Dealing with InterpolatingFunction in Compile

Question

I have rather large equations that profit a lot from compiling, unfortunately they require input from external numerics and need to be interpolated.

In the end this costs a lot of performance as InterpolatingFunction triggers a MainEvaluate.

A minimal example:

testInt = Interpolation[{{0., 0.}, {2.5, 2.5}, {5., 5.}, {10., 10.}, {15., 
 15.}}];

testCompile = With[{testInt = testInt},
Compile[{{x, _Real}, {a, _Real}},
testInt[a*x], CompilationTarget -> "C", 
"RuntimeOptions" -> "Speed", 
CompilationOptions -> {"InlineExternalDefinitions" -> True, 
  "InlineCompiledFunctions" -> True}, 
RuntimeAttributes -> {Listable}, Parallelization -> False
]];

CompilePrint[testCompile]

Out[3]= "
    2 arguments
    4 Real registers
    Underflow checking off
    Overflow checking off
    Integer overflow checking off
    RuntimeAttributes -> {Listable}

    R0 = A1
    R1 = A2
    Result = R3

1   R2 = R1 * R0
2   R3 = MainEvaluate[ Hold[InterpolatingFunction[{{0., 15.}}, <>]][ R2]]
3   Return
"

The options are set as in the case of my application.

Is there any way to access circumvent this the non compilabilty of InterpolatingFunction by accessing for example the resulting piece wise polynomial?

Answer 1

Using existing code from here to extract the piece-wise polynomial from the interpolation and compile it.

data = MapIndexed[
  Flatten[{#2, #1}] &, {2, 5, 9, 15, 22, 33, 50, 70, 100, 145, 200, 280, 375, 495, 635, 800, 1000, 1300, 1600, 2000, 2450, 3050, 3750, 4600, 5650, 6950}];

intF = Interpolation@data;
pwF[x_] = Piecewise[MapIndexed[{InterpolatingPolynomial[#1, x], x < 1 First[#2] + 2} &, Most[#]], InterpolatingPolynomial[Last@#1, x]] &@Partition[data, 4, 1];
compF = With[{}, Compile[{{x, _Real}}, Evaluate[N[pwf[x]]], CompilationTarget -> "C", "RuntimeOptions" -> "Speed", RuntimeAttributes -> {Listable}, CompilationOptions -> {"InlineExternalDefinitions" -> True}]];

compF[1.]//AbsoluteTiming
pwF[1.]//AbsoluteTiming
intF[1.]//AbsoluteTiming
 {7.38984*10^-6,2.}
 {0.0000640453,2.}
 {0.0000225801,2.}

This solves the problem at hand and even speeds up the evaluation.