연습문제

아래 문제들을 해결하는 코드를 lab06.py 파일에 작성하여 제출하라.

연습 1

아래 코드를 실행하고 23.5입력하면 ValueError 오류가 발생한다.

======

n = int(raw_input("Please enter a number: "))

======

위 코드를 아래 조건들이 만족되도록 수정해라.

정수가 입력되지 않으면 제대로된 정수를 입력하라는 메시지를 보여주고 동일한 입력창이 다시 보이도록 한다.
정수가 입력되면 "정확히 입력되었다" 라는 확인 메시지를 보여주고 실행을 멈춘다.

견본 답안 1: `while` 문 활용



In [1]:

    
while True:
    try:
        n = int(raw_input("Please enter a number: "))
        print("정확히 입력되었습니다.")
        break
    except ValueError:
        print("정수를 입력하시오.")









    



Please enter a number: 76a
정수를 입력하시오.
Please enter a number: 234
정확히 입력되었습니다.

견본 단안 2: 재귀함수 활용

재귀함수에 대해서는 이후에 배울 예정임



In [2]:

    
# 아래 `inpint()` 함수는 재귀함수이다.

def inpint():
    try:
        n = int(raw_input("Please enter a number: "))
        print("정확히 입력되었습니다.")
    except ValueError as e:
        print("정수를 입력하시오.")
        inpint()
        
inpint()









    



Please enter a number: 87a
정수를 입력하시오.
Please enter a number: 765
정확히 입력되었습니다.

연습 2

아래 코드를 실행하면 왜 어떤 결과가 나오는지 설명하라.

try:
    x = float(raw_input("Your number: "))
    inverse = 1.0 / x
finally:
    print("There may or may not have been an exception.")
print("The inverse: ", inverse)

견본답안

0이 아닌 숫자를 입력하면 입력한 숫자의 역원를 보여준다.
숫자 0을 입력하면 ZeroDivisionError가 발생한다.
숫자가 아닌 문자열을 입력하면 IOError 오류가 발생한다.
어떤 경우든 "There may or may not have been an exception." 라는 문장이 보여진다.

연습 3

아래 코드를 실행하면 왜 어떤 결과가 나오는지 설명하라.

try:
    x = float(raw_input("Your number: "))
    inverse = 1.0 / x
except ValueError:
    print "You should have given either an int or a float"
except ZeroDivisionError:
    print "Infinity"
finally:
    print("There may or may not have been an exception.")

견본답안

숫자 0을 입력하면 Infinity 문자열이 보여지며 예외처리가 발생한다.
숫자가 아닌 문자열을 입력하면 "You should have given either an int or a float" 문장이 보여지며 예외처리 발생한다.
어떤 경우든 "There may or may not have been an exception." 라는 문장이 보여진다.

연습 4

아래 코드를 exception_test.py에 저장하라.

=========

import sys
file_name = sys.argv[1]
text = []
try:
    fh = open(file_name, 'r')
except IOError:
    print 'cannot open', file_name
else:
    text = fh.readlines()
    fh.close()

if text:
    print text[100]

==========

이제 터미널에서 아래 명령을 실행하면 왜 어떤 일이 발생할 수 있는지 설명하라.

python exception_test.py integers.txt

(주의: 위 명령은 exception_test.py 파일이 저장되어 있는 디렉토리에서 실행해야 한다.)

견본답안

integers.txt 파일이 해당 폴더에 존재하지 않으면 아래 문장이 보여지면 예외처리 된다.
```
  'cannot open', integers.txt
```
integers.txt 파일이 존재할 경우:
- 파일에 한 줄도 없으면, 즉 비어 있으면:
  - 아무 결과도 보여지지 않는다.
- 파일에 한 줄이 있지만 첫째줄에 100개 이하의 문자가 있다면:
  - IndexError 오류 발생
- 파일에 한 줄 이상 있고 첫째줄에 100개 이상의 문자가 있다면:
  - 첫째줄의 백번째 문자를 보여줌.

연습 5

아래 코드를 실행하면 AssertionError가 발생한다. 아래 코드를 raise 함수를 이용하여 동일한 결과가 나오도록 수정하라.

x = 5
y = 3
assert x < y, "x has to be smaller than y"

견본답안



In [3]:

    
x=5
y=3
if(not(x<y)):
    raise AssertionError ('x has to be smaller than y')









    



---------------------------------------------------------------------------
AssertionError                            Traceback (most recent call last)
<ipython-input-3-88b248158f56> in <module>()
      2 y=3
      3 if(not(x<y)):
----> 4     raise AssertionError ('x has to be smaller than y')

AssertionError: x has to be smaller than y

연습 6

함수 f가 아래와 같이 정의되었다.

f(x) = sin(x) - 0.5 * x + 30

f(x) = x를 만족시키는 x를 함수 f의 고정점(fixed-point)이라 한다.

