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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}]
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