Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?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
 for real data,
A
 =
U
H
*U
 for complex data
if
uplo
=
'U'
A
 =
L*L
T
 for real data,
A
 =
L*L
H
 for complex data
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).
If
transr
 =
'N'
, the Normal
transr
 of RFP
A
 is stored.
If
transr
 =
'T'
, the Transpose
transr
 of RFP
A
 is stored.
If
transr
 =
'C'
, the Conjugate-Transpose
transr
 of RFP
A
 is stored.
uplo
Must be
'U'
 or
'L'
.
Indicates whether the upper or lower triangular part of
A
 is stored:
If
uplo
 =
'U'
, the array
a
 stores the upper triangular part of the matrix
A
.
If
uplo
 =
'L'
, the array
a
 stores the lower triangular part of the matrix
A
.
n
The order of the matrix
A
;
n
≥
 0.
a
Array, size
(
n
*(
n
+1)/2)
. The array
a
 contains the matrix
A
 in the RFP format.
Output Parameters
a
a
 is overwritten by the Cholesky factor
U
 or
L
, as specified by
uplo
 and
trans
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
 =
-i
, parameter
i
 had an illegal value.
If
info
 =
i
, the leading minor of order
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
.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.