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:

LinearMatrixSolver<Matrix,Vector>, LinearSolver<Matrix>

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

This solver solves a real linear system of equations where the coefficient matrix is lower triangular. That is, solves the systems $Lx=b$ or $LX=B$ where $L$ is a lower triangular matrix. This is accomplished using a simple forward substitution.

See Also:

• ComplexForwardSolver

Field Summary

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

enforceLower, isUnit, RANK_CONDITION, 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	solve(Matrix L, PermutationMatrix P)	Solves a linear system $LX=P$ for $X$ where $L$ is a lower triangular matrix and $P$ is a permutation matrix.
Matrix	solveIdentity(Matrix L)	Performs forward substitution for a unit lower triangular matrix $L$ and 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

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 false, the coefficient matrix is expected to be lower triangular but not necessarily unit lower.

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 false, the coefficient matrix is expected to be lower triangular but not necessarily unit lower.

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 $Lx=b$ for $x$ where $L$ is lower triangular.

Parameters:

L - Lower triangular coefficient matrix $L$. L is assumed to be lower triangular and only entries at and below the principle diagonal will be accessed.

b - Constant vector $b$.

Returns:

The result of solving the linear system $Lx=b$ where $L$ is a lower triangular.

Throws:

SingularMatrixException - If L is singular (i.e. has at least one zero on the principle diagonal).

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 $LX=B$ for $X$ where $L$ is lower triangular.

Parameters:

L - Lower triangular coefficient matrix $L$. L is assumed to be lower triangular and only entries at and below the principle diagonal will be accessed.

B - The constant matrix in the linear system.

b - Constant matrix $B$.

Returns:

The result of solving the linear system $LX=B$ where $L$ is a lower triangular.

Throws:

SingularMatrixException - If L is singular (i.e. has at least one zero on the principle diagonal).

solve

public Matrix solve(Matrix L,
 PermutationMatrix P)

Solves a linear system $LX=P$ for $X$ where $L$ is a lower triangular matrix and $P$ is a permutation matrix.

Specified by:

solve in class ForwardSolver<Matrix,Vector,double[]>

Parameters:

L - Lower triangular coefficient matrix $L$.

P - Constant permutation matrix $P$.

Returns:

The solution to $X$ in the linear system $LX=P$.

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 $LX=I$ where $L$ is a lower triangular matrix and $I$ is the appropriately sized identity matrix.

Parameters:

L - Lower triangular coefficient matrix, $L$. If L is not lower triangular, it will be treated as if it were and only data in the lower triangular portion will be accessed.

Returns:

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

Throws:

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