Vector function containing quadratic basis in a n-dimensional vector space. Composed of (n+1)*(n+2)/2 functions: 1, x_1, ..., x_n, 0.5*x_1^2, 0.5*x_2^2, ..., 0.5*x_n^2, x_1*x_2, x_1*x_3, ..., x_1*x_n, ..., x_2*x_3, ..., x_2*x_n, ..., ..., x_n-1*x_n. More...

Inheritance diagram for IG.Num.QuadraticBasis:

Collaboration diagram for IG.Num.QuadraticBasis:

Public Member Functions
	QuadraticBasis (int dimension)
	Constructs a vector function containing quadratic basis for the specified dimension. Composed of (n+1)(n+2)/2 functions: 1, x_1, ..., x_n, 0.5x_1^2, 0.5x_2^2, ..., 0.5x_n^2, x_1x_2, x_1x_3, ..., x_1x_n, ..., x_2x_3, ..., x_2x_n, ..., ..., x_n-1x_n. More...

int[]	GetFunctionDefinition (int which)
	Returns a table of indices defining the specified function of the quadratic basis. Table contains up to two indices of variables whose product represents the specific basis function. [] (empty array) means constant term, [1] means x1, [2] means x2, [1,1] means x1^2, [2,2] means x2^2, [1,2] means x1x2, [3,5] means x4x5, etc. More...

void	GetFunctionDefinition (int which, out int numTerms, out int firstVariableIndex, out int secondVariableIndex)
	Returns data about the specific function of this vector function containing quadratic basis. Examples: numTerms = 0: constant (1) numTerms = 1: linear terms, firstVariableIndex is index of the variable. numTerms = 2: quadratic terms, firstVariableIndex and secondVariableIndex are indices of variables whose product gives this basis function. More...

override double	Value (IVectorFunctionResults evaluationData, int which)
	Calculates and returns the particular component of the vector function value. More...

override double	Derivative (IVectorFunctionResults evaluationData, int which, int component)
	Calculates and returns the particular component of the vector function's derivative. More...

override double	SecondDerivative (IVectorFunctionResults evaluationData, int which, int rowNum, int columnNum)
	Calculates and returns the particular component of the vector function's second derivative (Hessian). More...

Public Member Functions inherited from IG.Num.VectorFunctionBaseComponentWise
override void	Evaluate (IVectorFunctionResults evaluationData)
	Performs evaluation of requwester function results and writes them to the provided data structure. Uses Evaluate(IVector, ref bool, ref List{double}, ref bool, ref List{IVector}, ref bool, ref List{IMatrix}) to do the job. More...

override void	Evaluate (IVector parameters, ref bool calculateValues, ref List< double > values, ref bool calculateGradients, ref List< IVector > gradients, ref bool calculateHessians, ref List< IMatrix > hessians)
	Calculation of values, gradients, and hessians of the vector function according to request flags. Uses functions for component-wise evaluation to do the job. More...

Public Member Functions inherited from IG.Num.VectorFunctionBaseGeneral
	VectorFunctionBaseGeneral ()

void	SetNumParameters (int num)
	Sets number of parameters of the current vector function to the specified value. More...

void	SetNumValues (int num)
	Sets number of values of the vector function to the specified value. More...

virtual double	Value (IVector parameters, int which)
	Calculates and returns the particular component of the vector function value. More...

virtual double	Derivative (IVector parameters, int which, int component)
	Calculates and returns the particular component of the vector function derivative. More...

virtual double	SecondDerivative (IVector parameters, int which, int rowNum, int columnNum)
	Calculates and returns the particular component of the vector function's second derivative (Hessian). More...

void	Value (IVector parameters, ref List< double > values)
	Returns the value of vector function at the specified parameter. More...

void	Derivative (IVector parameters, ref List< IVector > gradients)
	Returns the first derivative of this function at the specified parameter. More...

void	SecondDerivative (IVector parameters, ref List< IMatrix > hessians)
	Returns the second derivative (Hessian) of this function at the specified arameter. More...

