IG.Num.Func Class Reference

Creation of a number of standard real mathematical functions in one dimension. Conttains subclasses for specific functions ans corresponding static creator methods. Creator methods come in 3 different version: for reference form of the function (e.g. just Exp[x]), for form shifted and stretched in x direction, and general form shifted and stretched in both directions. More...

Classes
class	Constant
	A RealFunction class representing a constant function. More...
class	Cubic
	Cubic function, f(x) = a3*x*x*x + a2*x*x + a1*x + a0. Specific properties: Zero - returns a zero. Zero1 - returns the fierst zero. Zero2 - returns the second zero. Zero3 - returns the third zero. NumZeros - returns number of zeros (0, 1 or 3). HasZero - either the function has a zero or not. Min - returns function's strict minimum. Max - returns function's strict maximum. More...
class	Exp
	A RealFunction class representing exponential function. More...
class	Identity
	A RealFunction class representing identity (or linear) function. More...
class	Linear
	Linear function, f(x) = a1*x + a0. Specific properties: Zero - returns a zero. HasZero - either the function has a zero or not. More...
class	PenaltyPower
	Penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Formula: hh*((x - xx0)/dd)^pp where: dd: Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height. hh: Characteristic barrier height. Value of the function at transition point plus characteristic length. xx0: Transition point where function starts to be non-zero. pp: Power. Must be greater than 0; for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc. More...
class	Quadratic
	Quadratic function, f(x) = a2*x*x + a1*x + a0. Specific properties: Zero - returns a zero. Zero1 - returns the fierst zero. Zero2 - returns the second zero. NumZeros - 0, 1 or 2, returns number of zeros. HasZero - either the function has a zero or not. More...
class	ReciprocalPower
	A RealFunction class representing a reciprocal power function. More...
class	WeightGauss
	A RealFunction class representing bell like polynomial weighting function with finite support, based on Gaussian function (exp(-x^2)). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...
class	WeightPol3
	A RealFunction class representing bell like polynomial weighting function with finite support. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
class	WeightPol4
	A RealFunction class representing bell like polynomial weighting function with finite support, based on 4th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
class	WeightPol5
	A RealFunction class representing bell like polynomial weighting function with finite support, based on 5th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
class	WeightPol7
	A RealFunction class representing bell like polynomial weighting function with finite support, based on 7th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
class	WeightReciprocalPower
	A RealFunction class representing bell like polynomial weighting function with finite support, based on reciprocal power function (1/(1+|x|^p) where p>0 is an integer power). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...

