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

Class RealBackSolver

java.lang.Object

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

org.flag4j.linalg.solvers.exact.triangular.RealBackSolver

All Implemented Interfaces:

LinearSolver<Matrix,Vector>

public class RealBackSolver
extends BackSolver<Matrix,Vector,double[]>

This solver solves linear systems of equations where the coefficient matrix in an upper triangular real dense matrix and the constant vector is a real dense vector or matrix. That is, solves a linear system of equations U*x=b or U*X=B where U is an upper triangular matrix.

Field Summary

Fields

Modifier and Type	Field	Description
protected double	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
RealBackSolver()	Creates a solver for solving linear systems for upper triangular coefficient matrices.
RealBackSolver(boolean enforceTriU)	Creates a solver for solving linear systems for upper triangular coefficient matrices.

Method Summary

Modifier and Type	Method	Description
double	getDet()	Gets the determinant computed during the last solve.
Matrix	solve(Matrix U, Matrix B)	Solves the linear system of equations given by U*X=B where the coefficient matrix U is an upper triangular matrix.
Vector	solve(Matrix U, Vector b)	Solves the linear system of equations given by U*x=b where the coefficient matrix U is an upper triangular matrix.
Matrix	solveIdentity(Matrix 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.
Matrix	solveLower(Matrix U, Matrix 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 double det

For computing determinant of coefficient matrix during solve.

Constructor Details

RealBackSolver

public RealBackSolver()

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 * RealBackSolver(boolean).

RealBackSolver

public RealBackSolver(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 double getDet()

Gets the determinant computed during the last solve.

solve

public Vector solve(Matrix U,
 Vector 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 enforceTriU was set to false when this solver instance was created and 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. has a zero on the principle diagonal).

solve

public Matrix solve(Matrix U,
 Matrix 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 enforceTriU was set to false when this solver instance was created and 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 U*X=B.

Throws:

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

solveIdentity

public Matrix solveIdentity(Matrix 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. This essentially inverts the upper triangular matrix since U*U^-1=I.

Parameters:

U - Upper triangular coefficient matrix in the linear system. If enforceTriU was set to false when this solver instance was created and 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 Matrix solveLower(Matrix U,
 Matrix 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 in the linear system. If enforceTriU was set to false when this solver instance was created and U is not actually upper triangular, it will be treated as if it were.

L - Lower triangular constant matrix. This is not explicit checked. If L is not lower triangular, values above the principle diagonal will be ignored and the result will still be correctly computed.

Returns:

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