Manipulating Slot objects in Compile

*To*: mathgroup at smc.vnet.net*Subject*: [mg24584] Manipulating Slot objects in Compile*From*: "Johannes Ludsteck" <ludsteck at zew.de>*Date*: Tue, 25 Jul 2000 00:56:16 -0400 (EDT)*Organization*: Zentr. f. Europ. Wirtschaftsforsch*Sender*: owner-wri-mathgroup at wolfram.com

Dear Mathgroup Members, I want to write a program which computes the gradient of any function and then compiles this expression. I tried to do this by manipulating Slot objects. Unfortunately there is the following problem: First I define an example function. f[{x_, y_}] := x^2 y^3, Then I generate a list of (unique) variables for differentiation: arg = Table[Unique[], {2}] {$1,$2} and compute the gradient: grad = Map[D[f[arg], #] &, arg] {2 $1 $2^3, 3 $1^2 $2^2} Then I generate a set of replacement rules rules = Table[arg[[i]] -> Slot[][[i]], {i, 2}] and use them in order to get compiled code by applying r to grad c = Compile[{{cArg, _Real, 1}}, Evaluate[Evaluate[grad /. r] &[cArg]]] Unfortunately, Mathematica doesn't replace the Slot[] object by cArg and I get the following Output: CompiledFunction[{cArg}, ( { 2 Slot[][[1]] Slot[][[2]]^3, 3 Slot[][[1]]^2 Slot[][[2]]^2 } & )[cArg], -CompiledCode-] Thus I tried to circumvent the problem by using Slot[1] instead: rules = Table[arg[[i]] -> Slot[][[i]], {i, 2}] Now the Slot[1] object disappeared, but Slot[1][[1]] was replaced by 1 and I got again the false result: c = Compile[{{cArg, _Real, 1}}, Evaluate[Evaluate[grad /. r] &[cArg]]] now evaluates to CompiledFunction[{cArg}, { 2 cArg[[2]]^3, 3 cArg[[2]]^2}, -CompiledCode-] The Problem here is that Slot[1][[1]] is replaced by 1. How can I force Mathematica to replace Slot[][[i]] by cArg[[i]] or to replace Slot[[1]][[1]] by cArg[[1]] instead, or is there any other way to get a compiled gradient from any function? Any suggestions? Of course, the seemingly awkward usage of Unique[] and Tables of rules is in order to collect the pieces of code into one Module which does the job for any function of any dimension (lenArg is the dimension of the argument list of function fun): compiledGradient[fun_, lenArg_] := Module[{arg, rules, grad}, arg = Table[Unique[], {lenArg}]; grad = Map[D[fun[arg], #] &, arg]; rules = Table[arg[[i]] -> Slot[][[i]], {i, lenArg}]; Compile[{{cArg, _Real, 1}}, Evaluate[Evaluate[grad /. rules] &[cArg]]]] Thank you and best regards, Johannes Ludsteck Johannes Ludsteck Centre for European Economic Research (ZEW) Department of Labour Economics, Human Resources and Social Policy Phone (+49)(0)621/1235-157 Fax (+49)(0)621/1235-225 P.O.Box 103443 D-68034 Mannheim GERMANY Email: ludsteck at zew.de