C200留学生代做、Computer Science代写、代做Python程序、Python语言代写

日期：2019-04-11 10:52

C200 Programming Assignment № 10

Computer Science

School of Informatics, Computing, and Engineering

Indiana University, Bloomington, IN, USA

April 5, 2019

Contents

Introduction 1

Problem 1: Random Walk 3

Starting Code for Problem One . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Using 100000 Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Random Output for Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Deliverables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Problem 2: Making Maps 7

Starting Code for Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Deliverables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Problem 3: It’s Not Real Butter 8

Geometry of Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Starting Code to Problem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Output to Problem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Deliverables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Assignment №10 Maps and Matrices and Correlation Page 1

Introduction

In this homework, you’ll work on translating critical thinking to programming. This homework is

a bit less intense than the last one to give you a little breather! :)

Add a new folder to your C200 folder named Assignment10. In this folder, you will have:

– randomwalk.py

– mymap.py and hellobloomington.html

– complex.py

Make sure and commit your project and modules by 11pm, April 10th 2019.

As always, all the work should be your own. You will submit your work by committing your code

to your GitHub repository. You will not turn anything in on canvas. If your timestamp is 11:01P

or greater, the homework cannot be graded. So do not wait until 10:58P to commit your code.

Assignment №10 Maps and Matrices and Correlation Page 2

Problem 1: Random Walk

A random walk is a stochastic process. A stochastic process is a series of values that are

not determined functionally, but probabilistically. The random walk is supposed to describe an

inebriated person who, starting from the bar, intends to walk home, but because of intoxication

instead randomly takes single steps either forward or backward, left or right. The person has

no memory of any steps taken, so theoretically, the person shouldn’t move too far from where

he or she starts. Random walks are used to model many phenomena, like the size of the web

or changes in financial instruments. We will model a 2D random walk with two arrays x and y

where x represents moving left or right and y represents forward or backward. The index i will

represent the step and x[i],y[i] will represent the location at step i. So, for i=0, we have x[0],y[0]

(starting place). Using random we choose from the list [1,2,3,4]. If the value is one then we

move right from the previous x position:

1 x[i] = x[i-1] + 1

2 y[i] = y[i-1]

If the value is two, then we move left from the previous x position:

1 x[i] = x[i-1] - 1

2 y[i] = y[i-1]

If the value is three, we move up from the previous y position:

1 x[i] = x[i-1]

2 y[i] = y[i-1] + 1

And when the value is four, we move down from the previous y position:

1 x[i] = x[i-1]

2 y[i] = y[i-1] - 1

Here is another way to describe this:

step(0) = 0 (1)

left step(n  1)

right step(n 1)

up step(n 1)

down step(n 1)

(2)

Assignment №10 Maps and Matrices and Correlation Page 3

Figure 1: The first few steps of a random walk.

1 import numpy as np

2 import matplotlib.pyplot as plt

3 import random as rn

4

5

6 #translates a random int into a step along the random walk

7 #parameters: int i for the step index, numpy array x for tracking the left←-

/right location at index i,

8 #numpy array y for tracking the forward/backward location at index i

9 #return: none

10 def step(x,y,i):

11 direction = rn.randint(1,4)

12 #TO DO: implement this function

13

14

15 def graphit(x,y,n):

16 plt.title("Random {0} Walk\nLast Location {1},{2}".format(n,int(x[n←-

-1]),int(y[n-1])) )

17 plt.plot(x,y)

18 plt.plot([x[1],x[1]],[y[1]-10,y[1]+10], "b-")

19 plt.plot([x[1]-10,x[1]+10],[y[1],y[1]], "b-")

Assignment №10 Maps and Matrices and Correlation Page 4

20 plt.plot([x[n-1]-10,x[n-1]+10],[y[n-1],y[n-1]], "r-")

21 plt.plot([x[n-1],x[n-1]],[y[n-1]-10,y[n-1]+10], "r-")

22 plt.savefig("rand_walk"+str(n)+".png",bbox_inches="tight",dpi=600)

23 plt.show()

24

25

26 n = int(input("Number of steps: "))

27

28 x = np.zeros(n)

29 y = np.zeros(n)

30

31 for i in range(1,n):

32 step(x,y,i)

33

34 graphit(x,y,n)

Session Output

Number of Steps: 100000

Figure 2: The blue cross is where we started and the red cross is where we ended.

