Skip to main content

compile - Catching and debugging numerical errors in compiled functions


I have a compiled function (that was created using the second method of this question). Basically it's using a compiled closure. The problem is that for some parameter values it does not evaluate. Here is a small example:


(*just some function that has a singularity at x=5*)
f = Compile[{{x, _Real, 0}, {a, _Real, 0}}, Sin[a*x*Pi/180]/(x - 5)
   , RuntimeOptions -> {"Speed", "EvaluateSymbolically" -> False}];


(*The wrapper just increments the x values by diff. Aa is the 
variable that is supposed to be inlined in the closure*)
Block[{Aa},
  With[{wrapper = 
     Compile[{{x, _Real, 0}, {diff, _Real, 0}}, 
      Evaluate@f[x + diff, Aa]]},
   min = Compile[{{xs, _Real, 1}, {Aa, _Real, 0}, {diff, _Real, 0}},
     First@Sort[wrapper[#, diff] & /@ xs]
     , CompilationOptions -> {"InlineCompiledFunctions" -> True, 

       "InlineExternalDefinitions" -> True, 
       "ExpressionOptimization" -> True}, 
     RuntimeOptions -> {"Speed"}](*compile*)
   ]
  ];

(*The warning is harmeless*)
(*CompiledFunction::cfsa:Argument diff+x at position 1 should be a machine-size real number. >>*)

(*The function is compiled*)

Needs["CompiledFunctionTools`"]
CompilePrint[min]


        3 arguments
        9 Integer registers
        11 Real registers
        3 Tensor registers
        Underflow checking off
        Overflow checking off

        Integer overflow checking off
        RuntimeAttributes -> {}

        T(R1)0 = A1
        R0 = A2
        R1 = A3
        I7 = 0
        I6 = -5
        I3 = 1
        R6 = 3.141592653589793

        I5 = 180
        Result = R7

1   I2 = Length[ T(R1)0]
2   I8 = I7
3   T(R1)1 = Table[ I2]
4   I4 = I7
5   goto 20
6   R3 = GetElement[ T(R1)0, I4]
7   R2 = R1

8   R5 = R2 + R3
9   R4 = R0
10  R8 = I5
11  R9 = Reciprocal[ R8]
12  R8 = R6 * R9
13  R9 = R4 * R5 * R8
14  R8 = Sin[ R9]
15  R9 = I6
16  R10 = R5 + R9
17  R9 = Reciprocal[ R10]

18  R8 = R8 * R9
19  Element[ T(R1)1, I8] = R8
20  if[ ++ I4 < I2] goto 6
21  T(R1)2 = Sort[ T(R1)1]]
22  R7 = Part[ T(R1)2, I3]
23  Return

But then here are the use cases:


(*everything works OK even though the singularity is in the arguments*)
min[{1,5,5},1,0]

(*=> -0.0043631*)

But for some arguments it does not:


(*But if all the arguments are singularites: BLAM!*)
min[{5,5,5},1,0]

(*=> CompiledFunction[{x,a},Sin[(a x \[Pi])/180]/(x-5),-CompiledCode-][5,Aa] *)


   CompiledFunction::cfne: Numerical error encountered; proceeding with uncompiled evaluation. >>

   CompiledFunction::cfse: Compiled expression Aa should be a machine-size real number. >>
   CompiledFunction::cfex: Could not complete external evaluation at instruction 2; proceeding with uncompiled evaluation. >>

Questions:



  • Why is this working if some of the arguments give division by zero, but does not evaluate if all of the arguments are incorrect?

  • How can one debug such problems? There is nothing obviously wrong at instruction 2 in the compiled output...

  • How to guard against and/or catch such errors in compiled code?




Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]
Post a Comment
Read more