Class Calculus

    • Constructor Detail

      • Calculus

        public Calculus()
    • Method Detail

      • integralTrapezoid

        public static final 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:
        Expression
      • derivative

        public static final 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:
        Expression
      • derivativeNth

        public static final 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:
        Expression
      • forwardDifference

        public static final 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:
        Expression, Argument
      • forwardDifference

        public static final 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:
        Expression, Argument
      • backwardDifference

        public static final 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:
        Expression, Argument
      • backwardDifference

        public static final 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:
        Expression, Argument
      • forwardDifference

        public static final 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:
        Expression, Argument
      • forwardDifference

        public static final 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 at the current value of the argument x.
        See Also:
        Expression, Argument
      • backwardDifference

        public static final 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:
        Expression, Argument
      • backwardDifference

        public static final 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 at the current value of the argument x.
        See Also:
        Expression, Argument
      • solveBrent

        public static final 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.