함수 f의 부동점을 구하기 위해서 f(x) 반복적으로 업데이트 하는 고정점반복 기술을 아래와 같이 적용한다:

x = sin(x) - a*x + 30

위 아래 코드가 고정점반복 기술을 적용하고 있다.

x = 0.5
a = 0.5
for i in range(200):
    x = sin(x) - a * x + 30   #(*)
print("The result after %s iteration is %s" % (i, x))

위 코드를 다음 조건이 만족되도록 수정하라.

아래의 절대값 조건이 만족될 때까지 고정점 계산 (*)이 반복되어야 한다.
```
  abs(f(x) - x) < 1e-8  
```
고정점 반복 계산이 200번 실행되었어도 앞서 언급된 절대값 조건이 만족되지 않으면 그 조건이 만족되지 않았다는 메시지를 보여주면서 에러가 발생하도록 해야 한다.



In [4]:

    
from math import sin

x = 0.5
a = 0.5
for i in range(200):
    y = sin(x) - a * x + 30
    if(abs(y - x) < 1e-8):
        print("The result after %s iteration is %s" % (i, x))
        break
    else:
        x = y
    
if(i == 199):
    raise ReferenceError("unsatisfied")









    



The result after 59 iteration is 20.6492743683

참고: 그래프 그리기

아래 등식

x = sin(x) - 0.5 * x + 30

를 만족시키는 x가 과연 존재하는지, 존재한다면 얼마정도인지를 먼저 확인할 필요가 있다. 그러기 위해서는 아래 함수의 그래프를 그려보아야 한다.

g(x) = sin(x) - 1.5 * x + 30

그래프를 그리는 방법은 나중에 배울 예정이지만, 아래와 같이 실행하면 된다.



In [5]:

    
%matplotlib inline

import matplotlib.pyplot as plt
import numpy as np

plt.axhline(y=0, color = 'r') # draw y =0 axes

x = np.arange(0, 10 * np.pi, 0.01) 
y = np.sin(x) - 1.5 * x +30
plt.plot(x, y) 
plt.show()

따라서 f(x) = sin(x) - 0.5 * x + 30의 고정점은 x = 20 근처에 존재함을 알 수 있다.

연습 7

다음과 같이 수열이 정의되어 있다.

x(n) = (sin(1/n))**2 / n

x(n) 값은 n이 증가함에 따라 0으로 수렴한다. x(n) >= 1e-9 조건을 만족하는 모든 x(n)들의 리스트를 구하는 코드를 작성하라.



In [6]:

    
n = 1
l = []

def x(n):
    return ((sin(1.0/n))**2) / n

while(x(n) >= 1e-9):
    l.append(x(n))
    n = n + 1

print("구해지는 리스트의 길이는 {}이다.\n".format(len(l)))
print(l)









    



구해지는 리스트의 길이는 999이다.

