Developer Reference

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

?hetrs_3

Solves a system of linear equations A * X = B with a complex Hermitian matrix using the factorization computed by
?hetrf_rk
.
call chetrs_3
(
uplo
,
n
,
nrhs
,
A
,
lda
,
e
,
ipiv
,
B
,
ldb
,
info
)
call zhetrs_3
(
uplo
,
n
,
nrhs
,
A
,
lda
,
e
,
ipiv
,
B
,
ldb
,
info
)
Description
?hetrs_3
solves a system of linear equations A * X = B with a complex Hermitian matrix A using the factorization computed by
?hetrf_rk
: A = P*U*D*(U
H
)*(P
T
) or A = P*L*D*(L
H
)*(P
T
), where U (or L) is unit upper (or lower) triangular matrix, U
H
(or L
H
) is the conjugate of U (or L), P is a permutation matrix, P
T
is the transpose of P, and D is a Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
This algorithm uses Level 3 BLAS.
Input Parameters
uplo
CHARACTER*1
Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
  • =
    'U'
    : Upper triangular; form is A = P*U*D*(U
    H
    )*(P
    T
    ).
  • =
    'L'
    : Lower triangular; form is A = P*L*D*(L
    H
    )*(P
    T
    ).
n
INTEGER
The order of the matrix A.
n
≥ 0.
nrhs
INTEGER
The number of right-hand sides; that is, the number of columns in the matrix B.
nrhs
≥ 0.
A
COMPLEX
for
chetrs_3
COMPLEX*16
for
zhetrs_3
Array, dimension (
lda
,
n
).
Diagonal of the block diagonal matrix D and factor U or L as computed by
?hetrf_rk
:
  • Only
    diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A; that is, D(
    k
    ,
    k
    ) = A(
    k
    ,
    k
    ). Superdiagonal (or subdiagonal) elements of D should be provided on entry in array
    e
    .
  • If
    uplo
    =
    'U'
    , factor U in the superdiagonal part of A. If
    uplo
    =
    'L'
    , factor L in the subdiagonal part of A.
lda
INTEGER
The leading dimension of the array
A
.
lda
≥ max(1,
n
).
e
COMPLEX
for
chetrs_3
COMPLEX*16
for
zhetrs_3
Array, dimension (
n
).
On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If
uplo
=
'U'
, e(
i
) = D(
i
-
1,
i
),
i
=2:N, and e(1) is not referenced. If
uplo
=
'L'
, e(
i
) = D(
i
+1,
i
),
i
=1:N
-
1, and e(
n
) is not referenced.
For 1-by-1 diagonal block D(
k
), where 1 ≤
k
n
, the element
e
(
k
) is not referenced in both the
uplo
=
'U'
and
uplo
=
'L'
cases.
ipiv
INTEGER
Array, dimension (
n
).
Details of the interchanges and the block structure of D as determined by
?hetrf_rk
.
B
COMPLEX
for
chetrs_3
COMPLEX*16
for
zhetrs_3
On entry, the right-hand side matrix B.
The second dimension of
B
must be at least max(1,
nrhs
).
ldb
INTEGER
The leading dimension of the array
B
.
ldb
≥ max(1,
n
).
Output Parameters
B
COMPLEX
for
chetrs_3
COMPLEX*16
for
zhetrs_3
On exit, the solution matrix X.
info
INTEGER
  • = 0: Successful exit.
  • < 0: If
    info
    =