mathjs/lib/function/matrix/cross.js

'use strict';

var array = require('../../utils/array');

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'));

  /**
   * Calculate the cross product for two vectors in three dimensional space.
   * The cross product of `A = [a1, a2, a3]` and `B = [b1, b2, b3]` is defined
   * as:
   *
   *    cross(A, B) = [
   *      a2 * b3 - a3 * b2,
   *      a3 * b1 - a1 * b3,
   *      a1 * b2 - a2 * b1
   *    ]
   *
   * If one of the input vectors has a dimension greater than 1, the output
   * vector will be a 1x3 (2-dimensional) matrix.
   *
   * Syntax:
   *
   *    math.cross(x, y)
   *
   * Examples:
   *
   *    math.cross([1, 1, 0],   [0, 1, 1]);       // Returns [1, -1, 1]
   *    math.cross([3, -3, 1],  [4, 9, 2]);       // Returns [-15, -2, 39]
   *    math.cross([2, 3, 4],   [5, 6, 7]);       // Returns [-3, 6, -3]
   *    math.cross([[1, 2, 3]], [[4], [5], [6]]); // Returns [[-3, 6, -3]]
   *
   * See also:
   *
   *    dot, multiply
   *
   * @param  {Array | Matrix} x   First vector
   * @param  {Array | Matrix} y   Second vector
   * @return {Array | Matrix}     Returns the cross product of `x` and `y`
   */
  var cross = typed('cross', {
    'Matrix, Matrix': function (x, y) {
      return matrix(_cross(x.toArray(), y.toArray()));
    },

    'Matrix, Array': function (x, y) {
      return matrix(_cross(x.toArray(), y));
    },

    'Array, Matrix': function (x, y) {
      return matrix(_cross(x, y.toArray()));
    },

    'Array, Array': _cross
  });

  cross.toTex = {
    2: '\\left(${args[0]}\\right)\\times\\left(${args[1]}\\right)'
  };

  return cross;

  /**
   * Calculate the cross product for two arrays
   * @param {Array} x  First vector
   * @param {Array} y  Second vector
   * @returns {Array} Returns the cross product of x and y
   * @private
   */
  function _cross(x, y) {
    var highestDimension = Math.max(array.size(x).length, array.size(y).length);

    x = array.squeeze(x);
    y = array.squeeze(y);

    var xSize = array.size(x);
    var ySize = array.size(y);

    if (xSize.length != 1 || ySize.length != 1 || xSize[0] != 3 || ySize[0] != 3) {
      throw new RangeError('Vectors with length 3 expected ' +
      '(Size A = [' + xSize.join(', ') + '], B = [' + ySize.join(', ') + '])');
    }

    var product = [
      subtract(multiply(x[1], y[2]), multiply(x[2], y[1])),
      subtract(multiply(x[2], y[0]), multiply(x[0], y[2])),
      subtract(multiply(x[0], y[1]), multiply(x[1], y[0]))
    ];

    if (highestDimension > 1) {
      return [product];
    } else {
      return product;
    }
  }
}

exports.name = 'cross';
exports.factory = factory;