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

Class ComplexBackSolver

java.lang.Object

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

org.flag4j.linalg.solvers.exact.triangular.ComplexBackSolver

All Implemented Interfaces:

LinearSolver<CMatrix,CVector>

public class ComplexBackSolver
extends BackSolver<CMatrix,CVector,CNumber[]>

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

Field Summary

Fields

Modifier and Type	Field	Description
protected CNumber	det	For computing determinant of coefficient matrix during solve.

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

enforceTriU, RANK_CONDITION, x, X, xCol

Constructor Summary

Constructors

Constructor	Description
ComplexBackSolver()	Creates a solver for solving linear systems for upper triangular coefficient matrices.
ComplexBackSolver(boolean enforceTriU)	Creates a solver for solving linear systems for upper triangular coefficient matrices.

Method Summary

Modifier and Type	Method	Description
CNumber	getDet()	Gets the determinant computed during the last solve.
CMatrix	solve(CMatrix U, CMatrix B)	Solves the linear system of equations given by U*X=B where the coefficient matrix U is an upper triangular matrix.
CVector	solve(CMatrix U, CVector b)	Solves the linear system of equations given by U*x=b where the coefficient matrix U is an upper triangular matrix.
CMatrix	solveIdentity(CMatrix U)	Solves the linear system of equations given by U*X=I where the coefficient matrix U is an upper triangular matrix and I is the identity matrix of appropriate size.
CMatrix	solveLower(CMatrix U, CMatrix L)	Solves a special case of the linear system U*X=L for X where the coefficient matrix U is an upper triangular matrix and the constant matrix L is lower triangular.

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

checkParams, checkSingular

Methods inherited from class java.lang.Object

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

Field Details

det

protected CNumber det

For computing determinant of coefficient matrix during solve.

Constructor Details

ComplexBackSolver

public ComplexBackSolver()

Creates a solver for solving linear systems for upper triangular coefficient matrices. Note, by default no check will be made to ensure the coefficient matrix is upper triangular. If you would like to enforce this, see ComplexBackSolver(boolean).

ComplexBackSolver

public ComplexBackSolver(boolean enforceTriU)

Creates a solver for solving linear systems for upper triangular coefficient matrices.

Parameters:

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

Method Details

getDet

public CNumber getDet()

Gets the determinant computed during the last solve.

solve

public CVector solve(CMatrix U,
 CVector b)

Solves the linear system of equations given by U*x=b where the coefficient matrix U is an upper triangular matrix.

Parameters:

U - Upper triangular coefficient matrix in the linear system. If U is not actually upper triangular, it will be treated as if it were.

b - Vector of constants in the linear system.

Returns:

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

Throws:

SingularMatrixException - If the matrix U is singular (i.e. if it has a zero along the principle diagonal).

solve

public CMatrix solve(CMatrix U,
 CMatrix B)

Solves the linear system of equations given by U*X=B where the coefficient matrix U is an upper triangular matrix.

Parameters:

U - Upper triangular coefficient matrix in the linear system. If U is not actually upper triangular, it will be treated as if it were.

B - Matrix of constants in the linear system.

Returns:

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

Throws:

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

solveIdentity

public CMatrix solveIdentity(CMatrix U)

Solves the linear system of equations given by U*X=I where the coefficient matrix U is an upper triangular matrix and I is the identity matrix of appropriate size.

Parameters:

U - Upper triangular coefficient matrix in the linear system. If U is not actually upper triangular, it will be treated as if it were.

Returns:

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

Throws:

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

solveLower

public CMatrix solveLower(CMatrix U,
 CMatrix L)

Solves a special case of the linear system U*X=L for X where the coefficient matrix U is an upper triangular matrix and the constant matrix L is lower triangular.

Parameters:

U - Upper triangular coefficient matrix

L - Lower triangular constant matrix.

Returns:

The result of solving the linear system U*X=L for the matrix X.