User defined functions

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The tutorial consists of more than 200 live examples from 50 sections. Each of the examples can be copied and run on your own environment. In addition, mXparser provides an extensive collection of over 500 built-in math functions, expressions and symbols. Familiarize yourself with the scope and the syntax. Live testing is the best way to learn. Good luck! 🙂

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Below is the code for JAVA, the code for C# is almost identical. To copy the code, double-click inside the frame.

You may also be interested in the following tutorial sections:

Case 1: Fast function definition (performance of creation)

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Function f = new Function("f", "x^2", "x");
Expression e = new Expression("f(2)", f);
mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Res 2: f(5) = " + f.calculate(5));

[mXparser-v.5.2.1] Res 1: f(2) = 4.0
[mXparser-v.5.2.1] Res 2: f(5) = 25.0

Case 2: Handy function constructor, but slower proces of function creation (performance of creation slower, but calculation the same)

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Function f = new Function("f(x) = x^2");
Expression e = new Expression("f(2)", f);
mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Res 2: f(5) = " + f.calculate(5));

[mXparser-v.5.2.1] Res 1: f(2) = 4.0
[mXparser-v.5.2.1] Res 2: f(5) = 25.0

Case 3: Function with more parameters

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Function f = new Function("f(a, b, c) = a+b+c");
Expression e = new Expression("f(1,2,3)", f);
mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Res 2: f(1,2,3) = " + f.calculate(1,2,3));

[mXparser-v.5.2.1] Res 1: f(1,2,3) = 6.0
[mXparser-v.5.2.1] Res 2: f(1,2,3) = 6.0

Case 4: Function in function

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Function g = new Function("g(x) = 2*x");
Function f = new Function("f(x) = g(x)^2", g);

mXparser.consolePrintln("Res 1: g(1) = " + g.calculate(1));
mXparser.consolePrintln("Res 2: f(1) = " + f.calculate(1));

[mXparser-v.5.2.1] Res 1: g(1) = 2.0
[mXparser-v.5.2.1] Res 2: f(1) = 4.0

Case 5: Implementing your own Function Extension

// JAVA: FunctionExtension interface implementation
// ...
import org.mariuszgromada.math.mxparser.*;

class Addition implements FunctionExtension {
   double x;
   double y;
   public Addition() {
      x = Double.NaN;
      y = Double.NaN;
   }
   public Addition(double x, double y) {
      this.x = x;
      this.y = y;
   }
   public int getParametersNumber() {
      return 2;
   }
   public void setParameterValue(int argumentIndex, double argumentValue) {
      if (argumentIndex == 0) x = argumentValue;
      if (argumentIndex == 1) y = argumentValue;
   }
   public String getParameterName(int parameterIndex) {
      switch (parameterIndex) {
         case 0: return "x";
         case 1: return "y";
         default: return "";
      }
   }
   public double calculate() {
      return x+y;
   }
   public FunctionExtension clone() {
      return new Addition(x, y);
   }
}

// C#: FunctionExtension interface implementation
// ...
using System;
using org.mariuszgromada.math.mxparser;

class Addition : FunctionExtension {
   double x;
   double y;
   public Addition() {
      x = Double.NaN;
      y = Double.NaN;
   }
   public Addition(double x, double y) {
      this.x = x;
      this.y = y;
   }
   public int getParametersNumber() {
      return 2;
   }
   public void setParameterValue(int argumentIndex, double argumentValue) {
      if (argumentIndex == 0) x = argumentValue;
      if (argumentIndex == 1) y = argumentValue;
   }
   public String getParameterName(int parameterIndex) {
      switch (parameterIndex) {
         case 0: return "x";
         case 1: return "y";
         default: return "";
      }
   }
   public double calculate() {
      return x+y;
   }
   public FunctionExtension clone() {
      return new Addition(x, y);
   }
}

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...

