MathUtils::LinearResidual Class Reference

Linear system residual functor: f(x) = ||Ax - b||^2. Useful for solving overdetermined linear systems via optimization. More...

#include <MathUtils_FunctorVector.hxx>

Public Member Functions
	LinearResidual (const math_Matrix &theA, const math_Vector &theB)
	Constructor from matrix and right-hand side.
bool	Value (const math_Vector &theX, double &theY) const
	Evaluates the residual ||Ax - b||^2.
bool	Gradient (const math_Vector &theX, math_Vector &theG) const
	Evaluates the gradient: g = 2 * A^T * (Ax - b).
bool	Values (const math_Vector &theX, double &theY, math_Vector &theG) const
	Evaluates both value and gradient.

Detailed Description

Linear system residual functor: f(x) = ||Ax - b||^2. Useful for solving overdetermined linear systems via optimization.

Usage:

math_Matrix A(1, 3, 1, 2);  // 3x2 overdetermined system
math_Vector b(1, 3);
// ... fill A and b ...
LinearResidual aRes(A, b);
math_Vector aStart(1, 2);
aStart.Init(0.0);
auto aResult = MathOpt::BFGS(aRes, aStart);

Constructor & Destructor Documentation

LinearResidual()

MathUtils::LinearResidual::LinearResidual ( const math_Matrix & theA, const math_Vector & theB )

inline

Constructor from matrix and right-hand side.

Parameters

theA	coefficient matrix (m x n)
theB	right-hand side vector (m)

Member Function Documentation

Gradient()

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

inline

Evaluates the gradient: g = 2 * A^T * (Ax - b).

Parameters

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

Returns

true (always succeeds)

Value()

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

inline

Evaluates the residual ||Ax - b||^2.

Parameters

[in]	theX	solution vector (n)
[out]	theY	squared residual norm

Returns

true (always succeeds)

Values()

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

inline

Evaluates both value and gradient.

Parameters

[in]	theX	solution vector
[out]	theY	squared residual norm
[out]	theG	gradient vector

Returns

true (always succeeds)

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

• MathUtils_FunctorVector.hxx