Initial commit

random_triangle_links_parallel.py

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+import time
+import random
+import math
+from multiprocessing import Process, Value, Lock, Pool
+
+def main():
+	start = time.time()
+	# number process
+	k=4
+	# points per process
+	n=250000000
+
+	unlinked=0
+	linked=0
+
+	pool = Pool(k)
+
+	results=[pool.apply_async(generate_data,args=(n,)) for i in range(k)]
+
+	for result in results:
+		result.wait()
+		output = result.get()
+		#print(output)
+		unlinked+=output[0]
+		linked+=output[1]
+
+	end = time.time()
+	print('Linked triangles: ' + str(linked))
+	print('Unlinked triangles: ' + str(unlinked))
+	print('Total time: ' + str(end-start))
+	p=1.0*linked/(n*k)
+	print('99% confidence interval for q: ' + str(p*4/18) + ' +/- ' +
+		str(2.575*4/18*math.sqrt(p*(1-p)/n)))
+
+def generate_data(n):
+	unlinked=0
+	linked=0
+	for i in range(n):
+		if random_triangles()==0:
+			unlinked+=1
+		else:
+			linked+=1
+	return [unlinked,linked]
+	
+
+def generate_coords(len=6):
+	pts=[]
+	for i in range(len):
+		pts.append(random.random())
+	return pts
+
+def random_triangles():
+	x=generate_coords()
+	y=generate_coords()
+	z=generate_coords()
+	#mathematica code to plot triangles
+#	print('Graphics3D[{Red,Line[{{'+str(x[0])+','+str(y[0])+','+str(z[0])+'},{'
+#		+str(x[1])+','+str(y[1])+','+str(z[1])+'},{'
+#		+str(x[2])+','+str(y[2])+','+str(z[2])+'},{'
+#		+str(x[0])+','+str(y[0])+','+str(z[0])+'}}],Blue,Line[{{'
+#		+str(x[3])+','+str(y[3])+','+str(z[3])+'},{'
+#		+str(x[4])+','+str(y[4])+','+str(z[4])+'},{'
+#		+str(x[5])+','+str(y[5])+','+str(z[5])+'},{'
+#		+str(x[3])+','+str(y[3])+','+str(z[3])+'}}]}]')
+
+	linknum = 0
+	for i in range(3):
+		for k in range(3):
+			j= (i+1) % 3
+			m=k+3
+			n= 3+( (k+1) % 3 )
+			linknum+=check_crossing([x[i],y[i],z[i]],[x[j],y[j],z[j]],
+				[x[m],y[m],z[m]],[x[n],y[n],z[n]])
+#	print(str(crossings))
+	return linknum
+
+
+def check_crossing(p1,p2,q1,q2):
+	# solve linear system for when two lines cross
+	dxp = p2[0]-p1[0]
+	dyp = p2[1]-p1[1]
+	dxq = q2[0]-q1[0]
+	dyq = q2[1]-q1[1]
+	dxc = q1[0]-p1[0]
+	dyc = q1[1]-p1[1]
+	det=dyp*dxq-dxp*dyq
+#	det=(p2[0]-p1[0])*(q1[1]-q2[1])-(q1[0]-q2[0])*(p2[1]-p1[1])
+	t=( dxq*dyc-dyq*dxc ) / det
+#	t=( (q1[1]-q2[1])*(q1[0]-p1[0])+(q2[0]-q1[0])*(q1[1]-p1[1]) ) / (
+#		det )
+	s=( dxp*dyc-dyp*dxc ) / det
+#	s=( (p1[1]-p2[1])*(q1[0]-p1[0])+(p2[0]-p1[0])*(q1[1]-p1[1]) ) / (
+#		det )
+
+	# check if the lines cross inside the segments from p1 to p2 and q1 to q2
+	if (0<t<1) and (0<s<1):
+		# segments cross, find which is the over crossing
+		if (p1[2] + t*(p2[2]-p1[2])) > (q1[2]+s*(q2[2]-q1[2])):
+			overunder= 1
+		else:
+			overunder= -1
+	else:
+		overunder= 0
+
+	# also check the possibility of numerical error
+	#if abs((p1[2] + t*(p2[2]-p1[2])) - (q1[2]+s*(q2[2]-q1[2])))<0.0000000001:
+	#	print('possible rounding error')
+
+	# now determine sign of crossing
+	if (det*overunder >0):
+		return 1
+	elif (det*overunder < 0):
+		return -1
+	else:
+		return 0
+
+
+if __name__ == "__main__":
+	main()
+
+# Linked triangles: 152402780
+# Unlinked triangles: 847597220
+# Total time: 11496.435719013214
+# 99% confidence interval for q: 0.033867284444444444 +/- 1.300726300256763e-05
+