Contents

# ?hesv_aa

Computes the solution to system of linear equations for HE matrices.
Description
?hesv_aa
computes the solution to a complex system of linear equations
A
*
X
=
B
, where
A
is an
n
-by-
n
Hermitian matrix and
X
and
B
are
n
-by-
nrhs
matrices. Aasen's algorithm is used to factor
A
as
A
=
U
*
T
*
U
H
if
uplo
= 'U', or
A
=
L
*
T
*
L
H
if
uplo
= 'L',
where
U
(or
L
) is a product of permutation and unit upper (lower) triangular matrices, and
T
is Hermitian and tridiagonal. The factored form of
A
is then used to solve the system of equations
A
*
X
=
B
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
If
uplo
= 'U': The upper triangle of
A
is stored.
If
uplo
= 'L': the lower triangle of
A
is stored.
n
The number of linear equations or the order of the matrix
A
.
n
0.
nrhs
The number of right hand sides or the number of columns of the matrix
B
.
nrhs
0.
a
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
The leading dimension of the array
a
.
lda
max(1,
n
).
b
Array of size
ldb
*
nrhs
. On entry, the
n
-by-
nrhs
right hand side matrix
B
.
ldb
The leading dimension of the array
b
.
ldb
max(1,
n
).
lwork
The length of
work
.
lwork
max(1, 2*
n
, 3*
n
-2), and for best performance
lwork
max(1,
n
*
nb
), where
nb
is the optimal blocksize for
?hetrf
.
If
lwork
<
n
, TRS is done with Level BLAS 2. If
lwork
n
, TRS is done with Level BLAS 3.
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, if
info
= 0, the tridiagonal matrix
T
and the multipliers used to obtain the factor
U
or
L
from the factorization
A
=
U
*
T
*
U
H
or
A
=
L
*
T
*
L
H
as computed by
?hetrf_aa
.
ipiv
Array of size (
n
) On exit, it contains the details of the interchanges: row and column
k
of
A
were interchanged with the row and column
ipiv
[
k
]
.
b
On exit, if
info
= 0, the
n
-by-
nrhs
solution matrix
X
.
work
Array of size (max(1,
lwork
)). On exit, if
info
= 0,
work

returns the optimal
lwork
.
Return Values
This function returns a value
info
.
If
info
= 0: successful exit.
If
info
< 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, so the solution could not be computed.

#### Product and Performance Information

1

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