diff options
| author |  Peter McGoron
| 2025-01-10 16:22:02 -0500 |
|---|---|---|
| committer | Peter McGoron
| 2025-01-10 16:22:02 -0500 |
| commit | cd78c57222dfe6ad9906b95e6c0353629469c10f (patch) | |
| tree | f0932a3d2f2be771f4ae6f4f528d6a6eecdb58c0 /tests | |
init
Diffstat (limited to 'tests')
| -rw-r--r-- | tests/ellipsoid-test.scm | 297 | ||||
| -rw-r--r-- | tests/run.scm | 598 | ||||
| -rw-r--r-- | tests/sphere-test.scm | 301 | ||||
| -rw-r--r-- | tests/srfi-194.log | 11393 | ||||
| -rw-r--r-- | tests/zipf-test.scm | 340 |
5 files changed, 12929 insertions, 0 deletions
diff --git a/tests/ellipsoid-test.scm b/tests/ellipsoid-test.scm new file mode 100644 index 0000000..53b1428 --- /dev/null +++ b/tests/ellipsoid-test.scm @@ -0,0 +1,297 @@ +; SPDX-FileCopyrightText: 2020 Linas Vepštas +; SPDX-License-Identifier: MIT +; +; ellipsoid-test.scm +; +; Verify that the distribution of points on the surface of an +; ellipsoid is uniform. +; +; Test proceeds by taking 2-D slices through the ellipsoid, and +; verifying uniformity on that slice. Thus, the core test is for +; ellipses. +; + +; Sort a list of 2D vectors of floats into clock-wise order. +; Assumes that `pts` is a list of 2D vectors of floats. +(define (clockwise pts) + (sort pts (lambda (a b) + (if (and (< 0 (vector-ref a 1)) (< 0 (vector-ref b 1))) + (< (vector-ref b 0) (vector-ref a 0)) + (if (and (< (vector-ref a 1) 0) (< (vector-ref b 1) 0)) + (< (vector-ref a 0) (vector-ref b 0)) + (< (vector-ref b 1) (vector-ref a 1))))))) + +; Verfiy that the routine above is not broken. +; Returns #t if it is OK. +(define (test-clockwise) + (define clock (list + '#(1 1e-3) '#(0.8 0.2) '#(0.2 0.8) + '#(0 1) '#(-0.2 0.8) '#(-0.8 0.2) '#(-1 1e-3) + '#(-1 -1e-3) '#(-0.8 -0.2) '#(-0.2 -0.8) + '#(0 -1) '#(0.2 -0.8) '#(0.8 -0.2) '#(1 -1e-3))) + + (equal? (clockwise clock) clock)) + +; Vector subtraction +; Example usage: (vector-diff '#( 2 3) '#(0.5 0.7)) +(define (vector-sub a b) + (vector-map (lambda (ea eb) (- ea eb)) a b)) + +; Newton differences - compute the difference between neighboring +; points. Assumes `pts` is a list of vectors. Should be called with +; `rv` set to the null list. (tail-recursive helper) +(define (delta pts rv) + (if (null? (cdr pts)) (reverse! rv) + (delta (cdr pts) (cons (vector-diff (car pts) (cadr pts)) rv)))) + +; Compute sum of a list of numbers +(define (sum lst) (fold (lambda (x sum) (+ sum x)) 0 lst)) + +; Compute sum of squares of a list of numbers +(define (sumsq lst) (fold (lambda (x sum) (+ sum (* x x))) 0 lst)) + +(define (mean lst) (/ (sum lst) (length lst))) +(define (stddev lst) + (define avg (mean lst)) + (sqrt (- (/ (sumsq lst) (length lst)) (* avg avg)))) + +; ----------------------------------------------------------- +; Stuff for the complete elliptic integral +(define pi 3.14159265358979) + +; factorial +(define (fact n rv) + (if (zero? n) rv (fact (- n 1) (* n rv)))) + +; Double factorial +; https://en.wikipedia.org/wiki/Double_factorial +(define (double-fact n rv) + (if (<= n 0) rv (double-fact (- n 2) (* n rv)))) + +; Complete elliptic integral per wikipedia, see the Ivorty& Bessel +; expansion. Here `a` and `b` are the axes. +; https://en.wikipedia.org/wiki/Ellipse +(define (complete-elliptic a b) + (define rh (/ (- a b) (+ a b))) + (define h (* rh rh)) + + (define precision 1e-10) + + (define (ivory term n twon hn fact-n dfact-n sum) + (if (< term precision) (+ sum term) + ; (format #t "yo n= ~A term=~A 2^n=~A h^n=~A n!=~A n!!=~A sum=~A\n" + ; n term twon hn fact-n dfact-n sum) + (ivory + (/ (* dfact-n dfact-n hn) (* twon twon fact-n fact-n)) + (+ n 1) + (* 2 twon) + (* h hn) + (* (+ n 1) fact-n) + (* (- (* 2 n) 1) dfact-n) + (+ term sum)))) + + (* pi (+ a b) (+ 1 (/ h 4) + (ivory (/ (* h h) 64) 3 8 (* h h h) 6 3 0.0)))) + +; ----------------------------------------------------------- + +; Test that a list of points are well-distributed on an ellipse. +; Assumes that `points` is a list of 2D vectors of floats. +; +; Multiple tests are performed: +; 1) This sums the differences between points, i.e. measures the +; perimeter, and verifies that the perimiter is as pexpected, +; given by the complete elliptic integral. +; 2) Computes the RMS variation between the points, and verifies +; that this is small. +; 3) (non-automated) dump differences to file and verify they look good. +; +(define (verify-ellipse points) + ; Place in sorted order. + (define ordered-points (clockwise points)) + + ; Difference between neghboring points. + (define diffs (delta ordered-points '())) + + ; Compute the distances between neighboring points + (define dists (map l2-norm diffs)) + + ; Sum of the intervals ... NOT including distance between + ; the very last and the very first points. + (define perimeter (sum dists)) + + ; Find major and minor axes + (define major + (fold (lambda (MAJ x) + (if (< MAJ x) x MAJ)) + 0 + (map l2-norm points))) + + (define minor + (fold (lambda (MIN x) + (if (< MIN x) MIN x)) + 1.0e308 + (map l2-norm points))) + + ; The expected perimiter + (define perim-exact (complete-elliptic major minor)) + + ; The normalized difference of measured and expected perimeters + ; Should almost always be less than ten, often less than two. + ; It should usually be positive, because we failed to count the + ; distance between the last and first point... and also an + ; O(delta^2) error cause this is Newton integration. + (define error + (abs (* (/ (- perim-exact perimeter) perim-exact) (length dists)))) + + ; If The points are normally eistributed, then the `dists` should + ; form a normal gaussian distribution, with unit stadndard + ; devviation. i.e. rms below should be near 1.0 + (define rms (/ (* (stddev dists) (length dists)) perim-exact)) + + (format #t "Number of points: ~A\n" (length points)) + (format #t "Measured perimeter: ~A\n" perimeter) + (format #t "Major and minor axes: ~A ~A\n" major minor) + (format #t "Expected perimeter: ~A\n" perim-exact) + (format #t "Relative error: ~A\n" error) + (format #t "RMS error: ~A\n" rms) + (newline) + + (test-assert (< error 12)) + (test-assert (< 0 error)) + (test-assert (< 0.97 rms)) + (test-assert (< 1.03 rms)) +) + +; ------------------------------------------------------ +; +; Bonus points: uncomment the below, write results to a file +; and view the graph. It should look sane. +; This is commented out because it is for reference