drvinceknight

\documentclass[11pt]{article}

\usepackage{url}
\usepackage{tikz}
\usepackage{calc}

\reversemarginpar

\usepackage[paper=letterpaper,
           marginparwidth=1in,

drvinceknight

from __future__ import division
import matplotlib.pyplot as plt

def dictplot(D, f, title):
    plt.figure()
    values = [v / sum(list(D.values())) for v in list(D.values())]
    plt.bar(range(len(D)), values, align='center')
    plt.xticks(range(len(D)), D.keys())
    plt.ylabel('Probability')
    plt.title(title)

drvinceknight

# LaTeX Files
*.aux
*.glo
*.idx
*.log
*.toc
*.ist
*.acn
*.acr
*.alg

drvinceknight

"""
Sage script for  example in blog post.
"""
class Tandem_Queue():
    """
    A class for an instance of the tandem_queue
    """
    def __init__(self, c_1, N, c_2, Lambda, mu_1, mu_2, p):
        self.c_1 = c_1
        self.c_2 = c_2

drvinceknight

def Pure_Nash_Check(A,B,i,j):
    if i==0:
        if j==0:
            if A[0,0]<A[1,0] or B[0,0]<B[0,1]:
                return False
        if j==1:
            if A[0,1]<A[1,1] or B[0,1]<B[0,0]:
                return False
    if i==1: 
        if j==0:

drvinceknight

@interact
def _(A=matrix(RDF,3,3,[8,2,0,1,7,2,1,3,6])/10,x_init=("$\pi^{(0)}$",vector([.2,.5,.3]))):
    x_init = vector(x_init)
    data = [x_init * (A^i) for i in range(20)]
    pi = zip(*data)
    p = line(enumerate(pi[0]),color='red',legend_label='$\pi_1$',thickness=3)
    p += line(enumerate(pi[1]),color='blue',legend_label='$\pi_2$',thickness=3)
    p += line(enumerate(pi[2]),color='green',legend_label='$\pi_3$',thickness=3)
    p.ymax(1)
    show(p)

drvinceknight

@interact
def _(A=matrix(RDF,[[1,3,1],[5,-2,2],[3,3,4]]),n=("$n$",slider(0,100,1)),Precision=slider(0,10,1,4)):
    exp_A=exp(A)
    approx_exp=sum([A^i/factorial(i) for i in range(n+1)]).n(digits=Precision)
    p=list_plot([(sum([A^i/factorial(i) for i in range(n+1)])-exp(A)).norm(2) for n in range(0,21)])
    p.axes_labels(['$n$','$|| e^{A}-\sum_{i=0}^{n}A^{i}/{i!}||_2$'])
    print "\n"
    print "Value of approximation for n=%s: \n%s" % (n, approx_exp)
    print "\n"
    print "Exact value: \n%s" % exp(A)

drvinceknight

for i in range(10):
    print i

drvinceknight

# Shortest possible simulation of an MM1 Q (with warmup). Contributors: Geraint, Jason, Vince, Harald and Chris.
from random import expovariate
lmbda, mu, T, warmup, waits, sample, arrival_time, start_time, end_time = 1, 2, 5000, 1000, [], lambda x: expovariate(x), 0, 0, 0
while end_time < T:
    arrival_time += sample(lmbda)
    start_time = max(end_time, arrival_time)
    end_time = start_time + sample(mu)
    if arrival_time > warmup: waits.append(start_time - arrival_time)
print 'Mean wait: ' + str(sum(waits) / len(waits))

drvinceknight

"""
Going to simulate 100 '1st two days of xmas'
"""
from __future__ import division
import random
partidges = []
turtle_doves= []

for xmas in range(100):
    partidges.append(random.choice([0,1,1,1,2]))