## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?hetrf_aa

Computes the factorization of a complex hermitian matrix using Aasen's algorithm.
Description
?hetrf_aa
computes the factorization of a complex Hermitian matrix
A
using Aasen's algorithm. The form of the factorization is
A
=
U
*
T
*
U
H
or
a
= L*T*L
H
where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is a Hermitian tridiagonal matrix. This is the blocked version of the algorithm, calling Level 3 BLAS.
Input Parameters
uplo
CHARACTER*1
.
= 'U': Upper triangle of
A
is stored; = 'L': Lower triangle of
a
is stored.
n
INTEGER
.
The order of the matrix
A
.
n
0.
a
COMPLEX
for
chetrf_aa
COMPLEX*16
for
zhetrf_aa
Array of size
(
lda
,
n
)
. On entry, the Hermitian matrix
A
.
If
uplo
n
-by-
n
upper triangular part of
a
contains the upper triangular part of the matrix
A
, and the strictly lower triangular part of
a
is not referenced.
If
uplo
n
-by-
n
lower triangular part of
a
contains the lower triangular part of the matrix
A
, and the strictly upper triangular part of
a
is not referenced.
lda
INTEGER
.
The leading dimension of the array
a
.
lda
max(1,
n
).
lwork
INTEGER
.
The length of
work
.
lwork
2*
n
. For optimum performance
lwork
n
*(1 +
nb
), where
nb
is the optimal block size. If
lwork
= -1, then a workspace query is assumed; the routine only calculates the optimal size of the
work
array, returns this value as the first entry of the
work
array, and no error message related to
lwork
is issued by
xerbla
.
Output Parameters
a
On exit, the tridiagonal matrix is stored in the diagonals and the subdiagonals of
a
just below (or above) the diagonals, and
L
is stored below (or above) the subdiagonals, when
uplo
is 'L' (or 'U').
ipiv
INTEGER
.
array, dimension (
n
) On exit, it contains the details of the interchanges: the row and column
k
of
a
were interchanged with the row and column
ipiv
(
k
)
.
work
COMPLEX
for
chetrf_aa
COMPLEX*16
for
zhetrf_aa
Array of size (max(1,
lwork
)). On exit, if
info
= 0,
work
(1)
returns the optimal
lwork
.
info
INTEGER
.
If
info
= 0: successful exit < 0: if
info
= -
i
, the
i
-th argument had an illegal value,
If
info
> 0: if
info
=
i
,
D
i
,
i
is exactly zero. The factorization has been completed, but the block diagonal matrix
D
is exactly singular, and division by zero will occur if it is used to solve a system of equations.