?pftrf
?pftrf
Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed
(RFP)
format
.
Syntax
lapack_int
LAPACKE_spftrf
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
float
*
a
);
lapack_int
LAPACKE_dpftrf
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
double
*
a
);
lapack_int
LAPACKE_cpftrf
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
a
);
lapack_int
LAPACKE_zpftrf
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
a
);
Include Files
- mkl.h
Description
The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, a Hermitian positive-definite matrix
A
:A = U T *U A = U H *U | if uplo ='U' |
A = L*L T A = L*L H | if uplo ='L' |
where
L
is a lower triangular matrix and U
is upper triangular.The matrix
A
is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes.This is the block version of the algorithm, calling Level 3 BLAS.
Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- transr
- Must be'N','T'(for real data) or'C'(for complex data).Iftransr='N', the Normaltransrof RFPAis stored.Iftransr='T', the Transposetransrof RFPAis stored.Iftransr='C', the Conjugate-Transposetransrof RFPAis stored.
- uplo
- Must be'U'or'L'.Indicates whether the upper or lower triangular part ofAis stored:Ifuplo='U', the arrayastores the upper triangular part of the matrixA.Ifuplo='L', the arrayastores the lower triangular part of the matrixA.
- n
- The order of the matrixA;n≥0.
- a
- Array, size(. The arrayn*(n+1)/2)acontains the matrixAin the RFP format.
Output Parameters
- a
- ais overwritten by the Cholesky factorUorL, as specified byuploandtrans.
Return Values
This function returns a value
info
.If , the execution is successful.
info
=0If , parameter
info
= -i
i
had an illegal value.If , the leading minor of order
info
= i
i
(and therefore the matrix A
itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A
.