aboutsummaryrefslogtreecommitdiff
path: root/src/extent-sampling.sc
blob: 48e65441feaa581f0589318b366f0cca73f78343 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
;;; nsmc --- n-sphere Monte Carlo method
;;; Copyright © 2021 Arun I <arunisaac@systemreboot.net>
;;; Copyright © 2021 Murugesan Venkatapathi <murugesh@iisc.ac.in>
;;;
;;; This file is part of nsmc.
;;;
;;; nsmc is free software: you can redistribute it and/or modify it
;;; under the terms of the GNU General Public License as published by
;;; the Free Software Foundation, either version 3 of the License, or
;;; (at your option) any later version.
;;;
;;; nsmc is distributed in the hope that it will be useful, but
;;; WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
;;; General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with nsmc.  If not, see <https://www.gnu.org/licenses/>.

(sc-include "macros/macros")

(pre-include "stddef.h")
(pre-include "gsl/gsl_integration.h")
(pre-include "gsl/gsl_rstat.h")
(pre-include "gsl/gsl_vector.h")
(pre-include "nd-random.h")
(pre-include "utils.h")
(pre-include "extent-sampling.h")

(sc-define-syntax (with-vector var size body ...)
  (with-alloc var gsl-vector*
              (gsl-vector-alloc size)
              gsl-vector-free
              body ...))

(sc-define-syntax (with-rstats var body ...)
  (with-alloc var gsl-rstat-workspace*
              (gsl-rstat-alloc) gsl-rstat-free
              body ...))

(sc-define-syntax (with-integration-workspace var intervals body ...)
  (with-alloc var gsl-integration-workspace*
              (gsl-integration-workspace-alloc intervals)
              gsl-integration-workspace-free
              body ...))

(sc-define-syntax (invoke-extent-oracle extent-oracle r x)
  ((: extent-oracle oracle) r x (: extent-oracle params)))

(pre-define CONFIDENCE-INTERVAL-FACTOR 1.96)

(pre-let* (VOLUME-MINIMUM-SAMPLES 100)
  (define (volume extent-oracle true-volume r dimension rtol stats)
    (double extent-oracle-t* double (const gsl-rng*) (unsigned int) double gsl-rstat-workspace*)
    (declare volume double)
    (let* ((vn double (ln-volume-of-ball dimension)))
      (with-vector x dimension
        (do-while (or (> (/ (* CONFIDENCE-INTERVAL-FACTOR
                               (gsl-rstat-sd-mean stats))
                            volume)
                         rtol)
                      (> (rerror volume true-volume) rtol)
                      (< (gsl-rstat-n stats) VOLUME-MINIMUM-SAMPLES))
          (random-direction-vector r x)
          (gsl-rstat-add (exp (+ vn (* dimension (log (invoke-extent-oracle extent-oracle r x)))))
                         stats)
          (set volume (gsl-rstat-mean stats)))))
    (return volume)))

(define (volume-window extent-oracle true-volume r dimension rtol number-of-samples)
  (double extent-oracle-t* double (const gsl-rng*) (unsigned int) double (unsigned int*))
  (declare volume double)
  (let* ((vn double (ln-volume-of-ball dimension))
         ;; This is the window length used in Volume.m of
         ;; Lovasz-Vempala's code.
         (window-length int (+ (* 4 dimension dimension) 500))
         (accurate-estimates int 0))
    (with-rstats stats
      (with-vector x dimension
        (do-while (< accurate-estimates window-length)
          (random-direction-vector r x)
          (gsl-rstat-add (exp (+ vn (* dimension (log (invoke-extent-oracle extent-oracle r x)))))
                         stats)
          (set volume (gsl-rstat-mean stats))
          (cond
           ((< (rerror volume true-volume) rtol)
            (set+ accurate-estimates 1))
           (else (set accurate-estimates 0)))))
      (set (pointer-get number-of-samples)
           (gsl-rstat-n stats))))
  (return volume))

(sc-define-syntax (invoke-integrand integrand r x)
  ((: integrand integrand) r x (: integrand params)))

