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replacement rules in packages


  • To: mathgroup@smc.vnet.net
  • Subject: [mg11235] replacement rules in packages
  • From: Silvia Heubach <silvi@cinenet.net>
  • Date: Mon, 2 Mar 1998 23:11:29 -0500
  • Organization: Cine Communications,Internet Access,Los Angeles;310-301-4500

My problem lies with replacement rules in packages. I have created
functions that use replacement rules both to utilize option arguments
as well as to get parameter values from built-in functions that have
answers in the form {a -> 20, b -> 30}. If I test my function in a
plain notebook, all is fine. If I make it a package following all the
info I found in Maeder, Tam, and others, it does not work. This has
happened twice to me recently, and the problem seems to lie with the
repalcement rules in the package. I have attached three files:

sinefit2.nb  - the function in a notebook, where it works fine TrigFit.m
- the package version
trial.nb 	- a notebook to check the package - lots of error messages

I am at the end of my wits - does anybody know how to fix this problem?

Please email me at silvi@cinenet.net  or if you use reply, make sure to
take out the nospam.

Thanks a lot

Silvia

(***********************************************************************

                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 3.0,
MathReader 3.0, or any compatible application. The data for the
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Cell[BoxData[
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--------------1199E6C87D7C1FBA8494D188 Content-Type: text/plain;
charset="us-ascii"; x-mac-type="54455854"; x-mac-creator="4F4D4547";
name="TrigFit.m" Content-Description: Mathematica 3.0 Document

BeginPackage["TrigFit`"]

Needs["Statistics`NonlinearFit`"]

SineFit::usage = 
  "SineFit[ls,amplitude,period,horizshift,vertshift,opts] fits 
  the data given in ls as pairs of values to a sine  function of the
form a*Sin(b x -c) + d. The parameters for the  function are amplitude
(>0), period (>0), hozizontal shift and vertical
 shift as estimated from the data. The first entry in ls may consist 
 of the names for the variables.The function will return a graph of 
 the data together with the fitted function. Optional arguments are
 plot ranges for input and output values in the usual form: 
 xplot -> {xmin,xmax},yplot ->{ymin,ymax}. Either one or both 
 may be given. The default values displays the function in the 
 range of the data"
		

Unprotect[SineFit]

Options[SineFit] = {xplot -> {minx,maxx},yplot -> {miny,maxy}}

Begin["`Private`"]

SineFit[ls_List,amplitude_?Positive,period_?Positive,horizshift_,vertshift_,
    opts___?OptionQ]:=
  Module[{A = ls,p1,p2,minx,maxx,xvals, xrange,
   miny,maxy,yvals, yrange,
   xlabel = " ", ylabel = " ", fitfun,
		 bstart = 2 Pi/period,
   cstart = 2 Pi*horizshift/period,
			dstart = vertshift, ampstart = amplitude, model,xr,yr},
		

					
		Off[General::spell1];
		Off[General::spell];	
				
  (* check whether names in first row *)  
  If[NumberQ[N[ls[[1,1]]]]==False,
          xlabel = A[[1,1]];
          ylabel = A[[1,2]];
              A = Rest[ls]];
 (* Check on proper values for ls and period *)
 If[ Length[A]<2, 
       Print[
        "There are not enough points to determine the function
uniquely"], (*else*)
					
   (* compute range for output *)
	 
          xvals = Transpose[A][[1]];
         xrange =  Max[xvals]- Min[xvals];
          minx =Min[xvals]-.1 xrange;
          maxx = Max[xvals]+.1 xrange;	
					
          yvals = Transpose[A][[2]];
          yrange =  Max[yvals]- Min[yvals];
          miny =Min[yvals]-.1 yrange;
          maxy = Max[yvals]+.1yrange;	
				

		Print[Options[SineFit]];
			
		{xr,yr} = {xplot,yplot} /. {opts} /. Options[SineFit];
			Print[{xr,yr}];
				
 (* actual curve fit *)   
  	Off[NonlinearFit::lmpnocon];
     Clear[xx];
    
			model = amp Sin[b xx - c] +d;
		pars = BestFitParameters /. NonlinearRegress[A,model,xx,
						{{amp,ampstart},{b,bstart},{c,cstart},{d,dstart}},
            RegressionReport ->BestFitParameters];
			Do[pars[[i,2]]=N[pars[[i,2]],2],{i,1,4}];
			
