def DecayTest(): X = [1.5,2,3,4,5,12] prior = MakeUniformSuite(0.001,1.5,1000) posterior = EstimateParameter(prior,X) myplot.Clf() myplot.Pmf(posterior) myplot.show()
def main():
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
# plot the distribution of actual speeds
pmf = Pmf.MakePmfFromList(speeds, 'actual speeds')
# myplot.Clf()
# myplot.Hist(pmf)
# myplot.Save(root='observed_speeds',
# title='PMF of running speed',
# xlabel='speed (mph)',
# ylabel='probability')
# plot the biased distribution seen by the observer
biased = BiasPmf(pmf, 7.5, name='observed speeds')
myplot.Clf()
myplot.Hist(biased)
myplot.Save(root='observed_speeds',
title='PMF of running speed',
xlabel='speed (mph)',
ylabel='probability')
cdf = Cdf.MakeCdfFromPmf(biased)
myplot.Clf()
myplot.Cdf(cdf)
myplot.show(root='observed_speeds_cdf',
title='CDF of running speed',
xlabel='speed (mph)',
ylabel='cumulative probability')
def EstimateTest(): evidence = [2.675, 0.198, 1.152, 0.787, 2.717, 4.269] prior = MakeUniformSuite(0.5,1.5,1000) posterior = EstimateParameter(prior,evidence) myplot.Clf() myplot.Pmf(posterior) myplot.show()
def main():
# Exercise 5.6
sample_size=365
for n in range(1,6):
distribution = []
for _ in range(sample_size):
distribution.append(get_bread(n))
print(np.mean(distribution), np.std(distribution))
found_distribution = []
for _ in range(sample_size):
found_distribution.append(int(get_bread(4)))
print('picking 4 loaves: mu={} sigma={}'.format(np.mean(found_distribution),np.std(found_distribution)))
expected_distribution = np.random.normal(np.mean(found_distribution), np.std(found_distribution), sample_size)
myplot.Cdfs(cdfs=(Cdf.MakeCdfFromList(found_distribution), Cdf.MakeCdfFromList(expected_distribution)))
myplot.show()
plt.hist(found_distribution, normed=True, bins=20, label='found')
plt.hist(expected_distribution, normed=True, bins=20, alpha=.75, label='expected')
plt.ylabel('Probability')
plt.xlabel('Bread Weight')
plt.legend()
plt.show()
# Exercise 5.7
men_heights = np.random.normal(loc=178, scale=59.4, size=99999)
women_heights = np.random.normal(loc=163, scale=52.8, size=99999)
pairs = zip(men_heights, women_heights)
l = [w>m for m, w in pairs]
print('In {}% of the pairs the woman will be taller than the man'.format(sum(l)/len(l)*100.0))
def HenriPoincare(): ave = 950 sigma = 50 weights = [] days= 360 n = 4 for i in range(days): p = 0.0 for j in range(n): temp = random.random() if p<temp: p = temp weights.append(erf.NormalCdfInverse(p,mu=ave,sigma = sigma)) mu, var = thinkstats.MeanVar(weights) print mu,math.sqrt(var) normal = [] for i in range(1000): normal.append(erf.NormalCdfInverse(random.random(),mu = mu,sigma = math.sqrt(var))) # histReal = Pmf.MakeHistFromList(weights,'real') # histStand = Pmf.MakeHistFromList(normal,'stand') # pmfReal = Pmf.MakePmfFromList(weights,"real") # pmfStand = Pmf.MakePmfFromList(normal,'stand') cdfReal = Cdf.MakeCdfFromList(weights) cdfStand = Cdf.MakeCdfFromList(normal) myplot.Clf() # myplot.Hists([histReal,histStand]) myplot.Cdfs([cdfReal,cdfStand]) # myplot.Pmfs([pmfReal,pmfStand]) myplot.show()
