Skip to main content

output formatting - Real and/or improved CForm of expressions


I'd quite like to be able to automatically generate C++ versions of certain mathematical expressions that I've manipulated in Mathematica. The resultant C++ code fragment is then going to be used independently of Mathematica.


Mathematica provides a CForm function, which almost seems like what I want, but I can't get it to do basic conversions nor tell it how to convert Mathematica symbols into my C++ identifiers.


For example, I would like the output from CForm[x[0]^2] or ToString[x[0]^2, CForm] to be "std::pow(obj.x_[0], 2)". This can be a string; it doesn't need to be usable in Mathematica any more. Of course, my actual expressions of interest are a lot more complicated than this.


But:



  • I don't have a way of telling Mathematica that symbol x is to be renamed to obj.x_ (not a valid symbol name in Mathematica so can't use it directly). String manipulation after conversion is too unreliable for this so a more direct method is preferred.

  • I can't tell Mathematica that x is an array, not a function, so it gives me x(0) instead of obj.x_[0].

  • Mathematica thinks I want to use its own Power function, but I'd really like to use std::pow.



Perhaps CForm isn't suited to this task, but I would still appreciate a solution using any other available method if possible. I really think that Mathematica should be able to help me here, because it knows where I need brackets and so on.


I've tried:


Format[x[a_], CForm] :=
"obj.x_[" <> ToString[a, CForm] <> "]"

Format[Power[a_, b_], CForm] :=
"std::pow(" <> ToString[a, CForm] <> ", " <> ToString[b, CForm] <> ")"

ToString[x[0]^2, CForm]


but of course Power is protected so the second SetDelayed gives me an error, and my ToString[x[0]^2, CForm] output is really weird (Power("obj.x_[0]",2)) because I've tried to use strings in the Format.



Answer



Using SymbolicC`


I suggest to use SymbolicC. It is a very flexible and robust way to generate C (or C++) code.


It is in fact pretty easy to override the standard rules for code generation. There is a GenerateCode function in SymbolicC` package, and if you inspect it, it has a number of definitions. The one relevant here is:


GenerateCode[CExpression[SymbolicC`Private`arg_], SymbolicC`Private`opts : OptionsPattern[]] := 
ToString[CForm[HoldForm[SymbolicC`Private`arg]]]

Since symbols like CExpression are inert (have no definitions), nothing prevents you from adding UpValues to them (but do it at your own risk, all the usual warnings about redefining some built-in functionality is in order. In particular, I would not recommend to use this simultaneously with compilation to C - but see below for the better version of this method):



CExpression /: GenerateCode[CExpression[Power[arg_, pow_]]] := 
"std::pow(" <> ToString[arg, CForm] <> ", " <> ToString[pow, CForm] <> ")"

Now, if you call


ToCCodeString[CExpression[a^2]]

you get


(* "std::pow(a, 2)" *)

This is, of course, a rather simplistic rule, and the rule can be much more complex, but this can be a start.



ClearAll[CExpression]

Making it safer


Now, let us see what can be done to make this redefinition safer / more local. My suggestion is to construct a dynamic environment for C++ code generation:


withModifiedCCodeGenerate = 
Function[code,
Block[{CExpression},
CExpression /: GenerateCode[CExpression[Power[arg_, pow_]]] :=
StringJoin[
"std::pow(",

ToString[arg, CForm],
", ",
ToString[pow, CForm],
")"
];
code
]
,
HoldAll
];


Now, when you need to generate your C++ code, you call your code-generation routine within this environment:


withModifiedCCodeGenerate @ ToCCodeString[CExpression[a^2]]

This is much safer since the changes to CExpression are now localized to the execution stack of the code you run inside this environment, while the global definitions are not affected.


Comments

Popular posts from this blog

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

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}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.