// Creating extended function
Function f = new Function("f", new Addition());
mXparser.consolePrintln("f.calculate(1,2) = " + f.calculate(1,2) );

// Using extended function in expression
Expression e = new Expression("f(2,3)", f);
mXparser.consolePrintln(e.getExpressionString() + " = " + e.calculate() );

[mXparser-v.5.2.1] f.calculate(1,2) = 3.0
[mXparser-v.5.2.1] f(2,3) = 5.0

Case 6: Getting list of missing user defined functions

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Expression e = new Expression("2sin(pi)+2f(1)g(3,4)+4*x");
mXparser.consolePrintln("syntax = " + e.checkSyntax());
mXparser.consolePrintln(e.getErrorMessage());
mXparser.consolePrintln("List of missing user defined functions:");
for (String fun : e.getMissingUserDefinedFunctions())
   mXparser.consolePrintln("Function '" + fun + "' has to be defined");
mXparser.consolePrintln("List of missing user defined arguments:");
for (String arg : e.getMissingUserDefinedArguments())
   mXparser.consolePrintln("Argument '" + arg + "' has to be defined");

[mXparser-v.5.2.1] syntax = false
[mXparser-v.5.2.1] [2sin(pi)+2f(1)g(3,4)+4*x]: Starting syntax check...
[2sin(pi)+2f(1)g(3,4)+4*x]: Token 'f', index 10: Invalid token.
[2sin(pi)+2f(1)g(3,4)+4*x]: Token 'g', index 15: Invalid token.
[2sin(pi)+2f(1)g(3,4)+4*x]: Token 'x', index 24: Invalid token.
[2sin(pi)+2f(1)g(3,4)+4*x]: Errors have been found.
[mXparser-v.5.2.1] List of missing user defined functions:
[mXparser-v.5.2.1] Function 'f' has to be defined
[mXparser-v.5.2.1] Function 'g' has to be defined
[mXparser-v.5.2.1] List of missing user defined arguments:
[mXparser-v.5.2.1] Argument 'x' has to be defined

Case 7: Possible conflict between Implied Multiplication and getting list of missing user defined functions + recommended solutions

mXparser has many built-in constants. This list can also be expanded by user-defined arguments. As a result, a list of keywords recognized by mXparser is created. By default, the parser operates in implied multiplication mode. In this case, in many situations, these known constants / arguments will be treated as “hidden” multiplication. This is best illustrated by an example where “e” is a builtin famous Euler’s number.

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Expression e = new Expression("3*CasterAttack(4,5)");
mXparser.consolePrintln("String '" + e.getExpressionString() + "' is interpreted as '" + e.getCanonicalExpressionString() + "'");
mXparser.consolePrintln("List of missing user defined functions:");
for (String fun : e.getMissingUserDefinedFunctions())
   mXparser.consolePrintln("Function '" + fun + "' has to be defined");
mXparser.consolePrintln("List of missing user defined arguments:");
for (String arg : e.getMissingUserDefinedArguments())
   mXparser.consolePrintln("Argument '" + arg + "' has to be defined");

[mXparser-v.5.2.1] String '3*CasterAttack(4,5)' is interpreted as '3*Cast*e*rAttack(4,5)'
[mXparser-v.5.2.1] List of missing user defined functions:
[mXparser-v.5.2.1] Function 'rAttack' has to be defined
[mXparser-v.5.2.1] List of missing user defined arguments:
[mXparser-v.5.2.1] Argument 'Cast' has to be defined

Solution #1 – turn off the Implied Multiplication Mode (locally)

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
mXparser.consolePrintln("Solution #1");
Expression e = new Expression("3*CasterAttack(4,5)");
e.disableImpliedMultiplicationMode();
mXparser.consolePrintln("String '" + e.getExpressionString() + "' is interpreted as '" + e.getCanonicalExpressionString() + "'");
mXparser.consolePrintln("List of missing user defined functions:");
for (String fun : e.getMissingUserDefinedFunctions())
   mXparser.consolePrintln("Function '" + fun + "' has to be defined");
mXparser.consolePrintln("List of missing user defined arguments:");
for (String arg : e.getMissingUserDefinedArguments())
   mXparser.consolePrintln("Argument '" + arg + "' has to be defined");

