Re: Random Normal deviates within compiled function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg62655] Re: Random Normal deviates within compiled function?*From*: "Ray Koopman" <koopman at sfu.ca>*Date*: Wed, 30 Nov 2005 00:07:33 -0500 (EST)*Organization*: http://groups.google.com*References*: <dln17e$gf4$1@smc.vnet.net><dmh9fg$8ul$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Lee Newman wrote: > I use the following two functions. The first generates a single value > from a normal distribution with mean and stdev specified in the > arguments. It avoids the use of Mathematica's built in distribution > functions. It will generate 10^6 values (using Table or Do) with > timing of about 4 seconds on my machine (2.8GHz P4 with 1GB RAM). The > second function is really fast. It uses the built-in NormalDistribution > function, and for some reason using RandomArray makes it quite fast. It > generates an array of 10^6 values in about 0.5seconds on my machine. > > > GaussianNoise = Compile[{{mean, _Real}, {stdev, _Real}}, > Module[{r = 0.0, x = 0.0, y = 0.0}, > While[r == 0.0 || r > 1, > x = Random[Real, {-1, 1}]; > y = Random[Real, {-1, 1}]; > r = x*x + y*y; > ]; > (x*Sqrt[-2Log[r]/r])*stdev + mean > ] > ]; > > GaussianArray = > RandomArray[NormalDistribution[#1, #2], #3] &; > (* the first argument is mean, second is the stdev and the third > specifies the length of the array. *) > > Cheers, > Lee Newman See my June 16, 2003, post "Warning -- another Random[] failure". Substituting your GaussianNoise[0,1] for Random[] in my code, and using n1 = n2 = 7, reps = 10^6, gives a residual vector z = {-3.41982, -4.12281, -.859585, -1.25571, -1.20193, -1.36457, .863248, -1.0381, .884148, 1.54233, 2.8457, 2.28917, 2.75297, 2.75567, 2.65074, 2.31981, 1.50249, 2.49637, -.324406, -.211185, -3.19893, -2.32533, -1.65605, -3.64346, -2.50297, -2.5255, -1.12445, -1.9046, -.786623, .151306, -.844143, -.570679, .6032, 1.3326, 1.1453, 1.50075, 1.76664, 3.94393, 3.67223, 1.75058, 2.30061, 1.93212, -1.00784, -.53217, -1.49742, .0818344, -.308665, -3.80073, -3.30265, -4.65006}, chisqr = 240.303, df = 49, p = 4.8*^-27. The plot is far from random.