double	LinearCombinationValue (IVectorFunctionResults evaluationData, IVector coefficients)
	Returns value of linear combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

void	LinearCombinationDerivative (IVectorFunctionResults evaluationData, IVector coefficients, ref IVector res)
	Returns gradient of linear combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

double	LinearCombinationDerivative (IVectorFunctionResults evaluationData, IVector coefficients, int component)
	Returns the specified component of gradient of combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

void	LinearCombinationSecondDerivative (IVectorFunctionResults evaluationData, IVector coefficients, ref IMatrix res)

double	LinearCombinationSecondDerivative (IVectorFunctionResults evaluationData, IVector coefficients, int rowNum, int columnNum)
	Returns the specified component of Hessian of combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

double	LinearCombinationValue (IVector parameters, IVector coefficients)
	Returns value of linear combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

void	LinearCombinationDerivative (IVector parameters, IVector coefficients, ref IVector res)
	Returns gradient of linear combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

double	LinearCombinationDerivative (IVector parameters, IVector coefficients, int component)
	Returns the specified component of gradient of combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

void	LinearCombinationSecondDerivative (IVector parameters, IVector coefficients, ref IMatrix res)
	Calculates second derivatives of the linear combination of components of vector functions and stores them to the specified matrix. More...

double	LinearCombinationSecondDerivative (IVector parameters, IVector coefficients, int rowNum, int columnNum)
	Returns the specified component of Hessian of combination of functions contained in this vector function, with specified coefficients at specified parameters. More...

virtual void	NumericalDerivative (IVector x, IVector stepSize, ref List< IVector > derivative)
	Calculates numerical derivative of this function. Central difference formula is used. More...

virtual void	NumericalSecondDerivative (IVector x, IVector stepsizes, ref List< IVector > secondDerivatives)
	Calculates numerical second order derivative of this function. Central difference formula is used. More...

Static Public Member Functions
static int	NumQuadraticBasisFunctions (int dimension)
	Returns number of basis functions in quadratic polynomial basis of the specified dimenson. This is a helper method. More...

static void	Example ()
	Example for this class, just runs examples form the LinearBasis class. More...

Protected Attributes
int[][]	functionDefinitions
	Definitions of basis functions. Each definition is an array of at most 2 indices specifying the product of which variables (zero-base) is a specific function. At index 0, length of array is 0. At indices 1 through n+1 it is 1 (linear terms), and at remaining indices it is 2. More...

int[,]	quatraticTerms
	2D table of indices specifying for each quadratic term which function it corresponds to (since up to quadratic terms this is trivial). More...

Protected Attributes inherited from IG.Num.VectorFunctionBaseGeneral
object	_lock = new object()

string	_name

string	_description

int	_numParameters = -1

int	_numValues = -1

bool	_valuesDefined = true

bool	_derivativeDefined = false

bool	_secondDerivativeDefined = false

bool	_componentEvaluation = false

Private Member Functions
	QuadraticBasis ()

int	GetConstantTermIndex ()
	Returns index of the constant function in this quadratic basis. More...

int	GetLinearTermIndex (int varIndex)
	Returns index of the specified linear function in this quadratic basis. More...

int	GetQuadraticTermIndex (int varIndex1, int varIndex2)
	Returns index of the specified quadratic function in this quadratic basis. Order of indices specifying the term is not important. More...

Additional Inherited Members
Properties inherited from IG.Num.VectorFunctionBaseComponentWise
override bool	ComponentWiseEvaluation `[get, protected set]`
	Returns true, indicating that individual components of functions and eventually their deirvatives is performed directly. More...

