/usr/share/doc/scm/examples/example.scm is in scm 5e5-3.2.
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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 | ;From Revised^4 Report on the Algorithmic Language Scheme
;William Clinger and Jonathon Rees (Editors)
; EXAMPLE
;INTEGRATE-SYSTEM integrates the system
; y_k' = f_k(y_1, y_2, ..., y_n), k = 1, ..., n
;of differential equations with the method of Runge-Kutta.
;The parameter SYSTEM-DERIVATIVE is a function that takes a system
;state (a vector of values for the state variables y_1, ..., y_n) and
;produces a system derivative (the values y_1', ..., y_n'). The
;parameter INITIAL-STATE provides an initial system state, and H is an
;initial guess for the length of the integration step.
;The value returned by INTEGRATE-SYSTEM is an infinite stream of
;system states.
(define integrate-system
(lambda (system-derivative initial-state h)
(let ((next (runge-kutta-4 system-derivative h)))
(letrec ((states
(cons initial-state
(delay (map-streams next states)))))
states))))
;RUNGE-KUTTA-4 takes a function, F, that produces a
;system derivative from a system state. RUNGE-KUTTA-4
;produces a function that takes a system state and
;produces a new system state.
(define runge-kutta-4
(lambda (f h)
(let ((*h (scale-vector h))
(*2 (scale-vector 2))
(*1/2 (scale-vector (/ 1 2)))
(*1/6 (scale-vector (/ 1 6))))
(lambda (y)
;; Y is a system state
(let* ((k0 (*h (f y)))
(k1 (*h (f (add-vectors y (*1/2 k0)))))
(k2 (*h (f (add-vectors y (*1/2 k1)))))
(k3 (*h (f (add-vectors y k2)))))
(add-vectors y
(*1/6 (add-vectors k0
(*2 k1)
(*2 k2)
k3))))))))
(define elementwise
(lambda (f)
(lambda vectors
(generate-vector
(vector-length (car vectors))
(lambda (i)
(apply f
(map (lambda (v) (vector-ref v i))
vectors)))))))
(define generate-vector
(lambda (size proc)
(let ((ans (make-vector size)))
(letrec ((loop
(lambda (i)
(cond ((= i size) ans)
(else
(vector-set! ans i (proc i))
(loop (+ i 1)))))))
(loop 0)))))
(define add-vectors (elementwise +))
(define scale-vector
(lambda (s)
(elementwise (lambda (x) (* x s)))))
;MAP-STREAMS is analogous to MAP: it applies its first
;argument (a procedure) to all the elements of its second argument (a
;stream).
(define map-streams
(lambda (f s)
(cons (f (head s))
(delay (map-streams f (tail s))))))
;Infinite streams are implemented as pairs whose car holds the first
;element of the stream and whose cdr holds a promise to deliver the rest
;of the stream.
(define head car)
(define tail
(lambda (stream) (force (cdr stream))))
;The following illustrates the use of INTEGRATE-SYSTEM in
;integrating the system
;
; dvC vC
; C --- = -i - --
; dt L R
;
; diL
; L --- = v
; dt C
;
;which models a damped oscillator.
(define damped-oscillator
(lambda (R L C)
(lambda (state)
(let ((Vc (vector-ref state 0))
(Il (vector-ref state 1)))
(vector (- 0 (+ (/ Vc (* R C)) (/ Il C)))
(/ Vc L))))))
(define the-states
(integrate-system
(damped-oscillator 10000 1000 .001)
'#(1 0)
.01))
(do ((i 10 (- i 1))
(s the-states (tail s)))
((zero? i) (newline))
(newline)
(write (head s)))
; #(1 0)
; #(0.99895054 9.994835e-6)
; #(0.99780226 1.9978681e-5)
; #(0.9965554 2.9950552e-5)
; #(0.9952102 3.990946e-5)
; #(0.99376684 4.985443e-5)
; #(0.99222565 5.9784474e-5)
; #(0.9905868 6.969862e-5)
; #(0.9888506 7.9595884e-5)
; #(0.9870173 8.94753e-5)
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