Hi Regina, On Sunday, 2009-06-28 20:20:17 +0200, Regina Henschel wrote:
> Searching around I come across an iterative solution from Peter > Deuflhard [1] (German). My tests as Basic macro results in an accuracy > of at least 12 digits. But it needs approximately order+x*1.1+30 > iterations. > [1] http://www.mathematik.uni-dortmund.de/ieem/BzMU/BzMU2007/Deuflhard.pdf > > So the question is, how much iterations are acceptable? Depends of course on the cost per iteration. Hard to say. How much time is a user willing to wait for an accurate result? Which still doesn't say anything about a series of values to be calculated. But, since a non-accurate solution wouldn't help much, I guess having to wait a little isn't too much.. so I just throw a number and say 10000. Does that help anything? > For example BESSELJ(3000;200) results in -7,79235815417491E-003 with the > current implementation with asymptotic formula, but the true value is > -1.186524260848996e-2. Gnumeric results -1.186524260848841E-002, my > Basic version of Deuflhard's algorithm results -1,18652426084901E-002. > But calculating this needs 3147 iterations. For order 200 you would need > x>520000 to result in at least 1 digit accuracy with the asymptotic > formula. > Second problem: The current implementation restricts the order to > integer values. In mathematic the order need not to be integer. ODF1.2 > also allows non-integer order. Are there plans to implement a solution > in OOo with non-integer orders? I personally have no idea how to do it. No plans. Is there any practical benefit in calculating non-integer orders? Does any spreadsheet application do it? > So the question is, shall I implement Deuflhard's algorithm nevertheless? > > Perhaps warn the user in the help, that large input values results in > long lasting calculations? What is "large" and what is "long lasting"? > Or return an error, if neither asymptotic > formula results at least 2 digits (How tell the user, that the result is > not accurate?) A few functions set errNoConvergence if a function can't determine a result. > nor Deuflhard's algorithm calculates in reasonable time > (where to cut?)? "reasonable time" depends on user perspective and intention. I don't think there is a general reasonable timeout. Btw, newer g++ compilers (>= 4.3) have some bessel functions built-in, as part of the TR1 extensions, see http://en.wikipedia.org/wiki/C%2B%2B_Technical_Report_1, it appears that MSVC does not have them though. Also the Boost library provides bessel functions, I don't know off-hand which library version introduced them and if it is in the one OOo uses. Maybe time to finally upgrade ;-) Eike -- OOo/SO Calc core developer. Number formatter stricken i18n transpositionizer. SunSign 0x87F8D412 : 2F58 5236 DB02 F335 8304 7D6C 65C9 F9B5 87F8 D412 OpenOffice.org Engineering at Sun: http://blogs.sun.com/GullFOSS Please don't send personal mail to the e...@sun.com account, which I use for mailing lists only and don't read from outside Sun. Use er...@sun.com Thanks.
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