Contents

# ?pstrf

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

## Syntax

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
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

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