Implement till 3.78

ex-3_73-82.scm

@@ -77,10 +77,62 @@
 (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-3.77 - lazy-integral\n")
+
+(define (integral delayed-integrand initial-value dt)
+  (define int
+    (cons-stream initial-value
+                 (let ((integrand (force delayed-integrand)))
+                   (add-streams (scale-stream integrand dt)
+                                int))))
+  int)
+
+(define (solve f y0 dt)
+  (define y (integral (delay dy) y0 dt))
+  (define dy (stream-map f y))
+  y)
+
+(assert (stream-ref (solve (lambda (y) y) 1 0.001) 1000) 2.716923932235896)
+
+(define (integral delayed-integrand initial-value dt)
+  (cons-stream
+    initial-value
+    (let ((integrand (force delayed-integrand)))
+      (if (stream-null? integrand)
+        the-empty-stream
+        (integral (delay (stream-cdr integrand))
+                  (+ (* dt (stream-car integrand)) initial-value)
+                  dt)))))
+
+(assert (stream-ref (solve (lambda (y) y) 1 0.001) 1000) 2.716923932235896)
+
+(display "\nex-3.78 - solve-2nd\n")
+
+; The output stream, modeling y, is generated by a network that contains a loop.
+; This is because the value of d2y/dt2 depends upon the values of y and dy/dt and
+; both of these are determined by integrating d2y/dt2. The diagram we would like
+; to encode is shown in figure 3.35. Write a procedure solve-2nd that takes as
+; arguments the constants a, b, and dt and the initial values y0 and dy0 for y
+; and dy/dt and generates the stream of successive values of y.
+
+(define (solve-2nd a b dt y0 dy0)
+  (define y (integral (delay dy) y0 dt))
+  (define dy (integral (delay ddy) dy0 dt))
+  (define ddy (add-streams (scale-stream dy a)
+                           (scale-stream y b)))
+  y)
+
+(assert (stream-ref (solve-2nd 1 0 0.0001 1 1) 10000)
+        2.7181459268252266) ; e
+(assert (stream-ref (solve-2nd 0 -1 0.0001 1 0) 10472)
+        0.5000240628699462) ; cos pi/3 = 0.5
+(assert (stream-ref (solve-2nd 0 -1 0.0001 0 1) 5236)
+        0.5000141490501059) ; sin pi/6 = 0.5
+
+(display "\nex-3.79 - solve-2nd-general\n")
+
+(define (solve-2nd-general a b) '())
 
-;(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")