SystemSolver class abstract

A solver for systems of linear equations whose coefficients are only real numbers. There must be n equations in n unknowns.

The coefficients of the various equations are put inside a square matrix, which is generally called A, and 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 vector x of the Ax = b equation.

Implementers

Constructors

SystemSolver({required int size, required List<List<double>> A, required List<double> b, 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.
SystemSolver.flatMatrix({required int size, required List<double> A, required List<double> b, 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.

Properties

equations ↔ RealMatrix: The equations of the system to be solved.
latefinal
hashCode → int: The hash code for this object.
no setteroverride
knownValues → List<double>: The vector containing the known values of the equation.
no setter
precision → double: The accuracy of the algorithm.
final
runtimeType → Type: A representation of the runtime type of the object.
no setterinherited
size → int: The dimension of the system (which is 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 containing the solutions of the system.
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.