I have some more observations on this poisson distribution threshold function: prthre=: [:~.!.0 [EMAIL PROTECTED]@[ +/\@:* 1 */\@, %&(1+i.1000)
First off, the plots plot [EMAIL PROTECTED]"0 i. 713 plot [EMAIL PROTECTED]"0 i. 800 are interesting. The first shows a nearly linear trend and the second shows a catastrophic decay when we hit this limits of our numeric representation. Anyways, if we are concerned about efficiency, maybe we should not be generating a full 1000 terms when they are not needed. In other words, since the curve is nearly linear, maybe we should use a first degree polynomial to estimate the number of terms we need. ([EMAIL PROTECTED]"0 i.713) %. (i.713)^/0 1 69.4126 1.24226 >./ ([EMAIL PROTECTED]"0 i.713) - 69.4126 1.24226 p. i. 713 11.388 11.388 + 69.4126 80.8006 In other words, the polynomial 81 1.25&p. should be more than generous. In fact >./ ([EMAIL PROTECTED]"0 i.713) - 81 1.25 p. i. 713 _2.25 we can use 79 1.25&p. and still have some room to spare. However, I am going to use 80, because all I am really going for here is a safe estimate: pth=: [: ~.!.0 [EMAIL PROTECTED]@[ +/\@:* 1 */\@, ]% 1 + 80 1.25 i.@>[EMAIL PROTECTED] ] *./ (pth -: prthre)"0 i. 713 1 This variation produces the same results as before, for integers in the domain of interest. And in some cases the speedup is noticable: ts=: 6!:2,7!:[EMAIL PROTECTED] 10000 ts 'pth 2' 2.67473e_5 4032 10000 ts 'prthre 2' 0.000248684 25600 I could tune this further, using a slightly different polynomial, for example, but I would expect to get into diminishing returns rather quickly. However, I should get around to looking at normal distributions, for cases where the floating point exponent of ieee 64 bit floating point numbers will not go low enough to properly represent the necessary terms. For example: pth 1000 0 FYI, -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
