Quote:
Originally Posted by Ether
1) How long did 4e10 trials take to run?
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About 16 hours. My laptop has an Intel Core i7-6700HQ Quad Core and I ran 4 copies of my program at once instead of implementing multithreading. This seemed to work as desired based on the cpu usage and left me with enough overhead to not impact my normal computer use.
Quote:
Originally Posted by Ether
2) Yes, please post your code.
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Internal points code:
Code:
import numpy as np
import time
def genPt(r_cir):
r = r_cir*(np.random.random()**0.5) #Square root correction ensures even probability distribution over area
theta = 2*np.pi*np.random.random()
x = r*np.cos(theta)
y = r*np.sin(theta)
return x,y
t = time.time()
trials = 10**9
r = 1.0
total = 0.0
for i in range(trials):
x1,y1 = genPt(r)
x2,y2 = genPt(r)
total += ((x2-x1)**2 + (y2-y1)**2)**0.5
if not i%10**7:
print(i)
print(total/(i+1))
print('')
print(total/trials)
print(time.time()-t)
Chord problem code:
Code:
import numpy as np
import time
t = time.time()
trials = 10**10 #Number of random samples
total = 0.0
r = 1.0
x1,y1 = 0.0,r
for i in range(trials):
theta = 2*np.pi*np.random.random()
x2 = r*np.cos(theta)
y2 = r*np.sin(theta)
total += ((x2-x1)**2 + (y2-y1)**2)**0.5
if not i%10**7:
print(i)
print(total/(i+1))
print('')
print(total/trials)
print(time.time()-t)
I have since made both programs about 2.5x faster by using the polar distance formula to cut down on trig functions (really add up after a few billion trials), by cutting the number of angles generated from 2 to 1 in each trial of the line segment problem, and by switching to using the math module trig functions instead of the NumPy ones. I was somewhat surprised to find that the math module ones are about twice as fast as NumPy's. I've often been impressed by the speed of doing things in NumPy, but it turns out that the Python developers also have some idea what they're doing
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Quote:
Originally Posted by Ether
3) What's the period of the PRNG you used?
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I used numpy.random.random(), which uses the Mersenne Twister sequence and has a period of 2^19937 − 1. Unfortunately I wasn't able to run quite that many trials.