mathjs/lib/function/statistics/median.js

'use strict';

module.exports = function (math) {
  var Matrix = math.type.Matrix,
      Unit = require('../../type/Unit'),
      BigNumber = math.type.BigNumber,
      collection = math.collection,

      isNumber = require('../../util/number').isNumber,
      isCollection = collection.isCollection,

      flatten = require('../../util/array').flatten;

  /**
   * 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
   *
   * @param {... *} args  A single matrix or or multiple scalar values
   * @return {*} The median
   */
  math.median = function median(args) {
    if (arguments.length == 0) {
      throw new SyntaxError('Function median requires one or more parameters (0 provided)');
    }

    if (isCollection(args)) {
      if (arguments.length == 1) {
        // median([a, b, c, d, ...])
        return _median(args.valueOf(), false);
      }
      else if (arguments.length == 2) {
        // median([a, b, c, d, ...], dim)
        // TODO: implement median(A, dim)
        throw new Error('median(A, dim) is not yet supported');
        //return collection.reduce(arguments[0], arguments[1], ...);
      }
      else {
        throw new SyntaxError('Wrong number of parameters');
      }
    }
    else {
      // median(a, b, c, d, ...)
      var argArr = new Array(arguments.length);
      for (var i = 0; i < argArr.length; ++i) {
        argArr[i] = arguments[i];
      }
      return _median(argArr, true);
    }
  };

  /**
   * Recursively calculate the median of an n-dimensional array
   * @param {Array} array
   * @param {Boolean} isFlat
   * @return {Number} median
   * @private
   */
  function _median(array, isFlat) {
    if (!isFlat) {
      array = flatten(array);
    }

    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 = math.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 (math.compare(array[i], left) > 0) {
          left = array[i];
        }
      }

      if (!isNumber(left) && !(left instanceof BigNumber) && !(left instanceof Unit)) {
        throw new math.error.UnsupportedTypeError('median', math['typeof'](left));
      }
      if (!isNumber(right) && !(right instanceof BigNumber) && !(right instanceof Unit)) {
        throw new math.error.UnsupportedTypeError('median', math['typeof'](right));
      }

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

      if (!isNumber(middle) && !(middle instanceof BigNumber) && !(middle instanceof Unit)) {
        throw new math.error.UnsupportedTypeError('median', math['typeof'](middle));
      }

      return middle;
    }
  }
};