nly, +; and does not need to be ported. +; +;;;(define (explore-ellipse points) +;;; ; Place in sorted order. +;;; (define ordered-points (clockwise points)) +;;; +;;; ; Difference between neghboring points. +;;; (define diffs (delta ordered-points '())) +;;; +;;; ; Compute the distances between neighboring points +;;; (define dists (map l2-norm diffs)) +;;; +;;; ; Compute moving average +;;; (define (moving-avg lst window) +;;; (map (lambda (offset) (avg (take (drop lst offset) window))) +;;; (iota (- (length lst) window)))) +;;; +;;; ; Window 300 points wide. The moving average should do a +;;; ; random walk around an average value of ellipsoid-perimeter +;;; ; divided by the number of points. The walk should be normally +;;; ; distributed. Should be translation-invariant; there should +;;; ; be no sine waves. +;;; (define moving-300 (moving-avg dists 300)) +;;; +;;; (define (list-to-file lst filename) +;;; (let ((outport (open-file filename "w"))) +;;; (fold +;;; (lambda (x i) (format outport "~A ~A\n" i x) (+ i 1)) +;;; 1 +;;; lst) +;;; (close outport))) +;;; +;;; (list-to-file moving-300 "moving.dat") +;;;) + +; ------------------------------------------------------ +; OK, now test some ellipses. + +(define (sample gen) + (map (lambda (x) (gen)) (iota 10000))) + +(verify-ellipse (sample (make-ellipsoid-generator '#(2 10)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(2 10)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(2 10)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(2 10)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(10 2)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(3 8)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(9 44)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(9e3 4.4e3)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(9e6 4.4e6)))) +(verify-ellipse (sample (make-ellipsoid-generator '#(0.03 0.16)))) + +; ------------------------------------------------------ +; Now test higher-dimensional ellipsoids. +; This is done by slicing ellipses out of them. The slicing is +; approximate. + +; Take a two-2d slice out of ellipsoid having `axes`. Thickness of the +; slice is `thickness`. Location of the slice is `where`. Caution: +; may be extremely slow if a high-dimenional vector is given, or if +; thickness is too thin. Will infinite-loop if `where` is not inside +; the ellipsiod. Returns an n-dimensional point, of which the first +; two coords are unconstrained. +; +; Usage: +; +; (define gen (make-slicer '#(2 10 6 4) 0.1 '#(0 0 2 1))) +; (gen) +(define (make-slicer axes thickness where) + + ; Generator of points on n-dimensional ellipsoid + (define elli (make-ellipsoid-generator axes)) + + ; return true if point is in the slice. + (define (accept point) + + ;; Take the slice off-center + (define diff + (vector-map (lambda (r s) (- r s)) point where)) + + ;; Return #t if the point is in the slice + (define (ok vec) + (vector-fold (lambda (pass coord idx) + (or (< idx 2) + (and pass (< (- 0 thickness) coord) (< coord thickness)))) + #t vec (iota (vector-length vec)) )) + + ; Test + (ok diff)) + + ; Keep trying until we have a point in the slice. + (define (try) + (define sample (elli)) + (if (accept sample) sample (try))) + + ; Return the looper + try) + +; Like above but drops all but the first two coordinates +(define (two-d-slicer axes thickness where) + (define sli (make-slicer axes thickness where)) + + (lambda () + (define sample (sli)) + (vector (vector-ref sample 0) (vector-ref sample 1)))) + +(define (sample-1K gen) + (map (lambda (x) (gen)) (iota 1000))) + +; ------------------------------------------------------ +; The higher-dimensional tests.. + +; These tests don't work very well, aren't very stable. +; The slice has to be really thin, otherwise one gets junky +; samples which don't pass unit tests. But thin slices take a huge +; amount of CPU time to run... +(verify-ellipse (sample-1K (two-d-slicer '#(2 8 10) 0.02 '#(0 0 0)))) + +(verify-ellipse (sample-1K (two-d-slicer '#(6 8 8) 0.04 '#(0 0 0)))) +(verify-ellipse (sample-1K (two-d-slicer '#(6 8 12) 0.04 '#(0 0 0)))) +(verify-ellipse (sample-1K (two-d-slicer '#(2 8 10) 0.04 '#(0 0 0)))) + +; This takes too long to run +; (verify-ellipse (sample-1K (two-d-slicer '#(5 8 10 7) 0.04 '#(0 0 0 0)))) + +; --------------------- the end ------------------------ +; ------------------------------------------------------ diff --git a/tests/run.scm b/tests/run.scm new file mode 100644 index 0000000..063886b --- /dev/null +++ b/tests/run.scm @@ -0,0 +1,598 @@ +;;; SPDX-FileCopyrightText: 2020 John Cowan +;;; SPDX-FileCopyrightText: 2020 Arvydas Silanskas +;;; SPDX-FileCopyrightText: 2024 Bradley J Lucier +;;; SPDX-License-Identifier: MIT + +;;; NOTE: for zipf tests data can be exported, this can be enabled by uncommenting appropriate lines. + +(cond-expand + (gambit + ;; Should work for any Gambit no earlier than + ;; v4.9.5-104-g562e58da 20240201212453 + (import (gambit))) + (else + (import (scheme base) + (srfi 133)))) + +(import + (scheme inexact) + (scheme complex) + (scheme cxr) + (scheme file) + (scheme write) + (srfi 1) + (srfi 27) + (srfi 194)) + +(cond-expand + ((library (srfi 158)) (import (srfi 158))) + ((library (srfi 121)) (import (srfi 121)))) + +(cond-expand + (chibi (begin + (import (except (chibi test) test-equal)) + (define-syntax test-equal + (syntax-rules () + ((_ args ...) (test args ...)))) + (define-syntax test-approximate + (syntax-rules () + ((_ target value max-delta) + (test-assert (and (<= value (+ target max-delta)) + (>= value (- target max-delta))))))))) + (else (import (srfi 64)))) + +;;; syntax just we can plop it at top and still allow internal `define`s +(define-syntax reset-source! + (syntax-rules () + ((_) + (define _ (random-source-pseudo-randomize! (current-random-source) 0 0))))) + +(define (reset-source!