import { Distribution } from "../../src/js/index"; import { expectErrorToBeBounded, failDefault } from "./TestHelpers"; import * as fc from "fast-check"; // Beware: float64Array makes it appear in an infinite loop. let arrayGen = () => fc.float32Array({ minLength: 10, maxLength: 10000, noDefaultInfinity: true, noNaN: true, }); describe("cumulative density function", () => { let n = 10000; // We should fix this. test.skip("'s codomain is bounded above", () => { fc.assert( fc.property(arrayGen(), fc.float(), (xs_, x) => { let xs = Array.from(xs_); // Should compute with squiggle strings once interpreter has `sample` let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: n, xyPointLength: 100 } ); let cdfValue = dist.cdf(x).value; let epsilon = 5e-7; expect(cdfValue).toBeLessThanOrEqual(1 + epsilon); }) ); }); test("'s codomain is bounded below", () => { fc.assert( fc.property(arrayGen(), fc.float(), (xs_, x) => { let xs = Array.from(xs_); // Should compute with squiggle strings once interpreter has `sample` let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: n, xyPointLength: 100 } ); let cdfValue = dist.cdf(x).value; expect(cdfValue).toBeGreaterThanOrEqual(0); }) ); }); // This may not be true due to KDE estimating there to be mass above the // highest value. These tests fail test.skip("at the highest number in the sample is close to 1", () => { fc.assert( fc.property(arrayGen(), (xs_) => { let xs = Array.from(xs_); let max = Math.max(...xs); // Should compute with squiggle strings once interpreter has `sample` let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: n, xyPointLength: 100 } ); let cdfValue = dist.cdf(max).value; expect(cdfValue).toBeCloseTo(1.0, 2); }) ); }); // I may simply be mistaken about the math here. test.skip("at the lowest number in the distribution is within epsilon of 0", () => { fc.assert( fc.property(arrayGen(), (xs_) => { let xs = Array.from(xs_); let min = Math.min(...xs); // Should compute with squiggle strings once interpreter has `sample` let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: n, xyPointLength: 100 } ); let cdfValue = dist.cdf(min).value; let max = Math.max(...xs); let epsilon = 5e-3; if (max - min < epsilon) { expect(cdfValue).toBeGreaterThan(4 * epsilon); } else { expect(cdfValue).toBeLessThan(4 * epsilon); } }) ); }); // I believe this is true, but due to bugs can't get the test to pass. test.skip("is <= 1 everywhere with equality when x is higher than the max", () => { fc.assert( fc.property(arrayGen(), fc.float(), (xs_, x) => { let xs = Array.from(xs_); let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: n, xyPointLength: 100 } ); let cdfValue = dist.cdf(x).value; let max = Math.max(...xs); if (x > max) { let epsilon = (x - max) / x; expect(cdfValue).toBeGreaterThan(1 * (1 - epsilon)); } else if (typeof cdfValue == "number") { expect(Math.round(1e5 * cdfValue) / 1e5).toBeLessThanOrEqual(1); } else { failDefault(); } }) ); }); test("is non-negative everywhere with zero when x is lower than the min", () => { fc.assert( fc.property(arrayGen(), fc.float(), (xs_, x) => { let xs = Array.from(xs_); let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: n, xyPointLength: 100 } ); let cdfValue = dist.cdf(x).value; if (x < Math.min(...xs)) { expect(cdfValue).toEqual(0); } else { expect(cdfValue).toBeGreaterThan(0); } }) ); }); }); // I no longer believe this is true. describe("probability density function", () => { let n = 1000; test.skip("assigns to the max at most the weight of the mean", () => { fc.assert( fc.property(arrayGen(), (xs_) => { let xs = Array.from(xs_); let max = Math.max(...xs); let mean = xs.reduce((a, b) => a + b, 0.0) / xs.length; // Should be from squiggleString once interpreter exposes sampleset let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: n, xyPointLength: 100 } ); let pdfValueMean = dist.pdf(mean).value; let pdfValueMax = dist.pdf(max).value; if (typeof pdfValueMean == "number" && typeof pdfValueMax == "number") { expect(pdfValueMax).toBeLessThanOrEqual(pdfValueMean); } else { expect(pdfValueMax).toEqual(pdfValueMean); } }) ); }); }); // // This should be true, but I can't get it to work. describe("mean is mean", () => { test.skip("when sampling twice as widely as the input", () => { fc.assert( fc.property( fc.float64Array({ minLength: 10, maxLength: 100000 }), (xs_) => { let xs = Array.from(xs_); let n = xs.length; let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: 2 * n, xyPointLength: 4 * n } ); let mean = dist.mean(); if (typeof mean.value == "number") { expectErrorToBeBounded( mean.value, xs.reduce((a, b) => a + b, 0.0) / n, 5e-1, 1 ); } else { failDefault(); } } ) ); }); test.skip("when sampling half as widely as the input", () => { fc.assert( fc.property( fc.float64Array({ minLength: 10, maxLength: 100000 }), (xs_) => { let xs = Array.from(xs_); let n = xs.length; let dist = new Distribution( { tag: "SampleSet", value: xs }, { sampleCount: Math.floor(n / 2), xyPointLength: 4 * n } ); let mean = dist.mean(); if (typeof mean.value == "number") { expectErrorToBeBounded( mean.value, xs.reduce((a, b) => a + b, 0.0) / n, 5e-1, 1 ); } else { failDefault(); } } ) ); }); });