mathjs/lib/function/statistics/quantileSeq.js
2015-07-18 13:22:38 +02:00

258 lines
8.4 KiB
JavaScript

'use strict';
var isInteger = require('../../utils/number').isInteger;
var isNumber = require('../../utils/number').isNumber;
var flatten = require('../../utils/array').flatten;
var isCollection = require('../../utils/collection/isCollection');
function factory (type, config, load, typed) {
var add = load(require('../arithmetic/add'));
var multiply = load(require('../arithmetic/multiply'));
var partitionSelect = load(require('../utils/partitionSelect'));
var compare = load(require('../relational/compare'));
/**
* Compute the prob order quantile of a matrix or a list with values.
* The sequence is sorted and the middle value is returned.
* Supported types of sequence values are: Number, BigNumber, Unit
* Supported types of probability are: Number, BigNumber
*
* In case of a (multi dimensional) array or matrix, the prob order quantile
* of all elements will be calculated.
*
* Syntax:
*
* math.quantileSeq(A, prob[, sorted])
* math.quantileSeq(A, [prob1, prob2, ...][, sorted])
* math.quantileSeq(A, N[, sorted])
*
* Examples:
*
* math.quantileSeq([3, -1, 5, 7], 0.5); // returns 4
* math.quantileSeq([3, -1, 5, 7], [1/3, 2/3]); // returns [3, 5]
* math.quantileSeq([3, -1, 5, 7], 2); // returns [3, 5]
* math.quantileSeq([-1, 3, 5, 7], 0.5, true); // returns 4
*
* See also:
*
* median, mean, min, max, sum, prod, std, var
*
* @param {Array, Matrix} data A single matrix or Array
* @param {Number, BigNumber, Array} probOrN prob is the order of the quantile, while N is
* the amount of evenly distributed steps of
* probabilities; only one of these options can
* be provided
* @param {Boolean} sorted=false is data sorted in ascending order
* @return {Number, BigNumber, Unit, Array} Quantile(s)
*/
function quantileSeq(data, probOrN, sorted) {
var probArr, dataArr, one;
if (arguments.length < 2 || arguments.length > 3) {
throw new SyntaxError('Function quantileSeq requires two or three parameters');
}
if (isCollection(data)) {
sorted = sorted || false;
if (typeof sorted === 'boolean') {
dataArr = data.valueOf();
if (isNumber(probOrN)) {
if (probOrN < 0) {
throw new Error('N/prob must be non-negative');
}
if (probOrN <= 1) {
// quantileSeq([a, b, c, d, ...], prob[,sorted])
return _quantileSeq(dataArr, probOrN, sorted);
}
if (probOrN > 1) {
// quantileSeq([a, b, c, d, ...], N[,sorted])
if (!isInteger(probOrN)) {
throw new Error('N must be a positive integer');
}
var nPlusOne = probOrN + 1;
probArr = new Array(probOrN);
for (var i = 0; i < probOrN;) {
probArr[i] = _quantileSeq(dataArr, (++i) / nPlusOne, sorted);
}
return probArr;
}
}
if (probOrN && probOrN.isBigNumber) {
if (probOrN.isNegative()) {
throw new Error('N/prob must be non-negative');
}
one = probOrN.constructor.ONE;
if (probOrN.lte(one)) {
// quantileSeq([a, b, c, d, ...], prob[,sorted])
return _quantileSeq(dataArr, probOrN, sorted);
}
if (probOrN.gt(one)) {
// quantileSeq([a, b, c, d, ...], N[,sorted])
if (!probOrN.isInteger()) {
throw new Error('N must be a positive integer');
}
// largest possible Array length is 2^32-1;
// 2^32 < 10^15, thus safe conversion guaranteed
var intN = probOrN.toNumber();
if (intN > 4294967295) {
throw new Error('N must be less than or equal to 2^32-1, as that is the maximum length of an Array');
}
var nPlusOne = new type.BigNumber(intN + 1);
probArr = new Array(intN);
for (var i = 0; i < intN;) {
probArr[i] = _quantileSeq(dataArr, new type.BigNumber(++i).div(nPlusOne), sorted);