Static Public Member Functions
static RealFunction	GetExp (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real exponential function object. More...
static RealFunction	GetExp (double Kx, double Sx)
	Creates and returns a new real exponential function object. More...
static RealFunction	GetExp ()
	Creates and returns a new real exponential function object. More...
static RealFunction	GetReciprocal (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real reciprocal power function object. More...
static RealFunction	GetReciprocal (double Kx, double Sx)
	Creates and returns a new real reciprocal power function object. More...
static RealFunction	GetReciprocal ()
	Creates and returns a new real reciprocal power function object. More...
static RealFunction	GetReciprocalPower (int power, double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real reciprocal power function object. More...
static RealFunction	GetReciprocalPower (int power, double Kx, double Sx)
	Creates and returns a new real reciprocal power function object. More...
static RealFunction	GetReciprocalPower (int power)
	Creates and returns a new real reciprocal power function object. More...
static RealFunction	GetIdentity (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real identity (or linear) function object. More...
static RealFunction	GetIdentity (double Kx, double Sx)
	Creates and returns a new real identity (or linear) function object. More...
static RealFunction	GetIdentity ()
	Creates and returns a new real identity (or linear) function object. More...
static RealFunction	GetConstant (double constantValue, double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real constant function object. More...
static RealFunction	GetConstant (double constantValue, double Kx, double Sx)
	Creates and returns a new constant function object. More...
static RealFunction	GetConstant (double constantValue)
	Creates and returns a new real identity (or linear) function object. More...
static Linear	GetLinearInterpolation (double x1, double y1, double x2, double y2)
	Creates and returns linear interpolation function with specified two values. More...
static Linear	GetLinearInterpolation (double x1, double y1, double d1)
	Creates and returns linear interpolation function with specified value and derivative. More...
static Linear	GetLinear (double a1, double a0)
	Creates and returns a new linear function with the specified coefficient. More...
static Quadratic	GetQuadraticInterpolation (double x1, double y1, double x2, double y2, double x3, double y3)
	Creates and returns quadratic interpolation function with specified two values. More...
static Quadratic	GetQuadraticInterpolation (double x1, double y1, double d1, double x2, double y2)
	Creates and returns quadratic interpolation function with specified two function values and one derivative. More...
static Quadratic	GetQuadraticInterpolation2der (double x1, double y1, double d1, double x2, double y2, double d2)
	Creates and returns quadratic interpolation function with specified two function values and two approximate derivatives. The returned interpolatinon is an average of interpolations obtained by taking into account one or another function. More...
static Quadratic	GetQuadratic (double a2, double a1, double a0)
	Creates and returns a new quadratic function with the specified coefficient. More...
static Cubic	GetCubicInterpolation (double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4)
	Creates and returns cubic interpolation function with specified two values. More...
static Cubic	GetCubicInterpolation (double x1, double y1, double d1, double x2, double y2, double d2)
	Creates and returns cubic interpolation function with specified two function values and one derivative. More...
static Cubic	GetCubic (double a3, double a2, double a1, double a0)
	Creates and returns a new cubic function with the specified coefficient. More...
static PenaltyPower	GetPenaltyPower (double barrierLength, double barrierHeght, int power)
	Creates and returns a new power penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Formula: hh*((x - xx0)/dd)^pp where: dd: Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height. hh: Characteristic barrier height. Value of the function at transition point plus characteristic length. xx0: Transition point where function starts to be non-zero. pp: Power. Must be greater than 0; for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc. More...
static PenaltyPower	GetPenaltyPower (double barrierLength, double barrierHeght, double zeroEnd, int power)
	Creates and returns a new power penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Formula: hh*((x - xx0)/dd)^pp where: dd: Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height. hh: Characteristic barrier height. Value of the function at transition point plus characteristic length. xx0: Transition point where function starts to be non-zero. pp: Power. Must be greater than 0; for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc. More...
static RealFunction	GetWeightGauss (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real polynomial weighting function object based on Gaussian function (exp(-x^2). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...
static RealFunction	GetWeightGauss (double Kx, double Sx)
	Creates and returns a new real polynomial weighting function object based on Gaussian function (exp(-x^2). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...
static RealFunction	GetWeightGauss ()
	Creates and returns a new real polynomial weighting function object based on Gaussian function (exp(-x^2). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...
static RealFunction	GetWeightReciprocalPower (int power, double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real polynomial weighting function object based on reciprocal power function (1/(1+|x|^p)). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...
static RealFunction	GetWeightReciprocalPower (int power, double Kx, double Sx)
	Creates and returns a new real polynomial weighting function object based on reciprocal power function (1/(1+|x|^p)). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...
static RealFunction	GetWeightReciprocalPower (int power)
	Creates and returns a new real polynomial weighting function object based on reciprocal power function (1/(1+|x|^p)). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1 More...
static RealFunction	GetWeightPol3 (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real polynomial weighting function object. Reference function: bell like function with final support, 0 less than or equal to |f(x)| less than or equall to 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol3 (double Kx, double Sx)
	Creates and returns a new real polynomial weighting function object. Reference function: bell like function with final support, 0 less than or equal to |f(x)| less than or equal to 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol3 ()
	Creates and returns a new real polynomial weighting function object. Reference function: bell like function with final support, 0 less than or equal to |f(x)| less than or equal to 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol4 (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real polynomial weighting function object based on 4th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol4 (double Kx, double Sx)
	Creates and returns a new real polynomial weighting function object based on 4th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol4 ()
	Creates and returns a new real polynomial weighting function object based on 4th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol5 (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real polynomial weighting function object based on 5th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol5 (double Kx, double Sx)
	Creates and returns a new real polynomial weighting function object based on 5th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol5 ()
	Creates and returns a new real polynomial weighting function object based on 5th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol7 (double Kx, double Sx, double Ky, double Sy)
	Creates and returns a new real polynomial weighting function object based on 7th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol7 (double Kx, double Sx)
	Creates and returns a new real polynomial weighting function object based on 7th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...
static RealFunction	GetWeightPol7 ()
	Creates and returns a new real polynomial weighting function object based on 7th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1 More...

