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    "info": {
        "author": "KenLeung",
        "author_email": "devyat192002@gmail.com",
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        "description": "ReadMe\r\nPDRandom  by Ken Leung\r\nThe MIT License (MIT)\r\nCopyright (c) 2015 Ken Leung\r\n###Update  1.0.2####\r\nNew Feature: \r\n1. support multiprocessing\r\nfor function: RandList, GetCountList, GenCountList, OutputRawRandom, OutputGenCountList,\r\nYou can set argument nproc=NUM_OF_PROCESS\r\ne.g. gen.OutputGenCountList(int(1e6),[100,100],\"cosine2\",nproc=4,foption='a')\r\n**for windows users, u should start the program with if __name__==\"__main__\":\r\n\r\n2. you can append the existing data files\r\nset foption='a' for appending\r\n*for appending a countlist file, the binNum should be matched with the file\r\n\r\n3. new function: GenCountList(number,binNum,nproc=1) ---- directly generate and return  a countlist\r\n\r\nmisc: tidy up\r\n\r\n*any bugs, tell me via email or github\r\n\r\n#===== Information =======\r\nGenerate random numbers according to your probability function, e.g. sin(x), cos(x) , sin(x)sin(y)\r\nf: R^n -> R\r\n\r\nLogic/Method:\r\nUse acceptance-rejection method,  Step Function to be the bound function\r\n\r\n\r\nHow TO Use:\r\n*** for dimension > 1 (multivariable function) , please pass list arguments\r\n\r\n1. Define Your probability density function, e.g.\r\ndef test(input):\r\n\treturn abs(math.sin(input))\r\n\r\n*If it is multivariable function, please pass a list argument. e.g.\r\n\ttest([1,2]) # for 2D function\r\n\r\n\r\n2. create a PDRandom object\r\nranObject = PDRandom.PDRandom(test, lowerBound, UpperBound, NumDiv, NumSubDiv, dimension )\r\n\r\n# test:  your density function\r\n#\r\n# lowerBound, UpperBound: x \u03f5 [lowerBound,UpperBound) \r\n#\t\t\tfor dim >1 :  x0 \u03f5 [lowerBound[0],UpperBound[0]), x1 \u03f5 [lowerBound[1],UpperBound[1]) , ..............\r\n#\r\n# NumDiv: divide the [UpperBound - LowerBound] into numbers of divisions for the Step function (bound function)\r\n#\t\t    NumDiv >=1 . NumDiv increases -> Rejection Rate decreases (i.e. increases the acceptance chance of random numbers) ,\r\n#\t\t\tBUT large NumDiv would cause performance hit \r\n#\t\t\t* this parameter related to the performance(Speed)\r\n#\r\n# NumSubDiv (Optional): used to find the maximum value in a division, related to the accuracy, and initialization time. \r\n#\t\te.g. 1000 or [10,10,10]\r\n#\r\n# Dimension: specify how many input varibles\r\n\r\n3. Some Class Function You can Use:\r\nNext(): return one random Number\r\n\r\nRandList(num): Return a list of random numbers\r\n\r\nGetCountList(binNum, randlist): \r\n\t#To count the numbers of random numbers within the range for bins (divisions)\r\n\t# if binLowerBound <= randomNum < binUpperBound, randomNum will be counted for the bin with value = binLowerBound\r\n\t#inclusive lowerbound, exclusive upper\r\n\t\r\n\targument: \r\n\t\tbinNum: divide the range into binNum bins\r\n\t\trandlist: generated by RandList(num)\r\n\r\n\treturn a countlist,e.g. [ [bin1x, bin1y ,count], [bin2x,bin2y,count] ....... ]  for two variable function\t\r\n\te.g.  randlist = [1.1, 2.4] # lowerBound = 0, UpperBound =5 , binNum = 5 , dimension=1\r\n\t\t\tcountlist= [ [0,0]\r\n\t\t\t\t\t\t[1,1]  # 1.1 counted for 1\r\n\t\t\t\t\t\t[2,1]\t# 2.4 counted for 2\r\n\t\t\t\t\t\t[3,0]\r\n\t\t\t\t\t\t[4,0]\r\n\r\n\t\t\t\t\t\t] # total 5 number of bins\r\n\r\nOutputCountList(countlist, filename) : output to a file with filename (space sperate format)\r\n\r\nOutputRawRandom(number, filename): generate rand numbers to a file with filename\r\n\r\nOutputGenCountList (number , binNum, filename): generate and directly output the count list\r\n\r\n#===================================================================\r\n\r\nExample:\r\n1-Dim case:\r\ndef cosine (input):\r\n\treturn abs(math.cos(input))\r\ngen = PDRandom.PDRandom(cosine, -1, math.pi, 10,dimension=1)\r\ngen.OutputGenCountList(100000,50,\"consine2\")\r\n\r\nn-Dim case: n>1\r\ndef sine3(input):\r\n\treturn abs(math.sin(input[0])*math.sin(input[1])*math.sin(input[2]))\r\ngen = PDRandom.PDRandom(sine3, [-1,0,1], [math.pi,math.pi,math.pi], [10,10,10],dimension=3)\r\nlis = gen.RandList(1000)\r\nprint (gen.GetCountList([10,10,10], lis))\r\ngen.OutputGenCountList(100000,[50,50,50],\"sine3\")\r\n\r\n\r\nmisc:\r\n\tcontact: devyat192002@gmail.com\r\n\tfeel free to contact me if any question, bug, opinion, I will response as soon as possible",
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