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MathGroup Archive 2005

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Re: Partial evaulation of function terms

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53321] Re: Partial evaulation of function terms
  • From: Erich Neuwirth <erich.neuwirth at univie.ac.at>
  • Date: Thu, 6 Jan 2005 02:51:54 -0500 (EST)
  • References: <cr8dve$r5g$1@smc.vnet.net> <crb3do$age$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

It turns out there is a simple solution to my speed problem.


Parfun[amps_, freqs_] := Function[t, Apply[Plus,
    MapThread[#1*Sin[2*Pi*#2*t] &, {amps, freqs}]]]


Now
Play[Parfun[1/Range[15], 55*2^Range[15]][t], {t, 0, 1}]
takes 7.5 seconds,
and
Play[Evaluate[Parfun[1/Range[15], 55*2^Range[15]][t]], {t, 0, 1}]
takes 0.25 seconds, which is a factor of 30
and good enough for my purposes.

Is there any reason Play does not automatically do the Evaluate for
sound expressions?


Peter Pein wrote:
> Erich Neuwirth wrote:
> 
>>I have the following function definition
>>
>>ParFun[amps_, freq_] := Function[t, Sum[amps[[i]]*Sin[2*Pi*freq*i*t], {
>>     i, Length[amps]}]]
>>
>>Then, the following works:
>>
>>ParFun[{1,1/2},220][t]//InputForm
>>Sin[440*Pi*t] + Sin[880*Pi*t]/2
>>
>>but
>>ParFun[{1,1/2},220]//InputForm
>>	yields
>>Function[t$, Sum[{1, 1/2}[[i]]*Sin[2*Pi*220*i*t$], {i, Length[{1, 1/2}]}]]
>>
>>Is there a way to force Mathematica to evaluate all
>>subterms which already can be evaluated?
>>This function will be called in Play very often, so it would make things 
>>much faster if you could assign the function with all possible
>>constants evaluated to a local variable and do the many calls to the 
>>function for producing numerical values with the "partially 
>>preevaluated" expression.
> 
>    ^^^^^^^^^^^^
> You almost got it!
> 
> You can speed things further up by using floats instead of exact numbers 
> and by compiling the function:
> 
> In[1]:=
> ParFun[amps_, freq_] := Function[t, Sum[amps[[i]]*Sin[2*Pi*freq*i*t], 
> {i, Length[amps]}]]
> 
> f1 is the original function:
> 
> In[2]:=
> f1 = ParFun[1./Range[15], 440.]
> Out[2]=
> Function[t$, Sum[{1., 0.5, 0.3333333333333333, 0.25, 0.2, 
> 0.16666666666666666,
>        0.14285714285714285, 0.125, 0.1111111111111111, 0.1, 
> 0.09090909090909091,
>        0.08333333333333333, 0.07692307692307693, 0.07142857142857142,
>        0.06666666666666667}[[i]]*Sin[2*Pi*440.*i*t$],
>     {i, 1, Length[{1., 0.5, 0.3333333333333333, 0.25, 0.2, 
> 0.16666666666666666,
>        0.14285714285714285, 0.125, 0.1111111111111111, 0.1, 
> 0.09090909090909091,
>        0.08333333333333333, 0.07692307692307693, 0.07142857142857142,
>        0.06666666666666667}]}]]
> 
> Map Evaluate onto f1 to get a preevaluated version:
> 
> In[3]:=
> f2 = Evaluate /@ f1
> Out[3]=
> Function[t$, 1.*Sin[2764.601535159018*t$] + 0.5*Sin[5529.203070318036*t$] +
>     0.3333333333333333*Sin[8293.804605477053*t$] + 
> 0.25*Sin[11058.406140636072*t$] +
>     0.2*Sin[13823.00767579509*t$] + 
> 0.16666666666666666*Sin[16587.609210954106*t$] +
>     0.14285714285714285*Sin[19352.210746113127*t$] + 
> 0.125*Sin[22116.812281272145*t$] +
>     0.1111111111111111*Sin[24881.413816431163*t$] + 
> 0.1*Sin[27646.01535159018*t$] +
>     0.09090909090909091*Sin[30410.616886749198*t$] +
>     0.08333333333333333*Sin[33175.21842190821*t$] + 0.07692307692307693*
>      Sin[35939.81995706724*t$] + 
> 0.07142857142857142*Sin[38704.421492226254*t$] +
>     0.06666666666666667*Sin[41469.02302738527*t$]]
> 
> and compile it:
> 
> In[4]:=
> f3 = f2 /. HoldPattern[Function[var_, expr_]] :> Compile[{var}, expr]
> Out[4]=
> CompiledFunction[]
> 
> In[5]:=
> {t1, t2, t3} = First /@
>     (Timing[snd = Sound[SampledSoundList[
>       Table[#1[t], {t, 0, 1, 1./22050}], 22050]]; ] & ) /@ {f1, f2, f3}
> Out[5]=
> {2.3129999999999997*Second, 1.2810000000000001*Second, 
> 0.21899999999999986*Second}
> 
> Peter
> 


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