Householder Class Template Reference
[Vector and Matrix mathematics]

#include <MatrixFunctors.hpp>

List of all members.

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Detailed Description

template<class T>
class gpstk::Householder< T >

The Householder transformation is simply an orthogonal transformation designed to make the elements below the diagonal zero.

It applies to any matrix.

Definition at line 694 of file MatrixFunctors.hpp.

Public Member Functions
	Householder ()
template<class BaseClass>
void	operator() (const ConstMatrixBase< T, BaseClass > &m) throw (MatrixException)
	Explicitly perform the transformation, one column at a time, without actually constructing the transformation matrix.
Public Attributes
Matrix< T >	A
	The upper triangular transformed matrix.

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Constructor & Destructor Documentation

Householder (   )  [inline]

Definition at line 697 of file MatrixFunctors.hpp.

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Member Function Documentation

void operator() (  const ConstMatrixBase< T, BaseClass > &  m  )  throw (MatrixException) [inline]

Explicitly perform the transformation, one column at a time, without actually constructing the transformation matrix. Let y be column k of the input matrix. y can be zeroed below the diagonal as follows: let sum=sign(y(k))*sqrt(y*y), and define vector u(k)=y(k)+sum, u(j)=y(j) (j.gt.k). This defines the transformation matrix as (1-bu*u), with b=2/u*u=1/sum*u(k). Redefine y(k)=u(k) and apply the transformation to elements of the input matrix below and to the right of the (k,k) element. This algorithm for each column k=0,n-1 in turn is equivalent to a single orthogonal transformation which triangularizes the matrix. Definition at line 710 of file MatrixFunctors.hpp. References SQRT, and gpstk::sum().

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Member Data Documentation

Matrix<T> A

The upper triangular transformed matrix. Definition at line 756 of file MatrixFunctors.hpp. Referenced by MatrixTest7(), SRI::operator+=(), SRI::Qbump(), and SRI::transformState().

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

• MatrixFunctors.hpp

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