Echelon forms

Macros
#define	mzd_slice_echelonize   mzd_slice_echelonize_ple
	Compute row echelon forms. More...

Functions
rci_t	mzd_slice_echelonize_ple (mzd_slice_t *A, int full)
	Compute row echelon forms using PLE decomposition. More...
static rci_t	mzed_echelonize_ple (mzed_t *A, int full)
	Compute row echelon forms using PLE decomposition. More...
rci_t	mzed_echelonize (mzed_t *A, int full)
	Compute row echelon forms. More...
rci_t	mzed_echelonize_naive (mzed_t *A, int full)
	Gaussian elimination. More...
rci_t	mzed_echelonize_newton_john (mzed_t *A, int full)
	Reduce matrix A to row echelon form using Gauss-Newton-John elimination. More...

Detailed Description

Macro Definition Documentation

#define mzd_slice_echelonize   mzd_slice_echelonize_ple

Compute row echelon forms.

Compute the (reduced) row echelon form of the matrix A. If full=0, then return the reduced REF.

Parameters

A	Matrix
full	REF or RREF.

Function Documentation

rci_t mzd_slice_echelonize_ple	(	mzd_slice_t *	A,
		int	full
	)

Compute row echelon forms using PLE decomposition.

Compute the (reduced) row echelon form of the matrix A. If full=0, then return the reduced row echelon. This function reduces echelon forms to PLE (or PLUQ) decomposition.

Parameters

A	Matrix
full	REF or RREF.

rci_t mzed_echelonize	(	mzed_t *	A,
		int	full
	)

Compute row echelon forms.

Compute the (reduced) row echelon form of the matrix A. If full=0, then return the reduced row echelon form.

Parameters

A	Matrix
full	REF or RREF.

rci_t mzed_echelonize_naive	(	mzed_t *	A,
		int	full
	)

Gaussian elimination.

Perform Gaussian elimination on the matrix A. If full=0, then it will do triangular style elimination, and if full=1, it will do Gauss-Jordan style, or full elimination.

Parameters

A	Matrix
full	Gauss-Jordan style or upper unit-triangular form only.

rci_t mzed_echelonize_newton_john	(	mzed_t *	A,
		int	full
	)

Reduce matrix A to row echelon form using Gauss-Newton-John elimination.

Parameters

A	Matrix to be reduced.
full	If set to true, the reduced row echelon form will be computed.

Todo:

we don't really compute the upper triangular form yet, we need to implement _mzed_gauss_submatrix() and a better table creation for that.

static rci_t mzed_echelonize_ple ( mzed_t *  A, int  full  )

inlinestatic

Compute row echelon forms using PLE decomposition.

Compute the (reduced) row echelon form of the matrix A. If full=0, then return the reduced REF. This function reduces echelon forms to PLE (or PLUQ) decomposition.

Parameters

A	Matrix
full	REF or RREF.

Note

This function converts A to bitslice representation and back. Hence, it uses more memory than using mzed_echelonize_newton_john() or mzd_slice_echelonize_ple()