def main():
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
# plot the distribution of actual speeds
pmf = Pmf.MakePmfFromList(speeds, 'actual speeds')
# myplot.Clf()
# myplot.Hist(pmf)
# myplot.Save(root='observed_speeds',
# title='PMF of running speed',
# xlabel='speed (mph)',
# ylabel='probability')
# plot the biased distribution seen by the observer
biased = BiasPmf(pmf, 7.5, name='observed speeds')
myplot.Clf()
myplot.Hist(biased)
myplot.Save(root='observed_speeds',
title='PMF of running speed',
xlabel='speed (mph)',
ylabel='probability')
cdf = Cdf.MakeCdfFromPmf(biased)
myplot.Clf()
myplot.Cdf(cdf)
myplot.show(root='observed_speeds_cdf',
title='CDF of running speed',
xlabel='speed (mph)',
ylabel='cumulative probability')
def NormalPlot(ys): n = len(ys) xs = [random.normalvariate(0,1) for i in range(n)] ys.sort() xs.sort() myplot.Clf() myplot.Plot(xs,ys) myplot.show()
def ResambleBirth(): pool,first,other = descriptive.MakeTables() allCdf = Cdf.MakeCdfFromPmf(pool.pmf) randomCdf = Cdf.MakeCdfFromList(Sample(allCdf,1000)) randomCdf.name = 'random birth' myplot.Clf() myplot.Cdfs([allCdf,randomCdf]) myplot.show()
def BirthDate(): pool,first,other = descriptive.MakeTables() pmf = pool.pmf print 'mean',pmf.Mean() print 'var',pmf.Var() cdf = Cdf.MakeCdfFromPmf(pmf) myplot.Clf() myplot.Cdf(cdf) myplot.show()
def main():
#Exercise 3.5
results = relay.ReadResults()
speeds = relay.GetSpeeds(results)
speedsCdf = Cdf.MakeCdfFromList(speeds, "race speeds")
mplt.Cdf(speedsCdf)
mplt.show(title="Race Speed CDF",
xlabel="speed in mph",
ylabel="probability")
def ParetovariateTest(): results = [] a=1 xm=0.5 for i in range(1000): results.append(random.paretovariate(a)*xm) cdf = Cdf.MakeCdfFromList(results) myplot.Clf() myplot.Cdf(cdf,complement=True,xscale = 'log',yscale = 'log') myplot.show()
def expovariateTest(): results = [] lamada = 1.0/32.6 for i in range(44): results.append(random.expovariate(lamada)) cdf = Cdf.MakeCdfFromList(results) myplot.Clf() myplot.Cdf(cdf,complement=True,xscale = 'linear',yscale = 'log') myplot.show()
def main():
data_dir = '../chap1/'
preg = survey.Pregnancies()
preg.ReadRecords(data_dir)
cdf = weight_cdf(preg)
myplot.Cdf(cdf)
myplot.show()
sample = Sample(cdf, 1000)
cdf_sample = Cdf.MakeCdfFromList(sample)
myplot.Cdf(cdf_sample)
myplot.Show()
def main():
data_dir = '../chap1/'
preg = survey.Pregnancies()
preg.ReadRecords(data_dir)
cdf = weight_cdf(preg)
myplot.Cdf(cdf)
myplot.show()
sample = Sample(cdf, 1000)
cdf_sample = Cdf.MakeCdfFromList(sample)
myplot.Cdf(cdf_sample)
myplot.Show()
def main():
pareto = paretovariate(1, 0.5)
cdf = Cdf.MakeCdfFromList(pareto)
myplot.Cdf(cdf)
myplot.show()
ccdf = ccdf_list(cdf)
plt = myplot.pyplot
plt.plot(cdf.Values(), ccdf)
plt.xscale('log')
plt.yscale('log')
plt.show()
def main():
