MathUtils::QuadraticForm Class Reference

Quadratic form functor: f(x) = x^T A x + b^T x + c. Commonly used for testing optimization algorithms. More...

#include <MathUtils_FunctorVector.hxx>

Public Member Functions
	QuadraticForm (const math_Matrix &theA, const math_Vector &theB, double theC)
	Constructor from matrix, vector, and constant.
bool	Value (const math_Vector &theX, double &theY) const
	Evaluates the quadratic form f(x) = x^T A x + b^T x + c.
bool	Gradient (const math_Vector &theX, math_Vector &theG) const
	Evaluates the gradient: g = 2*A*x + b.
bool	Values (const math_Vector &theX, double &theY, math_Vector &theG) const
	Evaluates both value and gradient.

Detailed Description

Quadratic form functor: f(x) = x^T A x + b^T x + c. Commonly used for testing optimization algorithms.

Usage:

math_Matrix A(1, 2, 1, 2);
A(1,1) = 2.0; A(1,2) = 0.0;
A(2,1) = 0.0; A(2,2) = 2.0;
math_Vector b(1, 2);
b(1) = -4.0; b(2) = -4.0;
QuadraticForm aFunc(A, b, 8.0);  // f(x) = 2*x1^2 + 2*x2^2 - 4*x1 - 4*x2 + 8
// Minimum at (1, 1) with value 4

Constructor & Destructor Documentation

QuadraticForm()

MathUtils::QuadraticForm::QuadraticForm ( const math_Matrix & theA, const math_Vector & theB, double theC )

inline

Constructor from matrix, vector, and constant.

Parameters

theA	quadratic coefficient matrix (must be square)
theB	linear coefficient vector
theC	constant term

Member Function Documentation

Gradient()

bool MathUtils::QuadraticForm::Gradient ( const math_Vector & theX, math_Vector & theG ) const

inline

Evaluates the gradient: g = 2*A*x + b.

Parameters

[in]	theX	input vector
[out]	theG	gradient vector

Returns

true if evaluation succeeded

Value()

bool MathUtils::QuadraticForm::Value ( const math_Vector & theX, double & theY ) const

inline

Evaluates the quadratic form f(x) = x^T A x + b^T x + c.

Parameters

[in]	theX	input vector
[out]	theY	function value

Returns

true if evaluation succeeded

Values()

bool MathUtils::QuadraticForm::Values ( const math_Vector & theX, double & theY, math_Vector & theG ) const

inline

Evaluates both value and gradient.

Parameters

[in]	theX	input vector
[out]	theY	function value
[out]	theG	gradient vector

Returns

true if evaluation succeeded

---

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

• MathUtils_FunctorVector.hxx