CGAL 5.1.5 - CGAL and Solvers
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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.
SparseLinearAlgebraTraits_d
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 . 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) . | |
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.
true
if the factorization is successful and false
otherwise. 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.
true
if the solver is successful and false
otherwise.