gausslu.h File Reference

#include <aims/config/aimsdata_config.h>
#include <aims/def/general.h>

Include dependency graph for gausslu.h:

Go to the source code of this file.

Namespaces
	carto

Functions
LU decomposition of matrix.
The source matrix is a. As output, a is the LU decomposition. indx is an output vector that records the row permutation effected by the partial pivoting. d is output as +1 or -1 depending wether the number of row interchanges was even or odd.
float	AimsDecompositionLU (carto::VolumeRef< float > &a, carto::VolumeRef< int32_t > &indx)
LU forward and backward substitution.
Solves the set of N linear equations A.X=B. Here a is input but in LU form. indx is input as the permutation vector returned by LU decomposition. b is input as the right-hand side vector B, and returns with the solution vector X.
void	AimsBackSubstitutionLU (const carto::VolumeRef< float > &a, const carto::VolumeRef< int32_t > &indx, carto::VolumeRef< float > &b)
Inverse of a matrix.
carto::VolumeRef< float >	AimsInversionLU (const carto::VolumeRef< float > &matrix)
	Inverse of a float matrix. More...
carto::VolumeRef< cfloat >	AimsInversionLU (const carto::VolumeRef< cfloat > &matrix)
	Inverse of a complex float matrix. More...
Resolution of the linear equation A.X = B.
carto::VolumeRef< float >	AimsLinearResolutionLU (const carto::VolumeRef< float > &matrix, const carto::VolumeRef< float > &b)
	Resolution in float. More...
carto::VolumeRef< cfloat >	AimsLinearResolutionLU (const carto::VolumeRef< cfloat > &matrix, const carto::VolumeRef< cfloat > &b)
	Resolution in complex float. More...
Determinant of a matrix.
float	AimsDeterminantLU (const carto::VolumeRef< float > &matrix)
Linear resolution of Toeplitz like system.
void	AimsToeplitz (const carto::VolumeRef< float > &r, const carto::VolumeRef< float > &y, carto::VolumeRef< float > &x)
	Resolution of system R.x = y where R is a toeplitz matrix decomposed in r=[r(-(N-1)), ...., r(-1), r(0), r(1), ..., r(N-1)]. More...

Function Documentation

AimsBackSubstitutionLU()

void AimsBackSubstitutionLU	(	const carto::VolumeRef< float > &	a,
		const carto::VolumeRef< int32_t > &	indx,
		carto::VolumeRef< float > &	b
	)

AimsDecompositionLU()

float AimsDecompositionLU	(	carto::VolumeRef< float > &	a,
		carto::VolumeRef< int32_t > &	indx
	)

AimsDeterminantLU()

float AimsDeterminantLU

(

const carto::VolumeRef< float > &

matrix

)

AimsInversionLU() [1/2]

carto::VolumeRef< cfloat > AimsInversionLU

(

const carto::VolumeRef< cfloat > &

matrix

)

Inverse of a complex float matrix.

AimsInversionLU() [2/2]

carto::VolumeRef<float> AimsInversionLU

(

const carto::VolumeRef< float > &

matrix

)

Inverse of a float matrix.

AimsLinearResolutionLU() [1/2]

carto::VolumeRef< cfloat > AimsLinearResolutionLU	(	const carto::VolumeRef< cfloat > &	matrix,
		const carto::VolumeRef< cfloat > &	b
	)

Resolution in complex float.

AimsLinearResolutionLU() [2/2]

carto::VolumeRef<float> AimsLinearResolutionLU	(	const carto::VolumeRef< float > &	matrix,
		const carto::VolumeRef< float > &	b
	)

Resolution in float.

AimsToeplitz()

void AimsToeplitz	(	const carto::VolumeRef< float > &	r,
		const carto::VolumeRef< float > &	y,
		carto::VolumeRef< float > &	x
	)

Resolution of system R.x = y where R is a toeplitz matrix decomposed in r=[r(-(N-1)), ...., r(-1), r(0), r(1), ..., r(N-1)].

The result is given in x