RE: Hold, HoldForm, ReleaseHold when Plotting multiple functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg25513] RE: [mg25481] Hold, HoldForm, ReleaseHold when Plotting multiple functions*From*: Ross Sean Civ AFRL/DELO <Sean.Ross at kirtland.af.mil>*Date*: Thu, 5 Oct 2000 23:50:32 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Thank you for your reply, but as I said to David Park, Evaluate[...] is one of the forms that generates error messages, is slower than the explicit form, but eventually works. This indicates that there is still some subtle difference between Plot[{bandwidth[28.5,x], bandwidth[28.7,x], bandwidth[28.9,x], bandwidth[29.1,x], bandwidth[29.3,x], bandwidth[29.5,x], bandwidth[29.7,x], bandwidth[29.9,x]},{x,140,200}, PlotRange->{-5,5},PlotStyle->Array[Hue[#/9.]&,9]] (*This form works quickly and generates no error messages*) ---and--- Plot[Evaluate[Map[bandwidth[#,x]&,{28.5,28.7,28.9,29.1,29.3,29.5,29.7,29.9}] ],{x,140,200}, PlotRange->{-5,5},PlotStyle->Array[Hue[#/9.]&,9]] (*This form works more slowly, generates lots of error messages associated with the functions called by bandwidth, especially the one that does root finding, but eventually plots the desired functions*) Using simple examples for the two-argument function, bandwidth, does not reveal the same issues that a complicated function does. There are many cases in which syntax that works for simple, one-line algebraic functions does not work the same way for complex functions that call other user-created functions or involve non-algebraic computations like numerical differentiation or root finding. If you have any further light to shed on this subject, please respond to sean.ross at kirtland.af.mil. Dr. Sean Ross AFRL/DELO 3550 Aberdeen Ave. Building 761 Kirtland AFB, NM 87117 Office: (505) 846-9148 Labs: (505) 853-6440/846-9289 Fax: (505) 853-0485 Email: sean.ross at kirtland.af.mil -----Original Message----- From: Matt.Johnson at autolivasp.com [mailto:Matt.Johnson at autolivasp.com] To: mathgroup at smc.vnet.net Subject: [mg25513] Re: [mg25481] Hold, HoldForm, ReleaseHold when Plotting multiple functions Sean- No Holds etc are necessary. When you Map the function over the values, a list of equations in y alone are returned. You must simply evaluate these inside Plot to get the graphics. In[15]:= \!\(\(f[x_, y_] := x\^2 + x\ y + y\^2;\)\n funs = Map[f[#, y] &, {2, 3, 4, 5}]\) Out[16]= \!\({4 + 2\ y + y\^2, 9 + 3\ y + y\^2, 16 + 4\ y + y\^2, 25 + 5\ y + y\^2}\) Plot[Evaluate[funs], {y, -10, 10}]; produces the desired type of plot. -matt Ross Sean Civ AFRL/DELO <Sean.Ross at kirtland.af.mil> on 10/02/2000 08:26:59 PM cc: Subject: [mg25513] [mg25481] Hold, HoldForm, ReleaseHold when Plotting multiple functions I wrote a function called bandwidth and want to print out a number of these functions on the same graph. Here is an example: In[1]:= Plot[{bandwidth[28.5,x], bandwidth[28.7,x], bandwidth[28.9,x], bandwidth[29.1,x], bandwidth[29.3,x], bandwidth[29.5,x], bandwidth[29.7,x], bandwidth[29.9,x]},{x,140,200}, PlotRange->{-5,5},PlotStyle->Array[Hue[#/9.]&,9]] Now, I personally think that listing out all those functions is a little clumsy. I would rather put some kind of a Map statement as the argument to Plot. Here is one that does the trick: In[2]:= Map[HoldForm[bandwidth[#,x]]&,{28.5,28.7,28.9,29.1,29.3,29.5,29.7,29.9}] However, using this code as the argument to Plot generates a lot of error messages and, ultimately, doesn't work. I know that the solution has something to do with Hold, HoldForm, ReleaseHold, Evaluate etc., but I have never been able to figure out what these things do or figure out which combination will work. Here are some combinations I have tried that kind of work: In[3]:= Plot[Evaluate[ReleaseHold[Map[HoldForm[bandwidth[#,x]] &,{28.5,28.7,28.9,29.1 ,29.3,29.5,29.7,29.9}]]],{x,140,200}, PlotRange->{-5,5},PlotStyle->Array[Hue[#/9.]&,9]] In[4]:= Plot[Evaluate[ReleaseHold[Map[Hold[bandwidth[#,x]] &,{28.5,28.7,28.9,29.1,29. 3,29.5,29.7,29.9}]]],{x,140,200}, PlotRange->{-5,5},PlotStyle->Array[Hue[#/9.]&,9]] In[3] and In[4] generate lots of error messages and take a long time, but print out the multiple graph. I have tried other combinations that don't work at all. I would greatly appreciate it if someone could tell me 1) what magic combination of Holds and Releases etc. would generate a multiple plot in the same time as the explicit version of In[1] and without generating error messages. (Please don't refer me to other packages or other kinds of solutions or approaches like MultipleListPlot or Show. I want to understand Holds and this is a good case in point.) 2) how I could have figured out what that magic combination was before hand by reading the Mathematica Book or something on the Wolfram web site. Please respond directly to Sean.Ross at kirtland.af.mil as I no longer subscribe to the mathgroup. Dr. Sean Ross AFRL/DELO 3550 Aberdeen Ave. Building 761 Kirtland AFB, NM 87117 Office: (505) 846-9148 Labs: (505) 853-6440/846-9289 Fax: (505) 853-0485 Email: sean.ross at kirtland.af.mil