Re: Nested numerical integral - speed: Is it suppose to be

*To*: mathgroup at smc.vnet.net*Subject*: [mg127644] Re: Nested numerical integral - speed: Is it suppose to be*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Fri, 10 Aug 2012 02:43:21 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20120809075343.71F12664F@smc.vnet.net>

You should get a slight (>10%) improvement if you rewrite the definition of trap to trap[t_, t1_, t2_, a_] = Piecewise[{ {a t, 0 <= t < t1}, {a t1, t1 <= t < t2}, {a (-t + t1 + t2), t2 <= t < t1 + t2}}, 0]; Bob Hanlon On Thu, Aug 9, 2012 at 3:53 AM, Sune <sunenj at gmail.com> wrote: > hello. > > Newbie here, working with Mathematica 8 on a Windows 7 64-bit system, Intel core i7-2600 @3.4Ghz and 16 GB of RAM. I'm doing a relatively simple double numerical integration of a function composed of trapezoids, but was surprised to see that the computation time was relatively high. The calculation that I need takes about 13 seconds as you can see below, and I need to evaluate it over many different parameters. Is there a way to significantly increase the speed of this execution? > > Code: > > In[19]:= trap[t_,t1_,t2_,a_]:=Piecewise[{{0,t<0||t>=t1+t2},{a t,t>=0&&t<t1},{a t1,t>=t1&&t<t2},{a (-t+t1+t2),t>=t2&&t<t1+t2}}] > In[20]:= Ga[t_,t1_,t2_,a_,\[CapitalDelta]_]:=trap[t,t1,t2,a]-trap[t-2\[CapitalDelta],t1,t2,a] > In[21]:= Fa[t_?NumericQ,g_,a_,\[CapitalDelta]_,\[Delta]_]:=NIntegrate[Ga[u,g/a,\[Delta]-g/a,a,\[CapitalDelta]],{u,0,t}] > In[22]:= ba[g_,a_,\[CapitalDelta]_,\[Delta]_]:=(2.675222/10)^2 NIntegrate[Fa[x,g,a,\[CapitalDelta],\[Delta]]^2,{x,0,\[Delta]+2 \[CapitalDelta]}] > In[23]:= Timing[ba[5.5,100000,12,0.25]] > Out[23]= {13.150999999999996,3.234694880849849} > > Sune >

**References**:**Nested numerical integral - speed: Is it suppose to be so slow?***From:*Sune <sunenj@gmail.com>