       Re: Recursive function

• To: mathgroup at smc.vnet.net
• Subject: [mg115914] Re: Recursive function
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Tue, 25 Jan 2011 06:31:14 -0500 (EST)

```On 25 Jan 2011, at 10:20, StatsMath wrote:

> I am trying to compute the following function:
>
> x[t] = a * x[t-1] + b * x[t-2]
> x = 1
> x = 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 = 1;
> x = 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 = 1;
> x = 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!
>
>

One, (rather obvious) thing you can do is:

x[t_Integer, a_, b_] :=
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, 30]], {a, -1, 1, 0.5}, {b, -1, 1, .5}]

Andrzej Kozlowski

```

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