IGLib  1.5
The IGLib base library for development of numerical, technical and business applications.
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IG.Num.Func.Linear Class Reference

Linear function, f(x) = a1*x + a0. Specific properties: Zero - returns a zero. HasZero - either the function has a zero or not. More...

+ Inheritance diagram for IG.Num.Func.Linear:
+ Collaboration diagram for IG.Num.Func.Linear:

Public Member Functions

 Linear (double a1, double a0)
 Creates a linear function, coefficients are specified in the descending order. More...
 
void SetCoefficients (double a1, double a0)
 Sets coefficients of the linear function represented by the current object. More...
 
void SetInterpolation (double x1, double y1, double x2, double y2)
 Initializes the linear interpolation function with specified two values. More...
 
void SetInterpolation (double x1, double y1, double d1)
 Initializes the linear interpolation function with specified value and derivative. More...
 
override bool HigherDerivativeDefined (int order)
 Tells whether the derivative of the given order is defined for this function (by implementation, not mathematically) More...
 
- Public Member Functions inherited from IG.Num.RealFunction
 RealFunction (DlgFunctionValue valueDelegate)
 Constructs a new function where delegates are provided for calculation of function valu. More...
 
 RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate)
 Constructs a new function where delegates are provided for calculation of function valu and first derivative. More...
 
 RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate)
 
 RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate, DlgFunctionValue integralDelegate)
 Constructs a new function where delegates are provided for calculation of function value, derivatives and integral. More...
 
 RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate, DlgFunctionValue integralDelegate, DlgFunctionValue inverseDelegate)
 Constructs a new function where delegates are provided for calculation of function value, derivatives, integral and inverse. More...
 
 RealFunction (DlgFunctionValue valueDelegate, DlgFunctionValue derivativeDelegate, DlgFunctionValue secondDerivativeDelegate, DlgFunctionHigherDerivative higherDerivativeDelegate, DlgFunctionValue integralDelegate, DlgFunctionValue inverseDelegate)
 Constructs a new function where delegates are provided for calculation of function value, derivatives, integral and inverse. More...
 
RealFunction CloneFunction ()
 
object Clone ()
 
double TransformedArgument (double t)
 
double InverseTransformedArgument (double x)
 
virtual void SetTransformationParameters (double kx, double sx, double ky, double sy)
 Sets parameters of the affine transformation parameters for both co-ordinates. More...
 
virtual void SetXTransformationParameters (double kx, double sx)
 Sets parameters of the affine transformation parameters for independent variable. More...
 
override double Value (double x)
 Returns the value of this function at the specified parameter. More...
 
override double Derivative (double x)
 Returns the first derivative of this function at the specified parameter. More...
 
override double Derivative (double x, int order)
 Returns the derivative of the given order of this function at the specified parameter. More...
 
override bool HigherDerivativeDefined (int order)
 Tells whether the derivative of the given order is defined for this function (by implementation, not mathematically). Returns true if either the internal variable indicates true or the appropriate delegate is non-null. More...
 
override double SecondDerivative (double x)
 Returns the second derivative of the given order of this function at the specified arameter. More...
 
override double Integral (double x)
 Returns definite integral of the current function from 0 to the function argument. More...
 
override double Inverse (double y)
 Returns value of the inverse of the current function at the specified value of dependent variable. More...
 
- Public Member Functions inherited from IG.Num.RealFunctionBase
void Tabulate (double from, double to, int numPoints)
 Tabulates the current function and its first and second derivatives (when available) on the specified interval, in the specified number of points. More...
 
void Tabulate (double from, double to, int numPoints, bool printDerivatives)
 Tabulates the current function and its first and eventually second derivatives (when available) on the specified interval, in the specified number of points. More...
 
void Tabulate (double from, double to, int numPoints, bool printDerivatives, bool printSecondDerivatives)
 Tabulates the current function and eventually its first and second derivatives (when available) on the specified interval, in the specified number of points. More...
 
virtual double NumericalIntegral (double from, double to, int numintervals)
 Calculates numerical integral of this function. Simpson's formula is used. More...
 
virtual double NumericalDerivative (double x, double stepsize)
 Calculates numerical derivative of this function. Central difference formula is used. More...
 
virtual double NumericalSecondDerivative (double x, double stepsize)
 Calculates numerical second order derivative of this function. Central difference formula is used. More...
 
virtual void Test ()
 Performs numerical tests with parameters adjusted for specific function. This function can be be overridden in derived classes, however its current implementation may be relatively well suited for most weighting and basic functions. More...
 
virtual void Test (double from, double to, int numProbes, double stepSize, double tolerance)
 Performs some numerical tests on the current function, such as correctness of first and second derivatives, integral and inverse of the function. Results are written to the standard output. Whenever a numerical result does not match the corresponding analytical value calculated by the function, a visible notification is written. More...
 
