Package org.flag4j.linalg.solvers.exact

Class ExactSolver<T extends MatrixMixin<T,?,?,?,?,?,U,?>,U extends VectorMixin<U,?,?,?,?,T,?,?>>

java.lang.Object

org.flag4j.linalg.solvers.exact.ExactSolver<T,U>

All Implemented Interfaces:

LinearSolver<T,U>

Direct Known Subclasses:

ComplexExactSolver, RealExactSolver

public abstract class ExactSolver<T extends MatrixMixin<T,?,?,?,?,?,U,?>,U extends VectorMixin<U,?,?,?,?,T,?,?>>
extends Object
implements LinearSolver<T,U>

Solves a well determined system of equations Ax=b in an exact sense by using a LU decomposition.

If the system is not well determined, i.e. A is square and full rank, then use a least-squares solver.

Field Summary

Fields

Modifier and Type	Field	Description
protected final LinearSolver<T,U>	backSolver	Backwards solver for solving system with upper triangular coefficient matrix.
protected final LinearSolver<T,U>	forwardSolver	Forward Solver for solving system with lower triangular coefficient matrix.
protected final LU<T>	lu	Decomposer to compute LU decomposition.
protected T	LU	The unit-lower and upper triangular matrices from the LU decomposition stored in a single matrix.
protected PermutationMatrix	rowPermute	Row permutation matrix for LU decomposition.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	ExactSolver(LU<T> lu, LinearSolver<T,U> forwardSolver, LinearSolver<T,U> backSolver)	Constructs an exact LU solver with a specified LU decomposer.

Method Summary

Modifier and Type	Method	Description
protected void	decompose(T A)	Decomposes A using an LU decomposition.
protected abstract T	permuteRows(T B)	Permute the rows of a matrix using the row permutation matrix from the LU decomposition.
protected abstract U	permuteRows(U b)	Permute the rows of a vector using the row permutation matrix from the LU decomposition.
T	solve(T A, T B)	Solves the set of linear system of equations given by A*X=B for the matrix X.
U	solve(T A, U b)	Solves the linear system of equations given by A*x=b for the vector x.

Methods inherited from class java.lang.Object

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

Field Details

forwardSolver

protected final LinearSolver<T extends MatrixMixin<T,?,?,?,?,?,U,?>,U extends VectorMixin<U,?,?,?,?,T,?,?>> forwardSolver

Forward Solver for solving system with lower triangular coefficient matrix.

backSolver

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

Backwards solver for solving system with upper triangular coefficient matrix.

lu

protected final LU<T extends MatrixMixin<T,?,?,?,?,?,U,?>> lu

Decomposer to compute LU decomposition.

LU

protected T extends MatrixMixin<T,?,?,?,?,?,U,?> LU

The unit-lower and upper triangular matrices from the LU decomposition stored in a single matrix.

rowPermute

protected PermutationMatrix rowPermute

Row permutation matrix for LU decomposition.

Constructor Details

ExactSolver

protected ExactSolver(LU<T> lu,
 LinearSolver<T,U> forwardSolver,
 LinearSolver<T,U> backSolver)

Constructs an exact LU solver with a specified LU decomposer.

Parameters:

lu - LU decomposer to employ in solving the linear system.

Throws:

IllegalArgumentException - If the LU decomposer does not use partial pivoting.

Method Details

decompose

protected void decompose(T A)

Decomposes A using an LU decomposition.

Parameters:

A - Matrix to decompose.

solve

public U solve(T A,
 U b)

Solves the linear system of equations given by A*x=b for the vector x. The system must be well determined.

Specified by:

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

Parameters:

A - Coefficient matrix in the linear system. Must be square and have full rank (i.e. all rows, or equivalently columns, must be linearly independent).

b - Vector of constants in the linear system.

Returns:

The solution to x in the linear system A*x=b.

Throws:

IllegalArgumentException - If the number of columns in A is not equal to the number of entries in b.

IllegalArgumentException - If A is not square.

SingularMatrixException - If A is singular.

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.

Specified by:

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

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.

Throws:

IllegalArgumentException - If the number of columns in A is not equal to the number of rows in B.

IllegalArgumentException - If A is not square.

SingularMatrixException - If A is singular.

permuteRows

protected abstract U permuteRows(U b)

Permute the rows of a vector using the row permutation matrix from the LU decomposition.

Parameters:

b - Vector to permute the rows of.

Returns:

A vector which is the result of applying the row permutation from the LU decomposition to the vector b.

permuteRows

protected abstract T permuteRows(T B)

Permute the rows of a matrix using the row permutation matrix from the LU decomposition.

Parameters:

B - matrix to permute the rows of.

Returns:

A matrix which is the result of applying the row permutation from the LU decomposition to the matrix B.