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[?] Use NestWhile using a function with 2 arguments one sets parameters?

Robert Curl

Robert Curl, Rice University

Posted 8 years ago

I want to use gf[x_, y_] := Module[{x1, x2, xtst, fnw, f1, xnw}, xtst = Total[x]/2;fnw = LAcr[xtst, 1/12., LAI, LBI, AF, a, b, c, d, 400000.,a, y]; f1 = LAcr[x[[1]], 1/12., LAI, LBI, AF, a, b, c, d, 400000., a, y]]; Return[If[Sign[fnw] == Sign[f1], {xtst, x[[2]]}, {x[[1]], xtst}]];] as the input to NestWhile[ gf, {500., 50000.}, #[[2]] - #[[1]] > 0.0001 &] where the return parameters are {xlowerfinal,xupperfinal} are the final values of { #[[1]],#[[2]]} and the value of y is to be supplied before entering NestWhile by using the Table function to introduce a list of y values. Can one convert a a 2 variable (here x, y) function into a 1 variable function of x by automatically introducing the y values using Table? Or is there some way of making ListWhile know which variable (x) to use?

POSTED BY: Robert Curl

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Robert Curl

Robert Curl, Rice University

Posted 8 years ago

I apologize for not following the rules. The code for my actual problem using the hints by Bill Simpson follows. Unfortunately I seem to not be able to think of a simple example. This is the solution to the problem I posted earlier today using the code for the actual problem. The functions and input paramaters are defined in another notebook. gf\[Beta][{x_, \[Beta]_}] := Module[{x1, x2, xtst, fnw, f1, xnw}, xtst = Total[x]/2; fnw = LAcr[xtst, 1/12., LAI, LBI, AF, a, b, c, d, 400000., \[Alpha]0, \[Beta]]; f1 = LAcr[x[[1]], 1/12., LAI, LBI, AF, a, b, c, d, 400000., \[Alpha]0, \[Beta]]; Return[If[Sign[fnw] == Sign[f1], {xtst, x[[2]]}, {x[[1]], xtst}]];] f1 = LAcr[x[[1]], 1/12., LAI, LBI, AF, a, b, c, d, 400000., \[Alpha]0, \[Beta]]; Return[If[Sign[fnw] == Sign[f1], {xtst, x[[2]]}, {x[[1]], xtst}]];]` f[x_] := gf\[Beta][{x, .6}] t works slightly differently from previously. What used to work, doesn't. In[27]:= NestWhile[f, {500., 50000.}, test &] Out[27]= {500., 50000.} However, if I add a large integer it does. In[28]:= NestWhile[f, {500., 50000.}, test &, 100] Out[28]= {35964.7, 35964.7} The integer seems to be the number of iterations.`enter code here` In[29]:= NestWhile[f, {500., 50000.}, test &, 3] Out[29]= {25250., 37625.}

I apologize for not following the rules. The code for my actual problem using the hints by Bill Simpson follows. Unfortunately I seem to not be able to think of a simple example.

This is the solution to the problem I posted earlier today using the code for the actual problem. 
The functions and input paramaters are defined in another notebook.
gf\[Beta][{x_, \[Beta]_}] := 
 Module[{x1, x2, xtst, fnw, f1, xnw}, xtst = Total[x]/2; 
  fnw = LAcr[xtst, 1/12., LAI, LBI, AF, a, b, c, d, 
    400000., \[Alpha]0, \[Beta]]; 
  f1 = LAcr[x[[1]], 1/12., LAI, LBI, AF, a, b, c, d, 
    400000., \[Alpha]0, \[Beta]]; 
  Return[If[Sign[fnw] == Sign[f1], {xtst, x[[2]]}, {x[[1]], xtst}]];]
  f1 = LAcr[x[[1]], 1/12., LAI, LBI, AF, a, b, c, d, 
    400000., \[Alpha]0, \[Beta]]; 
  Return[If[Sign[fnw] == Sign[f1], {xtst, x[[2]]}, {x[[1]], xtst}]];]`
f[x_] := gf\[Beta][{x, .6}]
t works slightly differently from previously.  What used to work, doesn't.
In[27]:= NestWhile[f, {500., 50000.}, test &]

Out[27]= {500., 50000.}
However, if I add a large integer it does.
In[28]:= NestWhile[f, {500., 50000.}, test &, 100]

Out[28]= {35964.7, 35964.7}
The integer seems to be the number of iterations.`enter code here`
In[29]:= NestWhile[f, {500., 50000.}, test &, 3]

Out[29]= {25250., 37625.}

POSTED BY: Robert Curl

Robert Curl

Robert Curl, Rice University

Posted 8 years ago

You have solved my problem. Thank you very much for your help! There is one peculiar feature that is no problem for me. If I use f[x_] := gf][{x, .5}], it works if I use NestWhile[f, {500., 50000.}, test &, 100], but it fails if I use NestWhile[f, {500., 50000.}, test &] , i.e. omit the last parameter, which I think is supposed to be the number of previous results available for use, it doesn't work. It just spits out the original input range. The peculiar thing is that if I make the original gf have only one parameter, i.e. set a value of y in the definition of gf and use gf as a function of one parameter, this extra parameter in NestWhile is not needed.

POSTED BY: Robert Curl

Bill Simpson

Posted 8 years ago

POSTED BY: Bill Simpson

Bill Simpson

Posted 8 years ago

A common trick to distinguish names when you have more than one # or more than one x is to introduce a named function. So try changing your NestWhile[ gf, {500., 50000.}, #[[2]] - #[[1]] > 0.0001 &] to test[p_] := p[[2]] - p[[1]] > 0.0001; NestWhile[f, {500., 50000.}, test] and now you could use a separate # inside your NestWhile without confusion. Next the trick to get NestWhile to work with two arguments is to give it a list of two items instead of two individual items. Thus gf[{x_, y_}]:= instead of gf[x_, y_] and then modify your NestWhile arguments to match. If you think about this a bit then it should give you enough of a hint that you can make this work.

POSTED BY: Bill Simpson

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