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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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