gram_schmidt.hpp File Reference

Provides some Gram Schmidt orthogonalization and orthonormalization algorithms. More...

#include <cassert>
#include <cmath>
#include <numeric>
#include "DPoint2d.hpp"
#include "linear_algebra.hpp"
#include "linear_algebra_traits.hpp"

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Namespaces
	slip
	This namespace corresponds to the kernel of the Simple Library on Image Processing (SLIP). That is to say that it contains the data structures and the algorithms needed by these data strucutres.

Functions
template<class RandomAccessIterator , class InnerProduct >
void	slip::gram_schmidt_normalization (RandomAccessIterator init_base_first, RandomAccessIterator init_base_end, RandomAccessIterator ortho_base_first, RandomAccessIterator ortho_base_end, InnerProduct inner_prod)
	Gram-Schmidt orthonormalization algorithm. More...
template<class RandomAccessIterator , class InnerProduct >
void	slip::modified_gram_schmidt_normalization (RandomAccessIterator init_base_first, RandomAccessIterator init_base_end, RandomAccessIterator ortho_base_first, RandomAccessIterator ortho_base_end, InnerProduct inner_prod)
	Modified Gram-Schmidt orthonormalization algorithm. More...
template<class RandomAccessIterator , class InnerProduct >
void	slip::gram_schmidt_orthogonalization (RandomAccessIterator init_base_first, RandomAccessIterator init_base_end, RandomAccessIterator ortho_base_first, RandomAccessIterator ortho_base_end, InnerProduct inner_prod)
	Gram-Schmidt orthogonalization algorithm. More...
template<class RandomAccessIterator , class InnerProduct >
void	slip::modified_gram_schmidt_orthogonalization (RandomAccessIterator init_base_first, RandomAccessIterator init_base_end, RandomAccessIterator ortho_base_first, RandomAccessIterator ortho_base_end, InnerProduct inner_prod)
	Modified Gram-Schmidt orthogonalization algorithm. More...
template<typename MatrixIterator1 , typename MatrixIterator2 , typename MatrixIterator3 >
void	slip::modified_gram_schmidt (MatrixIterator1 A_up, MatrixIterator1 A_bot, MatrixIterator2 Q_up, MatrixIterator2 Q_bot, MatrixIterator3 R_up, MatrixIterator3 R_bot)
	Modified Gram-Schmidt orthogonalization algorithm on a matrix. More...
template<class RandomAccessIterator , class RandomAccessIterator2d , class InnerProduct >
void	slip::gram_matrix (RandomAccessIterator init_base_first, RandomAccessIterator init_base_end, RandomAccessIterator2d matrix_upper_left, RandomAccessIterator2d matrix_bottom_right, InnerProduct inner_prod)
	Compute the Gram matrix from a base. More...

Detailed Description

Provides some Gram Schmidt orthogonalization and orthonormalization algorithms.

Since

1.0.0

Definition in file gram_schmidt.hpp.