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PDRandom  by Ken Leung
The MIT License (MIT)
Copyright (c) 2015 Ken Leung
###Update  1.0.2####
New Feature: 
1. support multiprocessing
for function: RandList, GetCountList, GenCountList, OutputRawRandom, OutputGenCountList,
You can set argument nproc=NUM_OF_PROCESS
e.g. gen.OutputGenCountList(int(1e6),[100,100],"cosine2",nproc=4,foption='a')

2. you can append the existing data files
set foption='a' for appending
*for appending a countlist file, the binNum should be matched with the file

3. new function: GenCountList(number,binNum,nproc=1) ---- directly generate and return  a countlist

misc: tidy up

*any bugs, tell me via email or github

#===== Information =======
Generate random numbers according to your probability function, e.g. sin(x), cos(x) , sin(x)sin(y)
f: R^n -> R

Logic/Method:
Use acceptance-rejection method,  Step Function to be the bound function


How TO Use:
*** for dimension > 1 (multivariable function) , please pass list arguments

1. Define Your probability density function, e.g.
def test(input):
	return abs(math.sin(input))

*If it is multivariable function, please pass a list argument. e.g.
	test([1,2]) # for 2D function


2. create a PDRandom object
ranObject = PDRandom.PDRandom(test, lowerBound, UpperBound, NumDiv, NumSubDiv, dimension )

# test:  your density function
#
# lowerBound, UpperBound: x ϵ [lowerBound,UpperBound) 
#			for dim >1 :  x0 ϵ [lowerBound[0],UpperBound[0]), x1 ϵ [lowerBound[1],UpperBound[1]) , ..............
#
# NumDiv: divide the [UpperBound - LowerBound] into numbers of divisions for the Step function (bound function)
#		    NumDiv >=1 . NumDiv increases -> Rejection Rate decreases (i.e. increases the acceptance chance of random numbers) ,
#			BUT large NumDiv would cause performance hit 
#			* this parameter related to the performance(Speed)
#
# NumSubDiv (Optional): used to find the maximum value in a division, related to the accuracy, and initialization time. 
#		e.g. 1000 or [10,10,10]
#
# Dimension: specify how many input varibles

3. Some Class Function You can Use:
Next(): return one random Number

RandList(num): Return a list of random numbers

GetCountList(binNum, randlist): 
	#To count the numbers of random numbers within the range for bins (divisions)
	# if binLowerBound <= randomNum < binUpperBound, randomNum will be counted for the bin with value = binLowerBound
	#inclusive lowerbound, exclusive upper
	
	argument: 
		binNum: divide the range into binNum bins
		randlist: generated by RandList(num)

	return a countlist,e.g. [ [bin1x, bin1y ,count], [bin2x,bin2y,count] ....... ]  for two variable function	
	e.g.  randlist = [1.1, 2.4] # lowerBound = 0, UpperBound =5 , binNum = 5 , dimension=1
			countlist= [ [0,0]
						[1,1]  # 1.1 counted for 1
						[2,1]	# 2.4 counted for 2
						[3,0]
						[4,0]

						] # total 5 number of bins

OutputCountList(countlist, filename) : output to a file with filename (space sperate format)

OutputRawRandom(number, filename): generate rand numbers to a file with filename

OutputGenCountList (number , binNum, filename): generate and directly output the count list

#===================================================================

Example:
1-Dim case:
def cosine (input):
	return abs(math.cos(input))
gen = PDRandom.PDRandom(cosine, -1, math.pi, 10,dimension=1)
gen.OutputGenCountList(100000,50,"consine2")

n-Dim case: n>1
def sine3(input):
	return abs(math.sin(input[0])*math.sin(input[1])*math.sin(input[2]))
gen = PDRandom.PDRandom(sine3, [-1,0,1], [math.pi,math.pi,math.pi], [10,10,10],dimension=3)
lis = gen.RandList(1000)
print (gen.GetCountList([10,10,10], lis))
gen.OutputGenCountList(100000,[50,50,50],"sine3")


misc:
	contact: devyat192002@gmail.com
	feel free to contact me if any question, bug, opinion, I will response as soon as possible