## Developer Reference

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

# ?hptrs

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

## 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 packed 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 arrays
ap
(containing
U
or
L
)and
ipiv
in the form returned by the factorization routine
?hptrf
.
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates how the input matrix
A
has been factored:
If
uplo
=
'U'
, the array
ap
stores the packed factor
U
of the factorization
A
=
U*D*U
H
. If
uplo
=
'L'
, the array
ap
stores the packed 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
?hptrf
.
ap
COMPLEX
for
chptrs
DOUBLE COMPLEX
for
zhptrs
.
The dimension of array
ap
(*)
must be at least max(1,
n
(
n
+1)/2). The array
ap
contains the factor
U
or
L
, as specified by
uplo
, in packed storage (see Matrix Storage Schemes).
b
COMPLEX
for
chptrs
DOUBLE COMPLEX
for
zhptrs
.
The array
b
(
ldb
,*)
contains the matrix
B
whose columns are the right-hand sides for the system of equations.
The second dimension of
b
must be at least
max(1,
nrhs
)
.
ldb
INTEGER
.