mathjs/test/function/probability/distribution.test.js
2016-07-16 15:07:49 +02:00

633 lines
23 KiB
JavaScript

var assert = require('assert');
var error = require('../../../lib/error/index');
var seed = require('seed-random');
var _ = require('underscore');
var math = require('../../../index');
math.import(require('../../../lib/function/probability/distribution'));
var Matrix = math.type.Matrix;
var distribution = math.distribution;
var assertApproxEqual = function(testVal, val, tolerance) {
var diff = Math.abs(val - testVal);
if (diff > tolerance) assert.equal(testVal, val);
else assert.ok(diff <= tolerance)
};
var assertUniformDistribution = function(values, min, max) {
var interval = (max - min) / 10
, count, i;
count = _.filter(values, function(val) { return val < min }).length;
assert.equal(count, 0);
count = _.filter(values, function(val) { return val > max }).length;
assert.equal(count, 0);
for (i = 0; i < 10; i++) {
count = _.filter(values, function(val) {
return val >= (min + i * interval) && val < (min + (i + 1) * interval)
}).length;
assertApproxEqual(count/values.length, 0.1, 0.02);
}
};
var assertUniformDistributionInt = function(values, min, max) {
var range = _.range(Math.floor(min), Math.floor(max)), count;
values.forEach(function(val) {
assert.ok(_.contains(range, val));
});
range.forEach(function(val) {
count = _.filter(values, function(testVal) { return testVal === val }).length;
assertApproxEqual(count/values.length, 1/range.length, 0.03);
});
};
describe('distribution', function () {
var originalRandom, uniformDistrib;
before(function () {
// replace the original Math.random with a reproducible one
originalRandom = Math.random;
Math.random = seed('key');
});
after(function () {
// restore the original random function
Math.random = originalRandom;
});
beforeEach(function() {
uniformDistrib = distribution('uniform')
});
describe('random', function() {
var originalRandom;
it('should pick uniformly distributed numbers in [0, 1]', function() {
var picked = [];
_.times(1000, function() {
picked.push(uniformDistrib.random())
});
assertUniformDistribution(picked, 0, 1);
});
it('should pick uniformly distributed numbers in [min, max]', function() {
var picked = [];
_.times(1000, function() {
picked.push(uniformDistrib.random(-10, 10));
});
assertUniformDistribution(picked, -10, 10);
});
it('should pick uniformly distributed random array, with elements in [0, 1]', function() {
var picked = [],
matrices = [],
size = [2, 3, 4];
_.times(100, function() {
matrices.push(uniformDistrib.random(size));
});
// Collect all values in one array
matrices.forEach(function(matrix) {
assert(Array.isArray(matrix));
assert.deepEqual(math.size(matrix), size);
math.forEach(matrix, function(val) {
picked.push(val);
})
});
assert.equal(picked.length, 2 * 3 * 4 * 100);
assertUniformDistribution(picked, 0, 1);
});
it('should pick uniformly distributed random array, with elements in [0, max]', function() {
var picked = [],
matrices = [],
size = [2, 3, 4];
_.times(100, function() {
matrices.push(uniformDistrib.random(size, 8));
});
// Collect all values in one array
matrices.forEach(function(matrix) {
assert(Array.isArray(matrix));
assert.deepEqual(math.size(matrix), size);
math.forEach(matrix, function(val) {
picked.push(val);
})
});
assert.equal(picked.length, 2 * 3 * 4 * 100);
assertUniformDistribution(picked, 0, 8);
});
it('should pick uniformly distributed random matrix, with elements in [0, 1]', function() {
var picked = [],
matrices = [],
size = math.matrix([2, 3, 4]);
_.times(100, function() {
matrices.push(uniformDistrib.random(size));
});
// Collect all values in one array
matrices.forEach(function(matrix) {
assert(matrix instanceof Matrix);
assert.deepEqual(matrix.size(), size.valueOf());
matrix.forEach(function(val) {
picked.push(val);
})
});
assert.equal(picked.length, 2 * 3 * 4 * 100);
assertUniformDistribution(picked, 0, 1);
});
it('should pick uniformly distributed random array, with elements in [min, max]', function() {
var picked = [],
matrices = [],
size = [2, 3, 4];
_.times(100, function() {
matrices.push(uniformDistrib.random(size, -103, 8));
});
// Collect all values in one array
matrices.forEach(function(matrix) {
assert.deepEqual(math.size(matrix), size);
math.forEach(matrix, function(val) {
picked.push(val);
})
});
assert.equal(picked.length, 2 * 3 * 4 * 100);
assertUniformDistribution(picked, -103, 8);
});
it.skip ('should throw an error if called with invalid arguments', function() {
assert.throws(function() { uniformDistrib.random(1, 2, [4, 8]); });
assert.throws(function() { uniformDistrib.random(1, 2, 3, 6); });
assert.throws( function () {uniformDistrib.random('str', 10)} );
assert.throws( function () {uniformDistrib.random(math.bignumber(-10), 10)} );
});
});
describe('randomInt', function() {
it('should pick uniformly distributed integers in [min, max)', function() {
var picked = [];
_.times(10000, function() {
picked.push(uniformDistrib.randomInt(-15, -5));
});
assertUniformDistributionInt(picked, -15, -5);
});
it('should pick uniformly distributed random array, with elements in [min, max)', function() {
var picked = [],
matrices = [],
size = [2, 3, 4];
_.times(1000, function() {
matrices.push(uniformDistrib.randomInt(size, -14.9, -2));
});
// Collect all values in one array
matrices.forEach(function(matrix) {
