IGLib 1.4
The IGLib base library for development of numerical, technical and business applications.

IG::Num::Func::Quadratic Class Reference

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...

Inheritance diagram for IG::Num::Func::Quadratic:
Collaboration diagram for IG::Num::Func::Quadratic:

List of all members.

Public Member Functions

 Quadratic (double a2, double a1, double a0)
 Creates a quadratic function, coefficients are specified in the descending order.
void SetCoefficients (double a2, double a1, double a0)
 Sets coefficients of the quadratic function represented by the current object.
void SetInterpolation (double x1, double y1, double x2, double y2, double x3, double y3)
 Initializes the quadratic interpolation function with specified three function values.
void SetInterpolation (double x1, double y1, double d1, double x2, double y2)
 Initializes the quadratic interpolation function with specified two function values and one derivative.
void SetInterpolation2der (double x1, double y1, double d1, double x2, double y2, double d2)
 Initializes the quadratic interpolation function with specified two function values and two approximate derivative. The interpolation becomes average between bunctio nobtained by taking into account the first derivative and the second derivative.
int Zeros (out double x1, out double x2)
 Calculates and returns real zeros of the function. Also returns the number of real zeros (0, 1 or 2).
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.

Protected Member Functions

override double RefValue (double x)
 Returns the value of reference (untransformed) function.
override double RefDerivative (double x)
 Returns the first derivative of reference (untransformed) function.
override double RefSecondDerivative (double x)
 Returns the second derivative of the given order of reference (untransformed) function.
override double RefDerivative (double x, int order)
 Returns the derivative of the given order of reference (untransformed) function.
internal override void setHighestDerivativeDefined (int order)
 Sets the internal variable that specifies which is the highest order derivative devined (-1 for unlimited).
override double RefIntegral (double x)
 Returns definite integral of reference (untransformed) function from 0 to the function argument.
override double RefInverse (double y)
 Returns inverse of the reference (untransformed) function.

Protected Attributes

double _a0

Properties

double a0 [get, set]
 Returns the constant term coefficient of the quadratic function.
double a2 [get, set]
 Returns the quadratic term coefficitne of the quadratic function.
double a1 [get, set]
 Returns the linear term coefficitne of the quadratic function.
double Zero [get]
 Returns the first zero of the current quadratic function. Throws InvalidOperationException if the function does not have real zeros.
double Zero1 [get]
 Returns the first zero of the current quadratic function. Throws InvalidOperationException if the function does not have real zeros.
double Zero2 [get]
 Returns the second zero of the current quadratic function. Throws InvalidOperationException if the function does not have two distinct real zeros.
bool HasZero [get]
 Returns true if this quadratic function has at least one real zero, false otherwise.
int NumZeros [get]
 Returns number of zeros of the current quadratic function.
bool HasMaximum [get]
 Returns true if this quadratic function has a strict maximum.
double Maximum [get]
 Gets strict maximum of this quadratic function. If the function does not have one then exeption is thrown.
bool HasMinimum [get]
 Returns true if this quadratic function has a strict minimum.
double Minimum [get]
 Gets strict minimum of this quadratic function. If the function does not have one then exeption is thrown.
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).
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).
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).
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).
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).

Private Attributes

double _a1
double _a2

Detailed Description

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.


Constructor & Destructor Documentation

IG::Num::Func::Quadratic::Quadratic ( double  a2,
double  a1,
double  a0 
) [inline]

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

Parameters:
a2quadratic term coefficient.
a1linear term coefficient.
a0constant term coefficient.

Member Function Documentation

void IG::Num::Func::Quadratic::SetCoefficients ( double  a2,
double  a1,
double  a0 
) [inline]

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

Parameters:
a2quadratic term coeficient.
a1linear term coefficient.
a0constant term coefficient.
void IG::Num::Func::Quadratic::SetInterpolation ( double  x1,
double  y1,
double  x2,
double  y2,
double  x3,
double  y3 
) [inline]

Initializes the quadratic interpolation function with specified three function values.

Parameters:
x1Abscissa of the first point.
y1Value at the first point.
x2Abscissa of the second point.
y2Value at the second point.
x3Abscissa of the third point.
y3Value at the third point.
void IG::Num::Func::Quadratic::SetInterpolation ( double  x1,
double  y1,
double  d1,
double  x2,
double  y2 
) [inline]

Initializes the quadratic interpolation function with specified two function values and one derivative.

Parameters:
x1Abscissa of the first point.
y1Value at the first point.
d1Derivative at the first point.
x2Abscissa of the second point.
y2Value at the second point.
void IG::Num::Func::Quadratic::SetInterpolation2der ( double  x1,
double  y1,
double  d1,
double  x2,
double  y2,
double  d2 
) [inline]

Initializes the quadratic interpolation function with specified two function values and two approximate derivative. The interpolation becomes average between bunctio nobtained by taking into account the first derivative and the second derivative.

Parameters:
x1Abscissa of the first point.
y1Value at the first point.
d1Derivative (approximate) in the first point.
x2Abscissa of the second point.
y2Value at the second point.
d2Derivative (approximate) in the second point.
int IG::Num::Func::Quadratic::Zeros ( out double  x1,
out double  x2 
) [inline]

Calculates and returns real zeros of the function. Also returns the number of real zeros (0, 1 or 2).

Parameters:
x1The first zero (output parameter).
x2The second zero (output parameter).
Returns:
Number of distinct real zeros.
override double IG::Num::Func::Quadratic::RefValue ( double  x) [inline, protected, virtual]

Returns the value of reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::Quadratic::RefDerivative ( double  x) [inline, protected, virtual]

Returns the first derivative of reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::Quadratic::RefSecondDerivative ( double  x) [inline, protected, virtual]

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

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::Quadratic::RefDerivative ( double  x,
int  order 
) [inline, protected, virtual]

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

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::Quadratic::HigherDerivativeDefined ( int  order) [inline]

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.

Reimplemented from IG::Num::RealFunction.

internal override void IG::Num::Func::Quadratic::setHighestDerivativeDefined ( int  order) [inline, protected, virtual]

Sets the internal variable that specifies which is the highest order derivative devined (-1 for unlimited).

Parameters:
orderHighest order for which derivative is defined. -1 means that all derivatives are defined.

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::Quadratic::RefIntegral ( double  x) [inline, protected, virtual]

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

Reimplemented from IG::Num::RealFunction.

override double IG::Num::Func::Quadratic::RefInverse ( double  y) [inline, protected, virtual]

Returns inverse of the reference (untransformed) function.

Reimplemented from IG::Num::RealFunction.


Member Data Documentation

double IG::Num::Func::Quadratic::_a0 [protected]

Property Documentation

double IG::Num::Func::Quadratic::a0 [get, set]

Returns the constant term coefficient of the quadratic function.

double IG::Num::Func::Quadratic::a2 [get, set]

Returns the quadratic term coefficitne of the quadratic function.

double IG::Num::Func::Quadratic::a1 [get, set]

Returns the linear term coefficitne of the quadratic function.

double IG::Num::Func::Quadratic::Zero [get]

Returns the first zero of the current quadratic function. Throws InvalidOperationException if the function does not have real zeros.

double IG::Num::Func::Quadratic::Zero1 [get]

Returns the first zero of the current quadratic function. Throws InvalidOperationException if the function does not have real zeros.

double IG::Num::Func::Quadratic::Zero2 [get]

Returns the second zero of the current quadratic function. Throws InvalidOperationException if the function does not have two distinct real zeros.

bool IG::Num::Func::Quadratic::HasZero [get]

Returns true if this quadratic function has at least one real zero, false otherwise.

int IG::Num::Func::Quadratic::NumZeros [get]

Returns number of zeros of the current quadratic function.

bool IG::Num::Func::Quadratic::HasMaximum [get]

Returns true if this quadratic function has a strict maximum.

double IG::Num::Func::Quadratic::Maximum [get]

Gets strict maximum of this quadratic function. If the function does not have one then exeption is thrown.

bool IG::Num::Func::Quadratic::HasMinimum [get]

Returns true if this quadratic function has a strict minimum.

double IG::Num::Func::Quadratic::Minimum [get]

Gets strict minimum of this quadratic function. If the function does not have one then exeption is thrown.

override bool IG::Num::Func::Quadratic::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::Quadratic::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::Quadratic::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::Quadratic::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).

Reimplemented from IG::Num::RealFunction.

override bool IG::Num::Func::Quadratic::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).

Reimplemented from IG::Num::RealFunction.


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