core/vnl/vnl_rank.h File Reference

Direct computation of the rank of a matrix, without using svd. More...

#include <vnl/vnl_matrix.h>

Go to the source code of this file.

Defines
#define	VNL_RANK_INSTANTIATE(T)   extern "please #include vnl/vnl_rank.txx instead"
Enumerations
enum	vnl_rank_type { vnl_rank_row, vnl_rank_column, vnl_rank_both }
enum	vnl_rank_pivot_type { vnl_rank_pivot_one, vnl_rank_pivot_all }
Functions
template<class T >
unsigned int	vnl_rank (vnl_matrix< T > const &mat, vnl_rank_type=vnl_rank_both)
	Returns the rank of a matrix.
template<class T >
vnl_matrix< T >	vnl_rank_row_reduce (vnl_matrix< T > const &mat, vnl_rank_pivot_type=vnl_rank_pivot_all)
	Row reduce a matrix.
template<class T >
vnl_matrix< T >	vnl_rank_column_reduce (vnl_matrix< T > const &mat, vnl_rank_pivot_type=vnl_rank_pivot_all)
	Column reduce a matrix.
template<class T >
vnl_matrix< T >	vnl_rank_row_column_reduce (vnl_matrix< T > const &mat, vnl_rank_pivot_type=vnl_rank_pivot_all)
	Row and column reduce a matrix.

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Detailed Description

Direct computation of the rank of a matrix, without using svd.

Author:

Peter Vanroose, Leuven

Date:

27 March 2003 The (row) rank of a matrix is its number of linearly independent rows. This turns out to be equal to the number of linearly independent columns, i.e., the column rank, so it is just called the rank of the matrix. This can be computed by row-reducing (or column-reducing) the matrix and then counting the number of non-zero rows (or columns).

Definition in file vnl_rank.h.

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Define Documentation

#define VNL_RANK_INSTANTIATE

(

T

)

extern "please #include vnl/vnl_rank.txx instead"

Definition at line 69 of file vnl_rank.h.

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Enumeration Type Documentation

enum vnl_rank_pivot_type

Enumerator:

vnl_rank_pivot_one
vnl_rank_pivot_all

Definition at line 19 of file vnl_rank.h.

enum vnl_rank_type

Enumerator:

vnl_rank_row
vnl_rank_column
vnl_rank_both

Definition at line 18 of file vnl_rank.h.

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Function Documentation

template<class T >

unsigned int vnl_rank	(	vnl_matrix< T > const &	mat,
		vnl_rank_type	= vnl_rank_both
	)

Returns the rank of a matrix.

By default, the row rank of the matrix is determined. Specify vnl_rank_column to obtain the column rank.

Definition at line 185 of file vnl_rank.txx.

template<class T >

vnl_matrix< T > vnl_rank_column_reduce	(	vnl_matrix< T > const &	mat,
		vnl_rank_pivot_type	= vnl_rank_pivot_all
	)

Column reduce a matrix.

Definition at line 57 of file vnl_rank.txx.

template<class T >

vnl_matrix< T > vnl_rank_row_column_reduce	(	vnl_matrix< T > const &	mat,
		vnl_rank_pivot_type	= vnl_rank_pivot_all
	)

Row and column reduce a matrix.

Perform both row reduction and column reduction on a matrix. The resulting matrix will in general no longer span the same row space (or column space) as the original matrix, but the rank will not have changed, and the number of nonzero elements will be minimal (viz at most one per row and one per column).

Definition at line 106 of file vnl_rank.txx.

template<class T >

vnl_matrix< T > vnl_rank_row_reduce	(	vnl_matrix< T > const &	mat,
		vnl_rank_pivot_type	= vnl_rank_pivot_all
	)

Row reduce a matrix.

First try to use 1 or -1 as pivot element in each row, to avoid divisions; then use any nonzero element as candidate pivot. Repeat this process until the matrix does not change any more. At that point, the matrix spans the same row space as before and contains as many zeros as possible.

When specifying vnl_rank_pivot_one is given as second argument, only elements with value 1 or -1 are used as candidate pivot elements.

Note that for integer matrices, the resulting matrix is still integer, and is guaranteed to be row equivalent with the original matrix.

Definition at line 8 of file vnl_rank.txx.