[mXparser-v.5.2.1] Solution #1
[mXparser-v.5.2.1] String '3*CasterAttack(4,5)' is interpreted as '3*CasterAttack(4,5)'
[mXparser-v.5.2.1] List of missing user defined functions:
[mXparser-v.5.2.1] Function 'CasterAttack' has to be defined
[mXparser-v.5.2.1] List of missing user defined arguments:

Solution #2 – turn off the Implied Multiplication Mode (globally)

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
mXparser.consolePrintln("Solution #2");
mXparser.disableImpliedMultiplicationMode();
Expression e = new Expression("3*CasterAttack(4,5)");
mXparser.consolePrintln("String '" + e.getExpressionString() + "' is interpreted as '" + e.getCanonicalExpressionString() + "'");
mXparser.consolePrintln("List of missing user defined functions:");
for (String fun : e.getMissingUserDefinedFunctions())
   mXparser.consolePrintln("Function '" + fun + "' has to be defined");
mXparser.consolePrintln("List of missing user defined arguments:");
for (String arg : e.getMissingUserDefinedArguments())
   mXparser.consolePrintln("Argument '" + arg + "' has to be defined");

[mXparser-v.5.2.1] Solution #2
[mXparser-v.5.2.1] String '3*CasterAttack(4,5)' is interpreted as '3*CasterAttack(4,5)'
[mXparser-v.5.2.1] List of missing user defined functions:
[mXparser-v.5.2.1] Function 'CasterAttack' has to be defined
[mXparser-v.5.2.1] List of missing user defined arguments:

Solution #3 – remove builtin keyword

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
mXparser.consolePrintln("Solution #3");
mXparser.removeBuiltinTokens("e");
Expression e = new Expression("3*CasterAttack(4,5)");
mXparser.consolePrintln("String '" + e.getExpressionString() + "' is interpreted as '" + e.getCanonicalExpressionString() + "'");
mXparser.consolePrintln("List of missing user defined functions:");
for (String fun : e.getMissingUserDefinedFunctions())
   mXparser.consolePrintln("Function '" + fun + "' has to be defined");
mXparser.consolePrintln("List of missing user defined arguments:");
for (String arg : e.getMissingUserDefinedArguments())
   mXparser.consolePrintln("Argument '" + arg + "' has to be defined");

[mXparser-v.5.2.1] Solution #3
[mXparser-v.5.2.1] String '3*CasterAttack(4,5)' is interpreted as '3*CasterAttack(4,5)'
[mXparser-v.5.2.1] List of missing user defined functions:
[mXparser-v.5.2.1] Function 'CasterAttack' has to be defined
[mXparser-v.5.2.1] List of missing user defined arguments:

Solution #4 – modify builtin keyword

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
mXparser.consolePrintln("Solution #4");
mXparser.modifyBuiltinToken("e", "ee");
Expression e = new Expression("3*CasterAttack(4,5)");
mXparser.consolePrintln("String '" + e.getExpressionString() + "' is interpreted as '" + e.getCanonicalExpressionString() + "'");
mXparser.consolePrintln("List of missing user defined functions:");
for (String fun : e.getMissingUserDefinedFunctions())
   mXparser.consolePrintln("Function '" + fun + "' has to be defined");
mXparser.consolePrintln("List of missing user defined arguments:");
for (String arg : e.getMissingUserDefinedArguments())
   mXparser.consolePrintln("Argument '" + arg + "' has to be defined");

[mXparser-v.5.2.1] Solution #4
[mXparser-v.5.2.1] String '3*CasterAttack(4,5)' is interpreted as '3*CasterAttack(4,5)'
[mXparser-v.5.2.1] List of missing user defined functions:
[mXparser-v.5.2.1] Function 'CasterAttack' has to be defined
[mXparser-v.5.2.1] List of missing user defined arguments: