IGLib  1.7.2
The IGLib base library for development of numerical, technical and business applications.
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IG.Num.Func2dQuadratic Class Reference

Quadratic function of 2 variables. More...

+ Inheritance diagram for IG.Num.Func2dQuadratic:
+ Collaboration diagram for IG.Num.Func2dQuadratic:

Public Member Functions

 Func2dQuadratic (mat2 hessian, vec2 gradient0, double scalarTerm)
 Creation of a quadratic 2D scalar function. More...
 
override double Value (vec2 parameters)
 Calculates and returns value of the current 2D quadratic function. More...
 
override vec2 Gradient (vec2 parameters)
 Calculates and returns gradient of the current 2D quadratic function. More...
 
override mat2 Hessian (vec2 parameters)
 Calculates and returns Hessian of the current 2D quadratic function and returns it (in the form of a mat2 struct). More...
 
- Public Member Functions inherited from IG.Num.Func2dVectorFormBase
 Func2dVectorFormBase ()
 Constructor. More...
 
override double Value (vec2 parameters)
 Calculates and returns value of the current 2D scalar function. More...
 
override vec2 Gradient (vec2 parameters)
 Calculates and returns gradient of the current 2D scalar function. More...
 
override mat2 Hessian (vec2 parameters)
 Calculates and returns Hessian of the current 2D scalar function and returns it (in the form of a mat2 struct). More...
 
sealed override double Value (double x, double y)
 Calculates and returns value of the current 2D scalar function. More...
 
sealed override void Gradient (double x, double y, out double gradx, out double grady)
 Calculates gradient of the current 2D scalar function and returns its components through the specified output variables. More...
 
sealed override void Hessian (double x, double y, out double dxx, out double dyy, out double dxy)
 Calculates Hessian of the current 3D scalar function and returns its component through the specified output variables. More...
 
- Public Member Functions inherited from IG.Num.Func2dBase
 Func2dBase ()
 
override double Value (IVector parameters)
 Returns the value of the current function at the specified parameters. More...
 
override void GradientPlain (IVector parameters, IVector gradient)
 Calculates first order derivatives (gradient) of this function at the specified parameters. WARNING: Plain function, does not check consistency of arguments. More...
 
override void HessianPlain (IVector parameters, IMatrix hessian)
 Calculates the second derivative (Hessian matrix) of this function at the specified parameters. WARNING: Plain function, does not check consistency of arguments. More...
 
- Public Member Functions inherited from IG.Num.ScalarFunctionUntransformedBase
virtual void Evaluate (IScalarFunctionResults data)
 Evaluates whatever needs to be evaluated and stores the results on the specified storage object. More...
 
virtual void Gradient (IVector parameters, ref IVector gradient)
 Calculates first order derivatives (gradient) of this function at the specified parameters. More...
 
virtual void Hessian (IVector parameters, ref IMatrix hessian)
 Calculates the second derivative (Hessian matrix) of this function at the specified parameters. More...
 
virtual void NumericalGradientForwardPlain (IVector x, IVector stepSizes, IVector gradient)
 Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
 
void NumericalGradientForward (IVector x, IVector stepSizes, ref IVector gradient)
 Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
 
void NumericalGradientForward (IVector x, double stepSize, ref IVector gradient)
 Calculates numerical derivatives (gradient) of this function. Forward difference formula is used. More...
 
virtual void NumericalGradientCentralPlain (IVector x, IVector stepSizes, IVector gradient)
 Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
 
void NumericalGradientCentral (IVector x, IVector stepSizes, ref IVector gradient)
 Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
 
void NumericalGradientCentral (IVector x, double stepSize, ref IVector gradient)
 Calculates numerical derivatives (gradient) of this function. Forward difference formula is normally used. More...
 
virtual void NumericalHessianForwardPlain (IVector x, IVector stepSizes, IVector aux, IMatrix hessian)
 Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. WARNING: Dimensions of vector arguments must match. This function does not check for consistency of argument dimensions. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianForward (IVector x, IVector stepSizes, ref IVector aux, ref IMatrix hessian)
 Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianForward (IVector x, double stepSize, ref IVector aux, ref IMatrix hessian)
 Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianCentralPlain (IVector x, IVector stepSizes, IVector aux1, IVector aux2, IMatrix hessian)
 Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. WARNING: Dimensions of vector arguments must match. This function does not check for consistency of argument dimensions. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianCentral (IVector x, IVector stepSizes, ref IVector aux1, ref IVector aux2, ref IMatrix hessian)
 Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianCentral (IVector x, double stepSize, ref IVector aux1, ref IVector aux2, ref IMatrix hessian)
 Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianCentralPlain (IVector x, IVector stepSizes, IVector aux1, IVector aux2, IMatrix hessian, bool useAnalyticalGradient)
 Calculates numerical second derivatives (Hessian) of this function by the central difference formula. WARNING: Dimensions of vector arguments must match. This function does not check for consistency of argument dimensions. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianCentral (IVector x, IVector stepSizes, ref IVector aux1, ref IVector aux2, ref IMatrix hessian, bool useAnalyticalGradient)
 Calculates numerical second derivatives (Hessian) of this function by the central difference formula. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
virtual void NumericalHessianCentral (IVector x, double stepSize, ref IVector aux1, ref IVector aux2, ref IMatrix hessian, bool useAnalyticalGradient)
 Calculates numerical second derivatives (Hessian) of this function. Forward difference formula is normally used. REMARK: if auxiliary vector or result matrix don't have correct dimensions or they are not allocated, then allocation is performed first. REMARK: Vector x is changed during operation, but is set to initial value before function returns (unless an exception is thrown). More...
 
void TestSpeed (IVector parameters, int numEvaluations, bool randomPerturbations, double relativePerturbationSize, bool calcValue, bool calcGradient, bool calcHessian, bool writeLastResult)
 Tests speed of evaluation of the current scalar function and writes results to the console. More...
 
void TestGradient (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeGradientComponents)
 Tests the calculation of gradients of the current scalar function. More...
 
void TestGradient (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeGradientComponents, bool useCentralDifference)
 Tests the calculation of gradients of the current scalar function. More...
 
void TestHessian (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeHessianComponents)
 Tests the calculation of Hessians of the current scalar function. More...
 
void TestHessian (IVector parameters, IVector stepSizes, int stepReductionFactor, int numStepReductions, bool checkNumerical, bool writeErrorComponents, bool writeHessianComponents, bool useCentralDifference)
 Tests the calculation of Hessians of the current scalar function. More...
 
void Test (IVector from, IVector to, int numProbes, IVector stepSizes, double tolerance, bool testDerivatives, bool testSecondDerivatives, bool printDifferences, bool printResults)
 Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. More...
 
void Test (IVector from, IVector to, int numProbes, IVector stepSizes, double tolerance)
 Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. This method tests first and second order derivatives, prints differences between analytical and numerical values to the console, and prints reports where absolute differences exceed rolerance. More...
 
void Test (IVector from, IVector to, int numProbes, double stepSize, double tolerance, bool testDerivatives, bool testSecondDerivatives, bool printDifferences, bool printResults)
 Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. More...
 
void Test (IVector from, IVector to, int numProbes, double stepSize, double tolerance)
 Performs numerical tests on the function, with output written to the console. Derivatives and second derivatives are tested and compared to numerical derivatives. More...
 

Static Public Member Functions

static int GetNumConstants ()
 Returns the number of scalar constants that specify the current function. More...
 
- Static Public Member Functions inherited from IG.Num.Func2dBase
static void Example ()
 Example of use of a 2D function. More...
 

Properties

mat2 HessianMatrix [get, protected set]
 Twice the matrix of quadratic coefficients (Hessian matrix of second derivatives). More...
 
vec2 Gradient0 [get, protected set]
 Vector of linear coefficients (equal to gradient of the function at x=0). More...
 
double ScalarTerm [get, protected set]
 Scalar additive constant. More...
 
- Properties inherited from IG.Num.Func2dBase
override bool ValueDefined [get, protected set]
 Whether calculation of function value is defined. Defaulet is true. More...
 
override bool GradientDefined [get, protected set]
 Whether calculation of functio ngradient is defined. Default is false. More...
 
override bool HessianDefined [get, protected set]
 Whether calculation of function Hessian is defined. Default is false. More...
 
int NumParam [get]
 Gets number of parameters. More...
 
- Properties inherited from IG.Num.ScalarFunctionUntransformedBase
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...
 
abstract bool ValueDefined [get, protected set]
 Tells whether value of the function is defined by implementation. More...
 
abstract bool GradientDefined [get, protected set]
 Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...
 
abstract bool HessianDefined [get, protected set]
 Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...
 
- Properties inherited from IG.Num.IScalarFunctionUntransformed
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 GradientDefined [get]
 Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...
 
bool HessianDefined [get]
 Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...
 
- Properties inherited from IG.Num.IFunc2d
bool ValueDefined [get]
 Whether calculation of function value is defined. More...
 
bool GradientDefined [get]
 Whether calculation of function ngradient is defined. More...
 
bool HessianDefined [get]
 Whether calculation of function Hessian is defined. More...
 

Private Member Functions

 Func2dQuadratic ()
 

Private Attributes

mat2 _G
 
vec2 _b
 
double _c
 

Additional Inherited Members

- Static Protected Member Functions inherited from IG.Num.Func2dBase
static void TestFunction (IFunc2d f)
 Demonstrates use of a 2D function by printing to the console 5 values and gradients of the function on the line connecting the two points (0, 0, 0) and (1, 1, 1). More...
 
static void TestFunction (IFunc2d f, double xmin, double xmax, double ymin, double ymax, int numPoints)
 Demonstrates use of a 2D function by printing to the console some values and gradients of the function on the line connecting the two specified points. More...
 
- Protected Attributes inherited from IG.Num.ScalarFunctionUntransformedBase
string _name
 
string _description
 

Detailed Description

Quadratic function of 2 variables.

Function is evaluated according to q(x) = (1/2)*x^T*G*x + b^T*x + c where x is vector of parameters, G is constant Hessian matrix, b is the vector of linear coefficients (gradient at x=0) and c is the scalar term (function value at x=0).

$A Igor Aug09;

Constructor & Destructor Documentation

IG.Num.Func2dQuadratic.Func2dQuadratic ( )
inlineprivate
IG.Num.Func2dQuadratic.Func2dQuadratic ( mat2  hessian,
vec2  gradient0,
double  scalarTerm 
)
inline

Creation of a quadratic 2D scalar function.

WARNING:

Matrix argument is interpreted as Hessian, i.e. twice the matrix of quadratic coefficients.

Parameters
hessianMatrix of second derivatives (Hessian).
gradient0Vector of linear coefficients - gradient of quadratic function at x = 0.
scalarTermConstant term.

Member Function Documentation

static int IG.Num.Func2dQuadratic.GetNumConstants ( )
inlinestatic

Returns the number of scalar constants that specify the current function.

override double IG.Num.Func2dQuadratic.Value ( vec2  parameters)
inline

Calculates and returns value of the current 2D quadratic function.

Parameters
parametersVector of function parameters (in form of the vec2) struct.
Returns
Function value.

Implements IG.Num.IFunc2d.

override vec2 IG.Num.Func2dQuadratic.Gradient ( vec2  parameters)
inline

Calculates and returns gradient of the current 2D quadratic function.

Parameters
parametersVector of parameters (in form of the vec2 struct)

<returnreturns>Gradient of the current 2D scalar function (in form of the vec2 struct)</returnreturns>

Implements IG.Num.IFunc2d.

override mat2 IG.Num.Func2dQuadratic.Hessian ( vec2  parameters)
inline

Calculates and returns Hessian of the current 2D quadratic function and returns it (in the form of a mat2 struct).

Implements IG.Num.IFunc2d.

Member Data Documentation

mat2 IG.Num.Func2dQuadratic._G
private
vec2 IG.Num.Func2dQuadratic._b
private
double IG.Num.Func2dQuadratic._c
private

Property Documentation

mat2 IG.Num.Func2dQuadratic.HessianMatrix
getprotected set

Twice the matrix of quadratic coefficients (Hessian matrix of second derivatives).

vec2 IG.Num.Func2dQuadratic.Gradient0
getprotected set

Vector of linear coefficients (equal to gradient of the function at x=0).

double IG.Num.Func2dQuadratic.ScalarTerm
getprotected set

Scalar additive constant.


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