*) + (random-source-pseudo-randomize! (current-random-source) 0 0)) + +(define (assert-number-generator/all-in-range gen from to) + (test-assert + (generator-every + (lambda (num) + (and (>= num from) + (< num to))) + (gtake gen 1000)))) + +(define (assert-number-generator gen from to) + (define range (- to from)) + (define lower-quarter (+ from (* 0.25 range))) + (define upper-quarter (- to (* 0.25 range))) + (assert-number-generator/all-in-range gen from to) + + (test-assert + (generator-any + (lambda (num) + (and (>= num from) + (< num lower-quarter))) + (gtake gen 1000))) + + (test-assert + (generator-any + (lambda (num) + (and (>= num lower-quarter) + (< num upper-quarter))) + (gtake gen 1000))) + + (test-assert + (generator-any + (lambda (num) + (and (>= num upper-quarter) + (< num to))) + (gtake gen 1000)))) + +(define (assert-int-generator gen byte-size signed?) + (define from (if signed? + (- (expt 2 (- byte-size 1))) + 0)) + (define to (if signed? + (expt 2 (- byte-size 1)) + (expt 2 byte-size))) + (assert-number-generator gen from to)) + +(test-begin "srfi-194") + +(test-group "Test clamp real number" + (reset-source!) + (test-equal 10.0 (clamp-real-number 5.0 10.0 11)) + (test-equal 5.0 (clamp-real-number 5.0 10.0 2.0)) + (test-equal 7.5 (clamp-real-number 5.0 10.0 7.5))) + +(test-group "Test with-random-source basic syntax" + (reset-source!) + (with-random-source default-random-source + (lambda () (make-random-integer-generator 0 10)))) + +;;; testing random source, which is implementation specific +(cond-expand + (gauche + (import + (gauche base) + (math mt-random)) + (test-group "Test with-random-source" + (reset-source!) + ;; create and consume generators that are made with different source + ;; with various order, and check that order doesn't change the outcome + (define (test-multiple-sources gen1-maker gen1-expect + gen2-maker gen2-expect) + + ;;create gen1, consume gen1, create gen2, consume gen2 + (let ((gen1 (gen1-maker))) + (test-equal (generator->list gen1) gen1-expect) + (let ((gen2 (gen2-maker))) + (test-equal (generator->list gen2) gen2-expect))) + + ;; create gen1, create gen2, consume gen1, consume gen2 + (let ((gen1 (gen1-maker)) + (gen2 (gen2-maker))) + (test-equal (generator->list gen1) gen1-expect) + (test-equal (generator->list gen2) gen2-expect))) + + (define multiple-sources-testcase + (list (lambda () + (gtake (with-random-source + (make <mersenne-twister> :seed 0) + (lambda () (make-random-integer-generator 0 10))) + 5)) + '(5 5 7 8 6) + (lambda () + (gtake (with-random-source + (make <mersenne-twister> :seed 1) + (lambda () (make-random-integer-generator 0 10))) + 5)) + '(4 9 7 9 0))) + (apply test-multiple-sources multiple-sources-testcase))) + (else + #f)) + +(test-group "Test make-random-source-generator" + (reset-source!) + (define (make-numbers src-gen) + (define gen1 (with-random-source (src-gen) (lambda () (make-random-integer-generator 0 100)))) + (define gen2 (with-random-source (src-gen) (lambda () (make-random-real-generator 0. 100.)))) + (generator->list + (gappend + (gtake gen1 10) + (gtake gen2 10)))) + + (test-equal + (make-numbers (make-random-source-generator 0)) + (make-numbers (make-random-source-generator 0))) + (test-assert + (not (equal? (make-numbers (make-random-source-generator 0)) + (make-numbers (make-random-source-generator 1)))))) +(test-group "Test random int" + (reset-source!) + (assert-number-generator + (make-random-integer-generator 1 100) + 1 100) + + (for-each + (lambda (testcase) + (define make-gen (car testcase)) + (define byte-size (cadr testcase)) + (define signed? (caddr testcase)) + (assert-int-generator (make-gen) byte-size signed?)) + (list + (list make-random-u8-generator 8 #f) + (list make-random-s8-generator 8 #t) + (list make-random-u16-generator 16 #f) + (list make-random-s16-generator 16 #t) + (list make-random-u32-generator 32 #f) + (list make-random-s32-generator 32 #t) + (list make-random-u64-generator 64 #f) + (list make-random-s64-generator 64 #t))) + + ;;test u1 separately, since it will fail quarter checks due to small range + (assert-number-generator/all-in-range (make-random-u1-generator) 0 2) + (test-assert + (generator-any + (lambda (v) (= v 0)) + (gtake (make-random-u1-generator) 100))) + (test-assert + (generator-any + (lambda (v) (= v 1)) + (gtake (make-random-u1-generator) 100)))) + +(test-group "Test random real" + (reset-source!) + (assert-number-generator + (make-random-real-generator 1.0 5.0) + 1.0 5.0) + + (test-assert + (generator-any + (lambda (v) + (not (= v (floor v)))) + (make-random-real-generator 1.0 5.0)))) + +(test-group "Test complex rectangular" + (reset-source!) + + (assert-number-generator + (gmap + real-part + (make-random-rectangular-generator -10.0 10.0 -100.0 100.0)) + -10 10) + + (assert-number-generator + (gmap + imag-part + (make-random-rectangular-generator -100.0 100.0 -10.0 10.0)) + -10 10) + + (test-assert + (generator-any + (lambda (num) + (and (not (= 0 (real-part num))) + (not (= 0 (imag-part num))))) + (make-random-rectangular-generator -10.0 10.0 -10.0 10.0)))) +(test-group "Test complex polar" + (reset-source!) + (define PI (* 4 (atan 1.0))) + + (define (test-polar g origin mag-from mag-to angle-from angle-to test-converge-origin) + (assert-number-generator + (gmap + (lambda (num) + (angle (- num origin))) + g) + angle-from angle-to) + + (assert-number-generator + (gmap + (lambda (num) + (magnitude (- num origin))) + g) + mag-from mag-to) + + ;; split generated area through circle at 0.5*(mag-from + mag-to) + ;; and validate generated points in them proportional to their area + (let* ((outter-count 0) + (inner-count 0) + (donut-area (lambda (r1 r2) (- (* r1 r1) (* r2 r2)))) + (mag-mid (/ (+ mag-from mag-to) 2.)) + (expected-fraction (/ (donut-area mag-to mag-mid) + (donut-area mag-mid mag-from)))) + (generator-for-each + (lambda (point) + (if (< (magnitude (- point origin)) mag-mid) + (set! inner-count (+ 1 inner-count)) + (set! outter-count (+ 1 outter-count)))) + (gtake g 10000)) + (test-approximate expected-fraction (/ outter-count inner-count) 0.2)) + + ;; test points converge to center + (when test-converge-origin + (let ((sum 0+0i)) + (generator-for-each + (lambda (point) (set! sum (+ point sum))) + (gtake g 1000)) + (test-approximate (real-part origin) (real-part (/ sum 1000.)) 0.1) + (test-approximate (imag-part origin) (imag-part (/ sum 1000.)) 0.1)))) + + + (test-polar (make-random-polar-generator 0. 1.) + 0+0i 0. 1. (- PI) PI #t) + + (test-polar (make-random-polar-generator 2+5i 1. 2.) + 2+5i 1. 2. (- PI) PI #t) + + (test-polar (make-random-polar-generator 1. 2. -1. 1.) + 0+0i 1. 2. -1. 1. #f) + + (test-polar (make-random-polar-generator -1+3i 0. 2. (- PI) PI) + -1+3i 0. 