# SICP 1.3.3 Procedures as General MethodsをPythonでやってみた

（一般的なメソッドの手順）

#### Finding roots of equations by the half-interval method

（平均化した半分間隔メソッドのルートを探し出す）

scheme

```(define (average x y)
(/ (+ x y) 2))
(define (search f neg-point pos-point)
(let ((midpoint (average neg-point pos-point)))
(if (close-enough? neg-point pos-point)
midpoint
(let ((test-value (f midpoint)))
(cond ((test-value)
(search f neg-point midpoint))
((negative? test-value)
(search f midpoint pos-point))
(else midpoint))))))
(define (close-enough? x y)
(< (abs (- x y)) 0.001))
(define (half-interval-method f a b)
(let ((a-value (f a))
(b-value (f b)))
(cond ((and (negative? a-value) (positive? b-value))
(search f a b))
((and (negative? b-value) (positive? a-value))
(search f b a))
(else
(error "Values are not of opposite sign" a b)))))
(half-interval-method sin 2.0 4.0);3.14111328125
(half-interval-method (lambda (x) (- (* x x x) (* 2 x) 3))
1.0
2.0);1.89306640625
```

python

```from math import sin

def average(x, y):
return (x + y) / 2
def search(f, neg_point, pos_point):
midpoint = average(neg_point, pos_point)
if close_enough(neg_point, pos_point):
return midpoint
test_value = f(midpoint)
if test_value > 0:
return search(f, neg_point, midpoint)
elif test_value <= 0:
return search(f, midpoint, pos_point)
else:
midpoint
def close_enough(x, y):
return abs(x - y) < 0.001
def half_interval_method(f, a, b):
a_value = f(a)
b_value = f(b)
if a_value <= 0 and b_value > 0:
return search(f, a, b)
elif b_value <= 0 and a_value > 0:
return search(f, b, a)
else:
print "Values are not of opposite sign %d %d" %(a, b)
print half_interval_method(lambda x:sin(x), 2.0 ,4.0) #3.14111328125
print half_interval_method(lambda x:x*x*x - 2*x - 3, 1.0, 2.0) #1.89306640625
```

#### Finding fixed points of functions

（関数の一定の効果を求める）

scheme

```(define tolerance 0.00001)
(define (fixed-point f first-guess)
(define (close-enough? v1 v2)
(< (abs (- v1 v2)) tolerance))
(define (try guess)
(let ((next (f guess)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))
(fixed-point cos 1.0);0.7390822985224023
```

python

```from math import cos

def tolerance():
return 0.00001
def fixed_point(f, first_guess):
def close_enough(v1, v2):
return abs(v1 - v2) < tolerance()
def f_try(guess):
next = f(guess)
if close_enough(guess, next):
return next
return f_try(next)
return f_try(first_guess)
print fixed_point(lambda x:cos(x), 1.0) #0.7390822985224023
```