This class implements the Gauss LU decomposition (Crout algorithm) with partial pivoting (rows interchange) of a square matrix and the different possible derived calculation : More...

#include <math_Gauss.hxx>

Public Member Functions
	math_Gauss (const math_Matrix &A, const Standard_Real MinPivot=1.0e-20)
	Given an input n X n matrix A this constructor performs its LU decomposition with partial pivoting (interchange of rows). This LU decomposition is stored internally and may be used to do subsequent calculation. If the largest pivot found is less than MinPivot the matrix A is considered as singular. Exception NotSquare is raised if A is not a square matrix. More...

Standard_Boolean	IsDone () const
	Returns true if the computations are successful, otherwise returns false. More...

void	Solve (const math_Vector &B, math_Vector &X) const
	Given the input Vector B this routine returns the solution X of the set of linear equations A . X = B. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B is not equal to the number of rows of A. More...

void	Solve (math_Vector &B) const
	Given the input Vector B this routine solves the set of linear equations A . X = B. B is replaced by the vector solution X. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B is not equal to the number of rows of A. More...

Standard_Real	Determinant () const
	This routine returns the value of the determinant of the previously LU decomposed matrix A. Exception NotDone may be raised if the decomposition of A was not done successfully, zero is returned if the matrix A was considered as singular. More...

void	Invert (math_Matrix &Inv) const
	This routine outputs Inv the inverse of the previously LU decomposed matrix A. Exception DimensionError is raised if the ranges of B are not equal to the ranges of A. More...

void	Dump (Standard_OStream &o) const
	Prints on the stream o information on the current state of the object. Is used to redefine the operator <<. More...

Protected Attributes
Standard_Boolean	Singular

math_Matrix	LU

math_IntegerVector	Index

Standard_Real	D

Detailed Description

This class implements the Gauss LU decomposition (Crout algorithm) with partial pivoting (rows interchange) of a square matrix and the different possible derived calculation :

solution of a set of linear equations.
inverse of a matrix.
determinant of a matrix.

Constructor & Destructor Documentation

◆ math_Gauss()

math_Gauss::math_Gauss	(	const math_Matrix &	A,
		const Standard_Real	MinPivot = `1.0e-20`
	)

Given an input n X n matrix A this constructor performs its LU decomposition with partial pivoting (interchange of rows). This LU decomposition is stored internally and may be used to do subsequent calculation. If the largest pivot found is less than MinPivot the matrix A is considered as singular. Exception NotSquare is raised if A is not a square matrix.

Member Function Documentation

◆ Determinant()

Standard_Real math_Gauss::Determinant ( ) const

This routine returns the value of the determinant of the previously LU decomposed matrix A. Exception NotDone may be raised if the decomposition of A was not done successfully, zero is returned if the matrix A was considered as singular.

◆ Dump()

void math_Gauss::Dump ( Standard_OStream & o ) const

Prints on the stream o information on the current state of the object. Is used to redefine the operator <<.

◆ Invert()

void math_Gauss::Invert ( math_Matrix & Inv ) const

This routine outputs Inv the inverse of the previously LU decomposed matrix A. Exception DimensionError is raised if the ranges of B are not equal to the ranges of A.

◆ IsDone()

Standard_Boolean math_Gauss::IsDone ( ) const

Returns true if the computations are successful, otherwise returns false.

◆ Solve() [1/2]

void math_Gauss::Solve	(	const math_Vector &	B,
		math_Vector &	X
	)		const

Given the input Vector B this routine returns the solution X of the set of linear equations A . X = B. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B is not equal to the number of rows of A.

◆ Solve() [2/2]

void math_Gauss::Solve ( math_Vector & B ) const

Given the input Vector B this routine solves the set of linear equations A . X = B. B is replaced by the vector solution X. Exception NotDone is raised if the decomposition of A was not done successfully. Exception DimensionError is raised if the range of B is not equal to the number of rows of A.