Package org.flag4j.linalg.solvers.lstsq

Class LstsqSolver<T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U>,U extends VectorMixin<U,U,?,CVector,?,T,T,CMatrix>>

java.lang.Object

org.flag4j.linalg.solvers.lstsq.LstsqSolver<T,U>

All Implemented Interfaces:

LinearSolver<T,U>

Direct Known Subclasses:

ComplexLstsqSolver, RealLstsqSolver

public abstract class LstsqSolver<T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U>,U extends VectorMixin<U,U,?,CVector,?,T,T,CMatrix>>
extends Object
implements LinearSolver<T,U>

This class solves a linear system of equations Ax=b in a least-squares sense. That is, minimizes ||Ax-b||₂ which is equivalent to solving the normal equations A^TAx=A^T b. This is done using a QR decomposition.

Field Summary

Fields

Modifier and Type	Field	Description
protected final LinearSolver<T,U>	backSolver	Solver for system with an upper triangular coefficient matrix.
protected T	Qh	Q The hermitian transpose of the orthonormal matrix from the QR decomposition.
protected final UnitaryDecomposition<T,?>	qr	Decomposer to compute the QR decomposition for using the least-squares solver.
protected T	R	R The upper triangular matrix from the QR decomposition.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	LstsqSolver(UnitaryDecomposition<T,?> qr, LinearSolver<T,U> backSolver)	Constructs a least-squares solver with a specified decomposer to use in the QR decomposition.

Method Summary

Modifier and Type	Method	Description
protected void	decompose(T A)	Computes the QR decomposition for use in this solver.
T	solve(T A, T B)	Solves the set of linear system of equations given by A*X=B for the matrix X where A, B, and X are matrices.
U	solve(T A, U b)	Solves the linear system given by Ax=b in the least-squares sense.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

backSolver

protected final LinearSolver<T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U>,U extends VectorMixin<U,U,?,CVector,?,T,T,CMatrix>> backSolver

Solver for system with an upper triangular coefficient matrix.

qr

protected final UnitaryDecomposition<T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U>,?> qr

Decomposer to compute the QR decomposition for using the least-squares solver.

Qh

protected T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U> Qh

Q The hermitian transpose of the orthonormal matrix from the QR decomposition.

R

protected T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U> R

R The upper triangular matrix from the QR decomposition.

Constructor Details

LstsqSolver

protected LstsqSolver(UnitaryDecomposition<T,?> qr,
 LinearSolver<T,U> backSolver)

Constructs a least-squares solver with a specified decomposer to use in the QR decomposition.

Parameters:

qr - The QR decomposer to use in the solver.

backSolver - The solver to solve the upper triangular system resulting from the QR decomposition which is equivalent to solving the normal equations

Method Details

solve

public U solve(T A,
 U b)

Solves the linear system given by Ax=b in the least-squares sense.

Specified by:

solve in interface LinearSolver<T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U>,U extends VectorMixin<U,U,?,CVector,?,T,T,CMatrix>>

Parameters:

A - Coefficient matrix in the linear system.

b - Vector of constants in the linear system.

Returns:

The least squares solution to x in the linear system Ax=b.

solve

public T solve(T A,
 T B)

Solves the set of linear system of equations given by A*X=B for the matrix X where A, B, and X are matrices.

Specified by:

solve in interface LinearSolver<T extends MatrixMixin<T,T,?,CMatrix,?,?,U,U>,U extends VectorMixin<U,U,?,CVector,?,T,T,CMatrix>>

Parameters:

A - Coefficient matrix in the linear system.

B - Matrix of constants in the linear system.

Returns:

The solution to X in the linear system A*X=B.

decompose

protected void decompose(T A)

Computes the QR decomposition for use in this solver.

Parameters:

A - Coefficient matrix in the linear system to solve.