(load "util.scm")

(define (integral integrand initial-value dt)
  (define int
    (cons-stream initial-value
                 (add-streams (scale-stream integrand dt)
                              int)))
  int)

(display "\nex-3.73 - RC\n")

(define (RC R C dt)
  (define (rc-proc i v0)
    (add-streams
      (scale-stream i R)
      (integral (scale-stream i (/ 1 C)) v0 dt)))
  rc-proc)

(define RC1 (RC 5 1 0.5))

(assert (take 5 (RC1 ones 4.2))
        '(9.2 9.7 10.2 10.7 11.2))

(display "\nex-3.74 - zero-crossings\n")

(define sense-data
  (list->stream
                 '(1  2  1.5  1  0.5  -0.1  -2  -3  -2  -0.5  0.2  3  4)))
(define response '(0  0    0  0    0    -1   0   0   0     0    1  0))

(define (sign-change-detector s2 s1)
  (cond
    ((and (< s1 0) (>= s2 0)) 1)
    ((and (>= s1 0) (< s2 0)) -1)
    (else 0)))

(define (make-zero-crossings input-stream last-value)
  (cons-stream
   (sign-change-detector (stream-car input-stream) last-value)
   (make-zero-crossings (stream-cdr input-stream)
                        (stream-car input-stream))))

(define zero-crossings (make-zero-crossings sense-data 0))

(assert (take 12 zero-crossings) response)

(define zero-crossings
  (stream-map sign-change-detector
              sense-data
              (cons-stream 0 sense-data)))

(assert (take 12 zero-crossings) response)

(display "\nex-3.75 - averaged zero-crossings\n")

; Louis' solution uses the average value as last-value which means that the new
; value and the previous average are used for averaging and not simply two
; consecutive values as proposed by Alyssa.

(define (make-zero-crossings-avg input-stream last-value last-avpt)
  (let ((avpt (/ (+ (stream-car input-stream) last-value) 2)))
    (cons-stream (sign-change-detector avpt last-avpt)
                 (make-zero-crossings-avg (stream-cdr input-stream)
                                          (stream-car input-stream)
                                          avpt))))

(display (take 12 (make-zero-crossings-avg sense-data 0 0))) (newline)

(display "\nex-3.76 - smooth zero-crossings\n")

(define (smooth xs)
  (stream-map average xs (stream-cdr xs)))

(define (make-zero-crossings-smoothed input-stream last-value)
  (make-zero-crossings (smooth input-stream) last-value))

(assert (take 11 (make-zero-crossings-smoothed sense-data 0))
        '(0  0    0  0    0    -1   0   0   0     0    1))

(display "\nex-3.77\n")

;(display "\nex-3.78\n")
;(display "\nex-3.79\n")
;(display "\nex-3.80\n")
;(display "\nex-3.81\n")
;(display "\nex-3.82\n")