ptems::ConstrainedLeastSquares< T > Class Template Reference

Class for solving a constrained least squares problem. More...

#include <ptems/linearalgebra.hpp>

Public Member Functions
	ConstrainedLeastSquares (std::size_t rows, std::size_t cols, std::size_t constraints)
	Create the constrained least squares problem: find \(x\in T^n\) which minimises. More...
std::size_t	ColumnCount () const
	Gets the size of the linear system. More...
std::size_t	RowCount () const
	Gets the size of the linear system. More...
std::size_t	ConstraintCount () const
	Gets the size of the linear system. More...
T &	operator() (std::size_t i, std::size_t j)
	Gets mutable reference to the specified entry of the matrix \(A\). More...
T &	Constraint (std::size_t i, std::size_t j)
	Gets mutable reference to the specified entry of the constraint matrix \(C\). More...
std::vector< T > &	Solve (std::vector< T > &rhs, const std::vector< T > &constraintRHS)
	Solves the constrained least squares problem. More...

Detailed Description

template<typename T>
class ptems::ConstrainedLeastSquares< T >

Class for solving a constrained least squares problem.

The constrained least squares problem is to find \(x\in T^n\) which minimises

\[\Vert Ax - b \Vert^2\]

subject to the constraints

\[Cx = d\]

where \(A\in T^{m\times n}\), \(C\in T^{p\times n}\), \(x\in T^m\) and \(d\in T^p\).

Template Parameters

T	The type of the entries of the least squares system

Constructor & Destructor Documentation

ConstrainedLeastSquares()

template<typename T >

ptems::ConstrainedLeastSquares< T >::ConstrainedLeastSquares ( std::size_t  rows, std::size_t  cols, std::size_t  constraints  )

inline

Create the constrained least squares problem: find \(x\in T^n\) which minimises.

\[\Vert Ax - b \Vert^2\]

subject to the constraints

\[Cx = d\]

where \(A\in T^{m\times n}\), \(C\in T^{p\times n}\), \(x\in T^m\) and \(d\in T^p\).

Parameters

rows	Number of rows ( \(m\)) in the matrix
cols	Number of columns ( \(n\)) in the matrix
constraints	Number of constraints ( \(p\))

Member Function Documentation

ColumnCount()

template<typename T >

std::size_t ptems::ConstrainedLeastSquares< T >::ColumnCount ( ) const

inline

Gets the size of the linear system.

Constraint()

template<typename T >

T& ptems::ConstrainedLeastSquares< T >::Constraint ( std::size_t  i, std::size_t  j  )

inline

Gets mutable reference to the specified entry of the constraint matrix \(C\).

Note

This method can only be called before Solve() is called

Exceptions

std::out_of_range	If the row or column index is greater or equal to the number or constraints or columns, respectively
std::logic_error	If Solve() has been called already

Parameters

i	The row index of the entry to get
j	The column index of the entry to get

Returns

Mutable reference to the constraint matrix entry

ConstraintCount()

template<typename T >

std::size_t ptems::ConstrainedLeastSquares< T >::ConstraintCount ( ) const

inline

Gets the size of the linear system.

operator()()

template<typename T >

T& ptems::ConstrainedLeastSquares< T >::operator() ( std::size_t  i, std::size_t  j  )

inline

Gets mutable reference to the specified entry of the matrix \(A\).

Note

This method can only be called before Solve() is called

Exceptions

std::out_of_range	If the row or column index is greater or equal to the number or rows or columns, respectively
std::logic_error	If Solve() has been called already

Parameters

i	The row index of the entry to get
j	The column index of the entry to get

Returns

Mutable reference to the matrix entry

RowCount()

template<typename T >

std::size_t ptems::ConstrainedLeastSquares< T >::RowCount ( ) const

inline

Gets the size of the linear system.

Solve()

template<typename T >

std::vector<T>& ptems::ConstrainedLeastSquares< T >::Solve ( std::vector< T > &  rhs, const std::vector< T > &  constraintRHS  )

inline

Solves the constrained least squares problem.

Exceptions

std::invalid_argument

If rhs.size() != number of columns, or constraintRHS.size() != number of constraints

Warning

LU factorisation is performed the first time Solve() is called, and the result is cached, overriding the original matrix. As such, the matrix entries cannot be changed after calling Solve().

Parameters

rhs	The mutable vector containing \(b\) which is updated with \(x\) on return
constraintRHS	The right hand side vector \(d\) for the constraints

Returns

Reference to rhs

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

• ptems/linearalgebra.hpp