Re: Partial evaulation of function terms
- To: mathgroup at smc.vnet.net
- Subject: [mg53245] Re: Partial evaulation of function terms
- From: Peter Pein <petsie at arcor.de>
- Date: Mon, 3 Jan 2005 04:29:22 -0500 (EST)
- References: <cr8dve$r5g$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Erich Neuwirth wrote: > I have the following function definition > > ParFun[amps_, freq_] := Function[t, Sum[amps[[i]]*Sin[2*Pi*freq*i*t], { > i, Length[amps]}]] > > Then, the following works: > > ParFun[{1,1/2},220][t]//InputForm > Sin[440*Pi*t] + Sin[880*Pi*t]/2 > > but > ParFun[{1,1/2},220]//InputForm > yields > Function[t$, 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 -- Peter Pein Berlin