How to get properties of interpolating function?

Questions
1

I have an InterpolatededFunction func and want to get some of its properties, namely:

  • Domain, Order, Method as shown in the output of func by clicking the plus-Button.
  • The functions pieces which are polynomials.
  • The value-range of the function within the domain.

I tried many things but did not succeed. The reason behind my problem is a complex plotting function that gets a function and a domain (= x-PlotRange), plots the function and many other things by Prolog and Epilog. I need a reasonable y-Plotrange which has at least to include the functions FunctionRange. Of course, I can use FindMaximum and FindMinimum, but its not so easy to get reasonable iteration starting points. Everything would be easier and faster if I had the information mentioned above.

Here is an example:

Block[{xs = {-2, 0, 1, 3, 4, 7}, ys = {0, 1, 3, 7, 2, -1}, data, xS, 
   xE, func, order = Automatic, method = "Spline"},
  xS = Min[xs]; xE = Max[xs];
  data = Thread[{xs, ys}];
  func = Interpolation[data, InterpolationOrder -> order, 
    Method -> method];
  Print[Column[{
     {xS, xE},
     data,
     {order, method},
     func,
     Plot[func[x], {x, xS, xE}, 
      Epilog -> {PointSize[Medium], Point[data]}, 
      AxesOrigin -> {0, 0}, ImageSize -> Small],
     Properties[func],
     FunctionRange[{func[x], xS <= x <= xE}, x, y]
     }]];
  ];

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2

Werner,

All that information is available by looking at the FullForm. Do

func // FullForm

to see the format and use Part to get the info. For example,

dom = func[[1]]

will give you the domain. You can even define your functions to pull the info out once you figure out what you need. For example, you can define

mydomain[x_InterpolatingFunction] := x[[1]]

Regards,

Neil

3

Recently I found a way to do it. Assume my InterpolatingFunction is stored in a variable, say x. Then

x["Methods"]

will return a list of available “fields”: {"Coordinates", "DerivativeOrder", "Domain", "ElementMesh", ...}. Then you can call any of them just like x["Coordinates"], x["Domain"] etc. By the may, there’re some fields regarding the “Method” of interpolation.

4

Thanks, Neil. This works, but is pretty tedious. I think Nicolay’s method is much clearer.

5

Thanks, Nicolay. This works indeed. I could not find that anywhere. Is it an undocumented feature?
If you write:

TableForm[{#,func[#]}&/@globFunc["Methods"]]

you get all the “properties” and you can see that the property “MethodInformation” needs more arguments and that the properties “Evaluate” and “GetPolynomial” do not work like this.

But I get the information which I really need: “InterpolationOrder”, “InterpolationMethod”, “Domain”, “Coordinates”, “ValuesOnGrid”.

This helps.

Block[{xs = {-2, 0, 1, 3, 4, 7}, ys = {0, 1, 3, 7, 2, -1}, data, xS, 
   xE, func, order = Automatic, method = "Spline"},
  xS = Min[xs]; xE = Max[xs];
  data = Thread[{xs, ys}];
  func = Interpolation[data, InterpolationOrder -> order, 
    Method -> method];
  Print[Column[{
     {xS, xE},
     data,
     {order, method},
     func,
     Plot[func[x], {x, xS, xE}, 
      Epilog -> {PointSize[Medium], Point[data]}, 
      AxesOrigin -> {0, 0}, ImageSize -> Small]
     }]];
  Print[Grid[{#, func[#]} & /@ globFunc["Methods"], 
    Alignment -> {{Right, Left}, Top}]]
  ];

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6

Interesting. I was not aware of that. Thank you.

However, we should report this as a bug because the interpolation function should support [“Properties”] which I tried before posting my response but it returned useless information. Changing to “Method” instead of “Properties” violates the latest standard used throughout the language.

Regards,

Neil

7

You are totally right, Neil. This is a bug.
I tried Properties, Options, Information before my post and searched on the net. None of them gives something helpful.

I think I once reported a bug, but don’t remember how to do this. Can you tell me?