From 5dddcd897c1dc732ff2e747458bcb0e78fa9d038 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Fri, 8 Jan 2021 06:28:39 -0500
Subject: [PATCH] Implement till 3.76

---
 ex-3_73-82.scm | 86 ++++++++++++++++++++++++++++++++++++++++++++++++++
 util.scm       |  5 +++
 2 files changed, 91 insertions(+)
 create mode 100644 ex-3_73-82.scm

diff --git a/ex-3_73-82.scm b/ex-3_73-82.scm
new file mode 100644
index 0000000..b279a88
--- /dev/null
+++ b/ex-3_73-82.scm
@@ -0,0 +1,86 @@
+(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")
diff --git a/util.scm b/util.scm
index 8212b3d..fde5c12 100644
--- a/util.scm
+++ b/util.scm
@@ -109,6 +109,11 @@
 (define (add-streams s1 s2)
   (stream-map + s1 s2))
 
+(define (list->stream xs)
+  (if (null? xs)
+    '()
+    (cons-stream (car xs) (list->stream (cdr xs)))))
+
 (define ones (cons-stream 1 ones))
 
 (define integers (cons-stream 1 (add-streams ones integers)))