Dense matrices over \(\mathbb{F}_{2^e}\) represented as packed matrices. More...

#include <m4ri/m4ri.h>
#include <m4rie/gf2e.h>
#include <m4rie/m4ri_functions.h>

Data Structures
struct	mzed_t
	Dense matrices over \(\mathbb{F}_{2^e}\) represented as packed matrices. More...

Macros
#define	mzed_sub mzed_add
	\( C = A+B \). More...

#define	_mzed_sub _mzed_add
	\( C = A+B \). More...

Functions
mzed_t *	mzed_init (const gf2e *ff, const rci_t m, const rci_t n)
	Create a new matrix of dimension m x n over ff. More...

void	mzed_free (mzed_t *A)
	Free a matrix created with mzed_init(). More...

static mzed_t *	mzed_concat (mzed_t C, const mzed_t A, const mzed_t *B)
	Concatenate B to A and write the result to C. More...

static mzed_t *	mzed_stack (mzed_t C, const mzed_t A, const mzed_t *B)
	Stack A on top of B and write the result to C. More...

static mzed_t *	mzed_submatrix (mzed_t S, const mzed_t M, const rci_t lowr, const rci_t lowc, const rci_t highr, const rci_t highc)
	Copy a submatrix. More...

static mzed_t *	mzed_init_window (const mzed_t *A, const rci_t lowr, const rci_t lowc, const rci_t highr, const rci_t highc)
	Create a window/view into the matrix A. More...

static void	mzed_free_window (mzed_t *A)
	Free a matrix window created with mzed_init_window(). More...

mzed_t *	mzed_add (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = A+B \). More...

mzed_t *	_mzed_add (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = A+B \). More...

mzed_t *	mzed_mul (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = A \cdot B \). More...

mzed_t *	mzed_addmul (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = C + A \cdot B \). More...

mzed_t *	_mzed_mul (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = A \cdot B \). More...

mzed_t *	_mzed_addmul (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = C + A \cdot B \). More...

mzed_t *	mzed_addmul_naive (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = C + A \cdot B \) using naive cubic multiplication. More...

mzed_t *	mzed_mul_naive (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = A \cdot B \) using naive cubic multiplication. More...

mzed_t *	_mzed_mul_naive (mzed_t C, const mzed_t A, const mzed_t *B)
	\( C = C + A \cdot B \) using naive cubic multiplication. More...

mzed_t *	mzed_mul_scalar (mzed_t C, const word a, const mzed_t B)
	\( C = a \cdot B \). More...

mzed_t *	_mzed_mul_init (mzed_t C, const mzed_t A, const mzed_t *B, int clear)

void	mzed_randomize (mzed_t *A)
	Fill matrix A with random elements. More...

mzed_t *	mzed_copy (mzed_t B, const mzed_t A)
	Copy matrix A to B. More...

void	mzed_set_ui (mzed_t *A, word value)
	Return diagonal matrix with value on the diagonal. More...

static word	mzed_read_elem (const mzed_t *A, const rci_t row, const rci_t col)
	Get the element at position (row,col) from the matrix A. More...

static void	mzed_add_elem (mzed_t *A, const rci_t row, const rci_t col, const word elem)
	At the element elem to the element at position (row,col) in the matrix A. More...

static void	mzed_write_elem (mzed_t *A, const rci_t row, const rci_t col, const word elem)
	Write the element elem to the position (row,col) in the matrix A. More...

static int	mzed_cmp (mzed_t A, mzed_t B)
	Return -1,0,1 if if A < B, A == B or A > B respectively. More...

static int	mzed_is_zero (const mzed_t *A)
	Zero test for matrix. More...

void	mzed_add_multiple_of_row (mzed_t A, rci_t ar, const mzed_t B, rci_t br, word x, rci_t start_col)

static void	mzed_add_row (mzed_t A, rci_t ar, const mzed_t B, rci_t br, rci_t start_col)

static void	mzed_rescale_row (mzed_t *A, rci_t r, rci_t start_col, const word x)
	Rescale the row r in A by X starting c. More...

static void	mzed_row_swap (mzed_t *M, const rci_t rowa, const rci_t rowb)
	Swap the two rows rowa and rowb. More...

static void	mzed_copy_row (mzed_t B, rci_t i, const mzed_t A, rci_t j)
	copy row j from A to row i from B. More...

static void	mzed_col_swap (mzed_t *M, const rci_t cola, const rci_t colb)
	Swap the two columns cola and colb. More...

static void	mzed_col_swap_in_rows (mzed_t *A, const rci_t cola, const rci_t colb, const rci_t start_row, rci_t stop_row)
	Swap the two columns cola and colb but only between start_row and stop_row. More...

static void	mzed_row_add (mzed_t *M, const rci_t sourcerow, const rci_t destrow)
	Add the rows sourcerow and destrow and stores the total in the row destrow. More...

static rci_t	mzed_first_zero_row (mzed_t *A)
	Return the first row with all zero entries. More...

rci_t	mzed_echelonize_naive (mzed_t *A, int full)
	Gaussian elimination. More...

void	mzed_print (const mzed_t *M)
	Print a matrix to stdout. More...

Detailed Description

Dense matrices over \(\mathbb{F}_{2^e}\) represented as packed matrices.

This file implements the data type mzed_t. That is, matrices over \(\mathbb{F}_{2^e}\) in row major representation.

For example, let \( a = \sum a_i x_i / <f>\) and \(b = \sum b_i x_i / <f>\) be elements in \(\mathbb{F}_{2^6}\) with minimal polynomial \(f\). Then, the \( 1 \times 2\) matrix [b a] would be stored as

 [...| 0 0 b5 b4 b3 b2 b1 b0 | 0 0 a5 a4 a3 a2 a1 a0]

Internally M4RI matrices are used to store bits with allows to re-use existing M4RI methods (such as mzd_add) when implementing functions for mzed_t.

This data type is preferable when Newton-John tables ought be used or when the matrix is small ( \( m \times n \times e < L2\)).

Author: Martin Albrecht marti.nosp@m.nral.nosp@m.brech.nosp@m.t@go.nosp@m.oglem.nosp@m.ail..nosp@m.com

Function Documentation

mzed_t* _mzed_mul_init	(	mzed_t *	C,
		const mzed_t *	A,
		const mzed_t *	B,
		int	clear
	)

Check whether C, A and B match in sizes and fields for multiplication

Parameters

C	Output matrix, if NULL a new matrix is created.
A	Input matrix.
B	Input matrix.
clear	Write zeros to C or not.

static int mzed_cmp	(	mzed_t *	A,
		mzed_t *	B
	)

inlinestatic

Return -1,0,1 if if A < B, A == B or A > B respectively.

Parameters

A	Matrix.
B	Matrix.

Note: This comparison is not well defined mathematically and relatively arbitrary since elements of \(\mathbb{F}_{2^e}\) don't have an ordering.

Examples:: tests/test_multiplication.c.

static int mzed_is_zero ( const mzed_t * A )

inlinestatic

Zero test for matrix.

Parameters

A	Input matrix.

Data Structures

Macros

Functions

Detailed Description

Function Documentation