[0.7080734182735712, 0.11492442353296507, 0.03568545653717533, 0.015302179763703412, 0.007893900599711491, 0.004586921140438527, 0.00289567277772019, 0.0019429736430847011, 0.0013661063672529153, 0.0009966711079379186, 0.0007492473425149478, 0.0005773653515447893, 0.0004542690800538189, 0.00036381212690660413, 0.00029585759886068815, 0.0002438228990834671, 0.00020330696712110295, 0.00017129142947522438, 0.00014565927685327378, 0.00012489586804935584, 0.00010789810717986602, 9.384968862357277e-05, 8.213775286234534e-05, 7.229611040501128e-05, 6.39658739476123e-05, 5.686771737599582e-05, 5.0782037100596544e-05, 4.553457098365615e-05, 4.0985842358676154e-05, 3.7023321647961474e-05, 3.355554319132099e-05, 3.050764531095079e-05, 2.781795771096899e-05, 2.5435367459342786e-05, 2.331726928914343e-05, 2.1427958350770015e-05, 1.973736080751594e-05, 1.8220024439701387e-05, 1.6854310847202272e-05, 1.562174506292192e-05, 1.4506488893976699e-05, 1.3494912128924682e-05, 1.257524161862428e-05, 1.1737272675019899e-05, 1.0972130609432933e-05, 1.0272072819873938e-05, 9.630323832538146e-06, 9.040937250852358e-06, 8.498679773451308e-06, 7.998933390220597e-06, 7.53761261303638e-06, 7.111094190349848e-06, 6.716157226707423e-06, 6.349932005944494e-06, 6.009856120326998e-06, 5.693636752927581e-06, 5.3992181591085695e-06, 5.124753554576237e-06, 4.868580749462157e-06, 4.6292009760958086e-06, 4.405260447157296e-06, 4.195534254391269e-06, 3.998912278932841e-06, 3.8143868348721154e-06, 3.6410418098361214e-06, 3.47804310160302e-06, 3.3246301793032677e-06, 3.180108622595751e-06, 3.0438435131402434e-06, 2.9152535703795023e-06, 2.7938059386348685e-06, 2.679011545252142e-06, 2.5704209603757106e-06, 2.467620698180839e-06, 2.3702299073075843e-06, 2.2778974050233472e-06, 2.1902990154684464e-06, 2.107135177355425e-06, 2.0281287908197197e-06, 1.9530232768588363e-06, 1.8815808260353137e-06, 1.8135808159279113e-06, 1.7488183792568472e-06, 1.6871031067345764e-06, 1.6282578705473773e-06, 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4.658243319423484e-07, 4.551571580745262e-07, 4.4481321097029315e-07, 4.34780340181013e-07, 4.250469392597759e-07, 4.15601917556728e-07, 4.064346736733118e-07, 3.9753507046645496e-07, 3.888934115016351e-07, 3.8050041886101834e-07, 3.7234721221957224e-07, 3.6442528910822556e-07, 3.5672650628885054e-07, 3.4924306217109797e-07, 3.419674802059784e-07, 3.348925931955705e-07, 3.280115284623877e-07, 3.213176938257772e-07, 3.1480476433628146e-07, 3.084666697221816e-07, 3.0229758250549763e-07, 2.9629190674754866e-07, 2.904442673867977e-07, 2.8474950013414804e-07, 2.7920264189311187e-07, 2.737989216743803e-07, 2.6853375197627444e-07, 2.634027206043707e-07, 2.584015829052903e-07, 2.535262543912081e-07, 2.487728037331076e-07, 2.441374461021688e-07, 2.396165368399513e-07, 2.352065654392192e-07, 2.3090414981836157e-07, 2.2670603087339618e-07, 2.2260906729250749e-07, 2.1861023061897246e-07, 2.147066005491669e-07, 2.1089536045313623e-07, 2.071737931059483e-07, 2.0353927661873367e-07, 1.9998928055896828e-07, 1.965213622501516e-07, 1.931331632416039e-07, 1.8982240593963242e-07, 1.8658689039181738e-07, 1.834244912166303e-07, 1.8033315467103944e-07, 1.7731089584916216e-07, 1.7435579600541506e-07, 1.714659999959695e-07, 1.686397138326645e-07, 1.6587520234384534e-07, 1.631707869368987e-07, 1.6052484345753793e-07, 1.5793580014115556e-07, 1.554021356518141e-07, 1.5292237720467917e-07, 1.5049509876792162e-07, 1.481189193403247e-07, 1.457925013010296e-07, 1.4351454882803739e-07, 1.4128380638226183e-07, 1.390990572540926e-07, 1.3695912216958242e-07, 1.3486285795352258e-07, 1.3280915624680612e-07, 1.3079694227561264e-07, 1.2882517367007e-07, 1.268928393301678e-07, 1.2499895833680553e-07, 1.2314257890596644e-07, 1.213227773841029e-07, 1.195386572829177e-07, 1.1778934835180974e-07, 1.1607400568634008e-07, 1.1439180887115109e-07, 1.1274196115584974e-07, 1.1112368866243344e-07, 1.0953623962290834e-07, 1.0797888364581211e-07, 1.0645091101041283e-07, 1.0495163198741686e-07, 1.0348037618506881e-07, 1.0203649191958183e-07, 1.0061934560888456e-07, 9.922832118871696e-08, 9.786281955015343e-08, 9.652225799767174e-08, 9.520606972692784e-08, 9.391370332143416e-08, 9.264462226737455e-08, 9.139830448582448e-08, 9.01742418816769e-08, 8.897193990860567e-08, 8.779091714942785e-08, 8.66307049112545e-08, 8.54908468348461e-08, 8.437089851761427e-08, 8.327042714973638e-08, 8.218901116287125e-08, 8.112623989098799e-08, 8.00817132428397e-08, 7.905504138563411e-08, 7.804584443947279e-08, 7.705375218214742e-08, 7.607840376390108e-08, 7.511944743177644e-08, 7.417654026319089e-08, 7.32493479083918e-08, 7.233754434146115e-08, 7.144081161955063e-08, 7.055883965004338e-08, 6.969132596534894e-08, 6.883797550505218e-08, 6.799850040514621e-08, 6.717261979409149e-08, 6.636005959545377e-08, 6.556055233688245e-08, 6.477383696520178e-08, 6.399965866739486e-08, 6.3237768697271e-08, 6.248792420761366e-08, 6.174988808761472e-08, 6.102342880540883e-08, 6.030832025552834e-08, 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연습문제

연습 1

견본 답안 1: while 문 활용

견본 단안 2: 재귀함수 활용

연습 2

견본답안

연습 3

견본답안

연습 4

견본답안

연습 5

견본답안

연습 6

참고: 그래프 그리기

연습 7

견본 답안 1: `while` 문 활용