mathjs/lib/function/matrix/det.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

'use strict';

var util = require('../../utils/index');

var object = util.object;
var string = util.string;

function factory(type, config, load, typed) {
  var matrix = load(require('../../type/matrix/function/matrix'));
  var subtract = load(require('../arithmetic/subtract'));
  var multiply = load(require('../arithmetic/multiply'));
  var unaryMinus = load(require('../arithmetic/unaryMinus'));
  var lup = load(require('../algebra/decomposition/lup'));
  /**
   * Calculate the determinant of a matrix.
   *
   * Syntax:
   *
   *    math.det(x)
   *
   * Examples:
   *
   *    math.det([[1, 2], [3, 4]]) // returns -2
   *
   *    const A = [
   *      [-2, 2, 3],
   *      [-1, 1, 3],
   *      [2, 0, -1]
   *    ]
   *    math.det(A) // returns 6
   *
   * See also:
   *
   *    inv
   *
   * @param {Array | Matrix} x  A matrix
   * @return {number} The determinant of `x`
   */

  var det = typed('det', {
    'any': function any(x) {
      return object.clone(x);
    },
    'Array | Matrix': function det(x) {
      var size;

      if (type.isMatrix(x)) {
        size = x.size();
      } else if (Array.isArray(x)) {
        x = matrix(x);
        size = x.size();
      } else {
        // a scalar
        size = [];
      }

      switch (size.length) {
        case 0:
          // scalar
          return object.clone(x);

        case 1:
          // vector
          if (size[0] === 1) {
            return object.clone(x.valueOf()[0]);
          } else {
            throw new RangeError('Matrix must be square ' + '(size: ' + string.format(size) + ')');
          }

        case 2:
          // two dimensional array
          var rows = size[0];
          var cols = size[1];

          if (rows === cols) {
            return _det(x.clone().valueOf(), rows, cols);
          } else {
            throw new RangeError('Matrix must be square ' + '(size: ' + string.format(size) + ')');
          }

        default:
          // multi dimensional array
          throw new RangeError('Matrix must be two dimensional ' + '(size: ' + string.format(size) + ')');
      }
    }
  });
  det.toTex = {
    1: "\\det\\left(${args[0]}\\right)"
  };
  return det;
  /**
   * Calculate the determinant of a matrix
   * @param {Array[]} matrix  A square, two dimensional matrix
   * @param {number} rows     Number of rows of the matrix (zero-based)
   * @param {number} cols     Number of columns of the matrix (zero-based)
   * @returns {number} det
   * @private
   */

  function _det(matrix, rows, cols) {
    if (rows === 1) {
      // this is a 1 x 1 matrix
      return object.clone(matrix[0][0]);
    } else if (rows === 2) {
      // this is a 2 x 2 matrix
      // the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12
      return subtract(multiply(matrix[0][0], matrix[1][1]), multiply(matrix[1][0], matrix[0][1]));
    } else {
      // Compute the LU decomposition
      var decomp = lup(matrix); // The determinant is the product of the diagonal entries of U (and those of L, but they are all 1)

      var _det2 = decomp.U[0][0];

      for (var _i = 1; _i < rows; _i++) {
        _det2 = multiply(_det2, decomp.U[_i][_i]);
      } // The determinant will be multiplied by 1 or -1 depending on the parity of the permutation matrix.
      // This can be determined by counting the cycles. This is roughly a linear time algorithm.


      var evenCycles = 0;
      var i = 0;
      var visited = [];

      while (true) {
        while (visited[i]) {
          i++;
        }

        if (i >= rows) break;
        var j = i;
        var cycleLen = 0;

        while (!visited[decomp.p[j]]) {
          visited[decomp.p[j]] = true;
          j = decomp.p[j];
          cycleLen++;
        }

        if (cycleLen % 2 === 0) {
          evenCycles++;
        }
      }

      return evenCycles % 2 === 0 ? _det2 : unaryMinus(_det2);
    }
  }
}

exports.name = 'det';
exports.factory = factory;