Re: Integrating Interpolation functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg89021] Re: Integrating Interpolation functions*From*: "David Park" <djmpark at comcast.net>*Date*: Sat, 24 May 2008 03:51:22 -0400 (EDT)*References*: <g15qk7$p9t$1@smc.vnet.net>

Hugh, Use Head and FunctionInterpolation. 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]] f3 = FunctionInterpolation[f1[x, t] f2[x, t], {x, 0, 1}, {t, 0, 1}] g1 = Head@Integrate[f1[x, t], {x, 0, 1}] Plot[g1[s], {s, 0, 1}] g3 = Head@Integrate[f3[x, t], {x, 0, 1}] Plot[g3[s], {s, 0, 1}] -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "Hugh Goyder" <h.g.d.goyder at cranfield.ac.uk> wrote in message news:g15qk7$p9t$1 at smc.vnet.net... > 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}] >