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%matplotlib inline
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import numpy as np
import matplotlib.pyplot as plt
mu, sigma = 100, 15
x = mu + sigma * np.random.randn(10000)
# the histogram of the data
n, bins, patches = plt.hist(x, 50, normed=1, facecolor='g', alpha=0.75)
plt.xlabel('Smarts')
plt.ylabel('Probability')
plt.title('Histogram of IQ')
plt.text(60, .025, r'$\mu=100,\ \sigma=15$')
plt.axis([40, 160, 0, 0.03])
plt.grid(True)
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from pylab import *
# fake up some data
spread= rand(50) * 100
center = ones(25) * 50
flier_high = rand(10) * 100 + 100
flier_low = rand(10) * -100
data =concatenate((spread, center, flier_high, flier_low), 0)
# basic plot
boxplot(data)
# notched plot
figure()
boxplot(data,1)
# change outlier point symbols
figure()
boxplot(data,0,'gD')
# don't show outlier points
figure()
boxplot(data,0,'')
# horizontal boxes
figure()
boxplot(data,0,'rs',0)
# change whisker length
figure()
boxplot(data,0,'rs',0,0.75)
# fake up some more data
spread= rand(50) * 100
center = ones(25) * 40
flier_high = rand(10) * 100 + 100
flier_low = rand(10) * -100
d2 = concatenate( (spread, center, flier_high, flier_low), 0 )
data.shape = (-1, 1)
d2.shape = (-1, 1)
#data = concatenate( (data, d2), 1 )
# Making a 2-D array only works if all the columns are the
# same length. If they are not, then use a list instead.
# This is actually more efficient because boxplot converts
# a 2-D array into a list of vectors internally anyway.
data = [data, d2, d2[::2,0]]
# multiple box plots on one figure
figure()
boxplot(data)
show()
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n, bins, patches = hist(randn(1000), 40, normed=1)
l, = plot(bins, normpdf(bins, 0.0, 1.0), 'r--', label='fit', linewidth=3)
legend([l, patches[0]], ['fit', 'hist'])
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from mpl_toolkits.mplot3d import axes3d
from matplotlib import cm
fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.3)
cset = ax.contourf(X, Y, Z, zdir='z', offset=-100, cmap=cm.coolwarm)
cset = ax.contourf(X, Y, Z, zdir='x', offset=-40, cmap=cm.coolwarm)
cset = ax.contourf(X, Y, Z, zdir='y', offset=40, cmap=cm.coolwarm)
ax.set_xlabel('X')
ax.set_xlim(-40, 40)
ax.set_ylabel('Y')
ax.set_ylim(-40, 40)
ax.set_zlabel('Z')
ax.set_zlim(-100, 100)
plt.show()
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import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon
# Generate some data from five different probability distributions,
# each with different characteristics. We want to play with how an IID
# bootstrap resample of the data preserves the distributional
# properties of the original sample, and a boxplot is one visual tool
# to make this assessment
numDists = 5
randomDists = ['Normal(1,1)',' Lognormal(1,1)', 'Exp(1)', 'Gumbel(6,4)',
'Triangular(2,9,11)']
N = 500
norm = np.random.normal(1,1, N)
logn = np.random.lognormal(1,1, N)
expo = np.random.exponential(1, N)
gumb = np.random.gumbel(6, 4, N)
tria = np.random.triangular(2, 9, 11, N)
# Generate some random indices that we'll use to resample the original data
# arrays. For code brevity, just use the same random indices for each array
bootstrapIndices = np.random.random_integers(0, N-1, N)
normBoot = norm[bootstrapIndices]
expoBoot = expo[bootstrapIndices]
gumbBoot = gumb[bootstrapIndices]
lognBoot = logn[bootstrapIndices]
triaBoot = tria[bootstrapIndices]
data = [norm, normBoot, logn, lognBoot, expo, expoBoot, gumb, gumbBoot,
tria, triaBoot]
fig, ax1 = plt.subplots(figsize=(10,6))
fig.canvas.set_window_title('A Boxplot Example')
plt.subplots_adjust(left=0.075, right=0.95, top=0.9, bottom=0.25)
bp = plt.boxplot(data, notch=0, sym='+', vert=1, whis=1.5)
plt.setp(bp['boxes'], color='black')
plt.setp(bp['whiskers'], color='black')
plt.setp(bp['fliers'], color='red', marker='+')
# Add a horizontal grid to the plot, but make it very light in color
# so we can use it for reading data values but not be distracting
ax1.yaxis.grid(True, linestyle='-', which='major', color='lightgrey',
alpha=0.5)
# Hide these grid behind plot objects
ax1.set_axisbelow(True)
ax1.set_title('Comparison of IID Bootstrap Resampling Across Five Distributions')
ax1.set_xlabel('Distribution')
ax1.set_ylabel('Value')
# Now fill the boxes with desired colors
boxColors = ['darkkhaki','royalblue']
numBoxes = numDists*2
medians = range(numBoxes)
for i in range(numBoxes):
box = bp['boxes'][i]
boxX = []
boxY = []
for j in range(5):
boxX.append(box.get_xdata()[j])
boxY.append(box.get_ydata()[j])
boxCoords = zip(boxX,boxY)
# Alternate between Dark Khaki and Royal Blue
#k = i % 2
#boxPolygon = Polygon(boxCoords, facecolor=boxColors[k])
#ax1.add_patch(boxPolygon)
# Now draw the median lines back over what we just filled in
#med = bp['medians'][i]
#medianX = []
#medianY = []
#for j in range(2):
# medianX.append(med.get_xdata()[j])
# medianY.append(med.get_ydata()[j])
# plt.plot(medianX, medianY, 'k')
#medians[i] = medianY[0]
# Finally, overplot the sample averages, with horizontal alignment
# in the center of each box
#plt.plot([np.average(med.get_xdata())], [np.average(data[i])],
# color='w', marker='*', markeredgecolor='k')
# Set the axes ranges and axes labels
ax1.set_xlim(0.5, numBoxes+0.5)
top = 40
bottom = -5
ax1.set_ylim(bottom, top)
xtickNames = plt.setp(ax1, xticklabels=np.repeat(randomDists, 2))
plt.setp(xtickNames, rotation=45, fontsize=8)
# Due to the Y-axis scale being different across samples, it can be
# hard to compare differences in medians across the samples. Add upper
# X-axis tick labels with the sample medians to aid in comparison
# (just use two decimal places of precision)
pos = np.arange(numBoxes)+1
upperLabels = [str(np.round(s, 2)) for s in medians]
weights = ['bold', 'semibold']
for tick,label in zip(range(numBoxes),ax1.get_xticklabels()):
k = tick % 2
ax1.text(pos[tick], top-(top*0.05), upperLabels[tick],
horizontalalignment='center', size='x-small', weight=weights[k],
color=boxColors[k])
# Finally, add a basic legend
plt.figtext(0.80, 0.08, str(N) + ' Random Numbers' ,
backgroundcolor=boxColors[0], color='black', weight='roman',
size='x-small')
plt.figtext(0.80, 0.045, 'IID Bootstrap Resample',
backgroundcolor=boxColors[1],
color='white', weight='roman', size='x-small')
plt.figtext(0.80, 0.015, '*', color='white', backgroundcolor='silver',
weight='roman', size='medium')
plt.figtext(0.815, 0.013, ' Average Value', color='black', weight='roman',
size='x-small')
plt.show()
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