bd_lu_solver.h File Reference

LU solver for TBCI::BdMatrix class (TBCI::lu_decomp). More...

#include "tbci/vector.h"
#include "tbci/band_matrix.h"
#include "tbci/matrix.h"

Include dependency graph for bd_lu_solver.h:

Go to the source code of this file.

Macros
#define	BDMLU_MINVAL   1e-16
#define	BDMLU_RES_WARN   1e-11

Functions
template<typename T>
NAMESPACE_TBCI int	lu_decomp (BdMatrix< T > &mat)
	LU decompose a TBCI::BdMatrix.
template<typename T>
TVector< T >	LU_fwd_subst (const BdMatrix< T > &lu, const Vector< T > &y)
template<typename T>
TVector< T >	LU_bkw_subst (const BdMatrix< T > &lu, const Vector< T > &y)
template<typename T>
TVector< T >	LU_solve (const BdMatrix< T > &lu, const Vector< T > &b)
	Solve the equation Ax = b where A IS already LU decomposed.
template<typename T>
TVector< T >	lu_solve (BdMatrix< T > &mat, const Vector< T > &b)
	Solve the equation Ax = b where A still needs to be LU decomposed.
template<typename T>
TMatrix< T >	LU_solve (const BdMatrix< T > &lu, const Matrix< T > &b)
template<typename T>
TMatrix< T >	lu_solve (BdMatrix< T > &mat, const Matrix< T > &b)
template<typename T>
T	LU_det (const BdMatrix< T > &lu)
	calculates determinant of an already LU decomposed BdMatrix
template<typename T>
T	lu_det (BdMatrix< T > &mat)
	calculates the determinant of a BdMatrix by doing an LU decomposition
template<typename T>
TMatrix< T >	LU_invert (const BdMatrix< T > &lu)
	return the inverse Matrix for an already LU decomposed BdMatrix
template<typename T>
TMatrix< T >	lu_invert (BdMatrix< T > &mat)
	return the inverse Matrix for a BdMatrix by doing an LU decomposition

Detailed Description

LU solver for TBCI::BdMatrix class (TBCI::lu_decomp).

LU decomposizes a BdMatrix and solves the Vector equation Ax = b

Definition in file bd_lu_solver.h.

Macro Definition Documentation

BDMLU_MINVAL

#define BDMLU_MINVAL   1e-16

Definition at line 33 of file bd_lu_solver.h.

Referenced by lu_decomp().

BDMLU_RES_WARN

#define BDMLU_RES_WARN   1e-11

Definition at line 38 of file bd_lu_solver.h.

Referenced by lu_solve().

Function Documentation

LU_bkw_subst()

template<typename T>

TVector< T > LU_bkw_subst	(	const BdMatrix< T > &	lu,
		const Vector< T > &	y )

Definition at line 224 of file bd_lu_solver.h.

References ALIGN2, BCHK, BdMatrix< T >::get(), BdMatrix< T >::getmaxoff(), i, MIN, MIN_ALIGN2, REGISTER, BdMatrix< T >::rows(), T, x, and y.

Referenced by LU_solve(), and LU_solve().

lu_decomp()

template<typename T>

NAMESPACE_TBCI int lu_decomp

(

BdMatrix< T > &

mat

)

LU decompose a TBCI::BdMatrix.

Decomposition is compactly stored in one BdMatrix The diagonal elements of the lower BdMatrix are all 1 (this is a feature of the algorithm)

Note

The BdMatrix passed will be changed!

Definition at line 57 of file bd_lu_solver.h.

References ALIGN2, BCHK, BDMLU_MINVAL, BdMatrix< T >::expand(), fabs(), BdMatrix< T >::get(), BdMatrix< T >::getmaxoff(), i, lu_decomp(), MATH__, MAX, MIN, MIN_ALIGN2, REGISTER, BdMatrix< T >::rows(), BdMatrix< T >::setval(), STD__, T, and UNLIKELY.

Referenced by lu_det(), lu_invert(), lu_solve(), and lu_solve().

LU_det()

template<typename T>

T LU_det

(

const BdMatrix< T > &

lu

)

calculates determinant of an already LU decomposed BdMatrix

Definition at line 317 of file bd_lu_solver.h.

References ALIGN2, BdMatrix< T >::get(), i, MIN_ALIGN2, REGISTER, BdMatrix< T >::rows(), and T.

Referenced by lu_det().

lu_det()

template<typename T>

T lu_det ( BdMatrix< T > & mat )

inline

calculates the determinant of a BdMatrix by doing an LU decomposition

Definition at line 329 of file bd_lu_solver.h.

References lu_decomp(), LU_det(), and T.

LU_fwd_subst()

template<typename T>

TVector< T > LU_fwd_subst	(	const BdMatrix< T > &	lu,
		const Vector< T > &	y )

Definition at line 207 of file bd_lu_solver.h.

References ALIGN2, BCHK, BdMatrix< T >::get(), BdMatrix< T >::getmaxoff(), i, MAX, MIN_ALIGN2, REGISTER, BdMatrix< T >::rows(), T, x, and y.

Referenced by LU_solve(), and LU_solve().

LU_invert()

template<typename T>

TMatrix< T > LU_invert

(

const BdMatrix< T > &

lu

)

return the inverse Matrix for an already LU decomposed BdMatrix

Definition at line 338 of file bd_lu_solver.h.

References BdMatrix< T >::columns(), inv(), LU_solve(), BdMatrix< T >::rows(), T, and y.

Referenced by TMatrix< T >::FGD, and lu_invert().

lu_invert()

template<typename T>

TMatrix< T > lu_invert ( BdMatrix< T > & mat )

inline

return the inverse Matrix for a BdMatrix by doing an LU decomposition

Definition at line 355 of file bd_lu_solver.h.

References lu_decomp(), and LU_invert().

Referenced by TMatrix< T >::FGD.

LU_solve() [1/2]

template<typename T>

TMatrix< T > LU_solve	(	const BdMatrix< T > &	lu,
		const Matrix< T > &	b )

Definition at line 279 of file bd_lu_solver.h.

References b, i, LU_bkw_subst(), LU_fwd_subst(), x, and y.

LU_solve() [2/2]

template<typename T>

TVector< T > LU_solve ( const BdMatrix< T > & lu, const Vector< T > & b )

inline

Solve the equation Ax = b where A IS already LU decomposed.

Definition at line 246 of file bd_lu_solver.h.

References b, LU_bkw_subst(), LU_fwd_subst(), and y.

Referenced by TMatrix< T >::FGD, LU_invert(), lu_solve(), and lu_solve().

lu_solve() [1/2]

template<typename T>

TMatrix< T > lu_solve ( BdMatrix< T > & mat, const Matrix< T > & b )

inline

Definition at line 295 of file bd_lu_solver.h.

References b, lu_decomp(), and LU_solve().

lu_solve() [2/2]

template<typename T>

TVector< T > lu_solve	(	BdMatrix< T > &	mat,
		const Vector< T > &	b )

Solve the equation Ax = b where A still needs to be LU decomposed.

Note

The BdMatrix passed will be changed by the LU decomposition!

Definition at line 260 of file bd_lu_solver.h.

References b, BDMLU_RES_WARN, BVector< T >::copy(), fabs(), lu_decomp(), LU_solve(), MATH__, res, STD__, UNLIKELY, and x.