RE: RE: Fast Integration of a product of 2 interpolating function s

*To*: mathgroup at smc.vnet.net*Subject*: [mg26620] RE: RE: Fast Integration of a product of 2 interpolating function s*From*: "Ersek, Ted R" <ErsekTR at navair.navy.mil>*Date*: Sat, 13 Jan 2001 22:36:03 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Earlier I wrote: --------------------- > Sebastien de Menten de Horne wanted to efficiently Integrate the product > of two IntegratingFunctions. I think the following will work. > > f=FunctionInterpolation[ Cos[x + y] + y^2, {x, -1., 1}, {y, -1., 1}]; > g=FunctionInterpolation[ Exp[y] + z/(y + 2), {y, -1., 1}, {z, -1., 1}]; > h=FunctionInterpolation[ f[x,y] g[y,z], {x,-1.,1.}, {y,-1.,1.}, > {z,-1.,1.}]; > int[x_,z_]:=Integrate[ h[x,y,z], {y, -1, 1} ] > > > The following standard package might also be helpful. > NumericalMath`NIntegrateInterpolatingFunct` > ----------------------- We can do much better because the code above performs the integration every time (int[x,z]) is used. Instead the following should be used to allow faster evaluation of int[x,z]. f=FunctionInterpolation[ Cos[x + y] + y^2, {x, -1., 1}, {y, -1., 1}]; g=FunctionInterpolation[ Exp[y] + z/(y + 2), {y, -1., 1}, {z, -1., 1}]; h=FunctionInterpolation[ f[x,y] g[y,z], {x,-1.,1.}, {y,-1.,1.}, {z,-1.,1.} ]; Clear[x,z] int[x_,z_]=Integrate[ h[x,y,z], {y, -1, 1} ] --------------- Notice I use int[x_,z_] = rather than int[x_,z_] := to ensure the integration is only done when (int) is defined. Use of Clear[x,z] is recommended since this would not work right if (x), or (z) have global values when (int) is defined. > -------------------- > Regards, > Ted Ersek >