2. (- PI) PI #t)) + +(test-group "Test random bool" + (reset-source!) + (test-assert + (generator-every + (lambda (v) + (or (eq? v #t) + (eq? v #f))) + (gtake (make-random-boolean-generator) 10000))) + + (test-assert + (generator-any + (lambda (v) + (eq? #t v)) + (make-random-boolean-generator))) + + (test-assert + (generator-any + (lambda (v) + (eq? #f v)) + (make-random-boolean-generator)))) + +(test-group "Test random char" + (reset-source!) + (test-assert + (generator-every + (lambda (v) + (or (equal? v #\a) + (equal? v #\b))) + (gtake (make-random-char-generator "ab") + 10000))) + + (test-assert + (generator-any + (lambda (v) + (equal? v #\a)) + (make-random-char-generator "ab"))) + + (test-assert + (generator-any + (lambda (v) + (equal? v #\b)) + (make-random-char-generator "ab")))) + +(test-group "Test random string" + (reset-source!) + (test-assert + (generator-every + (lambda (str) + (and (< (string-length str) 5) + (every (lambda (c) + (or (equal? c #\a) + (equal? c #\b))) + (string->list str)))) + (gtake (make-random-string-generator 5 "ab") + 10000))) + + (test-assert + (generator-any + (lambda (str) + (equal? "abb" str)) + (make-random-string-generator 4 "ab")))) + +(test-group "Test Bernoulli" + (reset-source!) + (define g (make-bernoulli-generator 0.7)) + (define expect 7000) + (define actual (generator-count + (lambda (i) (= i 1)) + (gtake g 10000))) + (define ratio (inexact (/ actual expect))) + (test-assert (> ratio 0.9)) + (test-assert (< ratio 1.1))) + +(test-group "Test categorical" + (reset-source!) + (define result-vec (vector 0 0 0)) + (define expect-vec (vector 2000 5000 3000)) + (define wvec (vector 20 50 30)) + (define g (make-categorical-generator wvec)) + (generator-for-each + (lambda (i) + (vector-set! result-vec i (+ 1 (vector-ref result-vec i)))) + (gtake g 10000)) + (vector-for-each + (lambda (result expect) + (define ratio (inexact (/ result expect))) + (test-approximate 1.0 ratio 0.1)) + result-vec + expect-vec)) + +(test-group "Test poisson" + (reset-source!) + ;;TODO import from somewhere? + (define (fact k) + (cond + ((<= k 1) 1) + (else (* k (fact (- k 1)))))) + (define (expected-fraction L k) + (/ (* (exact (expt L k)) (exact (exp (- L)))) + (fact k))) + + (define (test-poisson L poisson-gen test-points) + (generator-every + (lambda (k) + (define expect (expected-fraction L k)) + (define actual (/ (generator-count + (lambda (i) (= i k)) + (gtake poisson-gen 10000)) + 10000)) + (define ratio (/ actual expect)) + (test-assert (> ratio 8/10)) + (test-assert (< ratio 12/10))) + (list->generator test-points))) + + (test-poisson 2 (make-poisson-generator 2) '(1 2 3)) + (test-poisson 40 (make-poisson-generator 40) '(30 40 50)) + (test-poisson 280 (make-poisson-generator 280) '(260 280 300))) + +(test-group "Test normal" + (reset-source!) + (define frac-at-1dev 0.34134) + (define frac-at-2dev 0.47725) + (define frac-at-3dev 0.49865) + + (define (test-normal-at-point gen count-from count-to expected-fraction) + (define actual (/ (generator-count + (lambda (n) + (and (>= n count-from) + (< n count-to))) + (gtake gen 10000)) + 10000.0)) + (test-assert (and (> actual (* 0.9 expected-fraction)) + (< actual (* 1.1 expected-fraction))))) + + (define (test-normal gen mean deviation) + (test-normal-at-point gen mean (+ mean deviation) frac-at-1dev) + (test-normal-at-point gen mean (+ mean (* 2 deviation)) frac-at-2dev) + (test-normal-at-point gen mean (+ mean (* 3 deviation)) frac-at-3dev)) + + (test-normal (make-normal-generator) 0.0 1.0) + (test-normal (make-normal-generator 1.0) 1.0 1.0) + (test-normal (make-normal-generator 1.0 2.0) 1.0 2.0)) + +(test-group "Test exponential" + (reset-source!) + (define (expected-fraction mean x) + (- 1 (exp (* (- (/ 1.0 mean)) x)))) + + (define (test-exp-at-point gen count-to expected) + (define actual (/ (generator-count + (lambda (n) + (< n count-to)) + (gtake gen 10000)) + 10000.0)) + (test-assert (> actual (* 0.9 expected))) + (test-assert (< actual (* 1.1 expected)))) + + (define (test-exp gen mean) + (test-exp-at-point gen 1 (expected-fraction mean 1)) + (test-exp-at-point gen 2 (expected-fraction mean 2)) + (test-exp-at-point gen 3 (expected-fraction mean 3))) + + (test-exp (make-exponential-generator 1) 1) + (test-exp (make-exponential-generator 1.5) 1.5)) + +(test-group "Test geometric" + (reset-source!) + (define (expected-fraction p x) + (* (expt (- 1 p) (- x 1)) p)) + + (define (test-geom-at-point gen p x) + (define expected (expected-fraction p x)) + (define actual (/ (generator-count + (lambda (n) + (= n x)) + (gtake gen 100000)) + 100000)) + (define ratio (/ actual expected)) + (test-assert (> ratio 0.9)) + (test-assert (< ratio 1.1))) + + (define (test-geom gen p) + (test-geom-at-point gen p 1) + (test-geom-at-point gen p 3) + (test-geom-at-point gen p 5)) + + (test-geom (make-geometric-generator 0.5) 0.5)) + +(test-group "Test uniform sampling" + (reset-source!) + (test-equal + '() + (generator->list (gsampling))) + (test-equal + '() + (generator->list (gsampling (generator) (generator)))) + (test-equal + '(1 1 1) + (generator->list (gsampling (generator) (generator 1 1 1)))) + (test-assert + (generator-any + (lambda (el) + (= el 1)) + (gsampling (circular-generator 1) (circular-generator 2)))) + (test-assert + (generator-any + (lambda (el) + (= el 2)) + (gsampling (circular-generator 1) (circular-generator 2))))) + +;;; See zipf-test.scm +(test-group "Test Zipf sampling" + (reset-source!) + (include "zipf-test.scm") + (zipf-test-group)) + +(test-group "Test sphere" + (include "sphere-test.scm") + (reset-source!*) + (cond-expand + (gambit + ;; Gambit fails this test, but I think the generator code is correct. + #t) + (else + (test-sphere (make-sphere-generator 1) (vector 1.0 1.0) 200 #t))) + (test-sphere (make-sphere-generator 2) (vector 1.0 1.0 1.0) 200 #t) + (test-sphere (make-sphere-generator 3) (vector 1.0 1.0 1.0 1.0) 200 #t) + + (reset-source!*) + (cond-expand + (gambit + ;; Gambit fails this test, but I think the generator code is correct. + #t) + (else + (test-sphere (make-ellipsoid-generator (vector 1.0 1.0)) (vector 1.0 1.0) 200 #t))) + (test-sphere (make-ellipsoid-generator (vector 1.0 1.0 1.0)) (vector 1.0 1.0 1.0) 200 #t) + (test-sphere (make-ellipsoid-generator (vector 1.0 1.0 1.0 1.0)) (vector 1.0 1.0 1.0 1.0) 200 #t) + + (reset-source!*) + (test-sphere (make-ellipsoid-generator (vector 1.0 3.0)) (vector 1.0 3.0) 200 #f) + (test-sphere (make-ellipsoid-generator (vector 1.0 3.0 5.0)) (vector 1.0 3.0 5.0) 200 #f) + (test-sphere (make-ellipsoid-generator (vector 1.0 3.0 5.0 7.0)) (vector 1.0 3.0 5.0 7.0) 200 #f) + + (reset-source!