Re: Numerical integration and list of points

*To*: mathgroup at smc.vnet.net*Subject*: [mg87702] Re: Numerical integration and list of points*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Wed, 16 Apr 2008 04:59:02 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <ftvd4f$d89$1@smc.vnet.net> <fu1u4g$omu$1@smc.vnet.net>

guerom00 wrote: > Thank you for your answers. So this IS indeed the right method. > After some tests, it's just that my list contains 20'000 elements and > the integration takes forever to finish... > I thought Mathematica crashed because I thought it was a rather simple > thing to do but it turns out I would need to run this integration on a > powerful cluster or something :) Before going to the extremes, like using a cluster, you should try *Integrate[]* rather than *NIntegrate[]*. The symbolic integration tool *Integrate[]* works very well over *InterpolatingFunction* object and it is way faster (anything between about 40 and 100 times faster on my system). For instance, it can integrate over 100,000 points in 3/4th of a second. In[1]:= data = RandomReal[{-1000, 1000}, {10, 2}]; f = Interpolation[data]; Timing@Integrate[f[x], {x, f[[1, 1, 1]], f[[1, 1, 2]]}] Timing@NIntegrate[f[x], {x, f[[1, 1, 1]], f[[1, 1, 2]]}] %[[1]]/%%[[1]] Out[3]= {0.000163, -867887.} Out[4]= {0.017414, -867887.} Out[5]= 106.834 In[6]:= data = RandomReal[{-1000, 1000}, {100000, 2}]; f = Interpolation[data]; Timing@Integrate[f[x], {x, f[[1, 1, 1]], f[[1, 1, 2]]}] Out[8]= {0.79024, -3.53364*10^7} In[9]:= $Version Out[9]= "6.0 for Mac OS X x86 (64-bit) (February 7, 2008)" Regards, -- Jean-Marc