## Developer Reference

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

# ?hpsv

Computes the solution to the system of linear equations with a Hermitian coefficient matrix A stored in packed format, and multiple right-hand sides.

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine solves for
X
the system of linear equations
A*X
=
B
, where
A
is an
n
-by-
n
Hermitian matrix stored in packed format, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
The diagonal pivoting method is used to factor
A
as
A
=
U*D*U
H
or
A
=
L*D*L
H
, where
U
(or
L
) is a product of permutation and unit upper (lower) triangular matrices, and
D
is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
The factored form of
A
is then used to solve the system of equations
A*X
=
B
.
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular part of
A
is stored:
If
uplo
=
'U'
, the upper triangle of
A
is stored.
If
uplo
=
'L'
, the lower triangle of
A
is stored.
n
INTEGER
.
The order of matrix
A
;
n
0.
nrhs
INTEGER
.
The number of right-hand sides; the number of columns in
B
;
nrhs
0
.
ap
,
b
COMPLEX
for
chpsv
DOUBLE COMPLEX
for
zhpsv
.
Arrays:
ap
(size *)
,
b
(size
ldb
by *)
.
The dimension of
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).
The array
b
contains the matrix
B
whose columns are the right-hand sides for the systems of equations.
The second dimension of
b
must be at least
max(1,
nrhs
)
.
ldb
INTEGER
.
b
;
ldb
max(1,
n
)
.
Output Parameters
ap
The block-diagonal matrix
D
and the multipliers used to obtain the factor
U
(or
L
) from the factorization of
A
as computed by
?hptrf
, stored as a packed triangular matrix in the same storage format as
A
.
b
If
info
= 0,
b
is overwritten by the solution matrix
X
.
ipiv
INTEGER
.
Array, size at least
max(1,
n
)
. Contains details of the interchanges and the block structure of
D
, as determined by
?hptrf
.
If
ipiv
(
i
) =