This class implements the Crout algorithm used to solve a system A*X = B where A is a symmetric matrix. It can be used to invert a symmetric matrix. This algorithm is similar to Gauss but is faster than Gauss. Only the inferior triangle of A and the diagonal can be given. More...

#include <math_Crout.hxx>

Public Member Functions
	math_Crout (const math_Matrix &A, const double MinPivot=1.0e-20)
	Given an input matrix A, this algorithm inverts A by the Crout algorithm. The user can give only the inferior triangle for the implementation. A can be decomposed like this: A = L * D * T(L) where L is triangular inferior and D is diagonal. If one element of A is less than MinPivot, A is considered as singular. Exception NotSquare is raised if A is not a square matrix.

bool	IsDone () const
	Returns True if all has been correctly done.

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

const math_Matrix &	Inverse () const
	returns the inverse matrix of A. Only the inferior triangle is returned. Exception NotDone is raised if NotDone.

void	Invert (math_Matrix &Inv) const
	returns in Inv the inverse matrix of A. Only the inferior triangle is returned. Exception NotDone is raised if NotDone.

double	Determinant () const
	Returns the value of the determinant of the previously LU decomposed matrix A. Zero is returned if the matrix A is considered as singular. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).

void	Dump (Standard_OStream &o) const
	Prints on the stream o information on the current state of the object.

Detailed Description

This class implements the Crout algorithm used to solve a system A*X = B where A is a symmetric matrix. It can be used to invert a symmetric matrix. This algorithm is similar to Gauss but is faster than Gauss. Only the inferior triangle of A and the diagonal can be given.

Constructor & Destructor Documentation

◆ math_Crout()

math_Crout::math_Crout	(	const math_Matrix &	A,
		const double	MinPivot = 1.0e-20 )

Given an input matrix A, this algorithm inverts A by the Crout algorithm. The user can give only the inferior triangle for the implementation. A can be decomposed like this: A = L * D * T(L) where L is triangular inferior and D is diagonal. If one element of A is less than MinPivot, A is considered as singular. Exception NotSquare is raised if A is not a square matrix.

Member Function Documentation

◆ Determinant()

double math_Crout::Determinant ( ) const

Returns the value of the determinant of the previously LU decomposed matrix A. Zero is returned if the matrix A is considered as singular. Exceptions StdFail_NotDone if the algorithm fails (and IsDone returns false).

◆ Dump()

void math_Crout::Dump ( Standard_OStream & o ) const

Prints on the stream o information on the current state of the object.

◆ Inverse()

const math_Matrix & math_Crout::Inverse ( ) const

returns the inverse matrix of A. Only the inferior triangle is returned. Exception NotDone is raised if NotDone.

◆ Invert()

void math_Crout::Invert ( math_Matrix & Inv ) const

returns in Inv the inverse matrix of A. Only the inferior triangle is returned. Exception NotDone is raised if NotDone.

◆ IsDone()

bool math_Crout::IsDone ( ) const

Returns True if all has been correctly done.

◆ Solve()

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

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

The documentation for this class was generated from the following file:

math_Crout.hxx

Public Member Functions