ysjj-system/node_modules/mathjs/lib/esm/function/statistics/variance.js

import { deepForEach } from '../../utils/collection.js';
import { isBigNumber } from '../../utils/is.js';
import { factory } from '../../utils/factory.js';
import { improveErrorMessage } from './utils/improveErrorMessage.js';
var DEFAULT_NORMALIZATION = 'unbiased';
var name = 'variance';
var dependencies = ['typed', 'add', 'subtract', 'multiply', 'divide', 'apply', 'isNaN'];
export var createVariance = /* #__PURE__ */factory(name, dependencies, _ref => {
  var {
    typed,
    add,
    subtract,
    multiply,
    divide,
    apply,
    isNaN
  } = _ref;
  /**
   * Compute the variance of a matrix or a  list with values.
   * In case of a multidimensional array or matrix, the variance over all
   * elements will be calculated.
   *
   * Additionally, it is possible to compute the variance along the rows
   * or columns of a matrix by specifying the dimension as the second argument.
   *
   * Optionally, the type of normalization can be specified as the final
   * 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)
   *
   *
   * Note that older browser may not like the variable name `var`. In that
   * case, the function can be called as `math['var'](...)` instead of
   * `math.var(...)`.
   *
   * Syntax:
   *
   *     math.variance(a, b, c, ...)
   *     math.variance(A)
   *     math.variance(A, normalization)
   *     math.variance(A, dimension)
   *     math.variance(A, dimension, normalization)
   *
   * Examples:
   *
   *     math.variance(2, 4, 6)                     // returns 4
   *     math.variance([2, 4, 6, 8])                // returns 6.666666666666667
   *     math.variance([2, 4, 6, 8], 'uncorrected') // returns 5
   *     math.variance([2, 4, 6, 8], 'biased')      // returns 4
   *
   *     math.variance([[1, 2, 3], [4, 5, 6]])      // returns 3.5
   *     math.variance([[1, 2, 3], [4, 6, 8]], 0)   // returns [4.5, 8, 12.5]
   *     math.variance([[1, 2, 3], [4, 6, 8]], 1)   // returns [1, 4]
   *     math.variance([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.5, 2]
   *
   * See also:
   *
   *    mean, median, max, min, prod, std, sum
   *
   * @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'.
   * @param dimension {number | BigNumber}
   *                        Determines the axis to compute the variance for a matrix
   * @return {*} The variance
   */
  return typed(name, {
    // variance([a, b, c, d, ...])
    'Array | Matrix': function ArrayMatrix(array) {
      return _var(array, DEFAULT_NORMALIZATION);
    },
    // variance([a, b, c, d, ...], normalization)
    'Array | Matrix, string': _var,
    // variance([a, b, c, c, ...], dim)
    'Array | Matrix, number | BigNumber': function ArrayMatrixNumberBigNumber(array, dim) {
      return _varDim(array, dim, DEFAULT_NORMALIZATION);
    },
    // variance([a, b, c, c, ...], dim, normalization)
    'Array | Matrix, number | BigNumber, string': _varDim,
    // variance(a, b, c, d, ...)
    '...': function _(args) {
      return _var(args, DEFAULT_NORMALIZATION);
    }
  });

  /**
   * Recursively calculate the variance of an n-dimensional array
   * @param {Array} array
   * @param {string} normalization
   *                        Determines how to normalize the variance:
   *                        - 'unbiased'    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)
   * @return {number | BigNumber} variance
   * @private
   */
  function _var(array, normalization) {
    var sum;
    var num = 0;
    if (array.length === 0) {
      throw new SyntaxError('Function variance requires one or more parameters (0 provided)');
    }

    // calculate the mean and number of elements
    deepForEach(array, function (value) {
      try {
        sum = sum === undefined ? value : add(sum, value);
        num++;
      } catch (err) {
        throw improveErrorMessage(err, 'variance', value);
      }
    });
    if (num === 0) throw new Error('Cannot calculate variance of an empty array');
    var mean = divide(sum, num);

    // calculate the variance
    sum = undefined;
    deepForEach(array, function (value) {
      var diff = subtract(value, mean);
      sum = sum === undefined ? multiply(diff, diff) : add(sum, multiply(diff, diff));
    });
    if (isNaN(sum)) {
      return sum;
    }
    switch (normalization) {
      case 'uncorrected':
        return divide(sum, num);
      case 'biased':
        return divide(sum, num + 1);
      case 'unbiased':
        {
          var zero = isBigNumber(sum) ? sum.mul(0) : 0;
          return num === 1 ? zero : divide(sum, num - 1);
        }
      default:
        throw new Error('Unknown normalization "' + normalization + '". ' + 'Choose "unbiased" (default), "uncorrected", or "biased".');
    }
  }
  function _varDim(array, dim, normalization) {
    try {
      if (array.length === 0) {
        throw new SyntaxError('Function variance requires one or more parameters (0 provided)');
      }
      return apply(array, dim, x => _var(x, normalization));
    } catch (err) {
      throw improveErrorMessage(err, 'variance');
    }
  }
});