## Developer Reference

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

# ?hetrs2

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

## Syntax

Include Files
• mkl.fi
,
lapack.f90
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
uplo
CHARACTER*1
.
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
INTEGER
.
The order of matrix
A
;
n
0.
nrhs
INTEGER
.
The number of right-hand sides;
nrhs
0.
a
,
b
COMPLEX
for
chetrs2
DOUBLE COMPLEX
for
zhetrs2
Arrays:
a
(
lda
,*)
,
b
(
ldb
,*)
.
The array
a
contains the block diagonal matrix
D
and the multipliers used to obtain the factor
U
or
L
as computed by
?hetrf
.
The array
b
contains the right-hand side matrix
B
.
The second dimension of
a
must be at least
max(1,
n
)
, and the second dimension of
b
at least
max(1,
nrhs
)
.
lda
INTEGER
.
a
;
lda
max(1,
n
)
.
ldb
INTEGER
.
b
;
ldb
max(1,
n
)
.
ipiv
INTEGER
.
Array of size
n
. The
ipiv
array contains details of the interchanges and the block structure of
D
as determined by
?hetrf
.
work