Re: Help with Loop to Rule Based Algorithm

*To*: mathgroup at smc.vnet.net*Subject*: [mg114780] Re: Help with Loop to Rule Based Algorithm*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 17 Dec 2010 03:27:00 -0500 (EST)*References*: <201012161048.FAA11817@smc.vnet.net>*Reply-to*: murray at math.umass.edu

Your pseudo-code seems to be using three different notations involving u: In first line, u{1} [braces, no subscript] In third line, u [ I presume alpha should be a number; but your x is, it would seem an array you're defining in the loop and your u seems to be an array, too; so is alpha a constant depending on the entire array u and the entire array x, or what ??] In fourth line, u_{i}, [ with a subscript] So first let me ask if the following, modified, pseudo-code is what you meant: x_{1} = u_{1}; for i = 2 to N alpha = f(x_{i-1}, u_{i-1}); x_{i} = x_{i-1} + alpha * (u_{i} - x_{i-1}); end for; If not, what DID you mean? If so, then in Mathematica: x[1] = u[1]; x[i_] := x[i] = x[i-1] + f[x[i-1], u[i-1]] (u[i] - x[i-1]) This is a recursive definition, of course, which may or may not suit your purposes. It gives two rules, the particular one for x at 1 (which as a particular rule takes precedence over a general rule about x), and the general, recursive rule. The latter uses the "x[i_] := x[i] = ... " expression in order to make Mathematica "remember" a value of x[i] as soon as it calculates it, in other words, to add a rule for, say, x[2] = .... and x[3] = ..., etc., as soon as they are first calculated, so the recursion doesn't have to descend to the base each time a new value is calculated. On 12/16/2010 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! > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Help with Loop to Rule Based Algorithm***From:*Daniel Lockhart <daniel.lockhart@gmail.com>