# math_Householder Class Reference

This class implements the least square solution of a set of linear equations of m unknowns (n >= m) using the Householder method. It solves A.X = B. This algorithm has more numerical stability than GaussLeastSquare but is longer. It must be used if the matrix is singular or nearly singular. It is about 16% longer than GaussLeastSquare if there is only one member B to solve. It is about 30% longer if there are twenty B members to solve. More...

`#include <math_Householder.hxx>`

## Public Member Functions

math_Householder (const math_Matrix &A, const math_Matrix &B, const Standard_Real EPS=1.0e-20)
Given an input matrix A with n>= m, given an input matrix B this constructor performs the least square resolution of the set of linear equations A.X = B for each column of B. If a column norm is less than EPS, the resolution can't be done. Exception DimensionError is raised if the row number of B is different from the A row number. More...

math_Householder (const math_Matrix &A, const math_Matrix &B, const Standard_Integer lowerArow, const Standard_Integer upperArow, const Standard_Integer lowerAcol, const Standard_Integer upperAcol, const Standard_Real EPS=1.0e-20)
Given an input matrix A with n>= m, given an input matrix B this constructor performs the least square resolution of the set of linear equations A.X = B for each column of B. If a column norm is less than EPS, the resolution can't be done. Exception DimensionError is raised if the row number of B is different from the A row number. More...

math_Householder (const math_Matrix &A, const math_Vector &B, const Standard_Real EPS=1.0e-20)
Given an input matrix A with n>= m, given an input vector B this constructor performs the least square resolution of the set of linear equations A.X = B. If a column norm is less than EPS, the resolution can't be done. Exception DimensionError is raised if the length of B is different from the A row number. More...

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

void Value (math_Vector &sol, const Standard_Integer Index=1) const
Given the integer Index, this routine returns the corresponding least square solution sol. Exception NotDone is raised if the resolution has not be done. Exception OutOfRange is raised if Index <=0 or Index is more than the number of columns of B. More...

const math_MatrixAllValues () const
Returns the matrix sol of all the solutions of the system A.X = B. Exception NotDone is raised is the resolution has not be done. More...

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

## Protected Member Functions

void Perform (const math_Matrix &A, const math_Matrix &B, const Standard_Real EPS)
This method is used internally for each constructor above and can't be used directly. More...

## Detailed Description

This class implements the least square solution of a set of linear equations of m unknowns (n >= m) using the Householder method. It solves A.X = B. This algorithm has more numerical stability than GaussLeastSquare but is longer. It must be used if the matrix is singular or nearly singular. It is about 16% longer than GaussLeastSquare if there is only one member B to solve. It is about 30% longer if there are twenty B members to solve.

## Constructor & Destructor Documentation

 math_Householder::math_Householder ( const math_Matrix & A, const math_Matrix & B, const Standard_Real EPS = `1.0e-20` )

Given an input matrix A with n>= m, given an input matrix B this constructor performs the least square resolution of the set of linear equations A.X = B for each column of B. If a column norm is less than EPS, the resolution can't be done. Exception DimensionError is raised if the row number of B is different from the A row number.

 math_Householder::math_Householder ( const math_Matrix & A, const math_Matrix & B, const Standard_Integer lowerArow, const Standard_Integer upperArow, const Standard_Integer lowerAcol, const Standard_Integer upperAcol, const Standard_Real EPS = `1.0e-20` )

Given an input matrix A with n>= m, given an input matrix B this constructor performs the least square resolution of the set of linear equations A.X = B for each column of B. If a column norm is less than EPS, the resolution can't be done. Exception DimensionError is raised if the row number of B is different from the A row number.

 math_Householder::math_Householder ( const math_Matrix & A, const math_Vector & B, const Standard_Real EPS = `1.0e-20` )

Given an input matrix A with n>= m, given an input vector B this constructor performs the least square resolution of the set of linear equations A.X = B. If a column norm is less than EPS, the resolution can't be done. Exception DimensionError is raised if the length of B is different from the A row number.

## Member Function Documentation

 const math_Matrix& math_Householder::AllValues ( ) const

Returns the matrix sol of all the solutions of the system A.X = B. Exception NotDone is raised is the resolution has not be done.

 void math_Householder::Dump ( Standard_OStream & o ) const

Prints informations on the current state of the object.

 Standard_Boolean math_Householder::IsDone ( ) const

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

 void math_Householder::Perform ( const math_Matrix & A, const math_Matrix & B, const Standard_Real EPS )
protected

This method is used internally for each constructor above and can't be used directly.

 void math_Householder::Value ( math_Vector & sol, const Standard_Integer Index = `1` ) const

Given the integer Index, this routine returns the corresponding least square solution sol. Exception NotDone is raised if the resolution has not be done. Exception OutOfRange is raised if Index <=0 or Index is more than the number of columns of B.

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