pareto = paretovariate(1,0.5)
cdf = Cdf.MakeCdfFromList(pareto)
myplot.Cdf(cdf)
myplot.show()
ccdf = ccdf_list(cdf)
plt = myplot.pyplot
plt.plot(cdf.Values(), ccdf)
plt.xscale('log')
plt.yscale('log')
plt.show()
def main():
"""when k=1 weibull would be liner"""
weibull = weibullvariate(1,1)
cdf = Cdf.MakeCdfFromList(weibull)
myplot.Cdf(cdf)
myplot.show()
ccdf = ccdf_list(cdf)
plt = myplot.pyplot
plt.plot(cdf.Values(), ccdf)
#plt.xscale('log')
plt.yscale('log')
plt.show()
def main():
"""when k=1 weibull would be liner"""
weibull = weibullvariate(1, 1)
cdf = Cdf.MakeCdfFromList(weibull)
myplot.Cdf(cdf)
myplot.show()
ccdf = ccdf_list(cdf)
plt = myplot.pyplot
plt.plot(cdf.Values(), ccdf)
#plt.xscale('log')
plt.yscale('log')
plt.show()
def WeibullDistribution(): results = [] k = 2 lamada = 1 sampleNum = 6000 for i in range(sampleNum): results.append(random.weibullvariate(lamada,k)) cdf = Cdf.MakeCdfFromList(results) myplot.Clf() myplot.Cdf(cdf,complement=True,xscale = 'log',yscale = 'log') # myplot.Cdf(cdf) myplot.show()
def Random100(): results = [] for i in range(1000): results.append(random.random()) pmf = Pmf.MakePmfFromList(results) cdf = Cdf.MakeCdfFromPmf(pmf) myplot.Clf() myplot.Pmf(pmf) myplot.show() myplot.Clf() myplot.Cdf(cdf) myplot.show()
def main():
n = 44
mean = 32.6
lambd = 1.0/mean
data = sample(lambd, n)
cdf = Cdf.MakeCdfFromList(data)
ccdf = [1 - p for x, p in cdf.Items()]
plt.plot(cdf.Values(),ccdf)
plt.xscale('log')
plt.show()
myplot.Cdf(cdf, complement=True,xscale='linear',yscale='log')
myplot.show()
def main():
# Exercise 4.1
mean = 32.6
lambd = 1 / mean # l for lambda
exp_values = []
for _ in range(44):
exp_values.append(random.expovariate(lambd))
exponential_distribution_cdf = Cdf.MakeCdfFromList(
exp_values, name='Exponential Distribution')
myplot.Cdf(exponential_distribution_cdf,
complement=True,
xscale='linear',
yscale='log')
myplot.show()
def Brfss_figs(): resp = brfss.Respondents() resp.ReadRecords() print len(resp.records) results = [r.wtkg2 for r in resp.records if r.wtkg2 != 'NA'] cdf = Cdf.MakeCdfFromList(results) t = results[:] t.sort() mean,var = thinkstats.TrimmedMeanVar(t) print 'len,mean,var',len(t),mean,var sigma = math.sqrt(var) myplot.Clf() xs,ps = continuous.RenderNormalCdf(mean,sigma,175) myplot.Plot(xs,ps) xs,ps = cdf.Render() myplot.Plot(xs,ps) myplot.show()
def CentralLimitTheorem(): num = 4 times = 100 maxX = 2 lamadas = [i+2 for i in range(num)] sumHist = Pmf.Hist() for i in range(times): sumRes = 0 x = random.random()*maxX for lamada in lamadas: sumRes += ExpLamadaX(lamada,x) sumHist.Incr(sumRes) cdf = Cdf.MakeCdfFromHist(sumHist) myplot.Clf() myplot.Cdf(cdf) myplot.show()
def main():
# Exercise 4.3
# function defined below
random_pareto_sample = []
for i in range(1000):
random_pareto_sample.append(paretovariate(1, .5))
random_pareto_sample_cdf = Cdf.MakeCdfFromList(random_pareto_sample)
myplot.Cdf(random_pareto_sample_cdf,
complement=True,
xscale='log',