			Which[pars[[1,2]]==1.,
									If[pars[[2,2]] == 1.,
																model = Sin[xx-c]+d,
																model = Sin[b xx -c]+d],
	            pars[[1,2]]!= 1.,
									If[pars[[2,2]] == 1.,
																model = amp Sin[xx-c]+d],
						True,model = amp Sin[b xx - c]+d];
		model = model /. Chop[pars];
     sifit[x_]:=model/.{xx->x};
			
 (*  display of data and function *)
	
			fitfun = ToString[NumberForm[sifit[x],{10,2}]];
     p1=ListPlot[A,PlotStyle ->PointSize[0.015],
             DisplayFunction ->Identity];
     p2 = 
        Plot[Evaluate[sifit[x]],{x,xr[[1]],xr[[2]]},
          AxesOrigin -> {xr[[1]],yr[[1]]},
      AxesLabel ->{xlabel,ylabel},
          PlotLabel -> StringJoin["Fitted Function: ",fitfun],  
          DisplayFunction -> Identity];
     Show[p2,p1, PlotRange ->{ xr,yr}, 
        DisplayFunction -> $DisplayFunction]]
  ]

End[]

Protect[SineFit]

EndPackage[]
--------------1199E6C87D7C1FBA8494D188 Content-Type: text/plain;
charset="us-ascii"; x-mac-type="54455854"; x-mac-creator="4F4D4547";
name="sinefit2.nb" Content-Description: Mathematica 3.0 Document

(***********************************************************************

                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 3.0,
MathReader 3.0, or any compatible application. The data for the
notebook  starts with the line of stars above.

To get the notebook into a Mathematica-compatible application, do one of
the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be sent
directly in email or through ftp in text mode.  Newlines can be CR, LF
or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the 
word CacheID, otherwise Mathematica-compatible applications may try to 
use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info@wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from  Wolfram
Research.
***********************************************************************)

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Notebook[{
Cell[BoxData[
    \(<< Statistics`NonLinearFit`\)], "Input",
  InitializationCell->True],

