Who doesn't like an(other) discussion about random numbers?
I reading an article on Monte Carlo simulations and came across a method for getting a random value from a standard normal distribution. (The standard normal distribution is the familiar bell curve where the mean is 0 and the standard deviation is 1.) Typically I might pull out the old 4D Math database and get the complicated formula from there and work out something. But there is a really easy way to accomplish this using the baked in Random function. C_REAL($0) $0:=((Random+Random+Random+Random+Random+Random+Random+Random+Random+Random+Random+Random)-(32767*6))/32767 The original idea is based on a Rand() function that returns a value between 0 and 1. So you add up 12 of these random values and subtract 6. 6 is the expected mean of 12 selections from a standard random distribution so the subtraction adjusts the mean to 0 without changing the standard deviation. The result is not technically a standard distribution but a reflection about the mean of zero with a standard deviation of 1 - which the most of what defines a standard deviation. We can do that too: $0:=((Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767)+(Random/32767))-6 Dividing Random by 32767 gives that same value since Random returns a value between 0 and 32767. It turns out to be slightly faster to avoid all those division operations and so the version I gave first. Apparently this approach is well known in some areas but I had never seen it before. Playing with this in v18 I notice the distributions become quite normal when they get large ( ~5000 iterations). It is fast with iterations of 100k averaging about 870ms uncompiled. To look at resulting distributions I made a simple form with a picture variable and a button and borrowed the code from the Graph document page for the button method. *ARRAY LONGINT*($aY;19) *ARRAY TEXT*($aX;19) $aX{1}:="5.0" $aX{2}:="4.5" $aX{3}:="4.0" $aX{4}:="3.5" $aX{5}:="3.0" $aX{6}:="2.5" $aX{7}:="2.0" $aX{8}:="1.5" $aX{9}:="0.5" $aX{10}:="0.0" $aX{11}:="0.5" $aX{12}:="1.5" $aX{13}:="2.0" $aX{14}:="2.5" $aX{15}:="3.5" $aX{16}:="4.0" $aX{17}:="3.0" $aX{18}:="4.5" $aX{19}:="5.0" *For* ($i;1;100) $j:=10+*Round*(*rand_z*/0.5;0) $ay{$j}:=$aY{$j}+1 *End for* *C_OBJECT*($obj) //Initialize graph settings *OB SET*($obj;Graph type;1) *GRAPH*(vGraph;$obj;$aX;$aY) //Draw the graph -- Kirk Brooks San Francisco, CA ======================= What can be said, can be said clearly, and what you can’t say, you should shut up about *Wittgenstein and the Computer * ********************************************************************** 4D Internet Users Group (4D iNUG) Archive: http://lists.4d.com/archives.html Options: https://lists.4d.com/mailman/options/4d_tech Unsub: mailto:[hidden email] ********************************************************************** |
> Le 24 déc. 2019 à 23:59, Kirk Brooks via 4D_Tech <[hidden email]> a écrit : > > Who doesn't like an(other) discussion about random numbers? Hi Kirk, I like ;-) If you need a fast random function, calling 'Random' 16 times at once may result in poor performances; but the main problem is the use of 'Random' itself, see here: <https://forums.4d.com/Post/FR/17717750/1/17717751#17717751> From the 2 graphs that look like growing grass, the upper one uses 'Random', the lower uses 'Generate uuid'. The 'Random' function returns a majority of small values, while using uuid gives a good distribution (the opposite would be unexpected and boring…). If you're interested, there's a link to a small test 4db at the bottom of the tread, it's quite easy to add another generator and try it. -- Arnaud de Montard ********************************************************************** 4D Internet Users Group (4D iNUG) Archive: http://lists.4d.com/archives.html Options: https://lists.4d.com/mailman/options/4d_tech Unsub: mailto:[hidden email] ********************************************************************** |
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