override string ToString ()
 

Protected Member Functions

override double RefValue (double x)
 Returns the value of reference (untransformed) function. More...
 
override double RefDerivative (double x)
 Returns the first derivative of reference (untransformed) function. More...
 
override double RefSecondDerivative (double x)
 Returns the second derivative of the given order of reference (untransformed) function. More...
 
override double RefDerivative (double x, int order)
 Returns the derivative of the given order of reference (untransformed) function. More...
 
override double RefIntegral (double x)
 Returns definite integral of reference (untransformed) function from 0 to the function argument. More...
 
override double RefInverse (double x)
 Returns inverse of the reference (untransformed) function. More...
 
- Protected Member Functions inherited from IG.Num.RealFunction
 RealFunction ()
 

Protected Attributes

double _a0
 
- Protected Attributes inherited from IG.Num.RealFunction
bool _valueDefined = false
 
bool _derivativeDefined = false
 
int _highestDerivativeDefined = 0
 
bool _secondDerivativeDefined = false
 
bool _integralDefined = false
 
bool _inverseDefined = false
 
- Protected Attributes inherited from IG.Num.RealFunctionBase
string _name
 
string _description
 

Properties

double a0 [get, protected set]
 Returns the constant term coefficient of the linear function. More...
 
double a1 [get, protected set]
 Returns the linear term coefficitne of the linear function. More...
 
double Zero [get]
 Returns zero of the current linear function. Throws InvalidOperationException if the function does not have zeros. More...
 
bool HasZero [get]
 Returns true if the linear function has a zero, false otherwise. More...
 
override bool ValueDefined [get, set]
 
override bool DerivativeDefined [get, set]
 
override bool SecondDerivativeDefined [get, set]
 
override bool IntegralDefined [get, set]
 
override bool InverseDefined [get, set]
 
- Properties inherited from IG.Num.RealFunction
override string Name [get, set]
 Returns a code name of the function (not necessarily unique). More...
 
override string Description [get, set]
 Returns a short description of the function (not necessarily unique). More...
 
override RealFunctionBase DerivativeFunction [get]
 Returns a function that represents a derivative of the current function. More...
 
override RealFunctionBase InverseFunction [get]
 Returns a function that represents inverse of the current function. More...
 
override RealFunctionBase IntegralFunction [get]
 Returns a function that represents definite integral of the current function from 0 to function argument. More...
 
bool DoTransform [get, private set]
 Whether or not transformation (stretch/shift) is applied to the reference function, either in x or to y. Setter sets value both for transformation in X and Y direction. More...
 
bool TransformX [get, private set]
 Whether or not reference function is stretched/shifted in x direction. More...
 
bool TransformY [get, private set]
 Whether or not reference function is stretched/shifted in x direction. More...
 
double ScaleX [get, set]
 Gets or sets the scaling factor for independent variable. More...
 
double ShiftX [get, set]
 Gets or sets the shift of independent variable. More...
 
double ScaleY [get, set]
 Gets or sets the scaling factor for function value. More...
 
double ShiftY [get, set]
 Gets or sets the shift for function value. More...
 
override bool ValueDefined [get, set]
 Tells whether value of the function is defined by implementation. Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...
 
override bool DerivativeDefined [get, set]
 Tells whether the first derivative is defined for this function (by implementation, not mathematically). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...
 
override bool SecondDerivativeDefined [get, set]
 Tells whether the second derivative is defined for this function (by implementation, not mathematically). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...
 
override bool IntegralDefined [get, set]
 Indicates whether integral is defined for this function (w.r. implementation). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...
 
override bool InverseDefined [get, set]
 Indicates whether inverse is defined for this function (w.r. implementation). Getter returns true if internal flag is set OR appropriate delegate is defined. Setter sets the internal flag (i.e. delegate must also be set to null if getter should return false). More...
 
- Properties inherited from IG.Num.RealFunctionBase
virtual string Name [get, set]
 Returns a short name of thecurrent function. More...
 
virtual string Description [get, set]
 Returns a short description of the current function. More...
 
virtual RealFunctionBase DerivativeFunction [get]
 Returns a function object that represents a derivative of this function. Returns null if this is not implemented. More...
 
virtual RealFunctionBase IntegralFunction [get]
 Returns a function object that represents a definite integral of this function from 0 to 1. Returns null if not implemented. More...
 
virtual RealFunctionBase InverseFunction [get]
 Returns a function object that represents an inverse function of this function. Returns null if not implemented. More...
 
abstract bool ValueDefined [get, set]
 Tells whether value of the function is defined by implementation. More...
 
abstract bool DerivativeDefined [get, set]
 Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...
 
abstract bool SecondDerivativeDefined [get, set]
 Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...
 
abstract bool IntegralDefined [get, set]
 Tells whether analytical itegral of the function is defined or not. More...
 
abstract bool InverseDefined [get, set]
 Tells whether analytical inverse function is defined or not. More...
 
