ymax_prev = 1 # for axis in plot, prev. step
ymin = -0.1 # min limit for y axis
for step in range(ns):
for p in range(np):
coin = random.randint(1, 2) # flip coin
if coin == HEAD:
positions[p] += 1 # one unit length to the right
elif coin == TAIL:
positions[p] -= 1 # one unit length to the left
# Statistics
mean_pos = numpy.mean(positions)
stdev_pos = numpy.std(positions)
pos, freq = compute_histogram(positions, nbins, piecewise_constant=True)
# Extend x axis limits?
if min(positions) < xmin: xmin -= 2 * numpy.sqrt(ns)
if max(positions) > xmax: xmax += 2 * numpy.sqrt(ns)
# "Intelligent" choice of y axis limits:
# estimate ymax on the y axis from 1.1*max(freq)
# (1.1 to get some space), do not change ymax
# unless it deviates more than 0.1 from the previous
# value, and let ymin = -0.1*ymax.
ymax = 1.1 * max(freq) # axis for freq
if abs(ymax - ymax_prev) < 0.1:
# Do not change axis
ymax = ymax_prev
import sys
N = int(sys.argv[1])
m = float(sys.argv[2])
s = float(sys.argv[3])
import numpy as np
np.random.seed(12)
samples = np.random.normal(m, s, N)
print np.mean(samples), np.std(samples)
import scitools.std as st
x, y = st.compute_histogram(samples, 20, piecewise_constant=True)
st.plot(x, y, hardcopy='tmp.eps',
title ='%d samples of Gaussian/normal numbers on (0,1)' % N)
try:
np = int(sys.argv[1]) # number of particles
ns = int(sys.argv[2]) # number of steps
except IndexError:
np = 2000
ns = 200
# Draw from 1, 2
moves = numpy.random.random_integers(1, 2, size=np*ns)
# Transform 1 to -1 and 2 to 1
moves = 2*moves - 3
moves.shape = (ns, np)
positions = numpy.zeros(np)
for step in range(ns):
positions += moves[step, :]
mean_pos = numpy.mean(positions)
stdev_pos = numpy.std(positions)
print mean_pos, stdev_pos
nbins = int(3*numpy.sqrt(ns)) # no of intervals in histogram
pos, freq = compute_histogram(positions, nbins,
piecewise_constant=True)
plot(positions, numpy.zeros(np), 'ko3',
pos, freq, 'r',
axis=[min(positions), max(positions), -0.01, 1.1*max(freq)],
hardcopy='tmp.eps')
import sys N = int(sys.argv[1]) m = float(sys.argv[2]) s = float(sys.argv[3]) import numpy as np np.random.seed(12) samples = np.random.normal(m, s, N) print np.mean(samples), np.std(samples) import scitools.std as st x, y = st.compute_histogram(samples, 20, piecewise_constant=True) st.plot(x, y, hardcopy="tmp.eps", title="%d samples of Gaussian/normal numbers on (0,1)" % N)
"""
As uniform_numbers1.py but the histogram is plotted both as a piecewise
constant curve and a piecewise linear curve. The number of bins is
read from the command line.
"""
import sys
N = int(sys.argv[1])
nbins = int(sys.argv[2])
import numpy as np
np.random.seed(12)
# Vectorized generation of random numbers
samples = np.random.random(size=N)
import scitools.std as st
x1, y1 = st.compute_histogram(samples, nbins, piecewise_constant=True)
x2, y2 = st.compute_histogram(samples, nbins, piecewise_constant=False)
st.plot(x1, y1, 'r', x2, y2, 'b')
st.title('%d samples of uniform numbers on (0,1)' % N)
st.hardcopy('tmp.eps')
import sys
N = int(sys.argv[1])
import numpy as np
np.random.seed(12)
# Vectorized generation of random numbers
samples = np.random.random(size=N)
# Plot histogram
import scitools.std as st
x, y = st.compute_histogram(samples, nbins=20)
st.plot(x, y, title='%d samples of uniform numbers on [0,1)' % N)
st.hardcopy('tmp.eps')
# Exercise 8.20
# Author: Noah Waterfield Price
from time import time
from scitools.std import plot, compute_histogram
def diff_eq(x, a, c, m):
xn = (a * x + c) % m
yn = float(xn) / m
return xn, yn
def rand_gen(a, c, m, N=10, x=time()):
r = []
for i in range(N):
x, y = diff_eq(x, a, c, m)
r.append(y)
return r
a = 8121
c = 28411
m = 134456
N = 1000000
random_nos = rand_gen(a, c, m, N)
x, y = compute_histogram(random_nos, nbins=50)
plot(x, y, title='%d samples of psuedo-random numbers generated on (0, 1)' % N)
raw_input()
