一些models
Continuous
Discrete
Deterministic
Stochastic
Static
Dynamic
How would you randomly generate an even number x, 0 <= x < 100?
Fill out the definition for the function genEven().
Please generate a uniform distribution over the even numbers between 0 and 100 (not including 100).
In [37]: def genEven():
...: x = random.randint(0, 98)
...: while x % 2 != 0:
...: x = random.randint(0, 98)
...: return x
L2 Problem 3A
Write a deterministic program, deterministicNumber, that returns an even number between 9 and 21.
In [61]: def deterministicNumber():
...: random.seed(0) # This will be discussed in the video "Drunken Simulations"
...: return 2 * random.randint(5, 10)
...:
L2 Problem 3B
Write a uniformly distributed stochastic program, stochasticNumber, that returns an even number between 9 and 21.
In [42]: def stochasticNumber():
...: return 2 * random.randint(5, 10)
...:
L2 Problem 7
In [65]: random.seed(9001)
...: for i in range(random.randint(1, 10)):
...: print (random.randint(1, 10))
...:
5
In [66]: random.seed(9001)
...: d = random.randint(1, 10)
...: for i in range(random.randint(1, 10)):
...: print (d)
...:
1
1
1
1
1
In [67]: random.seed(9001)
...: d = random.randint(1, 10)
...: for i in range(random.randint(1, 10)):
...: if random.randint(1, 10) < 7:
...: print (d)
...: else:
...: random.seed(9001)
...: d = random.randint(1, 10)
...: print (random.randint(1, 10))
...:
1
1
5
1
1
课本代码练习：其中有些内容书上有错误
In [76]: class Location(object):
...: def __init__(self, x, y):
...: """x和y为数值型"""
...: self.x, self.y = x, y
...: def move(self, deltaX, deltaY):
...: """deltaX和deltaY为数值型"""
...: return Location(self.x + deltaX, self.y + deltaY)
...: def getX(self):
...: return self.x
...: def getY(self):
...: return self.y
...: def distFrom(self, other):
...: ox, oy = other.x, other.y
...: xDist, yDist = self.x - ox, self.y - oy
...: return (xDist**2 + yDist**2)**0.5
...: def __str__(self):
...: return '<' + str(self.x) + ', ' + str(self.y) + '>'
...: class Field(object):
...: def __init__(self):
...: self.drunks = {}
...: def addDrunk(self, drunk, loc):
...: if drunk in self.drunks:
...: raise ValueError('Duplicate drunk')
...: else:
...: self.drunks[drunk] = loc
...: def moveDrunk(self, drunk):
...: if drunk not in self.drunks:
...: raise ValueError('Drunk not in field')
...: xDist, yDist = drunk.takeStep()
...: currentLocation = self.drunks[drunk]
...: #使用Location的move方法获得一个新位置
...: self.drunks[drunk] = currentLocation.move(xDist, yDist)
...: def getLoc(self, drunk):
...: if drunk not in self.drunks:
...: raise ValueError('Drunk not in field')
...: return self.drunks[drunk]
...:
...: import random
...: class Drunk(object):
...: def __init__(self, name = None):
...: """假设name是字符串"""
...: self.name = name
...: def __str__(self):
...: if self != None:
...: return self.name
...: return 'Anonymous'
...: class UsualDrunk(Drunk):
...: def takeStep(self):
...: stepChoices = [(0,1), (0,-1), (1, 0), (-1, 0)]
...: return random.choice(stepChoices)
...: return random.choice(stepChoices)
...:
In [68]: def walk(f, d, numSteps):
...: """假设f是一个Field对象,d是f中的一个Drunk对象,numSteps是正整数。
...: 将d移动numSteps次;返回这次游走最终位置与开始位置之间的距离"""
...: start = f.getLoc(d)
...: for s in range(numSteps):
