Re: Recursive function

*To*: mathgroup at smc.vnet.net*Subject*: [mg115945] Re: Recursive function*From*: Achilleas Lazarides <achilleas.lazarides at gmx.com>*Date*: Thu, 27 Jan 2011 03:39:15 -0500 (EST)

For example, Manipulate[ Transpose[ NestList[{#[[2]], a #[[1]] + b #[[2]]} &, {1, 1}, 14] ] // Part[#, 2] &, {a, 1, 10, 1}, {b, 1, 10, 1} ] or you could extract the relevant numbers by eg Map[#[[2]]&,NestList[etc]] instead etc. On Jan26, 2011, at 11:06 AM, StatsMath wrote: > On Jan 25, 3:32 am, "Sjoerd C. de Vries" <sjoerd.c.devr... at gmail.com> > wrote: >> You need to make x explicitely depend on a and b as well: >> >> ClearAll[x]; >> x[t_, a_, b_] := a*x[t - 1, a, b] + b*x[t - 2, a, b] >> x[0, a_, b_] = 1; >> x[1, a_, b_] = 1; >> Manipulate[ >> Map[x[#, a, b] &, Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}] >> >> Cheers -- Sjoerd >> >> On Jan 25, 10:20 am, StatsMath <stats.ma... at gmail.com> wrote: >> >> >> >>> I am trying to compute the following function: >> >>> x[t] = a * x[t-1] + b * x[t-2] >>> x[0] = 1 >>> x[1] = 1 >> >>> For different values of a & b. >> >>> Would like to use Manipulate[] so that I can change the values of a & >>> b dynamically and observe what the resulting x[t] values are. >> >>> So wrote the following piece of code: >> >>> Clear["Global`*"] >>> x[t_Integer] := x[t] = a x[t - 1] + b x[t - 2] >>> x[0] = 1; >>> x[1] = 1; >>> Manipulate[Map[x[#] &, Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}] >> >>> Got the following results: >>> {1, 1, a + b, b + a (a + b)} >> >>> The a & b values are not being propagated so tried the following: >> >>> Clear["Global`*"] >>> x[t_Integer] := x[t] = a x[t - 1] + b x[t - 2] /; t > 2 >>> x[0] = 1; >>> x[1] = 1; >>> Manipulate[ >>> Map[(If[# == 0 || # == 1, 1, a x[# - 1] + b x[# - 2]]) &, >>> Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}] >> >>> Got the following result: >>> {1, 1, -2, -1 - a - b} >> >>> Finally got it working with the following code: >> >>> Clear["Global`*"] >>> Manipulate[ >>> Map[(If[# == 0 || # == 1, x[#] = 1, >>> x[#] = a x[# - 1] + b x[# - 2]]) &, Range[0, 20]], {a, -1, 1 , >>> 0.5}, {b, -1, 1, .5}] >> >>> The above code looks ugly, so wondering if there is a different way to >>> handle recursive functions. >> >>> Thanks!- Hide quoted text - >> >> - Show quoted text - > > Thanks for the above soln. > > Is there a way to use Nest[] or NestList[] for computing the recursive > fn and still be able to dynamically change 'a' & 'b' values with > Manipulate[]? > > Want to make sure I am not missing some technique in using Nest[] or > NestList[] to accomodate the above scenario. > > Thanks! >