Permutation matrices. More...

#include <m4ri/mzd.h>

Data Structures
struct	mzp_t
	Permutations. More...

Typedefs
typedef struct mzp_t	mzp_t
	Permutations.

Functions
mzp_t *	mzp_init (rci_t length)

void	mzp_free (mzp_t *P)

mzp_t *	mzp_init_window (mzp_t *P, rci_t begin, rci_t end)
	Create a window/view into the permutation P. More...

void	mzp_free_window (mzp_t *condemned)
	Free a permutation window created with mzp_init_mzp_t_window(). More...

mzp_t *	mzp_copy (mzp_t P, const mzp_t Q)
	copy permutation Q to P More...

void	mzp_set_ui (mzp_t *P, unsigned int value)
	Set the permutation P to the identity permutation. The only allowed value is 1. More...

void	mzd_apply_p_left (mzd_t A, mzp_t const P)

void	mzd_apply_p_left_trans (mzd_t A, mzp_t const P)

void	mzd_apply_p_right (mzd_t A, mzp_t const P)

void	mzd_apply_p_right_trans (mzd_t A, mzp_t const P)

void	mzd_apply_p_right_even_capped (mzd_t A, mzp_t const P, rci_t start_row, rci_t start_col)

void	mzd_apply_p_right_trans_even_capped (mzd_t A, mzp_t const P, rci_t start_row, rci_t start_col)

void	mzd_apply_p_right_trans_tri (mzd_t A, mzp_t const Q)

void	mzp_print (mzp_t const *P)

void	_mzd_compress_l (mzd_t *A, rci_t r1, rci_t n1, rci_t r2)

Detailed Description

Permutation matrices.

Author: Martin Albrecht M.R.A.nosp@m.lbre.nosp@m.cht@r.nosp@m.hul..nosp@m.ac.uk

Function Documentation

void _mzd_compress_l	(	mzd_t *	A,
		rci_t	r1,
		rci_t	n1,
		rci_t	r2
	)

Compresses the matrix L in a step in blockwise-recursive PLE decomposition.

Parameters

A	Matrix.
r1	Rank of left matrix.
n1	Column cut which separates left and right matrix.
r2	Rank of right matrix.

 We are compressing this matrix

           r1           n1
   ------------------------------------------
   | \ \____|___        | A01               |
   |  \     |   \       |                   |
 r1------------------------------------------ 
   |   |    |           | \  \_____         |
   | L1|    |           |  \       \________|
   |   |    |           | L2|               |
   ------------------------------------------

to this matrix

           r1           n1
   ------------------------------------------
   | \ \____|___        | A01               |
   |  \     |   \       |                   |
 r1------------------------------------------ 
   |    \   |           |    \_____         |
   |     \  |           |          \________|
   |      | |           |                   |
   ------------------------------------------

void mzd_apply_p_left	(	mzd_t *	A,
		mzp_t const *	P
	)

Apply the permutation P to A from the left.

This is equivalent to row swaps walking from 0 to length-1.

Parameters

A	Matrix.
P	Permutation.

Examples:: testsuite/test_ple.c.

void mzd_apply_p_left_trans	(	mzd_t *	A,
		mzp_t const *	P
	)

Apply the permutation P to A from the left but transpose P before.

This is equivalent to row swaps walking from length-1 to 0.

Parameters

A	Matrix.
P	Permutation.

void mzd_apply_p_right	(	mzd_t *	A,
		mzp_t const *	P
	)

Apply the permutation P to A from the right.

This is equivalent to column swaps walking from length-1 to 0.

Parameters

A	Matrix.
P	Permutation.

void mzd_apply_p_right_even_capped	(	mzd_t *	A,
		mzp_t const *	P,
		rci_t	start_row,
		rci_t	start_col
	)

Apply the permutation P to A from the right starting at start_row.

This is equivalent to column swaps walking from length-1 to 0.

Parameters

A	Matrix.
P	Permutation.
start_row	Start swapping at this row.
start_col	Start swapping at this column.

void mzd_apply_p_right_trans	(	mzd_t *	A,
		mzp_t const *	P
	)

Apply the permutation P to A from the right but transpose P before.

This is equivalent to column swaps walking from 0 to length-1.

Parameters

A	Matrix.
P	Permutation.

Apply the mzp_t P to A from the right but transpose P before.

This is equivalent to column swaps walking from 0 to length-1.

Parameters

A	Matrix.
P	Permutation.

Examples:: testsuite/test_ple.c.

void mzd_apply_p_right_trans_even_capped	(	mzd_t *	A,
		mzp_t const *	P,
		rci_t	start_row,
		rci_t	start_col
	)

Apply the permutation P^T to A from the right starting at start_row.

This is equivalent to column swaps walking from 0 to length-1.

Parameters

A	Matrix.
P	Permutation.
start_row	Start swapping at this row.
start_col	Start swapping at this column.

void mzd_apply_p_right_trans_tri	(	mzd_t *	A,
		mzp_t const *	Q
	)

Apply the permutation P to A from the right, but only on the upper the matrix A above the main diagonal.

This is equivalent to column swaps walking from length-1 to 0.

Parameters

A	Matrix.
Q	Permutation.

mzp_t* mzp_copy	(	mzp_t *	P,
		const mzp_t *	Q
	)

copy permutation Q to P

Parameters

P	Target permutation matrix (may be NULL)
Q	Source permutation matrix (must not be NULL)

void mzp_free ( mzp_t * P )

Free a mzp_t.

Parameters

P	Permutation to free.

Examples:: testsuite/test_ple.c.

void mzp_free_window ( mzp_t * condemned )

Free a permutation window created with mzp_init_mzp_t_window().

Parameters

condemned Permutation Matrix

mzp_t* mzp_init ( rci_t length )

Construct an identity permutation.

Parameters

length Length of the permutation.

Examples:: testsuite/bench_elimination.c, and testsuite/test_ple.c.

mzp_t* mzp_init_window	(	mzp_t *	P,
		rci_t	begin,
		rci_t	end
	)

Create a window/view into the permutation P.

Use mzp_free_mzp_t_window() to free the window.

Parameters

P	Permutation matrix
begin	Starting index (inclusive)
end	Ending index (exclusive)

void mzp_print ( mzp_t const * P )

Print the mzp_t P

Parameters

P	Permutation.

void mzp_set_ui	(	mzp_t *	P,
		unsigned int	value
	)

Set the permutation P to the identity permutation. The only allowed value is 1.

Parameters

P	Permutation
value	1

Note: This interface was chosen to be similar to mzd_set_ui().

Data Structures

Typedefs

Functions

Detailed Description

Function Documentation