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|
(*****************************************************************************
* *
* UNURAN -- Universal Non-Uniform Random number generator *
* *
*****************************************************************************
* *
* FILE: test_functionparser.m *
* *
* Create file with results of evaluations of algebraic expersions *
* and make C test file. *
* *
*****************************************************************************
* *
* Copyright (c) 2000-2006 Wolfgang Hoermann and Josef Leydold *
* Department of Statistics and Mathematics, WU Wien, Austria *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program; if not, write to the *
* Free Software Foundation, Inc., *
* 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA *
* *
*****************************************************************************)
(* === List of tests ========================================================*)
(* Input the function of testing in the following format :
{"function_string",{minimal_function_value,maximal_function_value,\
number_of_function_value} *)
Testsample = {
(* --- arithmetic operator --- *)
{"3.45+x", {-2, 2, 5}},
{"x-4.673", {-200, 200000, 5}},
{"3*x", {-2, 2, 5}},
{"x/5.8", {-2, 2, 5}},
{"x^12-3.345+5", {-2, 2, 5}},
{"3*x", {-2, 2, 5}},
{"2.894736*10^2", {-2, 2, 5}},
{"2.784e-2", {-2,2,5}},
{"2.784*e",{-2,2,5}},
{"-4.7285e-7*x",{-2,2,5}},
(* --- brackets --- *)
{"3*(x^5-x^4/(1.5-x))", {-2, 2, 5}},
(* --- relational operators --- *)
(*
(* Does not work for Mathematica 5.1 any more! *)
{"3*(x>1)" ,{-2,2,5}},
{"3*(x<1)" ,{-2,2,5}},
{"3*(x>=1)",{-2,2,5}},
{"3*(x<=1)",{-2,2,5}},
{"3*(x==1)",{-2,2,5}},
{"3*(2==x)",{-2,2,5}},
{"3*(x<>1)",{-2,2,5}},
{"3*(2<>x)",{-2,2,5}},
{"3*(2!=x)",{-2,2,5}},
{"3*(2=x)",{-2,2,5}},
*)
(* --- system functions --- *)
{"exp[-4*X]", {-2, 2, 5}},
{"log[x]", {1,6,6}},
{"sqrt[x]", {1,6,6}},
{"sin[x]", {1,6,6}},
{"mod[x,3]", {1,6,6}},
{"sgn[x]", {-2,2,5}},
{"sec[x]", {-2,2,5}},
{"exp[-x^2]+log[2]-Pi*sin[x+x*2]", {-5*10^1, 2.3454*10^2,7}},
{"Sin[x]*3*log[x]", {2, 4, 2}},
{"abs[x]-3*x", {-2, 2, 5}}
(*
(* does not work with Mathematica 3.0 *)
{"(sin[ ln[3*x*(cos[ 3*x^3-4.6789/(x+4)])]])-1", {-38.828,454.4*10^3,7}},
*)
(*
(* Does not work for Mathematica 5.1 any more! *)
{"exp[x^2]*(sin[x*cos[x^2-1]]+1)*((x-3*pi*x)<1)", {-3,7,5}}
*)
};
(* === Set Constants ========================================================*)
(* name of datafile file for running tests *)
DataFile = "t_functionparser.data";
(* === Define cosntants and functions for function parser ===================*)
(* --- Constants ----------------------------------------------------------- *)
pi = Pi;
e = E;
(* --- Functions ----------------------------------------------------------- *)
mod[x_,y_] := Mod[x,y];
exp[x_] := Exp[x];
log[x_] := Log[x];
sin[x_] := Sin[x];
cos[x_] := Cos[x];
tan[x_] := Tan[x];
sec[x_] := 1/Cos[x];
sqrt[x_] := Sqrt[x];
abs[x_] := Abs[x];
sgn[x_] := Sign[x];
(* === Define derivatives for these functions (according to function parser) *)
Unprotect[Derivative];
(* --- Relation Operators -------------------------------------------------- *)
Derivative[1][Sign][x_] := 0;
Derivative[1, 0][Unequal][x_, y_] := 0;
Derivative[0, 1][Unequal][x_, y_] := 0;
Derivative[1, 0][Greater][x_, y_] := 0;
Derivative[0, 1][Greater][x_, y_] := 0;
Derivative[1, 0][GreaterEqual][x_, y_] := 0;
Derivative[0, 1][GreaterEqual][x_, y_] := 0;
Derivative[1, 0][Less][x_, y_] := 0;
Derivative[0, 1][Less][x_, y_] := 0;
Derivative[1, 0][LessEqual][x_, y_] := 0;
Derivative[0, 1][LessEqual][x_, y_] := 0;
Derivative[1, 0][Mod][x_, y_] := 0;
Derivative[0, 1][Mod][x_, y_] := 0;
