trsm.h File Reference

Triangular system solving with Matrix routines. More...

#include "misc.h"
#include "packedmatrix.h"

Go to the source code of this file.

Functions
void	mzd_trsm_upper_right (mzd_t *U, mzd_t *B, const int cutoff)
	Solves X U = B with X and B matrices and U upper triangular.
void	_mzd_trsm_upper_right (mzd_t *U, mzd_t *B, const int cutoff)
	Solves X U = B with X and B matrices and U upper triangular.
void	mzd_trsm_lower_right (mzd_t *L, mzd_t *B, const int cutoff)
	Solves X L = B with X and B matrices and L lower triangular.
void	_mzd_trsm_lower_right (mzd_t *L, mzd_t *B, const int cutoff)
	Solves X L = B with X and B with matrices and L lower triangular.
void	mzd_trsm_lower_left (mzd_t *L, mzd_t *B, const int cutoff)
	Solves L X = B with X and B matrices and L lower triangular.
void	_mzd_trsm_lower_left (mzd_t *L, mzd_t *B, const int cutoff)
	Solves L X = B with X and B matrices and L lower triangular.
void	mzd_trsm_upper_left (mzd_t *U, mzd_t *B, const int cutoff)
	Solves U X = B with X and B matrices and U upper triangular.
void	_mzd_trsm_upper_left (mzd_t *U, mzd_t *B, const int cutoff)
	Solves U X = B with X and B matrices and U upper triangular.

---

Detailed Description

Triangular system solving with Matrix routines.

Author:

Clement Pernet <clement.pernet@gmail.com>

---

Function Documentation

void _mzd_trsm_lower_left	(	mzd_t *	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.

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

• L00 L10 B0 and B1 are possibly located at uneven locations.
• Their column dimension is lower than 64.
• The first column of L01, L11, B1 are aligned to words.

void _mzd_trsm_lower_right	(	mzd_t *	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 RADIX grid and that their dimension is a multiple of 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  |
     |____|____|
   

• L00 and B0 are possibly located at uneven locations.
• Their column dimension is lower than 64.
• The first column of L10, L11, B1 are aligned to words.

void _mzd_trsm_upper_left	(	mzd_t *	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.

     __________   ______
     \ U00|    | |      |
      \   |U01 | |      |
       \  |    | |  B0  |
        \ |    | |      |
         \|____| |______|
          \    | |      |
           \U11| |      |
            \  | |  B1  |
             \ | |      |
              \| |______|
     

• U00, B0 and B1 are possibly located at uneven locations.
• Their column dimension is greater than 64
• The first column of U01, U11, B0 and B1 are aligned to words.

void _mzd_trsm_upper_right	(	mzd_t *	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 |
     |___|___|
   

• U00 and B0 are possibly located at uneven locations.
• Their column dimension is lower than 64.
• The first column of U01, U11, B1 are aligned at words.

void mzd_trsm_lower_left	(	mzd_t *	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 *	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 *	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 *	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.