Interpreting the interpolating function and saving data to plot with external program

Question

So far I have been solving non-linear pdes with NDSolve and then plotting the result with the in-built Plot3D and ContourPlots.

An example file can be found here.

This is a two part question with part 1 leading in to part 2.

Part 1

How do I interpret the interpolating function (how do I read it)?

For instance, I can "expand" the InterpolatingFunction with

InterpolatingFunctionGrid[hSol]

This obviously has all the points that Plot3D plots with. How do I read this, say, row-wise or column-wise to make more sense of whats going on?

Part 2

How can I save this data to a .csv format or just some external file to use, say, gnuplot or some other plotting routine?

I have trid DumpSave etc . but the resulting huge files are generally not cross platform compatible.

Answer 1

It depends on what you want to do with your data afterwards

Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
l = Flatten[
   Table[{{x, y}, x^2 + y^2}, {x, -1, 1, .1}, {y, -1, 1, .1}], 1];
f = Interpolation[l];

(* To export as a text file*)
ListPlot3D[
 r = Flatten /@ Transpose[Flatten[#, 1] & /@ 
                       {InterpolatingFunctionGrid[f], InterpolatingFunctionValuesOnGrid[f]}]]

(* Export as a CSV file *)
Export["c:\\test.csv", r];

Note: Please note that the above is needed if your function is expensive to calculate, because the following is a lot easier to type:

 Export["c:\\test.csv", Table[{x,y,f@x},{x,0,1,.1},{y,0,1,.1}]];

---

Also, you may export for other pieces of s...oftware. Like Excel:

(*I don't mean to be rude, but the following is for Excel 3D plots (OMG)*)
Export["c:\\test.xls", InterpolatingFunctionValuesOnGrid[f]]

Answer 2

Interpolation stores it's data consistent with other Mathematica functions:

Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
f = Interpolation[
   Flatten[Table[{{x, y}, Sin[x y]}, {x, 0, 1, .25}, {y, 0, 2, .25}], 
    1]];
InterpolatingFunctionGrid[f] === 
 Table[{x, y}, {x, 0, 1, .25}, {y, 0, 2, .25}]
(* True *)

To export that raw data you could use Export