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 Standard_Real 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.

Standard_Boolean	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.

Standard_Real	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 Standard_Real	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()

Standard_Real 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()

Standard_Boolean 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