assert.deepEqual(math.size(matrix), size);
math.forEach(matrix, function(val) {
picked.push(val)
});
});
assert.equal(picked.length, 2 * 3 * 4 * 1000);
assertUniformDistributionInt(picked, -14.9, -2);
});
it('should throw an error if called with invalid arguments', function() {
assert.throws(function() {
uniformDistrib.randomInt(1, 2, [4, 8]);
});
assert.throws(function() {
uniformDistrib.randomInt(1, 2, 3, 6);
});
});
});
describe('pickRandom', function() {
it('should throw an error when providing a multi dimensional matrix', function() {
assert.throws(function () {
uniformDistrib.pickRandom(math.matrix([[1,2], [3,4]]));
}, /Only one dimensional vectors supported/);
});
it('should throw an error if the length of the weights doesn\'t match the length of the possibles', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 4],
number = 2;
assert.throws(function() {
uniformDistrib.pickRandom(possibles, weights);
}, /Weights must have the same length as possibles/);
assert.throws(function() {
uniformDistrib.pickRandom(possibles, number, weights);
}, /Weights must have the same length as possibles/);
assert.throws(function() {
uniformDistrib.pickRandom(possibles, weights, number);
}, /Weights must have the same length as possibles/);
});
it('should throw an error if the weights array contains a non integer value', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 0.2, 6],
number = 2;
assert.throws(function() {
uniformDistrib.pickRandom(possibles, weights);
}, /Weights must be an array of integers/);
weights = [1, 5, 2, "stinky", 6],
assert.throws(function() {
uniformDistrib.pickRandom(possibles, weights);
}, /Weights must be an array of integers/);
});
it('should return a single value if no number argument was passed', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 4, 6];
assert.notEqual(possibles.indexOf(uniformDistrib.pickRandom(possibles)), -1);
assert.notEqual(possibles.indexOf(uniformDistrib.pickRandom(possibles, weights)), -1);
});
it('should return the given array if the given number is equal its length', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 4, 6],
number = 5;
assert.equal(uniformDistrib.pickRandom(possibles, number), possibles);
assert.equal(uniformDistrib.pickRandom(possibles, number, weights), possibles);
assert.equal(uniformDistrib.pickRandom(possibles, weights, number), possibles);
});
it('should return the given array if the given number is greater than its length', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 4, 6],
number = 6;
assert.equal(uniformDistrib.pickRandom(possibles, number), possibles);
assert.equal(uniformDistrib.pickRandom(possibles, number, weights), possibles);
assert.equal(uniformDistrib.pickRandom(possibles, weights, number), possibles);
});
it('should return an empty array if the given number is 0', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 4, 6],
number = 0;
assert.equal(uniformDistrib.pickRandom(possibles, number).length, 0);
assert.equal(uniformDistrib.pickRandom(possibles, number, weights).length, 0);
assert.equal(uniformDistrib.pickRandom(possibles, weights, number).length, 0);
});
it('should return an array of length 1 if the number passed is 1', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 4, 6],
number = 1;
assert(Array.isArray(uniformDistrib.pickRandom(possibles, number)));
assert(Array.isArray(uniformDistrib.pickRandom(possibles, number, weights)));
assert(Array.isArray(uniformDistrib.pickRandom(possibles, weights, number)));
assert.equal(uniformDistrib.pickRandom(possibles, number).length, 1);
assert.equal(uniformDistrib.pickRandom(possibles, number, weights).length, 1);
assert.equal(uniformDistrib.pickRandom(possibles, weights, number).length, 1);
});
it('should pick the given number of values from the given array', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 5, 2, 4, 6],
number = 3;
assert.equal(uniformDistrib.pickRandom(possibles, number).length, number);
assert.equal(uniformDistrib.pickRandom(possibles, number, weights).length, number);
assert.equal(uniformDistrib.pickRandom(possibles, weights, number).length, number);
});
it('should pick a value from the given array following an uniform distribution if only possibles are passed', function() {
var possibles = [11, 22, 33, 44, 55],
picked = [],
count;
_.times(1000, function() {
picked.push(uniformDistrib.pickRandom(possibles));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
});
it('should pick a value from the given matrix following an uniform distribution', function() {
var possibles = math.matrix([11, 22, 33, 44, 55]),
picked = [],
count;
_.times(1000, function() {
picked.push(uniformDistrib.pickRandom(possibles));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
});
it('should pick a given number of values from the given array following an uniform distribution if no weights were passed', function() {
var possibles = [11, 22, 33, 44, 55],
number = 2,
picked = [],
count;
_.times(1000, function() {
picked.push.apply(picked, uniformDistrib.pickRandom(possibles, number));
});
assert.equal(picked.length, 2000);
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
});
it('should pick numbers from the given matrix following an uniform distribution', function() {
var possibles = math.matrix([11, 22, 33, 44, 55]),
number = 3,
picked = [],
count;
_.times(1000, function() {