Properties inherited from IG.Num.VectorFunctionBaseGeneral
object	Lock `[get]`

virtual string	Name `[get, set]`
	Returns a short name of the function. More...

virtual string	Description `[get, set]`
	Returns a short description of the function. More...

virtual int	NumParameters `[get, protected set]`
	Gets number of parameters of the current vector function (-1 for not defined, in case that function works with different numbers of parameters). More...

virtual int	NumValues `[get, protected set]`
	Gets number of values of the current vector function (-1 for not defined, e.g. in case that function works with different numbers of parameters and number of functions depends on number of parameters). More...

virtual bool	ComponentWiseEvaluation `[get, protected set]`
	Tells whether the function supports evaluation of individual components. If not then evaluation is performed through the Evaluate function. More...

virtual bool	ValueDefined `[get, protected set]`
	Tells whether value of the function is defined by implementation. More...

virtual bool	DerivativeDefined `[get, protected set]`
	Tells whether the first derivative is defined for this function (by implementation, not mathematically) More...

virtual bool	SecondDerivativeDefined `[get, protected set]`
	Tells whether the second derivative is defined for this function (by implementation, not mathematically) More...

IVectorFunctionResults	AuxResults `[get]`

VectorFunctionBase.ObjectStoreResults	ResultsStore `[get]`
	Store of result objects for reuse. More...

Properties inherited from IG.Num.IVectorFunction
string	Name `[get]`
	Returns a short name of the function. More...

string	Description `[get]`
	Returns a short description of the function. More...

int	NumParameters `[get]`
	Gets number of parameters of the current vector function (-1 for not defined, in case that function works with different numbers of parameters). More...

int	NumValues `[get]`
	Gets number of values of the current vector function (-1 for not defined, e.g. in case that function works with different numbers of parameters and number of functions depends on number of parameters). 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	ComponentWiseEvaluation `[get]`
	Tells whether the function supports evaluation of individual components. If not then evaluation is performed through the Evaluate function. More...

Properties inherited from IG.Lib.ILockable
object	Lock `[get]`

Detailed Description

Vector function containing quadratic basis in a n-dimensional vector space. Composed of (n+1)*(n+2)/2 functions: 1, x_1, ..., x_n, 0.5*x_1^2, 0.5*x_2^2, ..., 0.5*x_n^2, x_1*x_2, x_1*x_3, ..., x_1*x_n, ..., x_2*x_3, ..., x_2*x_n, ..., ..., x_n-1*x_n.

$A Igor xx Apr10;

Constructor & Destructor Documentation

IG.Num.QuadraticBasis.QuadraticBasis ( )

inlineprivate

IG.Num.QuadraticBasis.QuadraticBasis ( int dimension )

inline

Constructs a vector function containing quadratic basis for the specified dimension. Composed of (n+1)*(n+2)/2 functions: 1, x_1, ..., x_n, 0.5*x_1^2, 0.5*x_2^2, ..., 0.5*x_n^2, x_1*x_2, x_1*x_3, ..., x_1*x_n, ..., x_2*x_3, ..., x_2*x_n, ..., ..., x_n-1*x_n.

Parameters

dimension Space dimension.

Member Function Documentation

static int IG.Num.QuadraticBasis.NumQuadraticBasisFunctions ( int dimension )

inlinestatic

Returns number of basis functions in quadratic polynomial basis of the specified dimenson. This is a helper method.

Parameters

dimension Dimension of the space in which linear polynomial basis functions are calculated.

int [] IG.Num.QuadraticBasis.GetFunctionDefinition ( int which )

inline

Returns a table of indices defining the specified function of the quadratic basis. Table contains up to two indices of variables whose product represents the specific basis function. [] (empty array) means constant term, [1] means x1, [2] means x2, [1,1] means x1^2, [2,2] means x2^2, [1,2] means x1*x2, [3,5] means x4*x5, etc.

Parameters

which

Returns

void IG.Num.QuadraticBasis.GetFunctionDefinition	(	int	which,
		out int	numTerms,
		out int	firstVariableIndex,
		out int	secondVariableIndex
	)

inline

Returns data about the specific function of this vector function containing quadratic basis. Examples: numTerms = 0: constant (1) numTerms = 1: linear terms, firstVariableIndex is index of the variable. numTerms = 2: quadratic terms, firstVariableIndex and secondVariableIndex are indices of variables whose product gives this basis function.