- Properties inherited from IG.Num.IRealFunction
string Name [get]
 Returns a short name of the function. More...
 
string Description [get]
 Returns a short description of the function. More...
 
bool ValueDefined [get]
 Tells whether value of the function is defined by implementation. More...
 
bool DerivativeDefined [get]
 Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...
 
bool SecondDerivativeDefined [get]
 Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...
 
bool IntegralDefined [get]
 Tells whether analytical itegral of the function is defined or not. More...
 
bool InverseDefined [get]
 Tells whether analytical inverse function is defined or not. More...
 

Private Attributes

double _a1
 

Additional Inherited Members

- Static Public Member Functions inherited from IG.Num.RealFunction
static void TestSpeed ()
 Compares calculation times of three ways of evaluations of exponential function: directly by Math.Exp(), through a delegate initialized by this function, and through a Function object initialized by this function. The number of repetitions is pre-defined. More...
 
static void TestSpeed (long numiterations)
 Compares calculation times of three ways of evaluations of exponential function: directly by Math.Exp(), through a delegate initialized by this function, and through a Function object initialized by this function. More...
 
- Static Public Member Functions inherited from IG.Num.RealFunctionBase
static void ExampleTests ()
 

Detailed Description

Linear function, f(x) = a1*x + a0. Specific properties: Zero - returns a zero. HasZero - either the function has a zero or not.

Constructor & Destructor Documentation

IG.Num.Func.Linear.Linear ( double  a1,
double  a0 
)
inline

Creates a linear function, coefficients are specified in the descending order.

Parameters
a1Linear term coefficient.
a0Constant term coefficient.

Member Function Documentation

void IG.Num.Func.Linear.SetCoefficients ( double  a1,
double  a0 
)
inline

Sets coefficients of the linear function represented by the current object.

Parameters
a1
a0
void IG.Num.Func.Linear.SetInterpolation ( double  x1,
double  y1,
double  x2,
double  y2 
)
inline

Initializes the linear interpolation function with specified two values.

Parameters
x1Abscissa of the first point.
y1Value at the first point.
x2Abscissa of the second point.
y2Value at the second point.

Referenced by IG.Num.Func.GetLinearInterpolation().

void IG.Num.Func.Linear.SetInterpolation ( double  x1,
double  y1,
double  d1 
)
inline

Initializes the linear interpolation function with specified value and derivative.

Parameters
x1Abscissa of the first point.
y1Value at the first point.
d1Derivative at the first point.
override double IG.Num.Func.Linear.RefValue ( double  x)
inlineprotectedvirtual

Returns the value of reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.Linear.RefDerivative ( double  x)
inlineprotectedvirtual

Returns the first derivative of reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.Linear.RefSecondDerivative ( double  x)
inlineprotectedvirtual

Returns the second derivative of the given order of reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.Linear.RefDerivative ( double  x,
int  order 
)
inlineprotectedvirtual

Returns the derivative of the given order of reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

override bool IG.Num.Func.Linear.HigherDerivativeDefined ( int  order)
inline

Tells whether the derivative of the given order is defined for this function (by implementation, not mathematically)

Implements IG.Num.IRealFunction.

override double IG.Num.Func.Linear.RefIntegral ( double  x)
inlineprotectedvirtual

Returns definite integral of reference (untransformed) function from 0 to the function argument.

Reimplemented from IG.Num.RealFunction.

override double IG.Num.Func.Linear.RefInverse ( double  y)
inlineprotectedvirtual

Returns inverse of the reference (untransformed) function.

Reimplemented from IG.Num.RealFunction.

Member Data Documentation

double IG.Num.Func.Linear._a0
protected
double IG.Num.Func.Linear._a1
private

Property Documentation

double IG.Num.Func.Linear.a0
getprotected set

Returns the constant term coefficient of the linear function.

double IG.Num.Func.Linear.a1
getprotected set

Returns the linear term coefficitne of the linear function.

double IG.Num.Func.Linear.Zero
get

Returns zero of the current linear function. Throws InvalidOperationException if the function does not have zeros.

bool IG.Num.Func.Linear.HasZero
get

Returns true if the linear function has a zero, false otherwise.

override bool IG.Num.Func.Linear.ValueDefined
getset
override bool IG.Num.Func.Linear.DerivativeDefined
getset
override bool IG.Num.Func.Linear.SecondDerivativeDefined
getset
override bool IG.Num.Func.Linear.IntegralDefined
getset
override bool IG.Num.Func.Linear.InverseDefined
getset

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