) { if (len == null || len > arr.length) len = arr.length; for (var i = 0, arr2 = new Array(len); i < len; i++) { arr2[i] = arr[i]; } return arr2; }

function _iterableToArrayLimit(arr, i) { var _i = arr == null ? null : typeof Symbol !== "undefined" && arr[Symbol.iterator] || arr["@@iterator"]; if (_i == null) return; var _arr = []; var _n = true; var _d = false; var _s, _e; try { for (_i = _i.call(arr); !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"] != null) _i["return"](); } finally { if (_d) throw _e; } } return _arr; }

function _arrayWithHoles(arr) { if (Array.isArray(arr)) return arr; }

/* eslint-disable prefer-destructuring */
var Matrix = require('../..');

var _require = require('../../Error'),
    INVALID_SQUARE_MATRIX = _require.INVALID_SQUARE_MATRIX;
/**
 * Calculates the determinant of square Matrix.
 * If the Matrix size is larger than 3, it calculates the determinant using
 * LU decomposition, otherwise, using Leibniz Formula.<br><br>
 * The determinant is cached.
 * @memberof Matrix
 * @instance
 * @returns {number} Returns the determinant of square matrirx
 */


function det() {
  if (!this.isSquare()) {
    throw new Error(INVALID_SQUARE_MATRIX);
  }

  if (this._det !== undefined) {
    return this._det;
  }

  var matrix = this._matrix;
  var size = matrix.length;

  if (size === 0) {
    this._det = 1;
    return 1; // the determinant of 0x0 matrix must be 1
  }

  if (size === 1) {
    this._det = matrix[0][0];
    return this._det;
  }

  if (size === 2) {
    this._det = matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
    return this._det;
  }

  if (size === 3) {
    this._det = matrix[0][0] * matrix[1][1] * matrix[2][2] + matrix[0][1] * matrix[1][2] * matrix[2][0] + matrix[0][2] * matrix[1][0] * matrix[2][1] - matrix[0][2] * matrix[1][1] * matrix[2][0] - matrix[0][1] * matrix[1][0] * matrix[2][2] - matrix[0][0] * matrix[1][2] * matrix[2][1];
    return this._det;
  }

  var _Matrix$LU = Matrix.LU(this, true),
      _Matrix$LU2 = _slicedToArray(_Matrix$LU, 2),
      P = _Matrix$LU2[0],
      LU = _Matrix$LU2[1];

  var matrixLU = LU._matrix; // count whether the number of permutations <swap> is odd or even
  // O(n^2)

  var swap = 0;

  for (var i = 0; i < size; i++) {
    if (P[i] === i) {
      continue;
    }

    while (P[i] !== i) {
      var target = P[i];
      P[i] = P[target];
      P[target] = target;
      swap++;
    }
  }

  var result = 1;

  for (var _i2 = 0; _i2 < size; _i2++) {
    result *= matrixLU[_i2][_i2];
  }

  if (swap % 2 === 1) {
    this._det = result * -1;
    return this._det;
  }

  this._det = result;
  return result;
}

;
module.exports = det;