solve.h File Reference

System solving with matrix routines. More...

#include <m4ri/mzp.h>
#include <m4ri/mzd.h>

Go to the source code of this file.

Functions
int	mzd_solve_left (mzd_t *A, mzd_t *B, int const cutoff, int const inconsistency_check)
	Solves A X = B with A and B matrices. More...
int	mzd_pluq_solve_left (mzd_t const *A, rci_t rank, mzp_t const *P, mzp_t const *Q, mzd_t *B, int const cutoff, int const inconsistency_check)
	Solves (P L U Q) X = B. More...
int	_mzd_pluq_solve_left (mzd_t const *A, rci_t rank, mzp_t const *P, mzp_t const *Q, mzd_t *B, int const cutoff, int const inconsistency_check)
	Solves (P L U Q) X = B. More...
int	_mzd_solve_left (mzd_t *A, mzd_t *B, int const cutoff, int const inconsistency_check)
	Solves A X = B with A and B matrices. More...
mzd_t *	mzd_kernel_left_pluq (mzd_t *A, int const cutoff)
	Solve X for A X = 0. More...

Detailed Description

System solving with matrix routines.

Author

Jean-Guillaume Dumas Jean-.nosp@m.Guil.nosp@m.laume.nosp@m..Dum.nosp@m.as@im.nosp@m.ag.f.nosp@m.r

Function Documentation

int _mzd_pluq_solve_left	(	mzd_t const *	A,
		rci_t	rank,
		mzp_t const *	P,
		mzp_t const *	Q,
		mzd_t *	B,
		int const	cutoff,
		int const	inconsistency_check
	)

Solves (P L U Q) X = B.

A is an input matrix supposed to store both:

• an upper right triangular matrix U
• a lower left unitary triangular matrix L.

The solution X is stored inplace on B.

This version assumes that the matrices are at an even position on the m4ri_radix grid and that their dimension is a multiple of m4ri_radix.

Parameters

A	Input upper/lower triangular matrices.
rank	is rank of A.
P	Input row permutation matrix.
Q	Input column permutation matrix.
B	Input matrix, being overwritten by the solution matrix X.
cutoff	Minimal dimension for Strassen recursion (default: 0).
inconsistency_check	decide whether or not to perform a check for incosistency (faster without but output not defined if system is not consistent).

Returns

0 if a solution was found, -1 otherwise

0 if a solution was found, -1 otherwise

A is supposed to store L lower triangular and U upper triangular B is modified in place (Bi's in the comments are just modified versions of B) PLUQ = A 1) P B2 = B1 2) L B3 = B2 3) U B4 = B3 4) Q B5 = B4

FASTER without this check; update with the lower part of L

Default is to set the undefined bits to zero if inconsistency has been checked then Y2 bits are already all zeroes thus this clearing is not needed

int _mzd_solve_left	(	mzd_t *	A,
		mzd_t *	B,
		int const	cutoff,
		int const	inconsistency_check
	)

Solves A X = B with A and B matrices.

The solution X is stored inplace on B.

This version assumes that the matrices are at an even position on the m4ri_radix grid and that their dimension is a multiple of m4ri_radix.

Parameters

A	Input matrix (overwritten).
B	Input matrix, being overwritten by the solution matrix X.
cutoff	Minimal dimension for Strassen recursion (default: 0).
inconsistency_check	decide whether or not to perform a check for incosistency (faster without but output not defined if system is not consistent).

Returns

0 if a solution was found, -1 otherwise

0 if a solution was found, -1 otherwise

B is modified in place (Bi's in the comments are just modified versions of B) 1) PLUQ = A 2) P B2 = B1 3) L B3 = B2 4) U B4 = B3 5) Q B5 = B4

mzd_t* mzd_kernel_left_pluq	(	mzd_t *	A,
		int const	cutoff
	)

Solve X for A X = 0.

If r is the rank of the nr x nc matrix A, return the nc x (nc-r) matrix X such that A*X == 0 and that the columns of X are linearly independent.

Parameters

A	Input matrix (overwritten).
cutoff	Minimal dimension for Strassen recursion (default: 0).

See also

mzd_pluq()

Returns

X, NULL if kernel is empty

int mzd_pluq_solve_left	(	mzd_t const *	A,
		rci_t	rank,
		mzp_t const *	P,
		mzp_t const *	Q,
		mzd_t *	B,
		int const	cutoff,
		int const	inconsistency_check
	)

Solves (P L U Q) X = B.

A is an input matrix supposed to store both:

• an upper right triangular matrix U
• a lower left unitary triangular matrix L.

The solution X is stored inplace on B

This version assumes that the matrices are at an even position on the m4ri_radix grid and that their dimension is a multiple of m4ri_radix.

Parameters

A	Input upper/lower triangular matrices.
rank	is rank of A.
P	Input row permutation matrix.
Q	Input column permutation matrix.
B	Input matrix, being overwritten by the solution matrix X.
cutoff	Minimal dimension for Strassen recursion (default: 0).
inconsistency_check	decide whether or not to perform a check for incosistency (faster without but output not defined if system is not consistent).

Returns

0 if a solution was found, -1 otherwise

0 if a solution was found, -1 otherwise

int mzd_solve_left	(	mzd_t *	A,
		mzd_t *	B,
		int const	cutoff,
		int const	inconsistency_check
	)

Solves A X = B with A and B matrices.

The solution X is stored inplace on B.

Parameters

A	Input matrix (overwritten).
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion (default: 0).
inconsistency_check	decide wether or not to perform a check for incosistency (faster without but output not defined if system is not consistent).

Returns

0 if a solution was found, -1 otherwise