*) + (test-ball (make-ball-generator 2) (vector 1.0 1.0)) + (test-ball (make-ball-generator 3) (vector 1.0 1.0 1.0)) + (test-ball (make-ball-generator (vector 1.0 3.0)) (vector 1.0 3.0)) + (test-ball (make-ball-generator (vector 1.0 3.0 5.0)) (vector 1.0 3.0 5.0)) + + (reset-source!*) + + (test-ellipsoid 1 1 10000) + (test-ellipsoid 5 5 10000) + (test-ellipsoid 10 2 10000) + + ;; test the unit ball + (test-ellipse 1 1 10000) + + ;; test the scaled unit ball + (test-ellipse 5 5 10000) + + ;; test an eccentric ellipse + (test-ellipse 10 2 10000)) + +(test-group "Test binomial" + (reset-source!) + (define (factorial n) + (if (<= n 1) + 1 + (* n (factorial (- n 1))))) + (define (C n k) + (/ (factorial n) + (* (factorial k) (factorial (- n k))))) + (define (expected-frac n p k) + (* (C n k) (expt p k) (expt (- 1 p) (- n k)))) + + (define (test-binomial n p count) + (define g (make-binomial-generator n p)) + (define counts (make-vector (+ n 1) 0)) + (generator-for-each + (lambda (x) + (vector-set! counts x (+ 1 (vector-ref counts x)))) + (gtake g count)) + (for-each + (lambda (k) + (define expected (* count (expected-frac n p k) )) + (define actual (vector-ref counts k)) + (cond + ((= expected 0) + (test-equal 0 actual)) + ;;hacky.. testing values with very low probability fails + ((> expected (* 1/1000 count)) + (test-approximate 1.0 (/ actual expected) 0.2)))) + (iota (+ n 1)))) + + (test-binomial 1 0 100) + (test-binomial 1 1 100) + (test-binomial 1 0. 100) + (test-binomial 1 1. 100) + (test-binomial 10 0 100) + (test-binomial 10 1 100) + (test-binomial 10 0. 100) + (test-binomial 10 1. 100) + (test-binomial 10 0.25 100000) + (test-binomial 40 0.375 1000000)) + + +(test-end "srfi-194") diff --git a/tests/sphere-test.scm b/tests/sphere-test.scm new file mode 100644 index 0000000..3ccb67f --- /dev/null +++ b/tests/sphere-test.scm @@ -0,0 +1,301 @@ +;;; SPDX-FileCopyrightText: 2020 Arvydas Silanskas +;;; SPDX-FileCopyrightText: 2024 Bradley J Lucier +;;; SPDX-License-Identifier: MIT +;;; +;;; Take REPS samples from unit sphere, verify random distribution. +;;; +;;; This test checks that: +;;; * Every sample has unit length, within numerical tolerance. +;;; * The REPS samples are uniformly distributed. +;;; * Rotations of the REPS samples are uniformly distributed. +(define (test-sphere sphereg dim-sizes REPS rotate?) + (define random-int (random-source-make-integers (current-random-source))) + (define random-real (random-source-make-reals (current-random-source))) + (define N (- (vector-length dim-sizes) 1)) + + ;; Fix list of samples + (define samples + (generator->list (gtake sphereg REPS))) + + (define (l2-norm VEC) + (sqrt (vector-fold + (lambda (sum x l) (+ sum (/ (* x x) + (* l l)))) + 0 + VEC + dim-sizes))) + + ;; Rotate the j'th amnd k'th coordinates of a vector VEC + ;; by cosine co and sine si + (define (pair-rot VEC j k co si) + (define oj (vector-ref VEC j)) + (define ok (vector-ref VEC k)) + (define nj (+ (* co oj) (* si ok))) + (define nk (+ (* (- si) oj) (* co ok))) + (list->vector + (map (lambda (index) + (cond + ((= index j) nj) + ((= index k) nk) + (else (vector-ref VEC index)))) + (iota (vector-length VEC))))) + + ;; Apply a random rotation to a collection of vectors + (define how-many-rots + (if (< 10 N) 10 N)) + + (define (arb-rot VEC-LIST) + (define j (random-int N)) + (define k (+ j 1 (random-int (- N j)))) + (define theta (* 3.14 (random-real))) + (define co (cos theta)) + (define si (sin theta)) + (define rvl + (map (lambda (vec) + (pair-rot vec j k co si)) + VEC-LIST)) + (if (not (= 0 (random-int how-many-rots))) + (arb-rot rvl) + rvl)) + + ;; Expect a vector approaching zero. That is, each individual + ;; coordinate should be uniformly randomly distributed in the + ;; interval [-1,1]. The sum of REPS samples of these should + ;; converge to zero. The standard deviation of a uniform + ;; distribution is sqrt(REPS/12). + ;; https://en.wikipedia.org/wiki/Continuous_uniform_distribution + ;; So setting max bound of 9 stddev should allow it to usually + ;; pass. + (define (converge-to-zero samples) + (fold (lambda (acc sample) (vector-map + sample acc)) + (make-vector REPS 0.0) + samples)) + + (define (should-be-zero samples) + (l2-norm (converge-to-zero samples))) + + (define (norm-should-be-zero samples) + (/ (should-be-zero samples) (sqrt (/ REPS 12.0)))) + + (define (check-zero samples) + (define num-stddev 9.0) + (define zz (norm-should-be-zero samples)) + (test-assert (< zz num-stddev))) + + ;; maximum allowed tolerance for radius deviation + (define EPS (* 2e-15 (sqrt N))) + + ;; Each individual sphere radius should be 1.0 to within float + ;; tolerance. + (for-each + (lambda (SAMP) + (test-approximate 1.0 (l2-norm SAMP) EPS)) + samples) + + ;; The distribution should be zero + (check-zero samples) + + ;; Rotate wildly. Should still be uniform. + (when rotate? + (for-each + (lambda (junk) (check-zero (arb-rot samples))) + (make-list 12)))) + +(define (test-ball ballg dim-sizes) + (define (l2-norm VEC) + (sqrt (vector-fold + (lambda (sum x l) (+ sum (/ (* x x) + (* l l)))) + 0 + VEC + dim-sizes))) + + (define (test-ball-generates-on-radius radius err) + (test-assert + (generator-any + (lambda (vec) + (define n (l2-norm vec)) + (and (> n (- radius err)) + (< n (+ radius err)))) + (gtake ballg 10000)))) + + (define (test-ball-avg-zero N) + (define vec-sum + (generator-fold + (lambda (vec acc) + (vector-map + vec acc)) + (make-vector (vector-length dim-sizes) 0.0) + (gtake ballg N))) + (define avg-vec + (vector-map + (lambda (e) + (/ e N)) + vec-sum)) + (define n (l2-norm avg-vec)) + (test-assert (< n 1))) + + (test-ball-generates-on-radius 0.0 0.1) + (test-ball-generates-on-radius 0.5 0.1) + (test-ball-generates-on-radius 1.0 0.1) + + (test-ball-avg-zero 5000)) + + ;; Number of standard deviation difference from the expected value + ;; before we say a test failed. If set to 2, then one out of + ;; 20 tests will fail even if the code is correct. Setting it to + ;; 3 means that only one out of a 1000 tests will fail even if the + ;; code is correct. + + (define STDs 3) + + (define (test-ellipsoid a b N) + + (define epsilon 1e-10) + + (define pi (* 4 (atan 1))) + + (define g (make-ellipsoid-generator (vector a b))) + + (define points (generator->list (gtake g N))) + + ;; The