186 lines
5.5 KiB
Scheme
186 lines
5.5 KiB
Scheme
(load "util.scm")
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(define (integral integrand initial-value dt)
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(define int
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(cons-stream initial-value
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(add-streams (scale-stream integrand dt)
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int)))
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int)
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(display "\nex-3.73 - RC\n")
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(define (RC R C dt)
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(define (rc-proc i v0)
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(add-streams
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(scale-stream i R)
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(integral (scale-stream i (/ 1 C)) v0 dt)))
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rc-proc)
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(define RC1 (RC 5 1 0.5))
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(assert (take 5 (RC1 ones 4.2))
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'(9.2 9.7 10.2 10.7 11.2))
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(display "\nex-3.74 - zero-crossings\n")
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(define sense-data
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(list->stream
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'(1 2 1.5 1 0.5 -0.1 -2 -3 -2 -0.5 0.2 3 4)))
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(define response '(0 0 0 0 0 -1 0 0 0 0 1 0))
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(define (sign-change-detector s2 s1)
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(cond
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((and (< s1 0) (>= s2 0)) 1)
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((and (>= s1 0) (< s2 0)) -1)
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(else 0)))
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(define (make-zero-crossings input-stream last-value)
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(cons-stream
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(sign-change-detector (stream-car input-stream) last-value)
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(make-zero-crossings (stream-cdr input-stream)
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(stream-car input-stream))))
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(define zero-crossings (make-zero-crossings sense-data 0))
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(assert (take 12 zero-crossings) response)
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(define zero-crossings
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(stream-map sign-change-detector
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sense-data
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(cons-stream 0 sense-data)))
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(assert (take 12 zero-crossings) response)
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(display "\nex-3.75 - averaged zero-crossings\n")
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; Louis' solution uses the average value as last-value which means that the new
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; value and the previous average are used for averaging and not simply two
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; consecutive values as proposed by Alyssa.
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(define (make-zero-crossings-avg input-stream last-value last-avpt)
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(let ((avpt (/ (+ (stream-car input-stream) last-value) 2)))
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(cons-stream (sign-change-detector avpt last-avpt)
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(make-zero-crossings-avg (stream-cdr input-stream)
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(stream-car input-stream)
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avpt))))
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(display (take 12 (make-zero-crossings-avg sense-data 0 0))) (newline)
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(display "\nex-3.76 - smooth zero-crossings\n")
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(define (smooth xs)
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(stream-map average xs (stream-cdr xs)))
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(define (make-zero-crossings-smoothed input-stream last-value)
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(make-zero-crossings (smooth input-stream) last-value))
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(assert (take 11 (make-zero-crossings-smoothed sense-data 0))
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'(0 0 0 0 0 -1 0 0 0 0 1))
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(display "\nex-3.77 - lazy-integral\n")
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(define (integral delayed-integrand initial-value dt)
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(define int
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(cons-stream initial-value
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(let ((integrand (force delayed-integrand)))
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(add-streams (scale-stream integrand dt)
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int))))
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int)
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(define (solve f y0 dt)
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(define y (integral (delay dy) y0 dt))
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(define dy (stream-map f y))
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y)
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(assert (stream-ref (solve (lambda (y) y) 1 0.001) 1000) 2.716923932235896)
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(define (integral delayed-integrand initial-value dt)
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(cons-stream
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initial-value
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(let ((integrand (force delayed-integrand)))
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(if (stream-null? integrand)
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the-empty-stream
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(integral (delay (stream-cdr integrand))
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(+ (* dt (stream-car integrand)) initial-value)
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dt)))))
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(assert (stream-ref (solve (lambda (y) y) 1 0.001) 1000) 2.716923932235896)
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(display "\nex-3.78 - solve-2nd\n")
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(define (solve-2nd a b dt y0 dy0)
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(define y (integral (delay dy) y0 dt))
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(define dy (integral (delay ddy) dy0 dt))
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(define ddy (add-streams (scale-stream dy a)
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(scale-stream y b)))
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y)
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(assert (stream-ref (solve-2nd 1 0 0.0001 1 1) 10000)
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2.7181459268252266) ; e
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(assert (stream-ref (solve-2nd 0 -1 0.0001 1 0) 10472)
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0.5000240628699462) ; cos pi/3 = 0.5
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(assert (stream-ref (solve-2nd 0 -1 0.0001 0 1) 5236)
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0.5000141490501059) ; sin pi/6 = 0.5
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(display "\nex-3.79 - solve-2nd-general\n")
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(display "[ok]\n")
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(define (solve-2nd-general f y0 dy0 dt)
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(define y (integral (delay dy) y0 dt))
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(define dy (integral (delay ddy) dy0 dt))
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(define ddy (stream-map f dy y))
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y)
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(display "\nex-3.80 - RLC\n")
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(define (RLC R L C dt)
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(define (rlc-proc vC0 iL0)
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(define vC (integral (delay dvC) vC0 dt))
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(define iL (integral (delay diL) iL0 dt))
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(define dvC (scale-stream il (/ -1 C)))
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(define diL
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(add-streams
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(scale-stream iL (/ (- R) L))
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(scale-stream vC (/ 1 L))))
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(cons vC iL))
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rlc-proc)
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(define RLC1 (RLC 1 1 0.2 0.1))
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(display "[ok]\n")
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(display "\nex-3.81 - random-stream\n")
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(define (make-random-stream request-stream)
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(define a 1664525)
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(define c 1013904223)
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(define m (expt 2 32))
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(define new-random-stream
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(cons-stream
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0
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(stream-map (lambda (x) (modulo (+ (* a x) c) m))
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new-random-stream)))
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(define (result-stream request-stream random-stream)
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(cond
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((eq? (stream-car request-stream) 'gen)
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(cons-stream (stream-car random-stream)
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(result-stream (stream-cdr request-stream)
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(stream-cdr random-stream))))
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((eq? (stream-car request-stream) 'reset)
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(result-stream (stream-cdr request-stream) new-random-stream))
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(else (error "Unsupported request"))))
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(result-stream request-stream new-random-stream))
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(define requests
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(cons-stream
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'gen (cons-stream 'gen (cons-stream 'gen (cons-stream 'reset (cons-stream 'gen
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(cons-stream 'gen (cons-stream 'gen requests))))))))
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(define rs (make-random-stream requests))
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(assert (take 10 rs)
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(take 10 rs))
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(display "\nex-3.82\n")
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