Re: Slow plotting of reflected parametric "butterflies"

*To*: mathgroup at smc.vnet.net*Subject*: [mg124487] Re: Slow plotting of reflected parametric "butterflies"*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sat, 21 Jan 2012 05:17:39 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 1/20/12 at 1:52 AM, cy56 at comcast.net (Christopher Young) wrote: >On Jan 19, 2012, at 11:59 AM, Murray Eisenberg wrote: >>I don't have any suggestions, at least yet, on speeding up your >>code. >However, you should avoid naming things "C" and "D", since those >names stand for objects already built into Mathematica. In fact, >didn't you notice that running your code gives Shadowing warning >messages? >I know I shouldn't name globals "C" or "D", and I try to avoid it, >but isn't Mathematica now sophisticated enough to allow localized >variables "C" and "D" as long as they don't have the same form as >the functions? I.e., it allows "overloading" of those symbols. At >any rate, I'll see if avoiding that speeds things up. Meanwhile, my >guess is that using lists of functions in ParametricPlot3D is the >main source of the slow-down, so I'm rewriting the curves as regular >one-item functions. A few comments: In most cases, Mathematica is able to get the result you want using C etc as localized variables. But, this is still bad coding in my opinion for several reasons. It makes your code harder to understand. Clearly, when you overload built-in parameters Mathematica must do more to select the correct form. That must have some performance impact. =46inally, it makes your code more fragile. Any program with the complexity of Mathematica will always have some bugs or unintended side effects. These are far more likely to be a problem for code with potential conflicts such as using C for a local variable. Best practice is simply don not use a single uppercase letter as a variable. Then you are guaranteed no conflicts. As for your code, you are using FullSimplify every time in the function CurvedButterfly is called. FullSimply is generally an expensive function to use in terms of cpu time. But, it looks like you are supplying machine precision numbers for the values of A,B,C,D etc. If so, FullSimplify won't do anything. By default, Mathematica will evaluate your expression to a machine precision value whenever all values are numeric and at least one is machine precision. So, if I've understood your code, you will be feeding FullSimplify a machine number and there is nothing to simplify. Also, expr//Flatten[#,1]& does exactly the same thing as expr//Flatten using expr//Flatten will be faster. That is: In[7]:= d = RandomReal[1, {500, 500, 500}]; In[8]:= Timing[d // Flatten[#, 1] &;] Out[8]= {0.640754,Null} In[9]:= Timing[d // Flatten;] Out[9]= {0.449603,Null} As a general rule of thumb, using simpler forms is faster.