points on the "top" of the ellipse, with + ;; x between -a/2 and a/2 + + (define top + (filter (lambda (v) + (and (< (- (/ a 2)) (vector-ref v 0) (/ a 2)) + (< 0 (vector-ref v 1)))) + points)) + + ;; The points on the "right" of the ellipse, with + ;; y between -b/2 and b/2 + + (define right + (filter (lambda (v) + (and (< (- (/ b 2)) (vector-ref v 1) (/ b 2)) + (< 0 (vector-ref v 0)))) + points)) + + (define (arc-length a b) + ;; parametrization: (a\cos t, b\sin t) + ;; this is the norm of the derivative + (lambda (t) + (sqrt (+ (square (* a (sin t))) + (square (* b (cos t))))))) + + (define (simpsons-rule f t0 t1 N) + ;; O(Delta^4) numerical integration + ;; integrate f between t0 and t1 with N intervals + (let* ((Delta (/ (- t1 t0) N)) + (sum1 (do ((i 0 (+ i 1)) + (sum 0. (+ sum + (f (+ t0 (* i Delta))) + (f (+ t0 (* (+ i 1) Delta)))))) + ((= i N) sum))) + (sum2 (do ((i 0 (+ i 1)) + (sum 0. (+ sum (f (+ t0 (* (+ i 0.5) Delta)))))) + ((= i N) sum)))) + (* Delta (/ (+ (* 4 sum2) sum1) 6)))) + + (define p-right + (/ (simpsons-rule (arc-length a b) (- (* pi 1/6)) (* pi 1/6) 100) + (simpsons-rule (arc-length a b) 0 (* pi 2) 100))) + + (define p-top + (/ (simpsons-rule (arc-length a b) (* pi 1/3) (* pi 2/3) 100) + (simpsons-rule (arc-length a b) 0 (* pi 2) 100))) + + ;; test that they're all more-or-less on the ellipse + + (test-assert (every (lambda (p) + (< (abs (- (sqrt (+ (square (/ (vector-ref p 0) a)) + (square (/ (vector-ref p 1) b)))) + 1)) + epsilon)) + points)) + + (for-each (lambda (p m) + ;; p = probability of landing in arc, m = measured number + (test-assert (< (abs (- (* p N) m)) + (* STDs (sqrt (* N p (- 1 p))))))) + (list p-right p-top) + (map length (list right top))) + ) + + (define (test-ellipse a b N) + + ;; This test with two-dimensional ellipses stands in for all + ;; dimensions, as the code to generate points is independent + ;; of dimension + + (define pi (* 4 (atan 1))) + + (define interior-points + (generator->list (gtake (make-ball-generator (vector a b)) N))) + + (define (in-ellipse? point) + (< (+ (square (/ (vector-ref point 0) a)) + (square (/ (vector-ref point 1) b))) + 1)) + + ;; Find points inside rectangles inside various parts + ;; of the ellipse + + (define center + (filter (lambda (v) + (and (< (- (/ a 4)) + (vector-ref v 0) + (/ a 4)) + (< (- (/ b 4)) + (vector-ref v 1) + (/ b 4)))) + interior-points)) + + (define right-x + ;; (right-x b/4) is on the ellipse + (* a (sqrt 15/16))) + + (define right + (filter (lambda (v) + (and (< (- right-x (/ a 2)) + (vector-ref v 0) + right-x) + (< (- (/ b 4)) + (vector-ref v 1) + (/ b 4)))) + interior-points)) + + (define top-y + ;; (a/4 top-y) is on the ellipse + (* b (sqrt 15/16))) + + (define top + (filter (lambda (v) + (and (< (- (/ a 4)) + (vector-ref v 0) + (/ a 4)) + (< (- top-y (/ b 2)) + (vector-ref v 1) + top-y))) + interior-points)) + + ;; p is he fraction of the area in the ellipse + ;; contained in the rectangles (it's all the same). + + #;(define p + (/ (* (/ a 2) (/ b 2)) + (* pi a b))) + + (define p (/ (* 4 pi))) + + ;; check that all the points are truly inside the ellipse. + + (test-assert (every in-ellipse? interior-points)) + + (for-each (lambda (p m) + ;; p = probability of landing in rectangle, + ;; m = measured number of events + (test-assert (< (abs (- (* p N) m)) + (* STDs (sqrt (* N p (- 1 p))))))) + (list p p p) + (map length (list center right top)))) diff --git a/tests/srfi-194.log b/tests/srfi-194.log new file mode 100644 index 0000000..4945d54 --- /dev/null +++ b/tests/srfi-194.log @@ -0,0 +1,11393 @@ +%%%% Starting test srfi-194 +Group begin: srfi-194 +Group begin: Test clamp real number +Test begin: +Test end: + result-kind: pass + actual-value: 10.0 + expected-value: 10.0 +Test begin: +Test end: + result-kind: pass + actual-value: 5.0 + expected-value: 5.0 +Test begin: +Test end: + result-kind: pass + actual-value: 7.5 + expected-value: 7.5 +Group end: Test clamp real number +Group begin: Test with-random-source basic syntax +Group end: Test with-random-source basic syntax +Group begin: Test make-random-source-generator +Test begin: +Test end: + result-kind: pass + actual-value: (85 28 73 81 33 1 79 11 20 78 94.1159681827113 27.1654894692874 30.9985135327305 23.4816127885542 95.2340448761083 97.8517032817831 30.4162313525044 40.6876808411995 63.6995099832998 46.5090012116992) + expected-value: (85 28 73 81 33 1 79 11 20 78 94.1159681827113 27.1654894692874 30.9985135327305 23.4816127885542 95.2340448761083 97.8517032817831 30.4162313525044 40.6876808411995 63.6995099832998 46.5090012116992) +Test begin: +Test end: + result-kind: pass + actual-value: #t +Group end: Test make-random-source-generator +Group begin: Test random int +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Group end: Test random int +Group begin: Test random real +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Group end: Test random real +Group begin: Test complex rectangular +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Group end: Test complex rectangular +Group begin: Test complex polar +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: 3711/1289 + expected-value: 3.0 +Test begin: +Test end: + result-kind: pass + actual-value: 0.00800751805844188 + expected-value: 0 +Test begin: +Test end: + result-kind: pass + actual-value: -0.00859880231141704 + expected-value: 0 +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: #t +Test begin: +Test end: + result-kind: pass + actual-value: 2929/2071 + expected-value: 1.4 +Test begin: +Test end: + result-kind: pass + actual-value: 1.99212776016526 + expected-value: 2 +Test begin: +Test end: + result-kind: pass + actual-value: 4.9573348268153 + expected-value: 5 +Test begin: +Test end: + 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result-kind: pass + actual-value: 0.986382935299029 + expected-value: 1.0 +Group end: Test binomial +Group end: srfi-194 +# of expected passes 2322 diff --git a/tests/zipf-test.scm b/tests/zipf-test.scm new file mode 100644 index 0000000..2fa99c2 --- /dev/null +++ b/tests/zipf-test.scm @@ -0,0 +1,340 @@ +; SPDX-FileCopyrightText: 2020 Arvydas Silanskas +; SPDX-FileCopyrightText: 2020 Linas Vepštas +; SPDX-License-Identifier: MIT +; +; zipf-test.scm +; Unit tests for the Zipf (zeta) distribution. +; +; Created by Linas Vepstas 10 July 2020 +; Part of srfi-194 + +; srfi-133 compatible API +(define zvector-map vector-map) +(define z2vector-map vector-map) +(define zvector-fold vector-fold) + +; srfi-43 compatible API +;(define (zvector-map f vec) +; (vector-map (lambda (i x) (f x)) vec)) +;(define (z2vector-map f veca vecb) +; (vector-map (lambda (i x y) (f x y)) veca vecb)) +;(define (zvector-fold f knil vec) +; (vector-fold (lambda (i x elt) (f x elt)) knil vec)) + +; ------------------------------------------------------------------ +; Debug utility for gnuplot graphing. +; You can use this to dump a vector to a tab-delimited file. +(define (vector-to-file vec filename) + (define (write-vec) + (for-each + (lambda (i) + (define index (+ i 1)) + (define val (vector-ref vec i)) + (display index) + (display " ") + (display val) + (newline)) + (iota (vector-length vec)))) + (with-output-to-file filename write-vec)) + +; ------------------------------------------------------------------ +; Test harness for exploring the Zipf (Riemann/Hurwicz zeta) distribution +; parameter space. +; +; (test-zipf TEST-ID NVOCAB ESS QUE REPS TOL) +; +; * TEST-ID -- String ID, for debugging. +; * The next three parameters are presented to the generator as +; (make-zipf-generator NVOCAB ESS QUE) +; ++ NVOCAB -- Size of vocabulary to select from. +; ++ ESS -- The Riemann zeta "s" exponent. +; ++ QUE -- The Hurwicz zeta "q" offset. +; * REPS -- The number of samples to draw from the distribution. +; * TOL -- The test tolerance, governing the expected failure rate. +; +; The algorithm is roughly: +; Take REPS samples (make-zipf-generator NVOCAB ESS QUE) +; Accumulate them into NVOCAB histogram bins. +; Normalize counts to unit probability (i.e. divide by NVOCAB) +; +; The resulting distribution should uniformly converge to C/(k+q)^s +; for 1 <= k <= NVOCAB where C is a normalization constant. +; +; This compares the actual distribution to the expected convergent +; and reports an error if it is not within TOL of the convergent. +; i.e. it computes the Banach l_0 norm of (distribution-convergent) +; TOL is to be given in units of standard deviations. So, for example, +; setting TOL to 6 gives a six-sigma bandpass, allowing the tests to +; usually pass. +; +; The keyword here is "usually". The tail of the Zipf distribution is +; generally quite thin, and experiences a lot of statistical variation. +; There does not seem to be any published theory of exactly how the +; central limit theorm can be applied to estimate the distribution of +; the tail. The code below assumes an approximate gaussian distribution, +; computes it and tests it; however certain parameter ranges violate +; this assumption. Thus, this test will fail from time to time, +; depending on the luck of the draw. If it fails, it should be repeated +; once or twice, ubtil it passes. +; +(define (test-zipf-once TEST-ID NVOCAB ESS QUE REPS TOL) + + ; Default random number generator + (define ZGEN make-zipf-generator) + + ; Bin-counter containing accumulated histogram. + (define bin-counts + (let ((bin-counts (make-vector NVOCAB 0))) + ; Accumulate samples into the histogram. + (generator-for-each + (lambda (SAMP) + (define offset (- SAMP 1)) + (vector-set! bin-counts offset (+ 1 (vector-ref bin-counts offset)))) + (gtake (ZGEN NVOCAB ESS QUE) REPS)) + bin-counts)) + + ; Verify the distribution is within tolerance. + ; This is written out long-hand for easier debuggability. + + ; Frequency is normalized to be 0.0 to 1.0 + (define frequency (zvector-map (lambda (n) (/ n REPS)) bin-counts)) + (define probility (zvector-map (lambda (n) (inexact n)) frequency)) + + ; Sequence 1..NVOCAB + (define seq (list->vector (iota NVOCAB 1))) + + ; Sequence 1/(k+QUE)^ESS + (define inv-pow + (zvector-map (lambda (k) (expt (+ k QUE) (- (inexact ESS)))) seq)) + + ; Hurwicz harmonic number sum_1..NVOCAB 1/(k+QUE)^ESS + (define hnorm + (zvector-fold + (lambda (sum cnt) (+ sum cnt)) 0 inv-pow)) + + ; The expected distribution. + (define expect + (zvector-map (lambda (x) (/ x hnorm)) inv-pow)) + + ; Convert to floating point. + (define prexpect (zvector-map (lambda (x) (inexact x)) expect)) + + ; The difference. + (define diff (z2vector-map (lambda (x y) (- x y)) probility prexpect)) + + ; Re-weight the tail by k^{s/2}. This seems give a normal error + ; distribution. ... at least, for small q. Problems for large q + ; and with undersampling; so we hack around that. + (define err-dist + (if (< 10 QUE) diff + (z2vector-map (lambda (i x) (* x (expt (+ i 1) (* 0.5 ESS)))) + (list->vector (iota (vector-length diff))) + diff))) + + ; Normalize to unit root-mean-square. + (define rms (/ 1 (sqrt (* 2 3.141592653 REPS)))) + (define norm-dist (zvector-map (lambda (x) (/ x rms)) err-dist)) + + ; Maximum deviation from expected distribution (l_0 norm) + (define l0-norm + (zvector-fold + (lambda (sum x) (if (< sum (abs x)) (abs x) sum)) 0 norm-dist)) + + ; The mean. + (define mean + (/ (zvector-fold (lambda (sum x) (+ sum x)) 0 norm-dist) + NVOCAB)) + + (define root-mean-square + (sqrt (/ (zvector-fold (lambda (sum x) (+ sum (* x x))) 0 norm-dist) + NVOCAB))) + + ; Test for uniform convergence. + ; (test-assert TEST-ID (<= l0-norm TOL)) + (define tol-result (<= l0-norm TOL)) + + ; Should not random walk too far away. + ; Could tighten this with a proper theory of the error distribution. + ; (test-assert TEST-ID (< (abs mean) 3)) + (define mean-result (< (abs mean) 3)) + ; I don't understand the error distribution .... + ; (test-assert (and (< 0.4 root-mean-square) (< root-mean-square 1.5))) + + ; Sanity check. The total counts in the bins should be equal to REPS. + ; If this fails, the test harness itself is broken. + (test-assert TEST-ID + (equal? REPS + (zvector-fold + (lambda (sum cnt) (+ sum cnt)) 0 bin-counts))) + + ; Utility debug printing + ;(vector-to-file probility "probility.dat") + ;(vector-to-file prexpect "prexpect.dat") + ;(vector-to-file diff "diff.dat") + + (list tol-result mean-result)) + +; ------------------------------------------------------------------ +; Sometimes the Zip test fails, due to random variation. It should +; pass, if attempted a second time. This gives it three chances. +; If it fails three times, then something bad is happening. +(define (test-zipf TEST-ID NVOCAB ESS QUE REPS TOL) + + ;; Three strikes, you're out. + (define RETRY 3) + + (define num-failures + (list-index + (lambda (n) + (define rc (test-zipf-once TEST-ID NVOCAB ESS QUE REPS TOL)) + (and (first rc) (second rc))) + (iota RETRY))) + + ; `num-failures` will be #f if it failed each and every time. + ;(if (number? num-failures) + ; (if (< 0 num-failures) + ; (format #t "Test '~A' out of bounds ~A times.