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I have a set of data like:

matrix=Table[{x,y,x+y*c1},{x,0,1,0.1},{y,0,1,0.1}]

where 'c1' is a real constant. I'm trying to create an interpolation function called 'fun' like:

fun=Interpolation[matrix,Method->"Spline"]

It obviously creates a little problem beacuse 'c1' has not a numeric values. My question: is it possible to create an interpolation function with a non-numeric constant, like 'c1' in the previously case?

Thanks for any tips and helps!

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Clear["Global`*"]

The Interpolation data needs to be structured as {{x1, y1}, f1}, {x2, y2}, f2}, ...}

data = Flatten[Table[{{x, y}, x + y*c1}, {x, 0, 1, 0.1}, {y, 0, 1, 0.1}], 1];

f[c1_] = Interpolation[data]

enter image description here

Manipulate[
 Plot3D[f[c1][x, y], {x, 0, 1}, {y, 0, 1}],
 {{c1, 1}, 0, 10, 0.1, Appearance -> "Labeled"}]

enter image description here

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