SystemSolver class abstract base

An abstract class that represents a system of equations, which can be solved using various algorithms that manipulate the data of a matrix and a vector.

System solvers of linear equations require the coefficients to be real numbers and there must be n equations in n unknowns.

The coefficients of the various equations are put inside a square matrix, generally called A. The known values are represented by a vector, usually known as b. From this, we get an equation in the form Ax = b.

The method solve returns the x vector of the Ax = b equation.

Implementers

• CholeskySolver
• GaussianElimination
• GaussSeidelSolver
• JacobiSolver
• LUSolver
• SORSolver

Constructors

SystemSolver({required RealMatrix matrix, required List<double> knownValues, double precision = 1.0e-10})

Given an equation in the form Ax = b, A is a square matrix containing n equations in n unknowns and b is the vector of the known values. This class can only be built with square matrices. In particular:

Properties

hashCode → int

The hash code for this object.

no setter, override

knownValues → List<double>

The vector containing the known values of the equations.

final

matrix → RealMatrix

The equations to be solved.

final

precision → double

The algorithm accuracy.

final

runtimeType → Type

A representation of the runtime type of the object.

no setter, inherited

size → int

The dimension of the system (N equations in N unknowns).

no setter

Methods

determinant() → double

Computes the determinant of the associated matrix.

hasSolution() → bool

Computes whether the system can be solved or not.

noSuchMethod(Invocation invocation) → dynamic

Invoked when a nonexistent method or property is accessed.

inherited

solve() → List<double>

Solves the Ax = b equation and returns the x vector.

toString() → String

A string representation of this object.

override

toStringAugmented() → String

Prints the augmented matrix of this instance, which is the equations matrix plus the known values vector to the right. For example, if...

Operators

operator ==(Object other) → bool

The equality operator.

override

Static Methods

backSubstitution(List<List<double>> source, List<double> vector) → List<double>

Back substitution is an iterative process that solves equation matrices in the form Ux = b, where U is an upper triangular matrix.

forwardSubstitution(List<List<double>> source, List<double> vector) → List<double>

Forward substitution is an iterative process that solves equation matrices in the form Lx = b, where L is a lower triangular matrix.