Detailed Description

Creation of a number of standard real mathematical functions in one dimension. Conttains subclasses for specific functions ans corresponding static creator methods. Creator methods come in 3 different version: for reference form of the function (e.g. just Exp[x]), for form shifted and stretched in x direction, and general form shifted and stretched in both directions.

Contains subclasses that represent various commonly used functions.

Various commonly used real functions of one variable.

$A Igor xx;

Member Function Documentation

static RealFunction IG.Num.Func.GetExp ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real exponential function object.

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

Referenced by IG.Gr.PlotterZedGraph.ExampleDecorations(), and IG.Num.RealFunction.TestSpeed().

static RealFunction IG.Num.Func.GetExp ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real exponential function object.

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetExp ( )

inlinestatic

Creates and returns a new real exponential function object.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetReciprocal ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real reciprocal power function object.

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetReciprocal ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real reciprocal power function object.

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetReciprocal ( )

inlinestatic

Creates and returns a new real reciprocal power function object.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetReciprocalPower ( int  power, double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real reciprocal power function object.

Parameters

power	Power p. Reference function is f(x)=1/(x^p).
Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetReciprocalPower ( int  power, double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real reciprocal power function object.

Parameters

power	Power p. Reference function is f(x)=1/(x^p).
Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetReciprocalPower ( int  power )

inlinestatic

Creates and returns a new real reciprocal power function object.

Parameters

power

Power p. Reference function is f(x)=1/(x^p).

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetIdentity ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real identity (or linear) function object.

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

Referenced by IG.Num.GridGenerator1dFunc.MakeUniform(), and IG.Gr3d.VtkCurvePlot.SetCurveDefinition().

static RealFunction IG.Num.Func.GetIdentity ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real identity (or linear) function object.

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetIdentity ( )

inlinestatic

Creates and returns a new real identity (or linear) function object.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetConstant ( double  constantValue, double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real constant function object.

Parameters

constantValue	Value of the constant function.
Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

Referenced by IG.Gr3d.VtkCurvePlot.SetCurveDefinition().

static RealFunction IG.Num.Func.GetConstant ( double  constantValue, double  Kx, double  Sx  )

inlinestatic

Creates and returns a new constant function object.

Parameters

constantValue	Value of the constant function.
Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetConstant ( double  constantValue )

inlinestatic

Creates and returns a new real identity (or linear) function object.

Parameters

constantValue

Value of the constant function.

Returns

RealFunction object.

static Linear IG.Num.Func.GetLinearInterpolation ( double  x1, double  y1, double  x2, double  y2  )

inlinestatic

Creates and returns linear interpolation function with specified two values.

Parameters

x1	Abscissa of the first point.
y1	Value at the first point.
x2	Abscissa of the second point.
y2	Value at the second point.

References IG.Num.Func.Linear.SetInterpolation().

static Linear IG.Num.Func.GetLinearInterpolation ( double  x1, double  y1, double  d1  )

inlinestatic

Creates and returns linear interpolation function with specified value and derivative.

Parameters

x1	Abscissa of the first point.
y1	Value at the first point.
d1	Derivative at the first point.

