A.I.M.S


gausslu.h File Reference
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Classes

class  AimsData< T >
 

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.

AIMSDATA_API float AimsDecompositionLU (AimsData< float > &a, AimsData< 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.

AIMSDATA_API void AimsBackSubstitutionLU (AimsData< float > &a, AimsData< int32_t > &indx, AimsData< float > &b)
 
Inverse of a matrix.
AIMSDATA_API AimsData< float > AimsInversionLU (const AimsData< float > &matrix)
 Inverse of a float matrix. More...
 
AIMSDATA_API AimsData< cfloatAimsInversionLU (const AimsData< cfloat > &matrix)
 Inverse of a complex float matrix. More...
 
Resolution of the linear equation A.X = B.
AIMSDATA_API AimsData< float > AimsLinearResolutionLU (const AimsData< float > &matrix, const AimsData< float > &b)
 Resolution in float. More...
 
AIMSDATA_API AimsData< cfloatAimsLinearResolutionLU (const AimsData< cfloat > &matrix, const AimsData< cfloat > &b)
 Resolution in complex float. More...
 
Determinant of a matrix.
AIMSDATA_API float AimsDeterminantLU (const AimsData< float > &matrix)
 
Linear resolution of Toeplitz like system.
AIMSDATA_API void AimsToeplitz (const AimsData< float > &r, const AimsData< float > &y, AimsData< 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

AIMSDATA_API void AimsBackSubstitutionLU ( AimsData< float > &  a,
AimsData< int32_t > &  indx,
AimsData< float > &  b 
)
AIMSDATA_API float AimsDecompositionLU ( AimsData< float > &  a,
AimsData< int32_t > &  indx 
)
AIMSDATA_API float AimsDeterminantLU ( const AimsData< float > &  matrix)
AIMSDATA_API AimsData<float> AimsInversionLU ( const AimsData< float > &  matrix)

Inverse of a float matrix.

AIMSDATA_API AimsData< cfloat > AimsInversionLU ( const AimsData< cfloat > &  matrix)

Inverse of a complex float matrix.

AIMSDATA_API AimsData<float> AimsLinearResolutionLU ( const AimsData< float > &  matrix,
const AimsData< float > &  b 
)

Resolution in float.

AIMSDATA_API AimsData< cfloat > AimsLinearResolutionLU ( const AimsData< cfloat > &  matrix,
const AimsData< cfloat > &  b 
)

Resolution in complex float.

AIMSDATA_API void AimsToeplitz ( const AimsData< float > &  r,
const AimsData< float > &  y,
AimsData< 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