Static Public Member Functions
static double	IntegralSimpson (DlgFunctionValue f, double from, double to, int numintervals)
	Returns numerical integral of a function calculated by the composite Simpson's rule. Error: -(to-from)h^4f(4)(mi)/180 More...

static double	IntegralSimpson (double[] tabx, double[] tabf)
	Returns numerical integral of a function calculated by the Simpson's rule. Function is specified as a table of values in equidistant points. Intervals need to be equidistant, minimal number of points is 3 and must be odd. Error: -(to-from)h^4f(4)(mi)/180 More...

static double	IntegralTrapezoidal (DlgFunctionValue f, double from, double to, int numintervals)
	Returns numerical integral of a function calculated by the composite trapezoidal rule. Error: -(a-b)h^2f''(mi)/12 More...

static double	IntegralTrapezoidal (double[] tabx, double[] tabf)
	Returns numerical integral of a function calculated by the trapezoidal rule. Function is specified as a table of values in specified points. Intervals do not need to be equidistant, minimal number of points is 2. Error: -(a-b)h^2f''(mi)/12 More...

static double	DerivativeFD (DlgFunctionValue f, double x, double step)
	Calculates numerical derivative of a function according to the forward difference formula. Error: -h*f''(mi)/2 More...

static double	DerivativeBD (DlgFunctionValue f, double x, double step)
	Calculates numerical derivative of f according to the backward difference formula. Error: h*f''(mi)/2 More...

static double	DerivativeCD (DlgFunctionValue f, double x, double step)
	Calculates numerical derivative of a function according to the central difference formula. Error: -h^2*f(3)(mi)/6 More...

static double	Derivative4Point (DlgFunctionValue f, double x, double h)
	Calculates the derivative of a function with a 4 point formula. Error is of order O(h^4). More...

static double	SecondDerivativeCD (DlgFunctionValue f, double x, double step)
	Calculates numerical second derivative of a function according to the central difference formula. Error: -h^2*f(4)(mi)/12 More...

static double	SecondDerivative5Point (DlgFunctionValue f, double x, double h)
	Calculates the second order derivative of a function with a 5 point formula. Error is O(h^4). More...

static double	ThirdDerivative4Point (DlgFunctionValue f, double x, double h)
	Calculates the third order derivative of a function with a 5 point formula. Error is O(h^2). More...

static double	ThirdDerivative6Point (DlgFunctionValue f, double x, double h)
	Calculates the third order derivative of a function with a 5 point formula. Error is O(h^4). More...

static double	FourthDerivative5Point (DlgFunctionValue f, double x, double h)
	Calculates the fourth order derivative of a function with a 5 point formula. Error is O(h^2). More...

static double	FourthDerivative7Point (DlgFunctionValue f, double x, double h)
	Calculates the fourth order derivative of a function with a 5 point formula. Error is O(h^4). More...

static double	FifthDerivative7Point (DlgFunctionValue f, double x, double h)
	Calculates the fifth order derivative of a function with a 7 point formula. More...

static double	FifthDerivative9Point (DlgFunctionValue f, double x, double h)
	Calculates the fifth order derivative of a function with a 9 point formula. More...

static void	TestDifferentiation ()
	Tests numerical differentiation methods. More...

static void	TestIntegration ()
	Test for numerical integration methods. More...

Static Private Member Functions
static double	IntegralSimpsonTab (DlgFunctionValue f, double from, double to, int numintervals)
	Calculates numerical integral of a function by Simpson's rule, but through a table of values. More...

static double	IntegralTrapeZoidalTab (DlgFunctionValue f, double from, double to, int numintervals)
	Calculates numerical integral of a function by Trapezoidal rule, but through a table of values. More...

Member Function Documentation

static double IG.Num.Numeric.IntegralSimpson	(	DlgFunctionValue	f,
		double	from,
		double	to,
		int	numintervals
	)

inlinestatic

Returns numerical integral of a function calculated by the composite Simpson's rule. Error: -(to-from)*h^4*f(4)(mi)/180

Parameters

f	Function to be integrated.
from	Lower bound of integration interval.
to	Upper bound of integration interval.
numintervals	Number of sub-intervals (1 less than the numbe of evaluation points).

Returns: Integral approximation.

References IG.Num.s.

Referenced by IG.Num.RealFunctionBase.NumericalIntegral().

static double IG.Num.Numeric.IntegralSimpson	(	double[]	tabx,
		double[]	tabf
	)

inlinestatic

Returns numerical integral of a function calculated by the Simpson's rule. Function is specified as a table of values in equidistant points. Intervals need to be equidistant, minimal number of points is 3 and must be odd. Error: -(to-from)*h^4*f(4)(mi)/180

Parameters

tabx	Table of equidistant points at which function is evaluated.
tabf	Table of function values in points contained in tabx.

