       Help with Loop to Rule Based Algorithm

• To: mathgroup at smc.vnet.net
• Subject: [mg114761] Help with Loop to Rule Based Algorithm
• From: Daniel Lockhart <daniel.lockhart at gmail.com>
• Date: Thu, 16 Dec 2010 05:48:37 -0500 (EST)

```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!

```

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