mathjs/lib/function/statistics/median.js

'use strict';

var flatten = require('../../utils/array').flatten;
var reduce = require('../../utils/collection/reduce');
var containsCollections = require('../../utils/collection/containsCollections');

function factory (type, config, load, typed) {
  var add = load(require('../arithmetic/addScalar'));
  var divide = load(require('../arithmetic/divideScalar'));
  var compare = load(require('../relational/compare'));
  var partitionSelect = load(require('../matrix/partitionSelect'));

  /**
   * Compute the median of a matrix or a list with values. The values are
   * sorted and the middle value is returned. In case of an even number of
   * values, the average of the two middle values is returned.
   * Supported types of values are: Number, BigNumber, Unit
   *
   * In case of a (multi dimensional) array or matrix, the median of all
   * elements will be calculated.
   *
   * Syntax:
   *
   *     math.median(a, b, c, ...)
   *     math.median(A)
   *
   * Examples:
   *
   *     math.median(5, 2, 7);        // returns 5
   *     math.median([3, -1, 5, 7]);  // returns 4
   *
   * See also:
   *
   *     mean, min, max, sum, prod, std, var, quantileSeq
   *
   * @param {... *} args  A single matrix or or multiple scalar values
   * @return {*} The median
   */
  var median = typed('median', {
    // median([a, b, c, d, ...])
    'Array | Matrix': _median,

    // median([a, b, c, d, ...], dim)
    'Array | Matrix, number | BigNumber': function (array, dim) {
      // TODO: implement median(A, dim)
      throw new Error('median(A, dim) is not yet supported');
      //return reduce(arguments[0], arguments[1], ...);
    },

    // median(a, b, c, d, ...)
    '...': function (args) {
      if (containsCollections(args)) {
          throw new TypeError('Scalar values expected in function median');
      }

      return _median(args);
    }
  });


  /**
   * Recursively calculate the median of an n-dimensional array
   * @param {Array} array
   * @return {Number} median
   * @private
   */
  function _median(array) {
    array = flatten(array.valueOf());

    var num = array.length;
    if (num == 0) {
      throw new Error('Cannot calculate median of an empty array');
    }

    if (num % 2 == 0) {
      // even: return the average of the two middle values
      var mid = num / 2 - 1;
      var right = partitionSelect(array, mid + 1);

      // array now partitioned at mid + 1, take max of left part
      var left = array[mid];
      for (var i = 0; i < mid; ++i) {
        if (compare(array[i], left) > 0) {
          left = array[i];
        }
      }

      return middle2(left, right);
    }
    else {
      // odd: return the middle value
      var m = partitionSelect(array, (num - 1) / 2);

      return middle(m);
    }
  }

  // helper function to type check the middle value of the array
  var middle = typed({
    'number | BigNumber | Complex | Unit': function (value) {
      return value;
    }
  });

  // helper function to type check the two middle value of the array
  var middle2 = typed({
    'number | BigNumber | Complex | Unit, number | BigNumber | Complex | Unit': function (left, right) {
      return divide(add(left, right), 2);
    }
  });

  median.toTex = undefined; // use default template

  return median;
}

exports.name = 'median';
exports.factory = factory;