Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!neat.cs.toronto.edu!krj From: krj@na.toronto.edu (Ken Jackson) Newsgroups: ut.na Subject: NAgMAg v89 #23 Message-ID: <89Nov15.103350est.2796@neat.cs.toronto.edu> Date: 15 Nov 89 15:34:15 GMT Distribution: ut Organization: Department of Computer Science, University of Toronto Lines: 157 From: nagmag%ukc.ac.uk@NSFNET-RELAY.AC.UK Date: Wed, 15 Nov 89 07:13:53 EST Subject: NAgMAg v89 #23 NAgMAg Wednesday, November 15 1989 Volume 89 Issue 23 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% The official electronic digest of the NAG Users Association %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Today's Topics Random Numbers and the 'Marsaglia Effect' G05CBF New library routines Replies from NAG --------------------------- Date: Sun, 22 Oct 89 17:54:35 BST From: NMM1@phoenix.cambridge.ac.uk Subject: Random Numbers and the 'Marsaglia Effect' Jonathan Wheeler asked whether G05CAF suffers from the 'Marsaglia Effect' (i.e. that numbers fall on planes in a multi-dimensional lattice. The answer is "yes, but not seriously". All multiplicative congruential generators suffer from this effect, as well as some other kinds of generator. It is typically serious only when one of the following conditions is true: 1) The generator is frightful (e.g. the late (I hope) unlamented RANDU in SSP). 2) The random number has modulus P**Q and is broken apart into its constituent 'digits' (i.e. 0 to P-1 values). 3) The multi-dimensional simulation is very sensitive to such effects, AND uses a large number of random variates. G05CAF uses a modulus of 2**59 (much more than most comparable generators) and has been validated by Marsaglia's Spectral Test at least up to dimension 8. If a simulation uses less than 10**9 numbers, it would be very unlucky to have serious problems with this effect, and even larger ones will normally be all right. All 32-bit generators (prime modulus or not) are almost certain to be worse, which is why I do not recommend them. Nick Maclaren University of Cambridge Computer Laboratory nmm1 @ uk.ac.cam.phx --------------------------- Date: 06 Nov 89 13:16:14 gmt From: P.Visscher@ed.ac.uk Subject: G05CBF Dear Sir, Madam, I have the following unexplained problem with one of the NAG routines: My (Fortran77) simulation program consists of an outer loop (replicates) and an inner loop (samples). To initialise the Random number generator (G05DDF, which calls the uniform subr.) I call G05CBF, with a random integer seed as parameter. The problem occurs whenever I call G05CBF WITHIN the outer loop, that is for every replicate. Whenever i do this the variance generated is less than it should be. Not only the overall variance (over replicates) is reduced, but also the mean variance for each sample. At first i thought that the seeds were somehow correlated, but this does not seem to be the case. Can anybody tell me what is going on? I do realise i don't have to call the initialisation routine for each replicate, but i do have programs where such a strategy is required. For each replicate I read and write a random seed from a file. This random seed is generated within the program using a uniform distribution (not necessarily a NAG routine). Peter Visscher --------------------------- Date: Wed, 15 Nov 89 11:36 GMT From: trh@uk.ac.ukc Subject: New library routines Anybody out there desperate to see any new facilities in the main Fortran library. For example, would Toeplitz linear equation solvers be of use? Anyone else have their own favourite missing facility? Come now don't be shy - lets have your suggestions! Tim --------------------------- Date: Mon, 13 Nov 89 14:54 GMT From: Caroline J Foers Subject: Replies from NAG Reply to issue 22 ----------------- re: Random Number Generation ------------------------ The results of the spectral test on the NAG random number generator are given on page 2 of the routine document for G05CAF. These results show that G05CAF is only likely to display such effects at a higher number of dimensions than the six dimensions of RNDM. Geoff Morgan --------------------------- %% For NAGUA membership details contact: %% Janet Bentley, Administrator NAGUA, %% Shore Lane Farm, Blackstone Edge Old Road, %% LITTLEBOROUGH, Lancashire, OL15 0LQ, UK. %% %% For other NAGUA enquiries contact: %% Caroline J Foers %% NAGUA Coordinator, %% NAG Users Association, %% PO Box 426, %% Oxford, OX2 8SD, U.K. %% %% e-mail caroline@uk.co.nag.vax %% %% Replies or submissions to nagmag@uk.ac.ukc %% Distribution changes to nagmag-request@uk.ac.ukc %% %% END OF ISSUE --------------------- Reposted by Prof. Kenneth R. Jackson, krj@na.toronto.edu (on Internet, CSNet, Computer Science Dept., ARPAnet, BITNET) University of Toronto, krj@na.utoronto.ca (on CDNnet and other Toronto, Ontario, X.400 nets (Europe)) Canada M5S 1A4 ...!{uunet,pyramid,watmath,ubc-cs}!utai!krj (Phone: 416-978-7075) (on UUCP) (FAX: 416-978-4765)