mathjs/lib/function/matrix/kron.js

'use strict';

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

function factory(type, config, load, typed) {
  var matrix = load(require('../../type/matrix/function/matrix'));
  var multiplyScalar = load(require('../arithmetic/multiplyScalar'))
    /**
     * Calculates the kronecker product of 2 matrices or vectors.
     *
     * NOTE: If a one dimensional vector / matrix is given, it will be
     * wrapped so its two dimensions.
     * See the examples.
     *
     * Syntax:
     *
     *    math.kron(x, y)
     *
     * Examples:
     *
     *    math.kron([[1, 0], [0, 1]], [[1, 2], [3, 4]]);
     *    // returns [ [ 1, 2, 0, 0 ], [ 3, 4, 0, 0 ], [ 0, 0, 1, 2 ], [ 0, 0, 3, 4 ] ]
     *
     *    math.kron([1,1], [2,3,4]);
     *    // returns [ [ 2, 3, 4, 2, 3, 4 ] ]
     *
     * See also:
     *
     *    multiply, dot, cross
     *
     * @param  {Array | Matrix} x     First vector
     * @param  {Array | Matrix} y     Second vector
     * @return {Array | Matrix}       Returns the kronecker product of `x` and `y`
     */
    var kron = typed('kron', {
        'Matrix, Matrix': function(x, y) {
            return matrix(_kron(x.toArray(), y.toArray()));
        },

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

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

        'Array, Array': _kron
    });

    return kron;

    /**
     * Calculate the kronecker product of two matrices / vectors
     * @param {Array} a  First vector
     * @param {Array} b  Second vector
     * @returns {Array} Returns the kronecker product of x and y
     * @private
     */
    function _kron(a, b) {
        // Deal with the dimensions of the matricies.
        if (size(a).length === 1) {
          // Wrap it in a 2D Matrix
          a = [a];
        }
        if (size(b).length === 1) {
          // Wrap it in a 2D Matrix
          b = [b]
        }
        if (size(a).length > 2 || size(b).length > 2) {
            throw new RangeError('Vectors with dimensions greater then 2 are not supported expected ' +
            '(Size x = ' + JSON.stringify(a.length) + ', y = ' + JSON.stringify(b.length) + ')');
        }
        var t = [];
        var r = [];

        return a.map(function(a) {
            return b.map(function(b) {
                return a.map(function(y) {
                    return b.map(function(x) {
                        return r.push(multiplyScalar(y, x));
                    });
                }, t.push(r = []));
            });
        }, t = []) && t;
    }
}

exports.name = 'kron';
exports.factory = factory;