contrib/mul/mbl/mbl_mod_gram_schmidt.h File Reference

Orthogonalise a basis using modified Gram-Schmidt (and normalise) More...

#include <vnl/vnl_matrix.h>

Go to the source code of this file.

Functions
void	mbl_mod_gram_schmidt (const vnl_matrix< double > &v, vnl_matrix< double > &e)
	Orthogonalise a basis using modified Gram-Schmidt.
void	mbl_mod_gram_schmidt (const vnl_matrix< double > &v, vnl_matrix< double > &e, vnl_vector< double > &n)
	Convert input basis {v} to orthonormal basis {e}.

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Detailed Description

Orthogonalise a basis using modified Gram-Schmidt (and normalise)

Author:

Martin Roberts

Note: Modified Gram-Schmidt is more numerically stable than the classical version The partially constructed transformed jth vector is used in the successive projections rather than the untransformed

   Modifications
   Mar. 2011 - Patrick Sauer - added variant that returns normalisation multipliers
   

Definition in file mbl_mod_gram_schmidt.h.

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Function Documentation

void mbl_mod_gram_schmidt	(	const vnl_matrix< double > &	v,
		vnl_matrix< double > &	e
	)

Orthogonalise a basis using modified Gram-Schmidt.

Transform basis {vk} to orthonormal basis {ek} with k in range 1..N

 for j = 1 to N
     ej = vj
     for k = 1 to j-1
         ej = ej - <ej,ek>ek   //NB Classical GS has vj in inner product
     end
     ej = ej/|ej|
  end

Convert input basis {v} to orthonormal basis {e}. Each basis vector is a column of v, and likewise the orthonormal bases are returned as columns of e

Orthogonalise a basis using modified Gram-Schmidt.

Each basis vector is a column of v, and likewise the orthonormal bases are returned as columns of e

Definition at line 28 of file mbl_mod_gram_schmidt.cxx.

void mbl_mod_gram_schmidt	(	const vnl_matrix< double > &	v,
		vnl_matrix< double > &	e,
		vnl_vector< double > &	np
	)

Convert input basis {v} to orthonormal basis {e}.

Each basis vector is a column of v, and likewise the orthonormal bases are returned as columns of e The multipliers used to normalise each vector in {e} are returned in n.

Each basis vector is a column of v, and likewise the orthonormal bases are returned as columns of e The multipliers used to normalise each vector in {e} are returned in np

Definition at line 70 of file mbl_mod_gram_schmidt.cxx.