def simulate_n_paths_maxstorage(n, N, x0, p0, M, m):
self.simulations = zeros((n, N+1, 2))
for i in range(n):
x, p = simulate_one_path(N, x0, p0, M, m)
self.simulations[i,:,0] = x
self.simulations[i,:,1] = p
# show 5 random sample paths:
for i in range(0, n, n/5):
self.plot_path(x, 'sample paths of investment', 1)
self.plot_path(p, 'sample paths of interest rate', 2)
figure(1); hardcopy('tmp_sample_paths_investment.eps')
figure(2); hardcopy('tmp_sample_paths_interestrate.eps')
# compute average:
xm = mean(self.simulations[:,:,0], axis=1)
pm = mean(self.simulations[:,:,1], axis=1)
# compute standard deviation:
xs = std(self.simulations[:,:,0], axis=1)
ps = std(self.simulations[:,:,1], axis=1)
return xm, xs, pm, ps
def simulate_n_paths_maxstorage(n, N, x0, p0, M, m):
self.simulations = zeros((n, N + 1, 2))
for i in range(n):
x, p = simulate_one_path(N, x0, p0, M, m)
self.simulations[i, :, 0] = x
self.simulations[i, :, 1] = p
# show 5 random sample paths:
for i in range(0, n, n / 5):
self.plot_path(x, 'sample paths of investment', 1)
self.plot_path(p, 'sample paths of interest rate', 2)
figure(1)
hardcopy('tmp_sample_paths_investment.eps')
figure(2)
hardcopy('tmp_sample_paths_interestrate.eps')
# compute average:
xm = mean(self.simulations[:, :, 0], axis=1)
pm = mean(self.simulations[:, :, 1], axis=1)
# compute standard deviation:
xs = std(self.simulations[:, :, 0], axis=1)
ps = std(self.simulations[:, :, 1], axis=1)
return xm, xs, pm, ps
from scitools.std import *
N = int(sys.argv[1])
m = float(sys.argv[2])
s = float(sys.argv[3])
random.seed(12)
samples = random.normal(m, s, N)
x, y = compute_histogram(samples, 20, piecewise_constant=True)
print mean(samples), std(samples)
plot(x, y)
title('%d samples of Gaussian/normal numbers on (0,1)' % N)
hardcopy('tmp.eps')
from scitools.std import *
N = int(sys.argv[1]); m = float(sys.argv[2]); s = float(sys.argv[3])
random.seed(12)
samples = random.normal(m, s, N)
x, y = compute_histogram(samples, 20, piecewise_constant=True)
print mean(samples), std(samples)
plot(x, y)
title('%d samples of Gaussian/normal numbers on (0,1)' % N)
hardcopy('tmp.eps')
y = positions.copy() # y position is always 0
nbins = int(3 * xmax) # no of intervals in histogram
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_number.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 = mean(positions)
stdev_pos = std(positions)
pos, freq = compute_histogram(positions, nbins, piecewise_constant=True)
# extend x axis limits?
if min(positions) < xmin: xmin -= 2 * sqrt(ns)
if max(positions) > xmax: xmax += 2 * 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 math.abs(ymax - ymax_prev) < 0.1:
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 = 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 = zeros(np)
for step in range(ns):
positions += moves[step, :]
mean_pos, stdev_pos = mean(positions), std(positions)
print mean_pos, stdev_pos
nbins = int(3*sqrt(ns)) # no of intervals in histogram
pos, freq = compute_histogram(positions, nbins,
piecewise_constant=True)
plot(positions, zeros(np), 'ko3',
pos, freq, 'r',
axis=[min(positions), max(positions), -0.05, 1.1*max(freq)],
hardcopy='tmp.eps')
y = positions.copy() # y position is always 0
nbins = int(3*xmax) # no of intervals in histogram
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_number.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 = mean(positions)
stdev_pos = std(positions)
pos, freq = compute_histogram(positions, nbins,
piecewise_constant=True)
# extend x axis limits?
if min(positions) < xmin: xmin -= 2*sqrt(ns)
if max(positions) > xmax: xmax += 2*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
ns = int(sys.argv[2]) # number of steps
except IndexError:
np = 2000
ns = 200
# draw from 1, 2:
moves = 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 = zeros(np)
for step in range(ns):
positions += moves[step, :]
mean_pos, stdev_pos = mean(positions), std(positions)
print mean_pos, stdev_pos
nbins = int(3 * sqrt(ns)) # no of intervals in histogram
pos, freq = compute_histogram(positions, nbins, piecewise_constant=True)
plot(positions,
zeros(np),
'ko3',
pos,
freq,
'r',
axis=[min(positions),
max(positions), -0.05, 1.1 * max(freq)],
hardcopy='tmp.eps')