Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • 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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804