yscale='log')
myplot.show()
# Exercise 4.4
heights = []
for _ in range(6000000000):
heights.append(paretovariate(alpha=1.7, x_sub_m=100))
heights_cdf = Cdf.MakeCdfFromList(heights)
print(heights.Mean())
print(heights.Percentile(heights.Mean()))
print(heights.sort())
def main():
# Exercise 3.9
table = survey.Pregnancies()
table.ReadRecords()
unfilteredLiveBirthWeights = [(p.birthwgt_lb, p.birthwgt_oz)
for p in table.records if p.outcome == 1]
liveBirthWeights = [
lbs * 16 + oz for lbs, oz in unfilteredLiveBirthWeights
if type(lbs) == int and type(oz) == int and lbs * 16 + oz <= 200
]
liveBirthWeightsCdf = Cdf.MakeCdfFromList(liveBirthWeights,
name="live birth weights")
samepleListLiveBirthWeights = sample(liveBirthWeightsCdf, 1000)
myplot.Cdf(Cdf.MakeCdfFromList(samepleListLiveBirthWeights))
myplot.show(title="CDF of live births resampled")
# Exercise 3.10
randomList = [random.random() for x in range(1000)]
myplot.Pmf(Pmf.MakePmfFromList(randomList))
myplot.show(title="random pmf")
myplot.Cdf(Cdf.MakeCdfFromList(randomList))
myplot.Show(title="random cdf")
def main():
ran = generate_random_sample(1000)
pmf = Pmf.MakePmfFromList(ran)
cdf = Cdf.MakeCdfFromPmf(pmf)
myplot.Cdf(cdf)
myplot.show()
myplot.scatter(*cdf.Render())
myplot.show()
myplot.Hist(pmf)
myplot.show()
myplot.Pmf(pmf)
myplot.show()
mycsv.save([y for x in rho for y in x],
save_name=DATA + "/rho" + str(fig) + ".csv",
header=())
return fig, fbc
if __name__ == "__main__":
from sympy import *
import matplotlib.pyplot as plt
s = symbols('s')
import os
try:
os.makedirs(DATA)
except:
pass
fig = -1
import Example1_Single_FRF_Nano_Scale_Servo as ex1
import Example3_Another_Various_FRFs_Nano_Scale_Servo as ex3
fig, o, h = ex3.plant_data(fig, datapath=DATA)
fig, fbc = optimize(fig, o, h)
ex1.plotall(fig, fbc, ndata=NDATA, datapath=DATA)
myplot.show()
def population3(): results = populations.ReadData() cdf = Cdf.MakeCdfFromList(results) myplot.Clf() myplot.Cdf(cdf) myplot.show(xscale = 'log')
def Irs(): data = irs.ReadIncomeFile() hist, pmf, cdf = irs.MakeIncomeDist(data) myplot.Clf() myplot.Cdf(cdf) myplot.show(xscale = 'log')
def main():
maxQuestionAvg = 2000
minQuestionAvg = 400
questionInterval = (maxQuestionAvg - minQuestionAvg) / QUESTION_LIMIT
questionBank = [
fakeNormal.FakeNormalQuestion(i, midpoint_rating=r)
for i, r in enumerate(range(minQuestionAvg, maxQuestionAvg, questionInterval))
]
assert len(questionBank) == QUESTION_LIMIT
maxCompAvg = 1800
minCompAvg = 600
compInterval = (maxCompAvg - minCompAvg) / NUM_COMPETITORS
competitors = [
fakeNormal.FakeNormalCompetitor(questionBank, r) for r in range(minCompAvg, maxCompAvg, compInterval)
]
assert len(competitors) == NUM_COMPETITORS
for competitor in competitors:
competitor.init()
myplot.init()
for t in range(TRIALS):
selectedCompetitor1 = random.choice(competitors)
selectedCompetitor2 = selectedCompetitor1
while selectedCompetitor1 == selectedCompetitor2:
selectedCompetitor2 = random.choice(competitors)
