Integrating Interpolation functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg88983] Integrating Interpolation functions*From*: Hugh Goyder <h.g.d.goyder at cranfield.ac.uk>*Date*: Fri, 23 May 2008 03:05:18 -0400 (EDT)

Below I given an illustrative example where I have a two-dimensional interpolation function, f1[x,t], and I integrate over x and obtain a one-dimensional expression g1 which is an interpolation function depending on t. The interpolation function g1 has a built-in argument of t ie it ends in [t]. I would prefer it to be a pure function so that I could use any variable instead of t, like the original interpolation function, f1. I give a work-around which defines a new function independent of t. However, I feel that there should be 1. A better way of getting the interpolation function from Integrate without the built in t 2.A method of using NIntegrate rather than Integrate which should be able to use the information that the function is interpolated 3. A method that would work on a product of interpolating functions Thanks Hugh data1 = Table[{x, t, Exp[(-x)*t]}, {x, 0, 1, 0.1}, {t, 0, 1, 0.1}]; data2 = Table[{x, t, Sin[x*t]}, {x, 0, 1, 0.1}, {t, 0, 1, 0.1}]; f1 = Interpolation[Flatten[data1, 1]] f2 = Interpolation[Flatten[data2, 1]] g1 = Integrate[f1[x, t], {x, 0, 1}] g2[tt_] := Evaluate[g1 /. t -> tt] Plot[g2[t], {t, 0, 1}] g3 = Integrate[f1[x, t]*f2[x, t], {x, 0, 1}]