00001 // This is mul/mbl/mbl_mod_gram_schmidt.h 00002 #ifndef mbl_mod_gram_schmidt_h_ 00003 #define mbl_mod_gram_schmidt_h_ 00004 //: 00005 // \file 00006 // \brief Orthogonalise a basis using modified Gram-Schmidt (and normalise) 00007 // \author Martin Roberts 00008 // 00009 // Note: Modified Gram-Schmidt is more numerically stable than the classical version 00010 // The partially constructed transformed jth vector is used in the successive projections rather than the untransformed 00011 // \verbatim 00012 // Modifications 00013 // Mar. 2011 - Patrick Sauer - added variant that returns normalisation multipliers 00014 // \endverbatim 00015 00016 #include <vnl/vnl_matrix.h> 00017 00018 //======================================================================= 00019 //: Orthogonalise a basis using modified Gram-Schmidt 00020 // Transform basis {vk} to orthonormal basis {ek} with k in range 1..N 00021 // \code 00022 // for j = 1 to N 00023 // ej = vj 00024 // for k = 1 to j-1 00025 // ej = ej - <ej,ek>ek //NB Classical GS has vj in inner product 00026 // end 00027 // ej = ej/|ej| 00028 // end 00029 // \endcode 00030 00031 //: Convert input basis {v} to orthonormal basis {e} 00032 // Each basis vector is a column of v, and likewise the orthonormal bases are returned as columns of e 00033 void mbl_mod_gram_schmidt(const vnl_matrix<double>& v, 00034 vnl_matrix<double>& e); 00035 00036 //: Convert input basis {v} to orthonormal basis {e} 00037 // Each basis vector is a column of v, and likewise the orthonormal bases are returned as columns of e 00038 // The multipliers used to normalise each vector in {e} are returned in n. 00039 void mbl_mod_gram_schmidt( const vnl_matrix<double>& v, 00040 vnl_matrix<double>& e, vnl_vector<double>& n ); 00041 00042 #endif // mbl_mod_gram_schmidt_h_
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