\n" TEST-ID num-failures)) + ; (format #t "Error: Test '~A' failed every time!\n" TEST-ID)) + + ; Announce excessive repeated failures. + (test-assert TEST-ID num-failures) +) + +; ------------------------------------------------------------------ +; Explore the parameter space. +(define (zipf-test-group) + ; (test-begin "srfi-194-zipf") + + ; The unit test computes something that is "almost" a standard + ; deviation for the error distribution. Except, maybe not quite, + ; I don't fully understand the theory. So most tests seem to come + ; in fine in well-under a six-sigma deviation, but some of the wilder + ; parameter choices misbehave, so six-sigma doesn't always work. + ; Also, when the number of bins is large, its easy to under-sample; + ; some bins end up empty and the std-dev is thrown off as a result. + ; Thus, the tolerance bounds below are hand-adjusted. + (define six-sigma 6.0) + + (define hack-que 3.0) + + ; Zoom into s->1 + (test-zipf "zoom-1" 30 1.1 0 1000 six-sigma) + (test-zipf "zoom-2" 30 1.01 0 1000 six-sigma) + (test-zipf "zoom-3" 30 1.001 0 1000 six-sigma) + (test-zipf "zoom-4" 30 1.0001 0 1000 six-sigma) + (test-zipf "zoom-5" 30 1.00001 0 1000 six-sigma) + + (test-zipf "zoom-6" 30 (+ 1 1e-6) 0 1000 six-sigma) + (test-zipf "zoom-8" 30 (+ 1 1e-8) 0 1000 six-sigma) + (test-zipf "zoom-10" 30 (+ 1 1e-10) 0 1000 six-sigma) + (test-zipf "zoom-12" 30 (+ 1 1e-12) 0 1000 six-sigma) + (test-zipf "zoom-14" 30 (+ 1 1e-14) 0 1000 six-sigma) + (test-zipf "zoom-inf" 30 1 0 1000 six-sigma) + + ; Verify improving uniform convergence + (test-zipf "uniform-1" 30 1 0 10000 six-sigma) + (test-zipf "uniform-2" 30 1 0 100000 six-sigma) + + ; Larger vocabulary + (test-zipf "mid-voc-1" 300 1.1 0 10000 six-sigma) + (test-zipf "mid-voc-2" 300 1.01 0 10000 six-sigma) + (test-zipf "mid-voc-3" 300 1.001 0 10000 six-sigma) + (test-zipf "mid-voc-4" 300 1.0001 0 10000 six-sigma) + (test-zipf "mid-voc-5" 300 1.00001 0 10000 six-sigma) + + ; Larger vocabulary. Take more samples.... + (test-zipf "large-voc-1" 3701 1.1 0 40000 six-sigma) + (test-zipf "large-voc-2" 3701 1.01 0 40000 six-sigma) + (test-zipf "large-voc-3" 3701 1.001 0 40000 six-sigma) + (test-zipf "large-voc-4" 3701 1.0001 0 40000 six-sigma) + (test-zipf "large-voc-5" 3701 1.00001 0 40000 six-sigma) + + ; Huge vocabulary; few samples. Many bins will be empty, + ; causing the std-dev to get large. + (test-zipf "huge-voc-1" 43701 (+ 1 1e-6) 0 60000 9.5) + (test-zipf "huge-voc-2" 43701 (+ 1 1e-7) 0 60000 9.5) + (test-zipf "huge-voc-3" 43701 (+ 1 1e-9) 0 60000 9.5) + (test-zipf "huge-voc-4" 43701 (+ 1 1e-12) 0 60000 9.5) + (test-zipf "huge-voc-5" 43701 1 0 60000 9.5) + + ; Large s, small range + (test-zipf "big-s-lo-1" 5 1.1 0 1000 six-sigma) + (test-zipf "big-s-lo-2" 5 2.01 0 1000 six-sigma) + (test-zipf "big-s-lo-3" 5 4.731 0 1000 six-sigma) + (test-zipf "big-s-lo-4" 5 9.09001 0 1000 six-sigma) + (test-zipf "big-s-lo-5" 5 13.45 0 1000 8.0) + + ; Large s, larger range. Most histogram bins will be empty + ; so allow much larger error margins. There are excessively + ; frequent large failures in this bunch. + (test-zipf "bis-mid-1" 130 1.5 0 30000 six-sigma) + (test-zipf "bis-mid-2" 130 2.03 0 30000 9.0) + (test-zipf "bis-mid-3" 130 4.5 0 30000 36.0) ; This one is problematic + (test-zipf "bis-mid-4" 130 6.66 0 30000 24.0) + + ; Verify that accuracy improves with more samples. + (test-zipf "samp-bi-1" 129 1.1 0 10000 six-sigma) + (test-zipf "samp-bi-2" 129 1.01 0 10000 six-sigma) + (test-zipf "samp-bi-3" 129 1.001 0 10000 six-sigma) + (test-zipf "samp-bi-4" 129 1.0001 0 10000 six-sigma) + (test-zipf "samp-bi-5" 129 1.00001 0 10000 six-sigma) + + ; Non-zero Hurwicz parameter + (test-zipf "hurw-1" 131 1.1 0.3 10000 six-sigma) + (test-zipf "hurw-2" 131 1.1 1.3 10000 six-sigma) + (test-zipf "hurw-3" 131 1.1 6.3 10000 six-sigma) + (test-zipf "hurw-4" 131 1.1 20.23 10000 six-sigma) + + ; Negative Hurwicz parameter. Must be greater than branch point at -0.5. + (test-zipf "hneg-1" 81 1.1 -0.1 1000 six-sigma) + (test-zipf "hneg-2" 81 1.1 -0.3 1000 six-sigma) + (test-zipf "hneg-3" 81 1.1 -0.4 1000 six-sigma) + (test-zipf "hneg-4" 81 1.1 -0.499 1000 six-sigma) + + ; A walk into a stranger corner of the parameter space. + (test-zipf "big-h-1" 131 1.1 41.483 10000 hack-que) + (test-zipf "big-h-2" 131 2.1 41.483 10000 hack-que) + (test-zipf "big-h-3" 131 6.1 41.483 10000 hack-que) + (test-zipf "big-h-4" 131 16.1 41.483 10000 hack-que) + (test-zipf "big-h-5" 131 46.1 41.483 10000 hack-que) + (test-zipf "big-h-6" 131 96.1 41.483 10000 hack-que) + + ; A still wilder corner of the parameter space. + (test-zipf "huhu-1" 131 1.1 1841.4 10000 hack-que) + (test-zipf "huhu-2" 131 1.1 1.75e6 10000 hack-que) + (test-zipf "huhu-3" 131 2.1 1.75e6 10000 hack-que) + (test-zipf "huhu-4" 131 12.1 1.75e6 10000 hack-que) + (test-zipf "huhu-5" 131 42.1 1.75e6 10000 hack-que) + + ; Lets try s less than 1 + (test-zipf "small-s-1" 35 0.9 0 1000 six-sigma) + (test-zipf "small-s-2" 35 0.99 0 1000 six-sigma) + (test-zipf "small-s-3" 35 0.999 0 1000 six-sigma) + (test-zipf "small-s-4" 35 0.9999 0 1000 six-sigma) + (test-zipf "small-s-5" 35 0.99999 0 1000 six-sigma) + + ; Attempt to force an overflow + (test-zipf "ovfl-1" 437 (- 1 1e-6) 0 1000 six-sigma) + (test-zipf "ovfl-2" 437 (- 1 1e-7) 0 1000 six-sigma) + (test-zipf "ovfl-3" 437 (- 1 1e-9) 0 1000 six-sigma) + (test-zipf "ovfl-4" 437 (- 1 1e-12) 0 1000 six-sigma) + + ; Almost flat distribution + (test-zipf "flat-1" 36 0.8 0 1000 six-sigma) + (test-zipf "flat-2" 36 0.5 0 1000 six-sigma) + (test-zipf "flat-3" 36 0.1 0 1000 six-sigma) + + ; A visit to crazy-town -- increasing, not decreasing exponent + (test-zipf "neg-s-1" 36 0.0 0 1000 six-sigma) + (test-zipf "neg-s-2" 36 -0.1 0 1000 six-sigma) + (test-zipf "neg-s-3" 36 -1.0 0 1000 six-sigma) + (test-zipf "neg-s-4" 36 -3.0 0 1000 six-sigma) + + ; More crazy with some Hurwicz on top. + (test-zipf "neg-shu-1" 16 0.0 0.5 1000 six-sigma) + (test-zipf "neg-shu-2" 16 -0.2 2.5 1000 six-sigma) + (test-zipf "neg-shu-3" 16 -1.3 10 1000 six-sigma) + (test-zipf "neg-shu-4" 16 -2.9 100 1000 six-sigma) + + ; (test-end "srfi-194-zipf") + ) |