       Re: Help with Loop to Rule Based Algorithm

• To: mathgroup at smc.vnet.net
• Subject: [mg114789] Re: Help with Loop to Rule Based Algorithm
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Fri, 17 Dec 2010 03:28:39 -0500 (EST)
• References: <201012161048.FAA11817@smc.vnet.net>

```On Dec 16, 2010, at 5:48 AM, Daniel Lockhart wrote:

> Hi all,
>
> I have been a long time Mathematica user, but have always had problems
writing Mathematica code using rules from existing algorithms that
utilize loops.
>
> Suppose I want to write a simple smoothing filter, but not use any
built-in Mathematica algorithm. Just to make the point, I want the
smoothing gain/coefficient to be a nonlinear function. So, I want this
pseudocode:
>
> x_{1} = u{1};
> for i = 2 to N
>  alpha = f(x, u);
>  x_{i} = x_{i-1} + alpha * (u_{i} - x_{i-1});
> end for;
>
> if u is the input data, and f(x, u) is a nonlinear function of x and
u. If alpha was constant and 0 < alpha < 1, x would be some sort of
moving average of u.
>
> How can I do this in Mathematica without writing an explicit loop? I
am guessing some from of recursive Map, but I am at a loss on how to
start.
>
> Thanks!

You didn't specify u_{i}, I assume u_{i} = u_{1}, otherwise just use
Nest

Nest[#+f[#,u] (u-#)&,u,n]

Note, don't use capital N as a variable name, in general don't use
variable names with initial capital letters to avoid name collision with
predefined functions.

Regards,
Sseziwa

PS - If u_{i} /= u_{1} use Fold,

Fold[#+f[#,#2] (#2-#)&,First[u],Rest[u]]

Assuming u is a list of the u_{i}.

```

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