## Developer Reference

• 0.10
• 10/21/2020
• Public Content
Contents

# ?hetrs2

Solves a system of linear equations with a UDU- or LDL-factored Hermitian coefficient matrix.

## Syntax

Include Files
• mkl.h
Description
The routine solves a system of linear equations
A*X
=
B
with a complex Hermitian matrix
A
using the factorization of
A
:
if
uplo
=
'U'
,
A
=
U*D*U
H
if
uplo
=
'L'
,
A
=
L*D*L
H
where
• U
and
L
are upper and lower triangular matrices with unit diagonal
• D
is a Hermitian block-diagonal matrix.
The factorization is computed by
?hetrf
.
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 how the input matrix
A
has been factored:
If
uplo
=
'U'
, the array
a
stores the upper triangular factor
U
of the factorization
A
=
U*D*U
H
.
If
uplo
=
'L'
, the array
a
stores the lower triangular factor
L
of the factorization
A
=
L*D*L
H
.
n
The order of matrix
A
;
n
0.
nrhs
The number of right-hand sides;
nrhs
0.
a
The array
a
of size max(1,
lda
*
n
) contains the block diagonal matrix
D
and the multipliers used to obtain the factor
U
or
L
as computed by
?hetrf
.
b
The array
b
of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout contains the right-hand side matrix
B
.
lda
a
;
lda
max(1,
n
)
.
ldb
b
;
ldb
max(1,
n
) for column major layout and
ldb
nrhs
for row major layout
.
ipiv
Array of size
n
. The
ipiv
array contains details of the interchanges and the block structure of
D
as determined by
?hetrf
.
Output Parameters
b
Overwritten by the solution matrix
X
.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i