mathjs/src/function/statistics/median.js

'use strict'

const flatten = require('../../utils/array').flatten
const containsCollections = require('../../utils/collection/containsCollections')

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

  /**
   * 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
   */
  const 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) {
    try {
      array = flatten(array.valueOf())

      const 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
        const mid = num / 2 - 1
        const right = partitionSelect(array, mid + 1)

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

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

        return middle(m)
      }
    } catch (err) {
      throw improveErrorMessage(err, 'median')
    }
  }

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

  // helper function to type check the two middle value of the array
  const 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