Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?pstrf

Computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix.

Syntax

lapack_int LAPACKE_spstrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float*
a
,
lapack_int
lda
,
lapack_int*
piv
,
lapack_int*
rank
,
float
tol
);
lapack_int LAPACKE_dpstrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double*
a
,
lapack_int
lda
,
lapack_int*
piv
,
lapack_int*
rank
,
double
tol
);
lapack_int LAPACKE_cpstrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float*
a
,
lapack_int
lda
,
lapack_int*
piv
,
lapack_int*
rank
,
float
tol
);
lapack_int LAPACKE_zpstrf
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double*
a
,
lapack_int
lda
,
lapack_int*
piv
,
lapack_int*
rank
,
double
tol
);
Include Files
  • mkl.h
Description
The routine computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix. The form of the factorization is:
  • P
    T
     *
    A
     *
    P
     =
    U
    T
     *
    U
    , if
    uplo
     =
    'U'
     for real flavors,
  • P
    T
     *
    A
     *
    P
     =
    U
    H
     *
    U
    , if
    uplo
     =
    'U'
     for complex flavors,
  • P
    T
     *
    A
     *
    P
     =
    L
     *
    L
    T
    , if
    uplo
     =
    'L'
     for real flavors,
  • P
    T
     *
    A
     *
    P
     =
    L
     *
    L
    H
    , if
    uplo
     =
    'L'
     for complex flavors,
where
P
 is a permutation matrix stored as vector
piv
, and
U
 and
L
 are upper and lower triangular matrices, respectively.
This algorithm does not attempt to check that
A
 is positive semidefinite. This version of the algorithm calls level 3 BLAS.
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:
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
The order of matrix
A
;
n
≥
 0.
a
Array
a
, size
max(1,
lda
*
n
)
. The array
a
 contains either the upper or the lower triangular part of the matrix
A
 (see
uplo
). .
tol
User defined tolerance. If
tol
 < 0, then
n
*
ε
*max(
A
k
,
k
), where
ε
 is the machine precision, will be used (see Error Analysis for the definition of machine precision). The algorithm terminates at the
(
k
-1)
-st step, if the pivot
≤
tol
.
lda
The leading dimension of
a
; at least
max(1,
n
)
.
Output Parameters
a
If
info
 = 0
, the factor
U
 or
L
 from the Cholesky factorization
is as described in
Description
.
piv
Array, size at least
max(1,
n
)
. The array
piv
 is such that the nonzero entries are
P
piv
[
k
-1],
k
 (1
≤
k
≤
n
).
rank
The rank of
a
 given by the number of steps the algorithm completed.
Return Values
This function returns a value
info
.
If
info
 = 0
, the execution is successful.
If
info
 =
-k
, the
k-
th argument had an illegal value.
If
info
 > 0
, the matrix
A
 is either rank deficient with a computed rank as returned in
rank
, or is not positive semidefinite.

Product and Performance Information

1

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