References IG.Num.Func.Linear.SetInterpolation().

static Linear IG.Num.Func.GetLinear ( double  a1, double  a0  )

inlinestatic

Creates and returns a new linear function with the specified coefficient.

Parameters

a1	Leading coefficient - coefficient of the linear term.
a0	Constant term coefficient.

static Quadratic IG.Num.Func.GetQuadraticInterpolation ( double  x1, double  y1, double  x2, double  y2, double  x3, double  y3  )

inlinestatic

Creates and returns quadratic interpolation function with specified two values.

Parameters

x1	Abscissa of the first point.
y1	Value at the first point.
x2	Abscissa of the second point.
y2	Value at the second point.
x3	Abscissa of the third point.
y3	Value at the third point.

References IG.Num.Func.Quadratic.SetInterpolation().

static Quadratic IG.Num.Func.GetQuadraticInterpolation ( double  x1, double  y1, double  d1, double  x2, double  y2  )

inlinestatic

Creates and returns quadratic interpolation function with specified two function values and one derivative.

Parameters

x1	Abscissa of the first point.
y1	Value at the first point.
d1	Derivative at the first point.
x2	Abscissa of the second point.
y2	Value at the second point.

References IG.Num.Func.Quadratic.SetInterpolation().

static Quadratic IG.Num.Func.GetQuadraticInterpolation2der ( double  x1, double  y1, double  d1, double  x2, double  y2, double  d2  )

inlinestatic

Creates and returns quadratic interpolation function with specified two function values and two approximate derivatives. The returned interpolatinon is an average of interpolations obtained by taking into account one or another function.

Parameters

x1	Abscissa of the first point.
y1	Value at the first point.
d1	Derivative (approximate) in the first point.
x2	Abscissa of the second point.
y2	Value at the second point.
d2	Derivative (approximate) in the second point/

References IG.Num.Func.Quadratic.SetInterpolation2der().

static Quadratic IG.Num.Func.GetQuadratic ( double  a2, double  a1, double  a0  )

inlinestatic

Creates and returns a new quadratic function with the specified coefficient.

Parameters

a2	Leading coefficient - coefficient of the quadratic term.
a1	Linear term coefficient.
a0	Constant term coefficient.

static Cubic IG.Num.Func.GetCubicInterpolation ( double  x1, double  y1, double  x2, double  y2, double  x3, double  y3, double  x4, double  y4  )

inlinestatic

Creates and returns cubic interpolation function with specified two values.

Parameters

x1	Abscissa of the first point.
y1	Value at the first point.
x2	Abscissa of the second point.
y2	Value at the second point.
x3	Abscissa of the third point.
y3	Value at the third point.
x4	Abscissa of the fourth point.
y4	Value at the fifth point.

References IG.Num.Func.Cubic.SetInterpolation().

static Cubic IG.Num.Func.GetCubicInterpolation ( double  x1, double  y1, double  d1, double  x2, double  y2, double  d2  )

inlinestatic

Creates and returns cubic interpolation function with specified two function values and one derivative.

Parameters

x1	Abscissa of the first point.
y1	Value at the first point.
d1	Derivative at the first point.
x2	Abscissa of the second point.
y2	Value at the second point.
d2	Derivative in the second point.

References IG.Num.Func.Cubic.SetInterpolation().

static Cubic IG.Num.Func.GetCubic ( double  a3, double  a2, double  a1, double  a0  )

inlinestatic

Creates and returns a new cubic function with the specified coefficient.

Parameters

a3	Leading coefficient - coefficient of the cubic term.
a2	Coefficient of the quadratic term.
a1	Linear term coefficient.
a0	Constant term coefficient.