(pre-let* (INTEGRATION-INTERVALS 1000)
  (define (integral-per-direction integrand direction r n radius rtol)
    (double integrand-t* (const gsl-vector*) (const gsl-rng*) (unsigned int) double double)
    (define (f r params) (double double void*)
      (return (* (gsl-pow-uint r (- n 1))
                 (invoke-integrand integrand r direction))))
    (declare gsl-f (struct-variable gsl-function (function (address-of f)))
             result double
             error double)
    (with-integration-workspace w INTEGRATION-INTERVALS
      (gsl-integration-qag (address-of gsl-f)
                           0
                           radius
                           0
                           rtol
                           INTEGRATION-INTERVALS
                           GSL-INTEG-GAUSS15
                           w
                           (address-of result)
                           (address-of error)))
    (return (* (surface-area-of-ball n)
               result))))

(pre-let* (INTEGRAL-MINIMUM-SAMPLES 100)
  (define (integral integrand extent-oracle true-integral r dimension rtol stats)
    (double integrand-t* extent-oracle-t* double (const gsl-rng*) (unsigned int) double gsl-rstat-workspace*)
    (declare integral double
             error double)
    (with-vector x dimension
      (do-while (or (> error rtol)
                    (> (rerror integral true-integral) rtol)
                    (< (gsl-rstat-n stats) INTEGRAL-MINIMUM-SAMPLES))
        (random-direction-vector r x)
        (gsl-rstat-add (integral-per-direction integrand x r dimension
                                               (invoke-extent-oracle extent-oracle r x) rtol)
                       stats)
        (set integral (gsl-rstat-mean stats))
        (set error (/ (* CONFIDENCE-INTERVAL-FACTOR (gsl-rstat-sd-mean stats))
                      integral))))
    (cond
     ((> error rtol)
      (GSL-ERROR-VAL "Integral failed to converge" GSL-ETOL integral)))
    (return integral)))

(define (volume-cone extent-oracle r mean omega-min omega-max number-of-samples variance)
  (double extent-oracle-t* (const gsl-rng*) (const gsl-vector*) double double (unsigned int) double*)
  (declare volume double)
  (let* ((dimension (unsigned int) (: mean size))
         (vn double (ln-volume-of-ball dimension))
         (theta-min double (solid-angle->planar-angle (* omega-min (surface-area-of-ball dimension)) dimension))
         (theta-max double (solid-angle->planar-angle (* omega-max (surface-area-of-ball dimension)) dimension)))
    (with-rstats stats
      (with-vector x dimension
        (for-i i number-of-samples
          (hollow-cone-random-vector r mean theta-min theta-max x)
          (gsl-rstat-add (exp (+ vn (* dimension (log (invoke-extent-oracle extent-oracle r x)))))
                         stats)))
      (cond
       (variance (set (pointer-get variance) (gsl-rstat-variance stats))))
      (set volume (* (gsl-rstat-mean stats)
                     (- omega-max omega-min)))))
  (return volume))

(define (volume-experiment extent-oracle r mean samples-per-cone solid-angle-factor
                           solid-angle-threshold-exponent-factor number-of-samples)
  (double extent-oracle-t* (const gsl-rng*) (const gsl-vector*)
          (unsigned int) double double (unsigned int*))
  (define
    volume double 0
    omega-max double 0.5
    N int 0)
  (let* ((dimension int (: mean size)))
    (do-while (> omega-max (pow 2 (- (* dimension solid-angle-threshold-exponent-factor))))
      (let* ((omega-min double (/ omega-max solid-angle-factor)))
        (set+ volume (volume-cone extent-oracle r mean omega-min omega-max samples-per-cone NULL))
        (set+ N samples-per-cone)
        (set omega-max omega-min))))
  (set+ volume (volume-cone extent-oracle r mean 0 omega-max samples-per-cone NULL))
  (set+ N samples-per-cone)
  (cond
   (number-of-samples (set (pointer-get number-of-samples) N)))
  (return volume))