Assignment №10 Maps and Matrices and Correlation Page 5

Programming Problem 1: Random Walk

Complete the step function.

Experiment with different numbers of steps. Do you see any number of steps that

seems to always move significantly away from the start?

Put your code into a new module named randomwalk.py

Assignment №10 Maps and Matrices and Correlation Page 6

Problem 2: Maps

In this problem, you’ll use gmplot to make a map with markers for points of interest. The following

code centers the map at Showalter fountain (approximately). It then places two markers down,

one at Lindley Hall and one at Luddy Hall.

mymap.py

1 import gmplot

2

3 #create map Showalter Location

4 gmap = gmplot.GoogleMapPlotter(39.168451, -86.51891,15)

5

6 #Lindley Hall where we have C200

7 l1 = (39.165341,-86.523588)

8 #Luddy Hall the new SICE building

9 l2 = (39.172725,-86.523295)

10

11 #Indiana University -- Musical Arts Center

12

13

14 #list of points

15 lats = [l1[0],l2[0]]

16 lons = [l1[1],l2[1]]

17

18 #add points to map

19 gmap.scatter(lats, lons, ’red’, size=30, marker=False)

20 #add line

21 gmap.plot(lats,lons,’cornflowerblue’, size=30, marker=False)

22 #save to map

23 gmap.draw("Assignment10/hellobloomington.html")

Change

Install gmplot with pip.

Using the internet’s awesome power, find the longitude and latitude of IU’s Musical

Arts Center (where concerts are performed). Add the location to the code similar to

Lindley Hall and Luddy Hall and then add that point to the list of points and plot it.

Save the file into hellobloomington.html.

Put your code in a new module named mymap.py

Assignment №10 Maps and Matrices and Correlation Page 7

Problem 3: Imaginary Numbers

In class we discussed how complex numbers are a pair of real numbers, a, b ∈ R and i is the

solution to i

2 = 1. We called a the real part and b the imaginary part. We found that Python has

a complex class too, but engineers chose j for i. In this problem, we’re extending our complex

number class to include a few more operations. Subtraction is straightforward. Division is a little

strange, and we’ll just provide the solution:

Modulus is a property of a complex number that describes its magnitude, i.e., how large it

is. We write modulus of a complex number a + bi as |a + bi|. The formula is simple:

|a + bi| =2 + b2 (7)

Look at Figure 3. The abscissa is the real part of the complex number, and the ordinate axis is

the imaginary part. By changing the sign of the imaginary part, we’re reflecting as shown in the

figure’s dotted line. In fact, we can calculate both ρ and θ directly from a + bi:

(9)

As an example, x = 1 + i. Let’s find the polar representation (ρ, θ).

are in radians (so is Python by default). To convert to degrees we multiply by 180

πor simply

use a conversion function. You’ll see this in the interactive Sessions I, II. Observe that a call to

the the abs( ) function returns the modulus and also that we can get the polar representation by

using cmath.

Assignment №10 Maps and Matrices and Correlation Page 8

Figure 3: Complex Numbers as geometry. If we treat θ as time, any point on the line occurs at

the same time or what engineers call phase.

Session I with Complex Numbers

>>> x1 = complex(3,-1)

>>> x2 = complex(1,4)

>>> x1 + x2

(4+3j)

>>> x1*x2

(7+11j)

>>> x3 = complex(-3,1)

>>> x4 = complex(2,-4)

>>> x3+x4

(-1-3j)

>>> x3*x4

(-2+14j)

>>> x5 = complex(-2,1)

>>> x6 = complex(1,2)

>>> x5/x6

1j

>>> x7 = complex(0,3)

>>> x8 = complex(-1,-1)

>>> x7/x8

(-1.5-1.5j)

Assignment №10 Maps and Matrices and Correlation Page 9

Session II with Complex Numbers

>>> x9 = complex(1,-1)

>>> abs(x9)

1.4142135623730951

>>> x10 = complex(4,-3)

>>> abs(x10)

5.0

>>> x11 = complex(3,2)

>>> x11*x11.conjugate()

(13+0j)

>>> x12 = complex(1,1)

>>> import cmath

>>> cmath.polar(x12)

(1.4142135623730951, 0.7853981633974483)

>>> import math

>>> math.degrees(cmath.polar(x12)[1])

45.0

My Complex Numbers

1 import math

2

3 class MyComplexNumber:

4 def __init__(self, rpart, ipart):

5 self.rpart = rpart

6 self.ipart = ipart

7 self.cn = [self.rpart, self.ipart]

8

9 def get_real(self):

10 return self.rpart

11

12 def get_imag(self):

13 return self.ipart

14

15 def __str__(self):

16 return str(self.cn)

17

18 #adds two complex numbers

19 def add(self, ix):

20 real_part = self.get_real() + ix.get_real()

21 imag_part = self.get_imag() + ix.get_imag()

22 iy = MyComplexNumber(real_part, imag_part)

23 return iy

24

Assignment №10 Maps and Matrices and Correlation Page 10

25 #extends the ’+’ operator to add two complex numbers

26 #what’s the different between __add__(self,ix) and add(self,ix)?

27 def __add__(self,ix):

28 real_part = self.get_real() + ix.get_real()

29 imag_part = self.get_imag() + ix.get_imag()

30 iy = MyComplexNumber(real_part, imag_part)

31 return iy

32

33 #extends the ’-’ operator to subtract two complex numbers

34 #parameters: MyComplexNumber self, MyComplexNumber ix to subtract from←-

the MyComplexNumber self

35 #return: a new MyComplexNumber containing the result

36 def __sub__(self,ix):

37 #TO DO: implement this function

38

39 #extends the ’/’ operator to divide two complex numbers

40 #parameters: MyComplexNumber self, MyComplexNumber ix to divide into ←-

the MyComplexNumber self

41 #return: a new MyComplexNumber containing the result

42 def __truediv__(self,other):

43 #TO DO: implement this function

44

45 def __mul__(self,other):

46 real_part = self.get_real()*other.get_real() - self.get_imag()*←-

other.get_imag()

47 imag_part = self.get_real()*other.get_imag() + self.get_imag()*←-

other.get_real()

48 iy = MyComplexNumber(real_part, imag_part)

49 return iy

50

51 #calculates the modulus of the self MyComplexNumber

52 #parameters: MyComplexNumber self

53 #return: the value of the modulus

54 def modulus(self):

55 #TO DO: implement this function

56

57 #converts the self MyComplexNumber to polar representation

58 #parameters: MyComplexNumber self

59 #return: a tuple (rho, theta) as defined in the text, but where theta ←-

is in degrees not radians

60 def polar(self):

61 #TO DO: implement this function

62

63

64 #TEST CASES

65 x1 = MyComplexNumber(3,-1) #3-i

66 x2 = MyComplexNumber(1,4) #1+4i

Assignment №10 Maps and Matrices and Correlation Page 11

67 x3 = MyComplexNumber(-3,1) #-3+i

68 x4 = MyComplexNumber(2,-4) #2-4i

69 x5 = MyComplexNumber(-2,1)

70 x6 = MyComplexNumber(1,2)

71 x7 = MyComplexNumber(0,3)

72 x8 = MyComplexNumber(-1,-1)

73 x9 = MyComplexNumber(1,-1)

74 x10 = MyComplexNumber(4,-3)

75 x11 = MyComplexNumber(3,2)

76 x12 = MyComplexNumber(1,1)

77

78

79 print(x1 + x2)

80 print(x1 * x2)

81 print(x3 + x4)

82 print(x3 * x4)

83 print()

84 print(x5/x6)

85 print(x7/x8)

86 print(x9.modulus())

87 print(x10.modulus())

88 print()

89 print(x12.polar())

Session Output

[4, 3]

[7, 11]

[-1, -3]

[-2, 14]

[0.0, 1.0]

[-1.5, -1.5]

1.4142135623730951

5.0

(1.4142135623730951, 45.0)

Assignment №10 Maps and Matrices and Correlation Page 12

Deliverable for Problem 3: Complex Numbers

Complete Sessions I and II. The output of the sessions are the same output as your

class!

The file complex.py has the starting code for this problem.

Complete the TO DO’s to finish the implementation of the MyComplexNumber class.

assignment №10 Maps and Matrices and Correlation Page 13