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

Class ComplexForwardSolver

java.lang.Object

org.flag4j.linalg.solvers.exact.triangular.ForwardSolver<CMatrix,CVector,CNumber[]>

org.flag4j.linalg.solvers.exact.triangular.ComplexForwardSolver

All Implemented Interfaces:

LinearSolver<CMatrix,CVector>

public class ComplexForwardSolver
extends ForwardSolver<CMatrix,CVector,CNumber[]>

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

Field Summary

Fields

Modifier and Type	Field	Description
private CNumber	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
ComplexForwardSolver()	Creates a solver to solve a linear system where the coefficient matrix is lower triangular.
ComplexForwardSolver(boolean isUnit)	Creates a solver to solve a linear system where the coefficient matrix is lower triangular or unit lower triangular.
ComplexForwardSolver(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
CNumber	getDet()	Gets the determinant computed during the last solve.
CMatrix	solve(CMatrix L, CMatrix B)	Performs forward substitution for a unit lower triangular matrix L and a matrix B.
CVector	solve(CMatrix L, CVector b)	Performs forward substitution for a unit lower triangular matrix L and a vector b.
CMatrix	solveIdentity(CMatrix L)	Performs forward substitution for a unit lower triangular matrix L and the identity matrix.
private CMatrix	solveLower(CMatrix L, CMatrix B)	Solves a linear system where the coefficient matrix is lower triangular.
private CVector	solveLower(CMatrix L, CVector b)	Solves a linear system where the coefficient matrix is lower triangular.
private CMatrix	solveLowerIdentity(CMatrix 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 CMatrix	solveUnitLower(CMatrix L, CMatrix B)	Solves a linear system where the coefficient matrix is unit lower triangular.
private CVector	solveUnitLower(CMatrix L, CVector b)	Solves a linear system where the coefficient matrix is unit lower triangular.
private CMatrix	solveUnitLowerIdentity(CMatrix 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 CNumber det

For computing determinant of lower triangular matrix during solve.

Constructor Details

ComplexForwardSolver

public ComplexForwardSolver()

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

ComplexForwardSolver

public ComplexForwardSolver(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.

ComplexForwardSolver

public ComplexForwardSolver(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 CNumber getDet()

Gets the determinant computed during the last solve.

solve

public CVector solve(CMatrix L,
 CVector 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 - Unit lower triangular coefficient matrix. If L is not unit 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.

solve

public CMatrix solve(CMatrix L,
 CMatrix 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. If the lower triangular matrix L is singular (i.e. has a zero on the principle diagonal).

Throws:

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

solveIdentity

public CMatrix solveIdentity(CMatrix 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 CVector solveUnitLower(CMatrix L,
 CVector b)

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

Parameters:

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

b - Vector of constants in the linear system.

Returns:

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

solveUnitLowerIdentity

private CMatrix solveUnitLowerIdentity(CMatrix 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.

Throws:

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

solveLowerIdentity

private CMatrix solveLowerIdentity(CMatrix 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).

solveLower

private CVector solveLower(CMatrix L,
 CVector 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 CMatrix solveUnitLower(CMatrix L,
 CMatrix 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 CMatrix solveLower(CMatrix L,
 CMatrix 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).