(* --- Functions ----------------------------------------------------------- *)
Derivative[1][Abs][x_] := sgn[x];
(* ------------------------------------------------------------------------- *)
Protect[Derivative];
(* === Write results for an expression into data file ====================== *)
UnurWriteData[expression_,points__] := Module [
(* expression ... function term *)
(* points ... list {x_min, x_max, number of points} *)
(* local variables *)
{
funct, (* string use to compute expression with Mathematica *)
x, (* argument for function *)
xmin, (* minimal value for x *)
xmax, (* maximal value for x *)
xstep (* step width *)
},
(* convert to lower case letters *)
funct = ToLowerCase[expression];
(* print function string into data file *)
WriteString[DataFile,
"function=",
UnurTransformExpression[funct],
"\n"];
(* get values for x *)
xmin = points[[1]];
xmax = points[[2]];
xstep = (xmax - xmin) / (points[[3]]-1);
xmax += xstep/2;
(* print function and its derivative at all given points *)
Do[ UnurWriteLine[x,funct],{x,xmin,xmax,xstep}];
(* add blank line *)
WriteString[DataFile,"\n"];
]; (* end of UnurWriteData[] *)
(* --- Transform expression into string for function parser ---------------- *)
UnurTransformExpression[expression_] := Module [
(* expression ... function term *)
(* local variables *)
{fstr},
(* Replace square brackets by parenthesis *)
fstr = StringReplace[ expression, {"[" -> "(", "]" -> ")"}];
(* return result *)
Return[fstr];
]; (* end of UnurTransformExpression[] *)
(* --- Transform expression into string for Mathematica computation ----------*)
UnurTransformMathExpression[expression_] := Module [
(* expression ... function term *)
(* local variables *)
{fstr},
(* replace '<>' -> '!=' *)
fstr = StringReplace[expression, {"<>" -> "!="}];
(* replace 'and' -> '&&', 'or' -> '||' *)
fstr = StringReplace[fstr,{"and" -> "&&","or" -> "||"}];
(* replace '=' -> '==' *)
fstr = StringReplace[fstr,{"=" -> "=="}];
fstr = StringReplace[fstr,{"====" -> "==","<==" -> "<=",">=="->">=",
"!==" -> "!="}];
(* replace e.g'2.45e-3' -> '1.45*10^2' *)
fstr = StringReplace[fstr,{"0e" -> "0*10^","1e" -> "1*10^",
"2e" -> "2*10^","3e" -> "3*10^",
"3e" -> "3*10^","4e" -> "4*10^",
"5e" -> "5*10^","6e" -> "6*10^",
"7e" -> "7*10^","8e" -> "8*10^",
"8e" -> "8*10^","9e" -> "9*10^"}];
(* return result *)
Return[fstr];
]; (* end of UnurTransformMathExpression[] *)
(* --- Compute function and write line into date file ---------------- *)
UnurWriteLine[xarg_,funct_] := Module [
(* xarg ... argument *)
(* funct ... function term *)
(* local variables *)
{
xval, (* numerical value of argument x *)
fx, (* value of function at x *)
dfx, (* value of derivative of function at x *)
fstr (* function term *)
},
(* argument *)
xval = N[xarg];
WriteString[DataFile, CForm[xval],"\t"];
fstr = UnurTransformMathExpression[funct];
(* function *)
fx = N[ToExpression[fstr]] /. x -> xval /. {True -> 1, False -> 0};
(* if fx is Complex the output is 'inf' *)
If[Head[fx]===Complex,
WriteString[DataFile, "inf" ,"\t"],
WriteString[DataFile, CForm[fx],"\t"] ];
(* derivative *)
dfx = N[ D[ ToExpression[fstr], x ]] /. x -> xval /. {True -> 1, False -> 0};
(* if dfx is Complex the output is 'inf' *)
If[Head[dfx]===Complex,
WriteString[DataFile, "inf" ,"\n"],
WriteString[DataFile, CForm[dfx],"\n"] ];
]; (* end of UnurWriteLine[] *)
(* === Main ================================================================ *)
Do [
fstr = Testsample[[i]][[1]];
points = Testsample[[i]][[2]];
UnurWriteData[fstr, points],
{i, 1, Length[Testsample]}
];
(* === Exit ================================================================ *)
Quit[]
|
