triangular.h File Reference

Triangular system solving with Matrix routines. More...

#include <m4ri/mzd.h>

Go to the source code of this file.

Functions
void	mzd_trsm_upper_right (mzd_t const *U, mzd_t *B, const int cutoff)
	Solves X U = B with X and B matrices and U upper triangular. More...
void	_mzd_trsm_upper_right (mzd_t const *U, mzd_t *B, const int cutoff)
	Solves X U = B with X and B matrices and U upper triangular. More...
void	mzd_trsm_lower_right (mzd_t const *L, mzd_t *B, const int cutoff)
	Solves X L = B with X and B matrices and L lower triangular. More...
void	_mzd_trsm_lower_right (mzd_t const *L, mzd_t *B, const int cutoff)
	Solves X L = B with X and B with matrices and L lower triangular. More...
void	mzd_trsm_lower_left (mzd_t const *L, mzd_t *B, const int cutoff)
	Solves L X = B with X and B matrices and L lower triangular. More...
void	_mzd_trsm_lower_left (mzd_t const *L, mzd_t *B, const int cutoff)
	Solves L X = B with X and B matrices and L lower triangular. More...
void	mzd_trsm_upper_left (mzd_t const *U, mzd_t *B, const int cutoff)
	Solves U X = B with X and B matrices and U upper triangular. More...
void	_mzd_trsm_upper_left (mzd_t const *U, mzd_t *B, const int cutoff)
	Solves U X = B with X and B matrices and U upper triangular. More...
mzd_t *	mzd_trtri_upper (mzd_t *A)
	Invert the upper triangular matrix A by reduction to matrix multiplication. More...

Detailed Description

Triangular system solving with Matrix routines.

Author

Clement Pernet cleme.nosp@m.nt.p.nosp@m.ernet.nosp@m.@gma.nosp@m.il.co.nosp@m.m

Function Documentation

void _mzd_trsm_lower_left	(	mzd_t const *	L,
		mzd_t *	B,
		const int	cutoff
	)

Solves L X = B with X and B matrices and L lower triangular.

X is stored inplace on B.

Parameters

L	Input lower triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

void _mzd_trsm_lower_right	(	mzd_t const *	L,
		mzd_t *	B,
		const int	cutoff
	)

Solves X L = B with X and B with matrices and L lower triangular.

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. X is stored inplace on B.

Attention

Note, that the 'right' variants of TRSM are slower than the 'left' variants.

Parameters

L	Input lower triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

  |\
  | \
  |  \
  |L00\
  |____\
  |    |\
  |    | \
  |    |  \
  |L10 |L11\
  |____|____\
   _________
  |B0  |B1  |
  |____|____|

void _mzd_trsm_upper_left	(	mzd_t const *	U,
		mzd_t *	B,
		const int	cutoff
	)

Solves U X = B with X and B matrices and U upper triangular.

X is stored inplace on B.

Parameters

U	Input upper triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

void _mzd_trsm_upper_right	(	mzd_t const *	U,
		mzd_t *	B,
		const int	cutoff
	)

Solves X U = B with X and B matrices and U upper triangular.

X is stored inplace on B.

Attention

Note, that the 'right' variants of TRSM are slower than the 'left' variants.

Parameters

U	Input upper triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

  _________
  \U00|   |
   \  |U01|
    \ |   |
     \|___|
      \U11|
       \  |
        \ |
         \|
   _______
  |B0 |B1 |
  |___|___|

void mzd_trsm_lower_left	(	mzd_t const *	L,
		mzd_t *	B,
		const int	cutoff
	)

Solves L X = B with X and B matrices and L lower triangular.

X is stored inplace on B.

This is the wrapper function including bounds checks. See _mzd_trsm_lower_left() for implementation details.

Parameters

L	Input lower triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

void mzd_trsm_lower_right	(	mzd_t const *	L,
		mzd_t *	B,
		const int	cutoff
	)

Solves X L = B with X and B matrices and L lower triangular.

X is stored inplace on B.

This is the wrapper function including bounds checks. See _mzd_trsm_upper_right() for implementation details.

Attention

Note, that the 'right' variants of TRSM are slower than the 'left' variants.

Parameters

L	Input upper triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

void mzd_trsm_upper_left	(	mzd_t const *	U,
		mzd_t *	B,
		const int	cutoff
	)

Solves U X = B with X and B matrices and U upper triangular.

X is stored inplace on B.

This is the wrapper function including bounds checks. See _mzd_trsm_upper_left() for implementation details.

Parameters

U	Input upper triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

void mzd_trsm_upper_right	(	mzd_t const *	U,
		mzd_t *	B,
		const int	cutoff
	)

Solves X U = B with X and B matrices and U upper triangular.

X is stored inplace on B.

Attention

Note, that the 'right' variants of TRSM are slower than the 'left' variants.

This is the wrapper function including bounds checks. See _mzd_trsm_upper_right() for implementation details.

Parameters

U	Input upper triangular matrix.
B	Input matrix, being overwritten by the solution matrix X
cutoff	Minimal dimension for Strassen recursion.

mzd_t* mzd_trtri_upper

(

mzd_t *

A

)

Invert the upper triangular matrix A by reduction to matrix multiplication.

Parameters

A	Matrix to be inverted (overwritten).

Returns

Inverse of A or throws an error