mathjs/lib/function/statistics/std.js

'use strict';

function factory (type, config, load, typed) {
  var sqrt       = load(require('../arithmetic/sqrt'));
  var variance   = load(require('../statistics/var'));

  /**
   * Compute the standard deviation of a matrix or a  list with values.
   * The standard deviations is defined as the square root of the variance:
   * `std(A) = sqrt(var(A))`.
   * In case of a (multi dimensional) array or matrix, the standard deviation
   * over all elements will be calculated.
   *
   * Optionally, the type of normalization can be specified as second
   * parameter. The parameter `normalization` can be one of the following values:
   *
   * - 'unbiased' (default) The sum of squared errors is divided by (n - 1)
   * - 'uncorrected'        The sum of squared errors is divided by n
   * - 'biased'             The sum of squared errors is divided by (n + 1)
   *
   * Syntax:
   *
   *     math.std(a, b, c, ...)
   *     math.std(A)
   *     math.std(A, normalization)
   *
   * Examples:
   *
   *     math.std(2, 4, 6);                     // returns 2
   *     math.std([2, 4, 6, 8]);                // returns 2.581988897471611
   *     math.std([2, 4, 6, 8], 'uncorrected'); // returns 2.23606797749979
   *     math.std([2, 4, 6, 8], 'biased');      // returns 2
   *
   *     math.std([[1, 2, 3], [4, 5, 6]]);      // returns 1.8708286933869707
   *
   * See also:
   *
   *    mean, median, max, min, prod, sum, var
   *
   * @param {Array | Matrix} array
   *                        A single matrix or or multiple scalar values
   * @param {string} [normalization='unbiased']
   *                        Determines how to normalize the variance.
   *                        Choose 'unbiased' (default), 'uncorrected', or 'biased'.
   * @return {*} The standard deviation
   */
  var std = typed('std', {
    // std([a, b, c, d, ...])
    'Array | Matrix': _std,

    // std([a, b, c, d, ...], normalization)
    'Array | Matrix, string': _std,

    // std(a, b, c, d, ...)
    '...': function () {
      return _std(Array.prototype.slice.call(arguments));
    }
  });
  
  std.toTex = '\\mathrm{${name}}\\left(${args}\\right)';

  return std;

  function _std(array, normalization) {
    if (array.length == 0) {
      throw new SyntaxError('Function std requires one or more parameters (0 provided)');
    }

    return sqrt(variance.apply(null, arguments));
  }
}

exports.name = 'std';
exports.factory = factory;