Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • 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

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