actualRatingof1 = selectedCompetitor1.hiddenRating
actualRatingof2 = selectedCompetitor2.hiddenRating
currentRatingof1 = selectedCompetitor1.rating
currentRatingof2 = selectedCompetitor2.rating
print "Facing off competitor (", currentRatingof1,
print "/", actualRatingof1, ") vs. competitor (",
print currentRatingof2, "/", actualRatingof2, ")"
# 1 judges 2
numCorrectof2 = selectedCompetitor1.judge.judgeCompetitor(selectedCompetitor2.subject)
estRatingof2 = selectedCompetitor1.judge.guessCompetitorRating()
# 2 judges 1
numCorrectof1 = selectedCompetitor2.judge.judgeCompetitor(selectedCompetitor1.subject)
estRatingof1 = selectedCompetitor2.judge.guessCompetitorRating()
# Cannot predict on the first time
if estRatingof1 is not None and estRatingof2 is not None:
score1 = CORRECT_SCALE * numCorrectof1 - abs(estRatingof2 - currentRatingof2)
score2 = CORRECT_SCALE * numCorrectof2 - abs(estRatingof1 - currentRatingof1)
if score1 > score2:
print "First competitor is winner!"
score1 = 1.0
score2 = 0.0
elif score2 > score1:
print "Second competitor is winner!"
score1 = 0.0
score2 = 1.0
else:
print "Draw!"
score1 = 0.5
score2 = 0.5
newRating1, newRating2 = elo(score1, score2, currentRatingof1, currentRatingof2)
selectedCompetitor1.rating = newRating1
selectedCompetitor2.rating = newRating2
# myplot.plotCompRatings(competitors)
# myplot.draw()
# time.sleep(0.5)
# myplot.close()
selectedCompetitor1.finishCompetition(currentRatingof2)
selectedCompetitor2.finishCompetition(currentRatingof1)
myplot.plotCompRatings(competitors)
myplot.show()
def runGame(competitors):
myplot.init()
for t in range(TRIALS):
selectedCompetitor1 = random.choice(competitors)
selectedCompetitor2 = selectedCompetitor1
while selectedCompetitor1 == selectedCompetitor2:
selectedCompetitor2 = random.choice(competitors)
currentRatingof1 = selectedCompetitor1.rating
currentRatingof2 = selectedCompetitor2.rating
print "Facing off competitor (", currentRatingof1,
print "/", selectedCompetitor1.id, ") vs. competitor (",
print currentRatingof2, "/", selectedCompetitor2.id, ")"
# 1 judges 2
numCorrectof2 = selectedCompetitor1.judge.judgeCompetitor(selectedCompetitor2.subject)
estRatingof2 = selectedCompetitor1.judge.guessCompetitorRating()
selectedCompetitor2.totalCorrectAnswers += numCorrectof2
# 2 judges 1
numCorrectof1 = selectedCompetitor2.judge.judgeCompetitor(selectedCompetitor1.subject)
estRatingof1 = selectedCompetitor2.judge.guessCompetitorRating()
selectedCompetitor1.totalCorrectAnswers += numCorrectof1
# Cannot predict on the first time
if estRatingof1 is not None and estRatingof2 is not None:
score1 = CORRECT_SCALE*numCorrectof1-abs(estRatingof2-currentRatingof2)
score2 = CORRECT_SCALE*numCorrectof2-abs(estRatingof1-currentRatingof1)
if score1 > score2:
print "First competitor is winner!"
score1 = 1.0
score2 = 0.0
elif score2 > score1:
print "Second competitor is winner!"
score1 = 0.0
score2 = 1.0
else:
print "Draw!"