Returns: Integral approximation.

static double IG.Num.Numeric.IntegralTrapezoidal	(	DlgFunctionValue	f,
		double	from,
		double	to,
		int	numintervals
	)

inlinestatic

Returns numerical integral of a function calculated by the composite trapezoidal rule. Error: -(a-b)*h^2*f''(mi)/12

Parameters

f	Function to be integrated.
from	Lower bound of integration interval.
to	Upper bound of integration interval.
numintervals	Number of sub-intervals (1 less than the numbe of evaluation points).

Returns: Integral approximation.

References IG.Num.s.

static double IG.Num.Numeric.IntegralTrapezoidal	(	double[]	tabx,
		double[]	tabf
	)

inlinestatic

Returns numerical integral of a function calculated by the trapezoidal rule. Function is specified as a table of values in specified points. Intervals do not need to be equidistant, minimal number of points is 2. Error: -(a-b)*h^2*f''(mi)/12

Parameters

tabx	Table of equidistant points at which function is evaluated.
tabf	Table of function values in points contained in tabx.

Returns: Integral approximation.

static double IG.Num.Numeric.IntegralSimpsonTab	(	DlgFunctionValue	f,
		double	from,
		double	to,
		int	numintervals
	)

inlinestaticprivate

Calculates numerical integral of a function by Simpson's rule, but through a table of values.

static double IG.Num.Numeric.IntegralTrapeZoidalTab	(	DlgFunctionValue	f,
		double	from,
		double	to,
		int	numintervals
	)

inlinestaticprivate

Calculates numerical integral of a function by Trapezoidal rule, but through a table of values.

static double IG.Num.Numeric.DerivativeFD	(	DlgFunctionValue	f,
		double	x,
		double	step
	)

inlinestatic

Calculates numerical derivative of a function according to the forward difference formula. Error: -h*f''(mi)/2

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
step	Step size used in differentiation.

Returns: Derivative approximation.

static double IG.Num.Numeric.DerivativeBD	(	DlgFunctionValue	f,
		double	x,
		double	step
	)

inlinestatic

Calculates numerical derivative of f according to the backward difference formula. Error: h*f''(mi)/2

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
step	Step size used in differentiation.

Returns: Derivative approximation.

static double IG.Num.Numeric.DerivativeCD	(	DlgFunctionValue	f,
		double	x,
		double	step
	)

inlinestatic

Calculates numerical derivative of a function according to the central difference formula. Error: -h^2*f(3)(mi)/6

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
step	Step size used in differentiation.

Returns: Derivative approximation.

Referenced by IG.Num.RealFunctionBase.NumericalDerivative().

static double IG.Num.Numeric.Derivative4Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the derivative of a function with a 4 point formula. Error is of order O(h^4).

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static double IG.Num.Numeric.SecondDerivativeCD	(	DlgFunctionValue	f,
		double	x,
		double	step
	)

inlinestatic

Calculates numerical second derivative of a function according to the central difference formula. Error: -h^2*f(4)(mi)/12

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
step	Step size used in differentiation.

Returns: Derivative approximation.

Referenced by IG.Num.RealFunctionBase.NumericalSecondDerivative().

static double IG.Num.Numeric.SecondDerivative5Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the second order derivative of a function with a 5 point formula. Error is O(h^4).

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static double IG.Num.Numeric.ThirdDerivative4Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the third order derivative of a function with a 5 point formula. Error is O(h^2).

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static double IG.Num.Numeric.ThirdDerivative6Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the third order derivative of a function with a 5 point formula. Error is O(h^4).

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static double IG.Num.Numeric.FourthDerivative5Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the fourth order derivative of a function with a 5 point formula. Error is O(h^2).

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static double IG.Num.Numeric.FourthDerivative7Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the fourth order derivative of a function with a 5 point formula. Error is O(h^4).

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static double IG.Num.Numeric.FifthDerivative7Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the fifth order derivative of a function with a 7 point formula.

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static double IG.Num.Numeric.FifthDerivative9Point	(	DlgFunctionValue	f,
		double	x,
		double	h
	)

inlinestatic

Calculates the fifth order derivative of a function with a 9 point formula.

Parameters

f	Function whose derivative is calculated.
x	Value of independent variable at which derivative is calculated.
h	Step size.

static void IG.Num.Numeric.TestDifferentiation ( )

inlinestatic

Tests numerical differentiation methods.

References IG.Num.DlgFunctionValue().

static void IG.Num.Numeric.TestIntegration ( )

inlinestatic

Test for numerical integration methods.

References IG.Num.DlgFunctionValue().

The documentation for this class was generated from the following file:

igbase/numeric/FunctionNumeric.cs

Static Public Member Functions

Static Private Member Functions

Member Function Documentation