SUMMARY: NIntegrate: <XXX> should be a machine-size complex...

*To*: mathgroup at smc.vnet.net*Subject*: [mg19758] SUMMARY: NIntegrate: <XXX> should be a machine-size complex...*From*: Alessandro Simonetto <simonetto at ifp.mi.cnr.it>*Date*: Wed, 15 Sep 1999 03:53:07 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Thanks to Kevin McCann and Paul Abbott replies, I discovered that Mathematica's strange message was triggered by the option MaxPoints in NIntegrate, which forces it to use a QuasiMonteCarlo algorithm, and disappears using the default (MultiDimensional) algorithm. I had forced the QuasiMonteCarlo method because of the large computation times of the default method. Paul sent me an example that solved my problem:the integration times are dramatically reduced if the integrand is biased to avoid zero values for the integrand! (disclaimer: this is my summary, so any mistakes in the above statement are my own..) If f[x,y]==InterpolateFunction[something Real], 0<f[x,y]<1 for every x,y in the integration domain, then Timing[NIntegrate[f[x,y]^2,{x,xmin,xmax},{y,ymin,ymax},AccuracyGoal->5]]]=={249. 34*Second,...} Timing[NIntegrate[famp2[x,y]^2+2, {x,xmin,xmax},{y, ymax,ymax}, AccuracyGoal->5]-2*(xmax-xmin)*(ymax-ymin)]=={26.42*Second,...} Timing[NIntegrate[famp2[x,y]^2+1, {x,xmin,xmax},{y, ymax,ymax}, AccuracyGoal->5]-(xmax-xmin)*(ymax-ymin)]=={42.96*Second,...} Thanks again to Kevin and Paul! Alessandro