mathjs/es/function/matrix/det.js

import { isMatrix } from '../../utils/is';
import { clone } from '../../utils/object';
import { format } from '../../utils/string';
import { factory } from '../../utils/factory';
var name = 'det';
var dependencies = ['typed', 'matrix', 'subtract', 'multiply', 'unaryMinus', 'lup'];
export var createDet = /* #__PURE__ */factory(name, dependencies, function (_ref) {
  var typed = _ref.typed,
      matrix = _ref.matrix,
      subtract = _ref.subtract,
      multiply = _ref.multiply,
      unaryMinus = _ref.unaryMinus,
      lup = _ref.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`
   */
  return typed(name, {
    any: function any(x) {
      return clone(x);
    },
    'Array | Matrix': function det(x) {
      var size;

      if (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 clone(x);

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

        default:
          // multi dimensional array
          throw new RangeError('Matrix must be two dimensional ' + '(size: ' + format(size) + ')');
      }
    }
  });
  /**
   * 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 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 det = decomp.U[0][0];

      for (var _i = 1; _i < rows; _i++) {
        det = multiply(det, 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 ? det : unaryMinus(det);
    }
  }
});