NormalEquationSparseLinearAlgebraTraits_d Concept Reference

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.
typedef unspecified_type	Vector
	Vector type model of SparseLinearAlgebraTraits_d::Vector.
typedef unspecified_type	NT
	Number type.

Creation
	NormalEquationSparseLinearAlgebraTraits_d ()
	Default constructor.

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

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()

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.