Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • 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
.
lapack_int
LAPACKE_chetrs_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_float
*
A
,
lapack_int
lda
,
const
lapack_complex_float
*
e
,
const
lapack_int
*
ipiv
,
lapack_complex_float
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_zhetrs_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_double
*
A
,
lapack_int
lda
,
const
lapack_complex_double
*
e
,
const
lapack_int
*
ipiv
,
lapack_complex_double
*
B
,
lapack_int
ldb
);
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
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
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
The order of the matrix A.
n
 ≥ 0.
nrhs
The number of right-hand sides; that is, the number of columns in the matrix B.
nrhs
 ≥ 0.
A
Array of size max(1,
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
The leading dimension of the array
A
.
e
Array of size
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
-
1] is not referenced in both the
uplo
 =
'U'
 and
uplo
 =
'L'
 cases.
ipiv
Array of size (
n
.
 Details of the interchanges and the block structure of D as determined by
?hetrf_rk
.
B
On entry, the right-hand side matrix B.
The size of
B
 is at least max(1,
ldb
*
nrhs
) for column-major layout and max(1,
ldb
*
n
) for row-major layout.
ldb
The leading dimension of the array
B
.
ldb
 ≥ max(1,
n
) for column-major layout and
ldb
 ≥
nrhs
 for row-major layout.
Output Parameters
B
On exit, the solution matrix X.
Return Values
This function returns a value
info
.
= 0: Successful exit.
< 0: If
info
 =
-i
, the
i
th
 argument had an illegal value.

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804