Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?potrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix.

Syntax

lapack_int
LAPACKE_spotrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_dpotrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_cpotrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_zpotrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
);
Include Files
  • mkl.h
Description
The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, 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.
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Must be
'U'
 or
'L'
.
Indicates whether the upper or lower triangular part of
A
 is stored and how
A
 is factored:
If
uplo
 =
'U'
, the array
a
 stores the upper triangular part of the matrix
A
, and the strictly lower triangular part of the matrix is not referenced.
If
uplo
 =
'L'
, the array
a
 stores the lower triangular part of the matrix
A
, and the strictly upper triangular part of the matrix is not referenced.
n
Specifies the order of the matrix
A
. The value of
n
 must be at least zero.
a
Array, size max(1,
lda
*
n
. The array
a
 contains either the upper or the lower triangular part of the matrix
A
 (see
uplo
).
lda
The leading dimension of
a
. Must be at least max(1,
n
).
Output Parameters
a
The upper or lower triangular part of
a
 is overwritten by the Cholesky factor
U
 or
L
, as specified by
uplo
.
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
.
Application Notes
If
uplo
 =
'U'
, the computed factor
U
 is the exact factor of a perturbed matrix
A
 +
E
, where
Equation
c
(
n
)
 is a modest linear function of
n
, and
ε
 is the machine precision.
A similar estimate holds for
uplo
 =
'L'
.
The total number of floating-point operations is approximately
(1/3)
n
3
 for real flavors or
(4/3)
n
3
 for complex flavors.
After calling this routine, you can call the following routines:
to solve
A*X
 =
B
to estimate the condition number of
A
to compute the inverse of
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