nda::lapack::gelss_worker< T >

#include <nda/lapack/gelss_worker.hpp>

Detailed Description

template<typename T>
class nda::lapack::gelss_worker< T >

Worker class for solving linear least square problems.

Solving a linear least squares problem means finding the minimum norm solution \( \mathbf{x} \) of a linear system of equations, i.e.

\[ \min_x | \mathbf{b} - \mathbf{A x} |_2 \; , \]

where \( \mathbf{A} \) is a given matrix and \( \mathbf{b} \) is a given vector (although it can also be a matrix, in this case one gets a solution matrix \( \mathbf{X} \)).

See https://math.stackexchange.com/questions/772039/how-does-the-svd-solve-the-least-squares-problem for the notation used in this file.

Template Parameters

T	Value type of the given problem.

Definition at line 68 of file gelss_worker.hpp.

Public Member Functions
	gelss_worker (matrix< T > A_)
	Construct a new worker object for a given matrix \( \mathbf{A} \) .
int	n_var () const
	Get the number of variables of the given problem.
std::pair< matrix< T >, double >	operator() (matrix_const_view< T > B, std::optional< long >={}) const
	Solve the least-square problem for a given right hand side matrix \( \mathbf{B} \).
std::pair< vector< T >, double >	operator() (vector_const_view< T > b, std::optional< long >={}) const
	Solve the least-square problem for a given right hand side vector \( \mathbf{b} \).
array< double, 1 > const &	S_vec () const
	Get the singular value array.

Constructor & Destructor Documentation

gelss_worker()

template<typename T >

nda::lapack::gelss_worker< T >::gelss_worker ( matrix< T > A_ )

inline

Construct a new worker object for a given matrix \( \mathbf{A} \) .

It performs the SVD decomposition of the given matrix \( \mathbf{A} \) and calculates the (pseudo) inverse of \( \mathbf{A} \). Furthermore, it sets the null space term which determines the error of the least square problem.

Parameters

A_	Matrix to be decomposed by SVD.

Definition at line 107 of file gelss_worker.hpp.

Member Function Documentation

n_var()

template<typename T >

int nda::lapack::gelss_worker< T >::n_var ( ) const

inline

Get the number of variables of the given problem.

Returns

Number of columns of the matrix \( \mathbf{A} \) .

Definition at line 90 of file gelss_worker.hpp.

operator()() [1/2]

template<typename T >

std::pair< matrix< T >, double > nda::lapack::gelss_worker< T >::operator() ( matrix_const_view< T > B, std::optional< long > = {} ) const

inline

Solve the least-square problem for a given right hand side matrix \( \mathbf{B} \).

Parameters

B	Right hand side matrix.

Returns

A std::pair containing the solution matrix \( \mathbf{X} \) and the error of the least square problem.

Definition at line 134 of file gelss_worker.hpp.

operator()() [2/2]

template<typename T >

std::pair< vector< T >, double > nda::lapack::gelss_worker< T >::operator() ( vector_const_view< T > b, std::optional< long > = {} ) const

inline

Solve the least-square problem for a given right hand side vector \( \mathbf{b} \).

Parameters

b	Right hand side vector.

Returns

A std::pair containing the solution vector \( \mathbf{x} \) and the error of the least square problem.

Definition at line 151 of file gelss_worker.hpp.

S_vec()

template<typename T >

array< double, 1 > const & nda::lapack::gelss_worker< T >::S_vec ( ) const

inlinenodiscard

Get the singular value array.

Returns

1-dimensional array containing the singular values.

Definition at line 96 of file gelss_worker.hpp.

---

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

• nda/lapack/gelss_worker.hpp