picked.push.apply(picked, uniformDistrib.pickRandom(possibles, number));
});
assert.equal(picked.length, 3000);
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
});
it('should pick a value from the given array following a weighted distribution', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 4, 0, 2, 3],
picked = [],
count;
_.times(1000, function() {
picked.push(uniformDistrib.pickRandom(possibles, weights));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.1);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round((count)/picked.length, 1), 0.4);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.3);
});
it('should pick a value from the given matrix following a weighted distribution', function() {
var possibles = math.matrix([11, 22, 33, 44, 55]),
weights = [1, 4, 0, 2, 3],
picked = [],
count;
_.times(1000, function() {
picked.push(uniformDistrib.pickRandom(possibles, weights));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.1);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round((count)/picked.length, 1), 0.4);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.3);
});
it('should return an array of values from the given array following a weighted distribution', function() {
var possibles = [11, 22, 33, 44, 55],
weights = [1, 4, 0, 2, 3],
number = 2,
picked = [],
count;
_.times(1000, function() {
picked.push.apply(picked, uniformDistrib.pickRandom(possibles, number, weights));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.1);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round((count)/picked.length, 1), 0.4);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.3);
_.times(1000, function() {
picked.push.apply(picked, uniformDistrib.pickRandom(possibles, weights, number));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.1);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round((count)/picked.length, 1), 0.4);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.3);
});
it('should return an array of values from the given matrix following a weighted distribution', function() {
var possibles = math.matrix([11, 22, 33, 44, 55]),
weights = [1, 4, 0, 2, 3],
number = 2,
picked = [],
count;
_.times(1000, function() {
picked.push.apply(picked, uniformDistrib.pickRandom(possibles, number, weights));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.1);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round((count)/picked.length, 1), 0.4);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.3);
_.times(1000, function() {
picked.push.apply(picked, uniformDistrib.pickRandom(possibles, weights, number));
});
count = _.filter(picked, function(val) { return val === 11 }).length;
assert.equal(math.round(count/picked.length, 1), 0.1);
count = _.filter(picked, function(val) { return val === 22 }).length;
assert.equal(math.round((count)/picked.length, 1), 0.4);
count = _.filter(picked, function(val) { return val === 33 }).length;
assert.equal(math.round(count/picked.length, 1), 0);
count = _.filter(picked, function(val) { return val === 44 }).length;
assert.equal(math.round(count/picked.length, 1), 0.2);
count = _.filter(picked, function(val) { return val === 55 }).length;
assert.equal(math.round(count/picked.length, 1), 0.3);
});
});
describe('distribution.normal', function() {
it('should pick numbers in [0, 1] following a normal distribution', function() {
var picked = [], count, dist = distribution('normal');
_.times(100000, function() {
picked.push(dist.random())
});
count = _.filter(picked, function(val) { return val < 0 }).length;
assert.equal(count, 0);
count = _.filter(picked, function(val) { return val > 1 }).length;
assert.equal(count, 0);
count = _.filter(picked, function(val) { return val < 0.25 }).length;
assertApproxEqual(count/picked.length, 0.07, 0.01);
count = _.filter(picked, function(val) { return val < 0.4 }).length;
assertApproxEqual(count/picked.length, 0.27, 0.01);
count = _.filter(picked, function(val) { return val < 0.5 }).length;
assertApproxEqual(count/picked.length, 0.5, 0.01);
count = _.filter(picked, function(val) { return val < 0.6 }).length;
assertApproxEqual(count/picked.length, 0.73, 0.01);
count = _.filter(picked, function(val) { return val < 0.75 }).length;
assertApproxEqual(count/picked.length, 0.93, 0.01);
});
});
it('should throw an error in case of unknown distribution name', function() {
assert.throws(function () {
distribution('non-existing');
}, /Unknown distribution/)
});
it('created random functions should throw an error in case of wrong number of arguments', function() {
var dist = distribution('uniform');
assert.throws(function () {dist.random([2,3], 10, 100, 12); }, error.ArgumentsError);
assert.throws(function () {dist.randomInt([2,3], 10, 100, 12); }, error.ArgumentsError);
assert.throws(function () {dist.pickRandom(); }, error.ArgumentsError);
assert.throws(function () {dist.pickRandom([], 23, [], 9); }, error.ArgumentsError);
});
it('created random functions should throw an error in case of wrong type of arguments', function() {
var dist = distribution('uniform');
assert.throws(function () {dist.pickRandom(23); }, error.TypeError);
// TODO: more type testing...
});
it('should LaTeX distribution', function () {
var expression = math.parse('distribution("normal")');
assert.equal(expression.toTex(), '\\mathrm{distribution}\\left(\\mathtt{"normal"}\\right)');
});
});