Package org.mariuszgromada.math.mxparser.mathcollection

Class Calculus

java.lang.Object
org.mariuszgromada.math.mxparser.mathcollection.Calculus
public final class Calculus extends Object
Calculus - numerical integration, differentiation, etc...
Version:
5.2.0
Author:
Mariusz Gromada
MathParser.org - mXparser project page
mXparser on GitHub
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info@mathparser.org
ScalarMath.org - a powerful math engine and math scripting language
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MathSpace.pl

  • Field Details

  • Constructor Details

    • Calculus

      public Calculus()

  • Method Details

    • integralTrapezoid

      public static double integralTrapezoid(Expression f, Argument x, double a, double b, double eps, int maxSteps)
      Trapezoid numerical integration
      Parameters:
      f - the expression
      x - the argument
      a - form a ...
      b - ... to b
      eps - the epsilon (error)
      maxSteps - the maximum number of steps
      Returns:
      Integral value as double.
      See Also:

    • derivative

      public static double derivative(Expression f, Argument x, double x0, int derType, double eps, int maxSteps)
      Numerical derivative at x = x0
      Parameters:
      f - the expression
      x - the argument
      x0 - at point x = x0
      derType - derivative type (LEFT_DERIVATIVE, RIGHT_DERIVATIVE, GENERAL_DERIVATIVE
      eps - the epsilon (error)
      maxSteps - the maximum number of steps
      Returns:
      Derivative value as double.
      See Also:

    • derivativeNth

      public static double derivativeNth(Expression f, double n, Argument x, double x0, int derType, double eps, int maxSteps)
      Numerical n-th derivative at x = x0 (you should avoid calculation of derivatives with order higher than 2).
      Parameters:
      f - the expression
      n - the deriviative order
      x - the argument
      x0 - at point x = x0
      derType - derivative type (LEFT_DERIVATIVE, RIGHT_DERIVATIVE, GENERAL_DERIVATIVE
      eps - the epsilon (error)
      maxSteps - the maximum number of steps
      Returns:
      Derivative value as double.
      See Also:

    • forwardDifference

      public static double forwardDifference(Expression f, Argument x, double x0)
      Forward difference(1) operator (at x = x0)
      Parameters:
      f - the expression
      x - the argument name
      x0 - x = x0
      Returns:
      Forward difference(1) value calculated at x0.
      See Also:

    • forwardDifference

      public static double forwardDifference(Expression f, Argument x)
      Forward difference(1) operator (at current value of argument x)
      Parameters:
      f - the expression
      x - the argument name
      Returns:
      Forward difference(1) value calculated at the current value of argument x.
      See Also:

    • backwardDifference

      public static double backwardDifference(Expression f, Argument x, double x0)
      Backward difference(1) operator (at x = x0).
      Parameters:
      f - the expression
      x - the argument name
      x0 - x = x0
      Returns:
      Backward difference value calculated at x0.
      See Also:

    • backwardDifference

      public static double backwardDifference(Expression f, Argument x)
      Backward difference(1) operator (at current value of argument x)
      Parameters:
      f - the expression
      x - the argument name
      Returns:
      Backward difference(1) value calculated at the current value of argument x.
      See Also:

    • forwardDifference

      public static double forwardDifference(Expression f, double h, Argument x, double x0)
      Forward difference(h) operator (at x = x0)
      Parameters:
      f - the expression
      h - the difference
      x - the argument name
      x0 - x = x0
      Returns:
      Forward difference(h) value calculated at x0.
      See Also:

    • forwardDifference

      public static double forwardDifference(Expression f, double h, Argument x)
      Forward difference(h) operator (at the current value of the argument x)
      Parameters:
      f - the expression
      h - the difference
      x - the argument name
      Returns:
      Forward difference(h) value calculated at the current value of the argument x.
      See Also:

    • backwardDifference

      public static double backwardDifference(Expression f, double h, Argument x, double x0)
      Backward difference(h) operator (at x = x0)
      Parameters:
      f - the expression
      h - the difference
      x - the argument name
      x0 - x = x0
      Returns:
      Backward difference(h) value calculated at x0.
      See Also:

    • backwardDifference

      public static double backwardDifference(Expression f, double h, Argument x)
      Backward difference(h) operator (at the current value of the argument x)
      Parameters:
      f - the expression
      h - the difference
      x - the argument name
      Returns:
      Backward difference(h) value calculated at the current value of the argument x.
      See Also:

    • solveBrent

      public static double solveBrent(Expression f, Argument x, double a, double b, double eps, double maxSteps)
      Brent solver (Brent root finder)
      Parameters:
      f - Function given in the Expression form
      x - Argument
      a - Left limit
      b - Right limit
      eps - Epsilon value (accuracy)
      maxSteps - Maximum number of iterations
      Returns:
      Function root - if found, otherwise Double.NaN.