...: f.moveDrunk(d)
...: return start.distFrom(f.getLoc(d))
...: def simWalks(numSteps, numTrials, dClass):
...: """假设numSteps是非负整数,numTrials是正整数,
...: dClass是Drunk的一个子类。
...: 模拟numTrials次游走,每次游走numSteps步。
...: 返回一个列表,表示每次模拟的最终距离"""
...: Homer = dClass()
...: origin = Location(0, 0)
...: distances = []
...: for t in range(numTrials):
...: f = Field()
...: f.addDrunk(Homer, origin)
...: distances.append(round(walk(f, Homer, numTrials), 1))
...: return distances
...: def drunkTest(walkLengths, numTrials, dClass):
...: """假设walkLengths是非负整数序列
...: numTrials是正整数,dClass是Drunk的一个子类
...: 对于walkLengths中的每个步数,运行numTrials次simWalks函数,并输出结果"""
...: for numSteps in walkLengths:
...: distances = simWalks(numSteps, numTrials, dClass)
...: print(dClass.__name__, 'random walk of', numSteps, 'steps')
...: print(' Mean =', round(sum(distances)/len(distances), 4))
...: print(' Max =', max(distances), 'Min =', min(distances))
...:
In [77]: drunkTest((10, 100, 1000, 10000), 100, UsualDrunk)
UsualDrunk random walk of 10 steps
Mean = 9.233
Max = 20.9 Min = 0.0
UsualDrunk random walk of 100 steps
Mean = 8.663
Max = 19.0 Min = 1.4
UsualDrunk random walk of 1000 steps
Mean = 9.06
Max = 23.0 Min = 0.0
UsualDrunk random walk of 10000 steps
Mean = 8.435
Max = 22.7 Min = 0.0
In [78]: drunkTest((0, 1), 100, UsualDrunk)
UsualDrunk random walk of 0 steps
Mean = 8.698
Max = 22.8 Min = 0.0
UsualDrunk random walk of 1 steps
Mean = 8.394
Max = 19.8 Min = 0.0
修正simWalks 中,函数调用 walk(f, Homer, numTrials) 应该是 walk(f, Homer,numSteps)
In [79]: def walk(f, d, numSteps):
...: """假设f是一个Field对象,d是f中的一个Drunk对象,numSteps是正整数。
...: 将d移动numSteps次;返回这次游走最终位置与开始位置之间的距离"""
...: start = f.getLoc(d)
...: for s in range(numSteps):
...: f.moveDrunk(d)
...: return start.distFrom(f.getLoc(d))
...: def simWalks(numSteps, numTrials, dClass):
...: """假设numSteps是非负整数,numTrials是正整数,
...: dClass是Drunk的一个子类。
...: 模拟numTrials次游走,每次游走numSteps步。
...: 返回一个列表,表示每次模拟的最终距离"""
...: Homer = dClass()
...: origin = Location(0, 0)
...: distances = []
...: for t in range(numTrials):
...: f = Field()
...: f.addDrunk(Homer, origin)
...: distances.append(round(walk(f, Homer, numSteps), 1))
...: return distances
...: def drunkTest(walkLengths, numTrials, dClass):
...: """假设walkLengths是非负整数序列
...: numTrials是正整数,dClass是Drunk的一个子类
...: 对于walkLengths中的每个步数,运行numTrials次simWalks函数,并输出结果"""
...: for numSteps in walkLengths:
...: distances = simWalks(numSteps, numTrials, dClass)
...: print(dClass.__name__, 'random walk of', numSteps, 'steps')
...: print(' Mean =', round(sum(distances)/len(distances), 4))
...: print(' Max =', max(distances), 'Min =', min(distances))
...:
In [80]: drunkTest((0, 1), 100, UsualDrunk)
UsualDrunk random walk of 0 steps
Mean = 0.0
Max = 0.0 Min = 0.0
UsualDrunk random walk of 1 steps
Mean = 1.0
Max = 1.0 Min = 1.0
In [81]: drunkTest((10, 100, 1000, 10000), 100, UsualDrunk)
UsualDrunk random walk of 10 steps
Mean = 2.612
Max = 7.2 Min = 0.0
UsualDrunk random walk of 100 steps
Mean = 9.057
Max = 25.5 Min = 0.0
UsualDrunk random walk of 1000 steps
Mean = 29.859
Max = 74.1 Min = 2.8
UsualDrunk random walk of 10000 steps
Mean = 95.894
Max = 297.1 Min = 15.8
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