Parameters

which	Specifies the function whose definition is queried.
numTerms	Returns number of terms in the product that defines the function (0 for constant, 1 for linear terms, 2 for quadratic terms)
firstVariableIndex	Returns index of the first variable in the product. If 0 then the specific function is constant.
secondVariableIndex	Returns index of the second variable in the product. If 0 then the specific function is linear or constant.

int IG.Num.QuadraticBasis.GetConstantTermIndex ( )

inlineprivate

Returns index of the constant function in this quadratic basis.

int IG.Num.QuadraticBasis.GetLinearTermIndex ( int varIndex )

inlineprivate

Returns index of the specified linear function in this quadratic basis.

Parameters

varIndex Specifies which linear term to return.

int IG.Num.QuadraticBasis.GetQuadraticTermIndex	(	int	varIndex1,
		int	varIndex2
	)

inlineprivate

Returns index of the specified quadratic function in this quadratic basis. Order of indices specifying the term is not important.

Parameters

varIndex1	Index of the first variable in the product.
varIndex2	Index of the second variable of the product.

override double IG.Num.QuadraticBasis.Value	(	IVectorFunctionResults	evaluationData,
		int	which
	)

inlinevirtual

Calculates and returns the particular component of the vector function value.

Parameters

evaluationData	Evaluation data that contains function parameters and can store function resuts. If the function does not support component-wise evaluation then results will be stored to this structure and returned from it. This makes reuse possible - when different components are evaluated subsequently with the same parameters, results are calculated only for the first time.
which	Specifies which function to evaluate.

Implements IG.Num.VectorFunctionBaseComponentWise.

Reimplemented in IG.Num.QuadraticBasisSafer.

References IG.Num.IVectorFunctionResults.Parameters.

override double IG.Num.QuadraticBasis.Derivative	(	IVectorFunctionResults	evaluationData,
		int	which,
		int	component
	)

inlinevirtual

Calculates and returns the particular component of the vector function's derivative.

Parameters

evaluationData	Evaluation data that contains function parameters and can store function resuts. Not used in this class, can be null.
which	Specifies which function to take.
component	Specifies which compoonent of the gradient should be returned.

Implements IG.Num.VectorFunctionBaseComponentWise.

Reimplemented in IG.Num.QuadraticBasisSafer.

References IG.Num.IVectorFunctionResults.Parameters.

override double IG.Num.QuadraticBasis.SecondDerivative	(	IVectorFunctionResults	evaluationData,
		int	which,
		int	rowNum,
		int	columnNum
	)

inlinevirtual

Calculates and returns the particular component of the vector function's second derivative (Hessian).

Parameters

evaluationData	Evaluation data that contains function parameters and can store function resuts. Not used in this class, can be null.
which	Specifies which function to take.
rowNum	Specifies which row of the Hessian (matrix of second derivatives) should be returned.
columnNum	Specifies which column of the Hessian (matrix of second derivatives) should be returned.

Implements IG.Num.VectorFunctionBaseComponentWise.

Reimplemented in IG.Num.QuadraticBasisSafer.

References IG.Num.IVectorFunctionResults.Parameters.

static void IG.Num.QuadraticBasis.Example ( )

inlinestatic

Example for this class, just runs examples form the LinearBasis class.

References IG.Num.LinearBasis.Example().

Member Data Documentation

int [][] IG.Num.QuadraticBasis.functionDefinitions

protected

Definitions of basis functions. Each definition is an array of at most 2 indices specifying the product of which variables (zero-base) is a specific function. At index 0, length of array is 0. At indices 1 through n+1 it is 1 (linear terms), and at remaining indices it is 2.

int [,] IG.Num.QuadraticBasis.quatraticTerms

protected

2D table of indices specifying for each quadratic term which function it corresponds to (since up to quadratic terms this is trivial).

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

igbase/numeric/approximation/linear/ApproxBasis.cs

Public Member Functions

Static Public Member Functions

Protected Attributes

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation