def gauss():
"""
The driver for the generator based implementation
"""
from Disk import Disk
from Gaussian import Gaussian
from Mersenne import Mersenne
# inputs
N = 10**5
box = [(-1,1), (-1,1)]
B = functools.reduce(operator.mul, ((right-left) for left,right in zip(*box)))#@\label{line:mc:volume}@
# the point cloud generator
generator = Mersenne()
# the region of integration
disk = Disk(center=(0,0), radius=1)
# the integrand
gaussian = Gaussian(mean=(0,0), spread=1/3)
# the integration algorithm
# build the point sample
sample = generator.points(N, box)
# select the interior points
interior = disk.interior(sample)
# compute the integral
integral = B/N * sum(gaussian.eval(interior))#@\label{line:mc:integral}@
# print the estimate of the integral
print("integral: {:.8f}".format(integral))
return
def gauss():
"""
The driver for the generator based implementation
"""
from Disk import Disk
from Gaussian import Gaussian
from Mersenne import Mersenne
# inputs
N = 10**7
box = [(-1, -1), (1, 1)]
B = functools.reduce(operator.mul,
((right - left) for left, right in zip(*box)))
# the point cloud generator
generator = Mersenne()
# the region of integration
disk = Disk(center=(0, 0), radius=1)
# the integrand
gaussian = Gaussian(mean=(0, 0), spread=1 / 3)
# the integration algorithm
# build the point sample
sample = generator.points(N, box)
# select the interior points
interior = disk.interior(sample)
# compute the integral
integral = B / N * sum(gaussian.eval(interior))
# print out the estimate of the integral
print("integral: {0:.8f}".format(integral))
return
def gauss():
"""
The driver for the object oriented solution
"""
from Disk import Disk
from Mersenne import Mersenne
# inputs
N = 10**5
box = [(0,0), (1,1)]
# the point cloud generator
cloud = Mersenne()
# the region of integration
disk = Disk(center=(0,0), radius=1)
# the integration algorithm
total = 0
interior = 0
while total < N:
point = cloud.point(box)
if disk.interior(point):
interior += 1
total += 1
# print out the estimate of #@$\pi$@
print("pi: {0:.8f}".format(4*interior/N))
return
def gauss():
"""
The driver for the generator based implementation
"""
from Disk import Disk
from Mersenne import Mersenne
# inputs
N = 10**5
box = [(0, 1), (0, 1)]
# the point cloud
cloud = Mersenne()
# the region of integration
disk = Disk(center=(0, 0), radius=1)
# the integration algorithm
# build the point sample
sample = cloud.points(N, box)
# count the interior points
interior = count(disk.interior(sample))
# print the estimate of π
print("π: {:.8f}".format(4 * interior / N))
return
def gauss():
"""
The driver for the object oriented solution
"""
from Disk import Disk
from Mersenne import Mersenne
# inputs
N = 10**5
box = [(0,1), (0,1)]
# the point cloud generator
cloud = Mersenne()
# the region of integration
disk = Disk(center=(0,0), radius=1)
# the integration algorithm
interior = 0
for i in range(N):
point = cloud.point(box)
if disk.interior(point):
interior += 1
# print the estimate of π
print("π: {:.8f}".format(4*interior/N))
return
def gauss():
"""
The driver for the object oriented solution
"""
from Disk import Disk
from Mersenne import Mersenne
# inputs
N = 10**5
box = [(0, 1), (0, 1)]
# the point cloud generator
cloud = Mersenne()
# the region of integration
disk = Disk(center=(0, 0), radius=1)
# the integration algorithm
interior = 0
for i in range(N):
point = cloud.point(box)
if disk.interior(point):
interior += 1
# print the estimate of π
print("π: {:.8f}".format(4 * interior / N))
return
def gauss():
"""
The driver for the container based implementation
"""
from Disk import Disk
from Mersenne import Mersenne
# inputs
N = 10**5
box = [(0,1), (0,1)]
# the point cloud generator
cloud = Mersenne()
# the region of integration
disk = Disk(center=(0,0), radius=1)
# the integration algorithm
# build the point sample
sample = cloud.points(N, box)
# count the interior points
interior = len(disk.interior(sample))
# print the estimate of π
print("π: {:.8f}".format(4*interior/N))
return