Referenced by IG.Gr.PlotterZedGraph.ExampleDecorations().

static PenaltyPower IG.Num.Func.GetPenaltyPower ( double  barrierLength, double  barrierHeght, int  power  )

inlinestatic

Creates and returns a new power penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Formula: hh*((x - xx0)/dd)^pp where: dd: Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height. hh: Characteristic barrier height. Value of the function at transition point plus characteristic length. xx0: Transition point where function starts to be non-zero. pp: Power. Must be greater than 0; for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc.

Parameters

barrierLength	Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height.
barrierHeght	Characteristic barrier height. Value of the function at transition point plus characteristic length.
power	Power. Must be greater than 0, for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc.

Referenced by IG.Num.PenaltyEvaluator.CreatePenaltyFunction().

static PenaltyPower IG.Num.Func.GetPenaltyPower ( double  barrierLength, double  barrierHeght, double  zeroEnd, int  power  )

inlinestatic

Creates and returns a new power penalty function consisting of sticked together constant zero-valued function and a power function with positive integer exponent. Formula: hh*((x - xx0)/dd)^pp where: dd: Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height. hh: Characteristic barrier height. Value of the function at transition point plus characteristic length. xx0: Transition point where function starts to be non-zero. pp: Power. Must be greater than 0; for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc.

Parameters

barrierLength	Characteristic barrier length. Length of the interval on which function grows from 0 to characteristic height.
barrierHeght	Characteristic barrier height. Value of the function at transition point plus characteristic length.
zeroEnd	Transition point where function starts to be non-zero.
power	Power. Must be greater than 0, for 2 first derivative is continuous in transition points, for 3 second derivative is also continuous, etc.

static RealFunction IG.Num.Func.GetWeightGauss ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on Gaussian function (exp(-x^2). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

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

static RealFunction IG.Num.Func.GetWeightGauss ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on Gaussian function (exp(-x^2). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightGauss ( )

inlinestatic

Creates and returns a new real polynomial weighting function object based on Gaussian function (exp(-x^2). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightReciprocalPower ( int  power, double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on reciprocal power function (1/(1+|x|^p)). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1

Parameters

power	Power to which argument is raised.
Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightReciprocalPower ( int  power, double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on reciprocal power function (1/(1+|x|^p)). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1

Parameters

power	Power to whic argument is raised.
Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightReciprocalPower ( int  power )

inlinestatic

Creates and returns a new real polynomial weighting function object based on reciprocal power function (1/(1+|x|^p)). Reference function: bell like function with infinite support, 0 less than |f(x)| less than or equal to 1 f(0) = 1

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol3 ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real polynomial weighting function object. Reference function: bell like function with final support, 0 less than or equal to |f(x)| less than or equall to 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol3 ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real polynomial weighting function object. Reference function: bell like function with final support, 0 less than or equal to |f(x)| less than or equal to 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol3 ( )

inlinestatic

Creates and returns a new real polynomial weighting function object. Reference function: bell like function with final support, 0 less than or equal to |f(x)| less than or equal to 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol4 ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 4th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol4 ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 4th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol4 ( )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 4th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol5 ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 5th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol5 ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 5th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol5 ( )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 5th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol7 ( double  Kx, double  Sx, double  Ky, double  Sy  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 7th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.
Ky	Scaling factor for dependent variable.
Sy	Shift in dependent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol7 ( double  Kx, double  Sx  )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 7th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Parameters

Kx	Scaling factor for independent variable.
Sx	Shift in independent variable.

Returns

RealFunction object.

static RealFunction IG.Num.Func.GetWeightPol7 ( )

inlinestatic

Creates and returns a new real polynomial weighting function object based on 7th order polynomial. Reference function: bell like function with final support, 0 less or equal |f(x)| less or equal 1 f(x less than -1) = f(x greater than 1) = 0 f(0) = 1

Returns

RealFunction object.

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

• igbase/numeric/FunctionRealBasic.cs
• igbase/numeric/FunctionRealInterpolation.cs
• igbase/numeric/FunctionRealPenalty.cs
• igbase/numeric/FunctionRealWeight.cs