Cell[BoxData[
    \(\(SineFit[ls_List, amplitude_?Positive, period_?Positive,
horizshift_, 
        vertshift_, opts___?OptionQ] := \n\ \ 
      Module[{A\  = \ ls, p1, p2, minx, maxx, xvals, \ xrange, \n\ \ \
miny, 
          maxy, yvals, \ yrange, \n\ \ \ xlabel\  = \ "\< \>", \ 
          ylabel\  = \ "\< \>", \ fitfun, \n\t\t\ bstart\  = \ 2\
Pi/period, 
          \n\ \ \ cstart\  = \ 2\ Pi*horizshift/period, \n\t\t\t
          dstart\  = \ vertshift, \ ampstart\  = \ amplitude, \ model,
xr, 
          yr}, \n\t\t\n\n\t\t\t\t\t\n\t\tOff[General::spell1]; \n\t\t
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         (*\ check\ whether\ names\ in\ first\ row\ *) \ \ \n\ \ 
        If[NumberQ[N[ls[\([1, 1]\)]]] == False, \n\ \ \ \ \ \ \ \ \ \ 
          xlabel\  = \ A[\([1, 1]\)]; \n\ \ \ \ \ \ \ \ \ \ 
          ylabel\  = \ A[\([1, 2]\)]; \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ 
          A\  = \ Rest[ls]]; \n\ 
         (*\ Check\ on\ proper\ values\ for\ ls\ and\ period\ *) \n\ 
        If[\ Length[A] < 2, \ \n\ \ \ \ \ \ \ 
          Print["\<There are not enough points to determine the function
\ uniquely\>"], \n (*else*) \n\t\t\t\t\t\n\ \ \ 
           (*\ compute\ range\ for\ output\ *) \n\t\ \n\ \ \ \ \ \ \ \ \
\ 
          xvals\  = \ \(Transpose[A]\)[\([1]\)]; \n\ \ \ \ \ \ \ \ \ 
          xrange\  = \ \ Max[xvals] - \ Min[xvals]; \n\ \ \ \ \ \ \ \ \
\ 
          minx\  = Min[xvals] - .1\ xrange; \n\ \ \ \ \ \ \ \ \ \ 
          maxx\  = \ Max[xvals] + .1\ xrange; \t\n\t\t\t\t\t\n
          \ \ \ \ \ \ \ \ \ \ yvals\  = \ \(Transpose[A]\)[\([2]\)]; \n
          \ \ \ \ \ \ \ \ \ \ yrange\  = \ \ Max[yvals] - \ Min[yvals];
\n
          \ \ \ \ \ \ \ \ \ \ miny\  = Min[yvals] - .1\ yrange; \n
          \ \ \ \ \ \ \ \ \ \ maxy\  = \ Max[yvals] + .1  yrange;
\t\n\t\t\t\t
          \n\t\t\t\t
          Options[SineFit]\  = 
            \ {xplot\  -> \ {minx, maxx}, yplot\  -> \ {miny, maxy}}; \n
          \t\t\t\tPrint[Options[SineFit]]; \n\t\t\t\n
          \t\t\t{xr, yr}\  = \ 
            \({xplot, yplot}\  /. \ {opts}\)\  /. \ Options[SineFit];
\n\t\t\t
          Print[{xr, yr}]; \n\t\t\t\t\n\  (*\ actual\ curve\ fit\ *) \ \
\ \n
          \ \ \tOff[NonlinearFit::lmpnocon]; \n\ \ \ \ \ Clear[xx]; \n\
\ \ \ 
          \n\t\t\tmodel\  = \ amp\ Sin[b\ xx\  - \ c]\  + d; \n\t\t
          pars\  = \ 
            BestFitParameters\  /. \ 
              NonlinearRegress[A, model, xx, \n
                \t\t\t\t\t\t{{amp, ampstart}, {b, bstart}, {c, cstart},
{d, 
                    dstart}}, RegressionReport\  -> BestFitParameters];
\n
          \t\t\tDo[pars[\([i, 2]\)] = N[pars[\([i, 2]\)], 2], {i, 1,
4}]; \n
          \t\t\t\n\t\t\t
          Which[pars[\([1, 2]\)] == 1., \n\t\t\t\t\t\t\t\t\t
            If[pars[\([2, 2]\)]\  == \ 1.,
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
              model\  = \ Sin[xx - c] + d,
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
              model\  = \ Sin[b\ xx\  - c] + d], \n\t\ \ \ \ \ \ \ \ \ \
\ \ 
            pars[\([1, 2]\)] != \ 1., \n\t\t\t\t\t\t\t\t\t
            If[pars[\([2, 2]\)]\  == \ 1.,
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
              model\  = \ amp\ Sin[xx - c] + d], \n\t\t\t\t\t\tTrue, 
            model\  = \ amp\ Sin[b\ xx\  - \ c] + d]; \n\t\t
          model\  = \ model\  /. \ Chop[pars]; \n\ \ \ \ \ 
          sifit[x_] := model /. {xx -> x}; \n\t\t\t\n\ 
           (*\ \ display\ of\ data\ and\ function\ *) \n\t\n\t\t\t
          fitfun\  = \ ToString[NumberForm[sifit[x], {10, 2}]]; \n\ \ \
\ \ 
          p1 = ListPlot[A, PlotStyle\  -> PointSize[0.015], \n
              \ \ \ \ \ \ \ \ \ \ \ \ \ DisplayFunction\  -> Identity];
\n
          \ \ \ \ \ 
          p2\  = \ Plot[Evaluate[sifit[x]], {x, xr[\([1]\)],
xr[\([2]\)]}, 
              AxesOrigin\  -> \ {xr[\([1]\)], yr[\([1]\)]}, \n\ \ \ \ \
\ 
              AxesLabel\  -> {xlabel, ylabel}, 
              PlotLabel\  -> \ StringJoin["\<Fitted Function: \>",
fitfun], 
              \ \ DisplayFunction\  -> \ Identity]; \n\ \ \ \ \ 
          Show[p2, p1, \ PlotRange\  -> {\ xr, yr}, \ \n\ \ \ \ \ \ \ \ 
            DisplayFunction\  -> \ $DisplayFunction]]\n\ \ ]\n\)\)],
"Input"],

Cell[BoxData[
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Cell[BoxData[
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