       Re: Functions That Remember Values They Have Found

• To: mathgroup at smc.vnet.net
• Subject: [mg127610] Re: Functions That Remember Values They Have Found
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Tue, 7 Aug 2012 03:02:06 -0400 (EDT)
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• References: <20120806083728.AC1FE683B@smc.vnet.net>

```Clear[Hgeom, Hgeom2, Hgeom3]

Hgeom[n_] := H[n] = Sum[
(1 - 0.5)^i/(1 - 0.5^i) Hgeom[n - i],
{i, 1, n}]/n
Hgeom = 1;

Hgeom

0.203175

The memory is not effective when stored under a separate name

?? Hgeom

Use the same function name for the memory

Hgeom2[n_Integer] := Hgeom2[n] =
Sum[(1 - 0.5)^i/(1 - 0.5^i)
Hgeom2[n - i], {i, 1, n}]/n;
Hgeom2 = 1;

Hgeom2

0.203175

?? Hgeom2

You could also use exact values

Hgeom3[n_Integer] := Hgeom3[n] =
Sum[2^-i/(1 - 2^-i)
Hgeom3[n - i], {i, 1, n}]/n;
Hgeom3 = 1;

Hgeom3

64/315

?? Hgeom3

Note the timing differences

m = 18;

{Timing[Hgeom[m];][],
Timing[Hgeom2[m];][],
Timing[Hgeom3[m];][]}

{3.09407, 0.001196, 0.002241}

Demonstrating that the results are equal

And @@ Table[
Hgeom[n] == Hgeom2[n] == Hgeom3[n],
{n, 0, m}]

True

Bob Hanlon

On Mon, Aug 6, 2012 at 4:37 AM, Esteban Gonz=E1lez Morales
<yo8231 at gmail.com> wrote:
> Hi, I was trying to create a recursive function and I read the help about=
it, and wrote this code
>
> Hgeom[n_] :=
>  H[n] = Sum[(1 - 0.5)^i/(1 - 0.5^i) Hgeom[n - i], {i, 1, n}]/n
> Hgeom = 1;
>
> However, when I calculate Hgeom it gives me the right value, and then=
I ask for the information about Hgeom and get that it has values calculate=
d.
>
> Have you any idea what could have gone wrong?
>

```

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