}
return probArr;
}
}
if (Array.isArray(probOrN)) {
// quantileSeq([a, b, c, d, ...], [prob1, prob2, ...][,sorted])
probArr = new Array(probOrN.length);
for (var i = 0; i < probArr.length; ++i) {
var currProb = probOrN[i];
if (isNumber(currProb)) {
if (currProb < 0 || currProb > 1) {
throw new Error('Probability must be between 0 and 1, inclusive');
}
} else if (currProb && currProb.isBigNumber) {
one = currProb.constructor.ONE;
if (currProb.isNegative() || currProb.gt(one)) {
throw new Error('Probability must be between 0 and 1, inclusive');
}
} else {
throw new TypeError('Unexpected type of argument in function quantileSeq'); // FIXME: becomes redundant when converted to typed-function
}
probArr[i] = _quantileSeq(dataArr, currProb, sorted);
}
return probArr;
}
throw new TypeError('Unexpected type of argument in function quantileSeq'); // FIXME: becomes redundant when converted to typed-function
}
throw new TypeError('Unexpected type of argument in function quantileSeq'); // FIXME: becomes redundant when converted to typed-function
}
throw new TypeError('Unexpected type of argument in function quantileSeq'); // FIXME: becomes redundant when converted to typed-function
}
/**
* Calculate the prob order quantile of an n-dimensional array.
*
* @param {Array} array
* @param {Number, BigNumber} prob
* @param {Boolean} sorted
* @return {Number, BigNumber, Unit} prob order quantile
* @private
*/
function _quantileSeq(array, prob, sorted) {
var flat = flatten(array);
var len = flat.length;
if (len === 0) {
throw new Error('Cannot calculate quantile of an empty sequence');
}
if (isNumber(prob)) {
var index = prob * (len-1);
var fracPart = index % 1;
if (fracPart === 0) {
var value = sorted ? flat[index] : partitionSelect(flat, index);
validate(value);
return value;
}
var integerPart = Math.floor(index);
var left, right;
if (sorted) {
left = flat[integerPart];
right = flat[integerPart+1];
} else {
right = partitionSelect(flat, integerPart+1);
// max of partition is kth largest
left = flat[integerPart];
for (var i = 0; i < integerPart; ++i) {
if (compare(flat[i], left) > 0) {
left = flat[i];
}
}
}
validate(left);
validate(right);
// Q(prob) = (1-f)*A[floor(index)] + f*A[floor(index)+1]
return add(multiply(left, 1 - fracPart), multiply(right, fracPart));
}
// If prob is a BigNumber
var index = prob.times(len-1);
if (index.isInteger()) {
index = index.toNumber();
var value = sorted ? flat[index] : partitionSelect(flat, index);
validate(value);
return value;
}
var integerPart = index.floor();
var fracPart = index.minus(integerPart);
var integerPartNumber = integerPart.toNumber();
var left, right;
if (sorted) {
left = flat[integerPartNumber];
right = flat[integerPartNumber+1];
} else {
right = partitionSelect(flat, integerPartNumber+1);
// max of partition is kth largest
left = flat[integerPartNumber];
for (var i = 0; i < integerPartNumber; ++i) {
if (compare(flat[i], left) > 0) {
left = flat[i];
}
}
}
validate(left);
validate(right);
// Q(prob) = (1-f)*A[floor(index)] + f*A[floor(index)+1]
var one = fracPart.constructor.ONE;
return add(multiply(left, one.minus(fracPart)), multiply(right, fracPart));
}
/**
* Check if array value types are valid, throw error otherwise.
* @param {number | BigNumber | Unit} x
* @param {number | BigNumber | Unit} x
* @private
*/
var validate = typed({
'number | BigNumber | Unit': function (x) {
return x;
}
});
return quantileSeq;
}
exports.name = 'quantileSeq';
exports.factory = factory;