Set the FunctionInterpolation step

Question

Is there a way to specify the grid spacing for interpolation?

For example I would like the values of a to change in step of 0.34. How can I write this step in the FunctionInterpolation?

f = FunctionInterpolation[NIntegrate[-a*(x - 5)^2 - 3 Sqrt[y] + Cos[x], {x, 0, 10}, {y, 0, 3}], {a, 0, 3}]

And what is default step Mathematica uses?

Not an answer but I always used Interpolation and made the list using Table. — userrandrand, Oct 01 '22 at 16:31

Bob Hanlon · Answer 1 · 2022-10-01T17:28:29.853

3

$Version

(* "13.1.0 for Mac OS X x86 (64-bit) (June 16, 2022)" *)

Clear["Global`*"]

f[a_?NumericQ] := 
 NIntegrate[-a*(x - 5)^2 - 3 Sqrt[y] + Cos[x], {x, 0, 10}, {y, 0, 3}]

You can specify the step size using the standard form for an iterator.

fi = FunctionInterpolation[f[a], {a, 0, 3, 0.34}]

However, the iterator stops at 2.72 and the upper portion of the interval {0, 3} then requires extrapolation.

fi[2.9]
(* bInterpolatingFunction::dmval: Input value {2.9} lies outside the range of data in the interpolating function. Extrapolation will be used. *)
(* -830.555 *)
Plot[{f[a], fi[a]}, {a, 0, 3},
 PlotStyle -> {Automatic, Dashed},
 PlotLegends ->
  Placed["Expressions", {.8, .65}]]

edited Oct 01 '22 at 17:28

answered Oct 01 '22 at 17:18

Bob Hanlon

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When I write this line fi = FunctionInterpolation[f[a], {a, 0, 3, 0.34}] Mathematica highlights step (this part , 0.34) in red, like a mistake in syntax. – Mam Mam Oct 01 '22 at 18:26
Does the code execute as expected despite the red color? If not, what version are you running and on what OS? – Bob Hanlon Oct 01 '22 at 18:49
I'm running Mathematica 12.0 on Windows 10. But surprisingly it executes correctly. Is it possible to change it? – Mam Mam Oct 01 '22 at 20:27
I'm confused. If it executes correctly, what do you want to change? – Bob Hanlon Oct 01 '22 at 22:23
It's just weird to see some red code. – Mam Mam Oct 01 '22 at 23:09
Is there any way apply EvaluateMonitor to FunctionInterpolation to I can see changing? – Mam Mam Oct 01 '22 at 23:09
To see the insides of InterpolatingFunction see here – Bob Hanlon Oct 01 '22 at 23:14

Set the FunctionInterpolation step

1 Answers1