Re: Slow plotting of reflected parametric "butterflies"

*To*: mathgroup at smc.vnet.net*Subject*: [mg124536] Re: Slow plotting of reflected parametric "butterflies"*From*: Chris Young <cy56 at comcast.net>*Date*: Mon, 23 Jan 2012 02:58:02 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jf8ql4$3pl$1@smc.vnet.net> <jfe3io$a0v$1@smc.vnet.net>

Thanks very much for the good advice. I've rewritten my functions to avoid the problems. On 2012-01-21 10:21:12 +0000, Bill Rowe said: > 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. > > Finally, 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.