score1 = 0.5
score2 = 0.5
newRating1, newRating2 = elo(score1, score2, currentRatingof1, currentRatingof2)
selectedCompetitor1.rating = newRating1
selectedCompetitor2.rating = newRating2
# myplot.plotRatings(competitors)
# myplot.draw()
# time.sleep(0.5)
# myplot.close()
selectedCompetitor1.finishCompetition(currentRatingof2)
selectedCompetitor2.finishCompetition(currentRatingof1)
for competitor in competitors:
print competitor.id,
print ":",
print competitor.totalCorrectAnswers
myplot.plotRatings(competitors)
myplot.show()
def min_2norm(fig=0):
"""
2 norm optimization
:return:
"""
"""
CONDITION AND CONSTRAINTS
"""
MIN = JER # What to be minimized
TS = 0.001 # Sampling Period
TINIT = (0, 1)
START, END = 0, 1
TSAMPLE = np.linspace(0, TINIT[END], TINIT[END] / TS + 1)
QC = (0, 1.0)
VC = (0, 0)
AC = (0, 0)
JC = (0, 0)
CONSTRAINTS = (*QC, *VC, *AC, *JC)
LABEL_CONSTRAINTS = (POS, VEL, ACC, JER)
NCONSTRAINTS = len(CONSTRAINTS)
assert NCONSTRAINTS == len(LABEL_CONSTRAINTS) * 2
VMAX = 10000
AMAX = 10000
nc = NCONSTRAINTS + 60 # number of control points == number of theta
p = 4 # jerk continous
u = [TINIT[END] * i / (nc - 1) for i in range(nc)] # knots
bspl = Bspline(u, nc, p, verbose=True)
"""
QUDRATIC PROGRAMMING
"""
M = np.array(bspl.basis(TSAMPLE, der=MIN))
P = np.dot(M.T, M)
q = np.zeros(nc)
A = None
for d in LABEL_CONSTRAINTS:
for x in bspl.basis(TINIT, der=d):
if A is None:
A = np.array(x)
else:
A = np.block([[A], [np.array(x)]])
b = np.matrix(CONSTRAINTS).reshape((NCONSTRAINTS, 1))
if True:
G = np.array([*bspl.basis(TSAMPLE, der=VEL), *bspl.basis(TSAMPLE, der=ACC)])
hv = np.ones((len(TSAMPLE), 1)) * VMAX
ha = np.ones((len(TSAMPLE), 1)) * AMAX
h = np.append(hv, ha, axis=0)
G, h = mycvxopt.constraints(G, h, -h)
else:
G, h = None, None # No ineq
theta = mycvxopt.solve("qp", [P, q], G=G, h=h, A=A, b=b)
print(theta)
"""
Plot
"""
for d in STATES:
fig += 1
text = None
myplot.time(TSAMPLE, bspl.bspline(theta, TSAMPLE, der=d), fig, text=text,
save_name="data/" + LABELS[d][:-1].split()[0], label=("Time (s)", LABELS[d]))
myplot.show()
import Cdf
import myplot
import Pmf
import random
random_numbers = []
for i in range(1000):
random_numbers.append(random.random())
pmf = Pmf.MakePmfFromList(random_numbers)
cdf = Cdf.MakeCdfFromList(random_numbers)
myplot.Pmf(pmf)
myplot.show(title='PMF of random numbers 0-1',xlabel='value',ylabel='probability')
myplot.Cdf(cdf)
myplot.show(title='CDF of random numbers 0-1',xlabel='value', ylabel='probability')
import Cdf
import myplot
import Pmf
import random
random_numbers = []
for i in range(1000):
random_numbers.append(random.random())
pmf = Pmf.MakePmfFromList(random_numbers)
cdf = Cdf.MakeCdfFromList(random_numbers)
myplot.Pmf(pmf)
myplot.show(title='PMF of random numbers 0-1',
xlabel='value',
ylabel='probability')
myplot.Cdf(cdf)
myplot.show(title='CDF of random numbers 0-1',
xlabel='value',
ylabel='probability')
