-
Notifications
You must be signed in to change notification settings - Fork 0
/
common-stalingrad.vlad
145 lines (105 loc) · 4.17 KB
/
common-stalingrad.vlad
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
(define (car (cons x y)) x)
(define (cdr (cons x y)) y)
(define (not x) (if x #f #t))
(define (append x y) (if (null? x) y (cons (first x) (append (rest x) y))))
(define (length l) (if (null? l) 0 (+ (length (cdr l)) 1)))
(define (list-ref l i) (if (zero? i) (car l) (list-ref (cdr l) (- i 1))))
(define ((map f) l) (if (null? l) '() (cons (f (car l)) ((map f) (cdr l)))))
(define ((map2 f) l1 l2)
(if (null? l1) '() (cons (f (car l1) (car l2)) ((map2 f) (cdr l1) (cdr l2)))))
(define (equal? x y)
;; This doesn't compare procedures or transformed values.
(or
(and (null? x) (null? y))
(and (boolean? x) (boolean? y) (or (and x y) (and (not x) (not y))))
(and (real? x) (real? y) (= x y))
(and (pair? x) (pair? y) (equal? (car x) (car y)) (equal? (cdr x) (cdr y)))))
(define (max x y) (if (>= x y) x y))
(define (e i n) ((map-n (lambda (j) (if (= j i) (real 1) (real 0)))) n))
(define (j* x) (bundle x (perturb (zero x))))
(define ((derivative-F f) x)
(unperturb (tangent ((j* f) (bundle x (perturb (real 1)))))))
(define ((gradient-F f) x)
(let ((n (length x)))
((map-n (lambda (i)
(unperturb (tangent ((j* f) (bundle x (perturb (e i n))))))))
n)))
(define ((gradient-R f) x)
(cdr (unsensitize ((cdr ((*j f) (*j x))) (sensitize (real 1))))))
(define ((derivative-R f) x)
(cdr (unsensitize ((cdr ((*j f) (*j x))) (sensitize (real 1))))))
(define (first x) (car x))
(define (second x) (car (cdr x)))
(define (third x) (car (cdr (cdr x))))
(define (fourth x) (car (cdr (cdr (cdr x)))))
(define (rest x) (cdr x))
(define (sqr x) (* x x))
(define ((map-n f) n)
(letrec ((loop (lambda (i) (if (= i n) '() (cons (f i) (loop (+ i 1)))))))
(loop 0)))
(define ((reduce f i) l) (if (null? l) i (f (car l) ((reduce f i) (cdr l)))))
(define (map-reduce g i f l)
(if (null? l) i (g (f (first l)) (map-reduce g i f (rest l)))))
(define (remove-if p l)
(cond ((null? l) '())
((p (first l)) (remove-if p (rest l)))
(else (cons (first l) (remove-if p (rest l))))))
(define (v+ u v) ((map2 +) u v))
(define (v- u v) ((map2 -) u v))
(define (k*v k v) ((map (lambda (x) (* k x))) v))
(define (magnitude-squared x) ((reduce + (real 0)) ((map sqr) x)))
(define (magnitude x) (sqrt (magnitude-squared x)))
(define (distance-squared u v) (magnitude-squared (v- v u)))
(define (distance u v) (sqrt (distance-squared u v)))
(define (gradient-ascent-F f x0 n eta)
(if (zero? n)
(list x0 (f x0) ((gradient-F f) x0))
(gradient-ascent-F
f
((map2 (lambda (xi gi) (+ xi (* eta gi)))) x0 ((gradient-F f) x0))
(- n 1)
eta)))
(define (gradient-ascent-R f x0 n eta)
(if (zero? n)
(list x0 (f x0) ((gradient-R f) x0))
(gradient-ascent-R
f
((map2 (lambda (xi gi) (+ xi (* eta gi)))) x0 ((gradient-R f) x0))
(- n 1)
eta)))
(define (multivariate-argmin-F f x)
(let ((g (gradient-F f)))
(letrec ((loop
(lambda (x fx gx eta i)
(cond ((<= (magnitude gx) (real 1e-5)) x)
((= i (real 10)) (loop x fx gx (* (real 2) eta) (real 0)))
(else
(let ((x-prime (v- x (k*v eta gx))))
(if (<= (distance x x-prime) (real 1e-5))
x
(let ((fx-prime (f x-prime)))
(if (< fx-prime fx)
(loop x-prime fx-prime (g x-prime) eta (+ i 1))
(loop x fx gx (/ eta (real 2)) (real 0)))))))))))
(loop x (f x) (g x) (real 1e-5) (real 0)))))
(define (multivariate-argmax-F f x)
(multivariate-argmin-F (lambda (x) (- (real 0) (f x))) x))
(define (multivariate-max-F f x) (f (multivariate-argmax-F f x)))
(define (multivariate-argmin-R f x)
(let ((g (gradient-R f)))
(letrec ((loop
(lambda (x fx gx eta i)
(cond ((<= (magnitude gx) (real 1e-5)) x)
((= i (real 10)) (loop x fx gx (* (real 2) eta) (real 0)))
(else
(let ((x-prime (v- x (k*v eta gx))))
(if (<= (distance x x-prime) (real 1e-5))
x
(let ((fx-prime (f x-prime)))
(if (< fx-prime fx)
(loop x-prime fx-prime (g x-prime) eta (+ i 1))
(loop x fx gx (/ eta (real 2)) (real 0)))))))))))
(loop x (f x) (g x) (real 1e-5) (real 0)))))
(define (multivariate-argmax-R f x)
(multivariate-argmin-R (lambda (x) (- (real 0) (f x))) x))
(define (multivariate-max-R f x) (f (multivariate-argmax-R f x)))