Turning data into knowledge.

Simulation

Simulation models can be classified along three dimensions:

  • deterministic versus stochastic
    • Deterministic simulations are completely defined by the model. Rerunning a simulation will not change the outcome. Deterministic simulations are typically used when the system being modeled is too complex to analyze analytically.
    • Stochastic simulations include randomness. That means that different runs of the same simulation with the same initial conditions can generate different results.
  • static versus dynamic
  • discrete versus continuous
    • In a discrete model, the values of the pertinent variables are enumerable for example, the integers.
    • In a continuous model, they’re not enumerable.
class Location(object):
    def __init__(self, x, y):
        """x and y are floats"""
        self.x = x
        self.y = y
        
    def move(self, deltaX, deltaY):
        """deltaX and deltaY are floats"""
        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 = other.x
        oy = other.y
        xDist = self.x - ox
        yDist = 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 not drunk in self.drunks:
            raise ValueError('Drunk not in field')
        xDist, yDist = drunk.takeStep()
        currentLocation = self.drunks[drunk]
        #use move method of Location to get new location
        self.drunks[drunk] = currentLocation.move(xDist, yDist)
        
    def getLoc(self, drunk):
        if not drunk in self.drunks:
            raise ValueError('Drunk not in field')
        return self.drunks[drunk]

import random

class Drunk(object):
    def __init__(self, name):
        self.name = name
    def __str__(self):
        return 'This drunk is named ' + self.name

class UsualDrunk(Drunk):
    def takeStep(self):
        stepChoices =\
            [(0.0,1.0), (0.0,-1.0), (1.0, 0.0), (-1.0, 0.0)]
        return random.choice(stepChoices)

模拟醉汉的随机走向，建了3个class。UsualDrunk继承Drunk。

def walk(f, d, numSteps):
    """一个醉汉(d)在一个田里(f)走了几步(numSteps)"""
    start = f.getLoc(d) # get initial location
    for s in range(numSteps):
        f.moveDrunk(d)
    return(start.distFrom(f.getLoc(d)))

def simWalks(numSteps, numTrials):
    homer = UsualDrunk('Homer')
    origin = Location(0, 0)
    distances = []
    for t in range(numTrials):
        f = Field()
        f.addDrunk(homer, origin)
        distances.append(walk(f, homer, numSteps))
    return distances

def drunkTest(numTrials = 20):
    for numSteps in [10, 100, 1000, 10000]:
        distances = simWalks(numSteps, numTrials)
        print 'Random walk of ' + str(numSteps) + ' steps'
        print ' Mean =', sum(distances)/len(distances)
        print ' Max =', max(distances), 'Min =', min(distances)
        
drunkTest()

给出了3个function。

random.seed(0)可以帮助debug。

为了了解随着steps增加和distance之间的关系，我们可以用pylab把他们画出来。

def drunkTestP(numTrials = 50):
    stepsTaken = [10, 100, 1000, 10000]
    meanDistances = []
    for numSteps in stepsTaken:
        distances = simWalks(numSteps, numTrials)
        meanDistances.append(sum(distances)/len(distances))
    pylab.plot(stepsTaken, meanDistances)
    pylab.title('Mean Distance from Origin')
    pylab.xlabel('Steps Taken')
    pylab.ylabel('Steps from Origin')
    pylab.show()

还可以假定两种不同的走法，看距离是更远还是更近。

class ColdDrunk(Drunk):
    def takeStep(self):
        stepChoices =\
            [(0.0,0.95), (0.0,-1.0), (1.0, 0.0), (-1.0, 0.0)]
        return random.choice(stepChoices)

class EDrunk(Drunk):
    def takeStep(self):
        deltaX = random.random()
        if random.random() < 0.5:
            deltaX = -deltaX
        deltaY = random.random()
        if random.random() < 0.5:
            deltaY = -deltaY
        return (deltaX, deltaY)

Source code

Starting with abstract data types makes life easirer.

Subclassing is useful

Once basic structure in place, we can try different experiments