## Developer Reference

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

# ?hetrs

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

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine solves for
X
the system of linear equations
A*X
=
B
with a Hermitian matrix
A
, given the Bunch-Kaufman 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 and
D
is a symmetric block-diagonal matrix. The system is solved with multiple right-hand sides stored in the columns of the matrix
B
. You must supply to this routine the factor
U
(or
L
) and the array
ipiv
returned by the factorization routine
?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.
ipiv
INTEGER
.
Array, size at least
max(1,
n
)
.
The
ipiv
array, as returned by
?hetrf
.
a
,
b
COMPLEX
for
chetrs
DOUBLE COMPLEX
for
zhetrs
.
Arrays:
a
(
lda
,*)
,
b
(
ldb
,*)
.
The array
a
contains the factor
U
or
L
(see
uplo
).
The array
b
contains the matrix
B
whose columns are the right-hand sides for the system of equations.
The second dimension of
a
must be at least
max(1,
n
)
, the second dimension of
b
at least
max(1,
nrhs
)
.
lda
INTEGER
.