Package org.flag4j.linalg.solvers.exact.triangular

Class RealForwardSolver

java.lang.Object

org.flag4j.linalg.solvers.exact.triangular.ForwardSolver<Matrix,Vector,double[]>

org.flag4j.linalg.solvers.exact.triangular.RealForwardSolver

All Implemented Interfaces:

LinearSolver<Matrix,Vector>

public class RealForwardSolver
extends ForwardSolver<Matrix,Vector,double[]>

This solver solves linear systems of equations where the coefficient matrix in a lower triangular real dense matrix and the constant vector is a real dense vector.

Field Summary

Fields

Modifier and Type	Field	Description
private double	det	For computing determinant of lower triangular matrix during solve.

Fields inherited from class org.flag4j.linalg.solvers.exact.triangular.ForwardSolver

enforceLower, isUnit, RANK_CONDITION, x, X, xCol

Constructor Summary

Constructors

Constructor	Description
RealForwardSolver()	Creates a solver to solve a linear system where the coefficient matrix is lower triangular.
RealForwardSolver(boolean isUnit)	Creates a solver to solve a linear system where the coefficient matrix is lower triangular or unit lower triangular.
RealForwardSolver(boolean isUnit, boolean enforceLower)	Creates a solver to solve a linear system where the coefficient matrix is lower triangular or unit lower triangular.

Method Summary

Modifier and Type	Method	Description
double	getDet()	Gets the determinant computed during the last solve.
Matrix	solve(Matrix L, Matrix B)	Performs forward substitution for a unit lower triangular matrix L and a matrix B.
Vector	solve(Matrix L, Vector b)	Performs forward substitution for a unit lower triangular matrix L and a vector b.
Matrix	solveIdentity(Matrix L)	Performs forward substitution for a unit lower triangular matrix L and the identity matrix.
private Matrix	solveLower(Matrix L, Matrix B)	Solves a linear system where the coefficient matrix is lower triangular.
private Vector	solveLower(Matrix L, Vector b)	Solves a linear system where the coefficient matrix is lower triangular.
private Matrix	solveLowerIdentity(Matrix L)	Solves a linear system L*X=I where the coefficient matrix L is lower triangular and the constant matrix I is the appropriately sized identity matrix.
private Matrix	solveUnitLower(Matrix L, Matrix B)	Solves a linear system where the coefficient matrix is unit lower triangular.
private Vector	solveUnitLower(Matrix L, Vector b)	Solves a linear system where the coefficient matrix is unit lower triangular.
private Matrix	solveUnitLowerIdentity(Matrix L)	Solves a linear system where the coefficient matrix is unit lower triangular and the constant matrix is the identity matrix.

Methods inherited from class org.flag4j.linalg.solvers.exact.triangular.ForwardSolver

checkParams, checkSingular

Methods inherited from class java.lang.Object

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

Field Details

det

private double det

For computing determinant of lower triangular matrix during solve.

Constructor Details

RealForwardSolver

public RealForwardSolver()

Creates a solver to solve a linear system where the coefficient matrix is lower triangular.

RealForwardSolver

public RealForwardSolver(boolean isUnit)

Creates a solver to solve a linear system where the coefficient matrix is lower triangular or unit lower triangular.

Parameters:

isUnit - Flag which indicates if the coefficient matrix is unit lower triangular or not.
- If true, the coefficient matrix is expected to be unit lower triangular.
- If true, the coefficient matrix is expected to be lower triangular.

RealForwardSolver

public RealForwardSolver(boolean isUnit,
 boolean enforceLower)

Creates a solver to solve a linear system where the coefficient matrix is lower triangular or unit lower triangular.

Parameters:

isUnit - Flag which indicates if the coefficient matrix is unit lower triangular or not.
- If true, the coefficient matrix is expected to be unit lower triangular.
- If true, the coefficient matrix is expected to be lower triangular.

enforceLower - Flag indicating if an explicit check should be made that the coefficient matrix is lower triangular.

Method Details

getDet

public double getDet()

Gets the determinant computed during the last solve.

solve

public Vector solve(Matrix L,
 Vector b)

Performs forward substitution for a unit lower triangular matrix L and a vector b. That is, solves the linear system L*x=b where L is a lower triangular matrix.

Parameters:

L - Lower triangular coefficient matrix. If L is not lower triangular, it will be treated as if it were.

b - Constant vector.

Returns:

The result of solving the linear system L*x=b where L is a lower triangular matrix.

Throws:

SingularMatrixException - If

solve

public Matrix solve(Matrix L,
 Matrix B)

Performs forward substitution for a unit lower triangular matrix L and a matrix B. That is, solves the linear system L*X=B where L is a lower triangular matrix.

Parameters:

L - Lower triangular coefficient matrix. If L is not lower triangular, it will be treated as if it were.

B - Constant Matrix.

Returns:

The result of solving the linear system L*X=B where L is a lower triangular matrix.

Throws:

SingularMatrixException - If the matrix lower triangular L is singular (i.e. has a zero on * the principle diagonal).

solveIdentity

public Matrix solveIdentity(Matrix L)

Performs forward substitution for a unit lower triangular matrix L and the identity matrix. That is, solves the linear system L*X=I where L is a lower triangular matrix and I is the appropriately sized identity matrix.

Parameters:

L - Lower triangular coefficient matrix. If L is not lower triangular, it will be treated as if it were.

Returns:

The result of solving the linear system L*X=B where L is a lower triangular matrix.

Throws:

SingularMatrixException - If the matrix lower triangular L is singular (i.e. has a zero on the principle diagonal).

solveUnitLower

private Vector solveUnitLower(Matrix L,
 Vector b)

Solves a linear system where the coefficient matrix is unit lower triangular.

Parameters:

L - Unit lower triangular matrix.

b - Vector of constants in the linear system.

Returns:

The solution of x for the linear system L*x=b.

solveLower

private Vector solveLower(Matrix L,
 Vector b)

Solves a linear system where the coefficient matrix is lower triangular.

Parameters:

L - Unit lower triangular matrix.

b - Vector of constants in the linear system.

Returns:

The solution of x for the linear system L*x=b.

Throws:

SingularMatrixException - If the lower triangular matrix L is singular (i.e. has a zero on the principle diagonal).

solveUnitLower

private Matrix solveUnitLower(Matrix L,
 Matrix B)

Solves a linear system where the coefficient matrix is unit lower triangular.

Parameters:

L - Unit lower triangular matrix.

B - Matrix of constants in the linear system.

Returns:

The solution of X for the linear system L*X=b.

solveLower

private Matrix solveLower(Matrix L,
 Matrix B)

Solves a linear system where the coefficient matrix is lower triangular.

Parameters:

L - Unit lower triangular matrix.

B - Matrix of constants in the linear system.

Returns:

The solution of X for the linear system L*X=b.

Throws:

SingularMatrixException - If the lower triangular matrix L is singular (i.e. has a zero on the principle diagonal).

solveUnitLowerIdentity

private Matrix solveUnitLowerIdentity(Matrix L)

Solves a linear system where the coefficient matrix is unit lower triangular and the constant matrix is the identity matrix.

Parameters:

L - Unit lower triangular matrix.

Returns:

The solution of X for the linear system L*X=I.

solveLowerIdentity

private Matrix solveLowerIdentity(Matrix L)

Solves a linear system L*X=I where the coefficient matrix L is lower triangular and the constant matrix I is the appropriately sized identity matrix.

Parameters:

L - Unit lower triangular matrix (Note, this is not checked). If L is not lower triangular, it will be treated as if it were. No error will be thrown.

Returns:

The solution of X for the linear system L*X=I.

Throws:

SingularMatrixException - If the lower triangular matrix L is singular (i.e. has a zero on the principle diagonal).