#include <Concepts/NormalEquationSparseLinearAlgebraTraits_d.h>

Definition

Concept describing the set of requirements for solving the normal equation \( A^t A X = A^t B \), \( A \) being a matrix, \( At \) its transpose matrix, \( B \) and \( X \) being two vectors.

See also: SparseLinearAlgebraTraits_d

Has Models:: CGAL::Eigen_solver_traits<T>

Types
typedef unspecified_type	Matrix
	Matrix type model of `SparseLinearAlgebraTraits_d::Matrix` More...

typedef unspecified_type	Vector
	Vector type model of `SparseLinearAlgebraTraits_d::Vector` More...

typedef unspecified_type	NT
	Number type. More...

Creation
	NormalEquationSparseLinearAlgebraTraits_d ()
	Default constructor. More...

Operations
bool	normal_equation_factor (const Matrix &A)
	Factorize the sparse matrix `At * A`. More...

bool	normal_equation_solver (const Vector &B, Vector &X)
	Solve the sparse linear system `At * A * X = At * B`, with `A` being the matrix provided in `#normal_equation_factor()`, and `At` its transpose matrix. More...

bool	normal_equation_solver (const Matrix &A, const Vector &B, Vector &X)
	Equivalent to a call to `normal_equation_factor(A)` followed by a call to `normal_equation_solver(B,X)` . More...

Member Typedef Documentation

◆ Matrix

typedef unspecified_type NormalEquationSparseLinearAlgebraTraits_d::Matrix

Matrix type model of SparseLinearAlgebraTraits_d::Matrix

◆ NT

typedef unspecified_type NormalEquationSparseLinearAlgebraTraits_d::NT

Number type.

◆ Vector

typedef unspecified_type NormalEquationSparseLinearAlgebraTraits_d::Vector

Vector type model of SparseLinearAlgebraTraits_d::Vector

Constructor & Destructor Documentation

◆ NormalEquationSparseLinearAlgebraTraits_d()

NormalEquationSparseLinearAlgebraTraits_d::NormalEquationSparseLinearAlgebraTraits_d ( )

Default constructor.

Member Function Documentation

◆ normal_equation_factor()

bool NormalEquationSparseLinearAlgebraTraits_d::normal_equation_factor ( const Matrix & A )

Factorize the sparse matrix At * A.

This factorization is used in normal_equation_solver() to solve the system for different right-hand side vectors.

Returns: true if the factorization is successful and false otherwise.

◆ normal_equation_solver() [1/2]

bool NormalEquationSparseLinearAlgebraTraits_d::normal_equation_solver	(	const Matrix &	A,
		const Vector &	B,
		Vector &	X
	)

Equivalent to a call to normal_equation_factor(A) followed by a call to normal_equation_solver(B,X) .

◆ normal_equation_solver() [2/2]

bool NormalEquationSparseLinearAlgebraTraits_d::normal_equation_solver	(	const Vector &	B,
		Vector &	X
	)

Solve the sparse linear system At * A * X = At * B, with A being the matrix provided in #normal_equation_factor(), and At its transpose matrix.

Returns: true if the solver is successful and false otherwise.