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

Class ForwardSolver<T extends MatrixMixin<T,?,?,?,?,?,U,?>,U extends VectorMixin<U,?,?,?,?,T,?,?>,V>

java.lang.Object

org.flag4j.linalg.solvers.exact.triangular.ForwardSolver<T,U,V>

Type Parameters:

T - Type of coefficient matrix.

U - Vector type equivalent to the coefficient matrix.

V - Type of the internal storage datastructures in the matrix and vector.

All Implemented Interfaces:

LinearSolver<T,U>

Direct Known Subclasses:

ComplexForwardSolver, RealForwardSolver

public abstract class ForwardSolver<T extends MatrixMixin<T,?,?,?,?,?,U,?>,U extends VectorMixin<U,?,?,?,?,T,?,?>,V>
extends Object
implements LinearSolver<T,U>

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. That is, solves, L*x=b or L*X=B for the vector x or the matrix X respectively where L is a lower triangular matrix.

Field Summary

Fields

Modifier and Type	Field	Description
protected final boolean	enforceLower	Flag indicating if an explicit check should be made that the coefficient matrix is lower triangular.
protected final boolean	isUnit	Flag indicating if lower-triangular matrices passed to this solver will be unit lower-triangular (true) or simply lower-triangular (false).
protected static final double	RANK_CONDITION	Threshold for determining if a determinant is to be considered zero when checking if the coefficient matrix is full rank.
(package private) U	x	Storage for solution in solves which return a vector.
(package private) T	X	Storage for solution in solves which return a 00000000
protected V	xCol	Temporary storage for columns of the solution matrix.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	ForwardSolver(boolean isUnit, boolean enforceLower)	Creates a solver for solving a lower-triangular system.

Method Summary

Modifier and Type	Method	Description
protected void	checkParams(T coeff, int constantRows)	Ensures passed parameters are valid for the back solver.
protected void	checkSingular(double detAbs, int numRows, int numCols)	Checks if the coefficient matrix is singular based on the computed determinant.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.flag4j.linalg.solvers.LinearSolver

solve, solve

Field Details

RANK_CONDITION

protected static final double RANK_CONDITION

Threshold for determining if a determinant is to be considered zero when checking if the coefficient matrix is full rank.

isUnit

protected final boolean isUnit

Flag indicating if lower-triangular matrices passed to this solver will be unit lower-triangular (true) or simply lower-triangular (false).

enforceLower

protected final boolean enforceLower

Flag indicating if an explicit check should be made that the coefficient matrix is lower triangular. If false, the matrix will simply be assumed to be lower triangular.

X

T extends MatrixMixin<T,?,?,?,?,?,U,?> X

Storage for solution in solves which return a 00000000

x

U extends VectorMixin<U,?,?,?,?,T,?,?> x

Storage for solution in solves which return a vector.

xCol

protected V xCol

Temporary storage for columns of the solution matrix. This can be used to improve cache performance when columns need to be traveled.

Constructor Details

ForwardSolver

protected ForwardSolver(boolean isUnit,
 boolean enforceLower)

Creates a solver for solving a lower-triangular system.

Parameters:

isUnit - Flag indicating if coefficient matrices passed will be unit lower-triangular or simply lower-triangular in general.

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

Method Details

checkParams

protected void checkParams(T coeff,
 int constantRows)

Ensures passed parameters are valid for the back solver.

Parameters:

coeff - Coefficient matrix in the linear system.

constantRows - Number of rows in the constant vector or matrix.

Throws:

IllegalArgumentException - If coeff is not square, coeff.numRows()!=constantRows, or if enforceTriU is true and coeff is not upper triangular.

checkSingular

protected void checkSingular(double detAbs,
 int numRows,
 int numCols)

Checks if the coefficient matrix is singular based on the computed determinant.

Parameters:

detAbs - Absolute value of computed determinant.

numRows - Number of rows in the coefficient matrix.

numCols - Number of columns in the coefficient matrix.