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:

5.0.0

Author:

Mariusz Gromada
MathParser.org - mXparser project page
mXparser on GitHub
INFIMA place to purchase a commercial MathParser.org-mXparser software license
info@mathparser.org
ScalarMath.org - a powerful math engine and math scripting language
Scalar Lite
Scalar Pro
MathSpace.pl

Field Summary

Fields

Modifier and Type	Field	Description
static int	GENERAL_DERIVATIVE
static int	LEFT_DERIVATIVE	Derivative type specification
static int	RIGHT_DERIVATIVE

Constructor Summary

Constructors

Constructor	Description
Calculus()

Method Summary

Modifier and Type	Method	Description
static double	backwardDifference(Expression f, double h, Argument x)	Backward difference(h) operator (at the current value of the argument x)
static double	backwardDifference(Expression f, double h, Argument x, double x0)	Backward difference(h) operator (at x = x0)
static double	backwardDifference(Expression f, Argument x)	Backward difference(1) operator (at current value of argument x)
static double	backwardDifference(Expression f, Argument x, double x0)	Backward difference(1) operator (at x = x0).
static double	derivative(Expression f, Argument x, double x0, int derType, double eps, int maxSteps)	Numerical derivative at x = x0
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).
static double	forwardDifference(Expression f, double h, Argument x)	Forward difference(h) operator (at the current value of the argument x)
static double	forwardDifference(Expression f, double h, Argument x, double x0)	Forward difference(h) operator (at x = x0)
static double	forwardDifference(Expression f, Argument x)	Forward difference(1) operator (at current value of argument x)
static double	forwardDifference(Expression f, Argument x, double x0)	Forward difference(1) operator (at x = x0)
static double	integralTrapezoid(Expression f, Argument x, double a, double b, double eps, int maxSteps)	Trapezoid numerical integration
static double	solveBrent(Expression f, Argument x, double a, double b, double eps, double maxSteps)	Brent solver (Brent root finder)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

LEFT_DERIVATIVE

public static final int LEFT_DERIVATIVE

Derivative type specification

See Also:

Constant Field Values

RIGHT_DERIVATIVE

public static final int RIGHT_DERIVATIVE

See Also:

Constant Field Values

GENERAL_DERIVATIVE

public static final int GENERAL_DERIVATIVE

See Also:

Constant Field Values

Constructor Detail

Calculus

public Calculus()

Method Detail

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:

Expression

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:

Expression

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:

Expression

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:

Expression, Argument

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:

Expression, Argument

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:

Expression, Argument

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:

Expression, Argument

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:

Expression, Argument

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 at the current value of the argument x.

See Also:

Expression, Argument

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:

Expression, Argument

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 at the current value of the argument x.

See Also:

Expression, Argument

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.