Commit e44ae3c0 authored by Mike Bostock's avatar Mike Bostock
Browse files

Merge branch 'random-tests' of https://github.com/DanGoldbach/d3 into random-tests

parents 3234f47a cdbb9b78
......@@ -53,7 +53,8 @@
"devDependencies": {
"smash": "~0.0.12",
"uglify-js": "2.4.0",
"vows": "0.7.0"
"vows": "0.7.0",
"seedrandom": "0.1.6"
},
"scripts": {
"test": "node_modules/.bin/vows"
......
var vows = require("vows"),
load = require("../load"),
assert = require("../assert");
assert = require("../assert"),
seedrandom = require('seedrandom');
var suite = vows.describe("d3.random");
/**
* Testing a random number generator is a bit more complicated than testing
* deterministic code, so we use different techniques.
*
* If the RNG is correct, each test in this suite will pass with probability
* at least P. The tests have been designed so that P ≥ 98%. Specific values
* of P are given above each case. We use the seedrandom module to get around
* this non-deterministic aspect -- so it is safe to assume that if the tests
* fail, then d3's RNG is broken.
*
* More on RNG testing here:
* @see http://www.johndcook.com/Beautiful_Testing_ch10.pdf
*/
// Overwrites Math.random to a seeded random function.
// (by default Math.random is seeded with current time)
Math.seedrandom('a random seed.');
suite.addBatch({
"random": {
topic: load("math/random").expression("d3.random"),
"normal": {
"topic": function(random) {
return random.normal();
},
"returns a number": function(r) {
assert.typeOf(r(), "number");
}
"topic": function(random) { return random.normal(-43289, 38.8); },
// P = 98%
"has normal distribution" : KSTest(normalCDF(-43289, 38.8))
},
"logNormal": {
"topic": function(random) {
return random.logNormal();
},
"returns a number": function(r) {
assert.typeOf(r(), "number");
}
// Use reasonable values for mean here because random.logNormal() grows
// exponentially with the mean.
"topic": function(random) { return random.logNormal(10, 2.5); },
// P = 98%
"has log-normal distribution" : KSTest(logNormalCDF(10, 2.5))
},
"irwinHall": {
"topic": function(random) {
return random.irwinHall(10);
},
"returns a number": function(r) {
assert.typeOf(r(), "number");
}
"topic": function(random) { return random.irwinHall(10); },
// P = 98%
"has Irwin-Hall distribution" : KSTest(irwinHallCDF(10))
}
}
});
/**
* A macro that that takes a RNG and performs a Kolmogorov-Smirnov test:
* asserts that the values generated by the RNG could be generated by the
* distribution with cumulative distribution function `cdf'. Each test runs in
* O(n log n) * O(cdf).
*
* Passes with P≈98%.
*
* @param cdf function(x) { returns CDF of the distribution evaluated at x }
* @param n number of sample points. Higher n = better evaluation, slower test.
* @return function(rng) {
* // asserts that rng produces values fitting the distribution
* }
*/
function KSTest(cdf, n) {
return function(rng) {
var n = 1000;
var values = [];
for (var i = 0; i < n; i++) {
values.push(rng());
}
values.sort(function(a, b) { return a - b; });
K_positive = -Infinity; // Identity of max() function
for (var i = 0; i < n; i++) {
var edf_i = i / n; // Empirical distribution function evaluated at x=values[i]
K_positive = Math.max(K_positive, edf_i - cdf(values[i]));
}
K_positive *= Math.sqrt(n);
// Derivation of this interval is difficult.
// @see K-S test in Knuth's AoCP vol.2
assert.inDelta(K_positive, 0.723255, 0.794145);
}
}
function normalCDF(mean, stddev) {
// Logistic approximation to normal CDF around N(mean, stddev).
return function(x) {
return 1 / (1 + Math.exp(-0.07056 * Math.pow((x-mean)/stddev, 3) - 1.5976 * (x-mean)/stddev));
}
}
function logNormalCDF(mean, stddev) {
// @see http://en.wikipedia.org/wiki/Log-normal_distribution#Similar_distributions
var exponent = Math.PI / (stddev * Math.sqrt(3));
var numerator = Math.exp(mean);
return function(x) {
return 1 / (Math.pow(numerator / x, exponent) + 1);
}
}
function irwinHallCDF(n) {
var normalisingFactor = factorial(n);
// Precompute binom(n, k), k=0..n for efficiency. (this array gets stored
// inside the closure, so it is only computed once)
var binoms = [];
for (var k = 0; k <= n; k++) {
binoms.push(binom(n, k));
}
// @see CDF at http://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution
return function(x) {
var t = 0;
// What d3 calls Irwin-Hill distribution is actually a Bates distribution:
// the Irwin-Hall distribution divided by n. So we multiply the Bates
// distribution's x-value by n to get the Irwin-Hall CDF at x.
x *= n;
for (var k = 0; k < x; k++) {
t += Math.pow(-1, k % 2) * binoms[k] * Math.pow(x - k, n);
}
return t / normalisingFactor;
}
}
function factorial(n) {
var t = 1;
for (var i = 2; i <= n; i++) {
t *= i;
}
return t;
}
function binom(n, k) {
if (k < 0 || k > n) return undefined; // only defined for 0 <= k <= n
return factorial(n) / (factorial(k) * factorial(n - k));
}
suite.export(module);
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