Contents

# hetrf (USM Version)

Computes the Bunch-Kaufman factorization of a complex Hermitian matrix. This routine belongs to the
oneapi::mkl::lapack
namespace.

## Description

The routine computes the factorization of a complex Hermitian matrix
A
using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is:
• if
uplo=uplo::upper
,
A = U*D*UH
• if
uplo=uplo::lower
,
A = L*D*LH,
where
A
is the input matrix,
U
and
L
are products of permutation and triangular matrices with unit diagonal (upper triangular for
U
and lower triangular for
L
), and
D
is a Hermitian block-diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks.
U
and
L
have 2-by-2 unit diagonal blocks corresponding to the 2-by-2 blocks of
D
.

## API

Syntax
``````namespace oneapi::mkl::lapack {
cl::sycl::event hetrf(cl::sycl::queue &queue,
mkl::uplo uplo,
std::int64_t n,
T *a,
std::int64_t lda,
std::int64_t *ipiv,
const std::vector<cl::sycl::event> &events = {})
}``````
hetrf
(USM version) supports the following precisions and devices:
T
Devices supported
std::complex<float>
Host and CPU
std::complex<double>
Host and CPU
Input Parameters
queue
The device queue where calculations will be performed.
uplo
Indicates whether the upper or lower triangular part of
A
is stored and how
A
is factored:.
If
uplo = uplo::upper
, the arraya stores the upper triangular part of
A
and
A
is factored as
U
*
D
*
U
H
.
If
uplo = uplo::lower
, the arraya stores the lower triangular part of
A
and
A
is factored as
L
*
D
*
L
H
.
n
The order of the matrix
A
(0≤n)
.
a
The pointer to coefficients of matrix
A
, size
max(1,lda*n)
, containing either the upper or the lower triangular part of the matrix
A
(see uplo). The second dimension of a must be at least
max(1,n)
.
lda
Pointer to scratchpad memory to be used by the routine for storing intermediate results.
Size of scratchpad memory as a number of floating point elements of type
T
. Size should not be less than the value returned by the hetrf_scratchpad_size function.
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
a
The upper or lower triangular part of
a
is overwritten by details of the block-diagonal matrix
D
and the multipliers used to obtain the factor
U
(or
L
).
ipiv
Pointer to memory array of size at least
max(1, n)
. Contains details of the interchanges and the block structure of
D
. If
ipiv(i) = k >0
, then
dii
is a 1-by-1 block, and the
i
-th row and column of
A
was interchanged with the
k
-th row and column.
If
uplo
= mkl::uplo::upper and
ipiv
(
i
) =
ipiv
(
i
-1) = -
m
< 0, then
D
has a 2-by-2 block in rows/columns
i
and
i-1
, and (
i-1
)-th row and column of
A
was interchanged with the
m
-th row and column.
If
uplo
= mkl::uplo::lower and
ipiv
(
i
) =
ipiv
(
i
+1) = -
m
< 0, then
D
has a 2-by-2 block in rows/columns
i
and
i+1
, and (
i+1
)-th row and column of
A
was interchanged with the
m
-th row and column.
Exceptions
Exception
Description
mkl::lapack::exception
This exception is thrown when problems occur during calculations. You can obtain the info code of the problem using the info() method of the exception object:
If
info = -i
, the
i
-th parameter had an illegal value.
If
info = i
,
d
:sub:
`i
i`
is 0. The factorization has been completed, but
D
is exactly singular. Division by 0 will occur if you use
D
for solving a system of linear equations.
If
info
is equal to the value passed as scratchpad size, and detail() returns non zero, then the passed scratchpad has an insufficient size, and the required size should not be less than the value returned by the detail() method of the exception object.
Return Values
Output event to wait on to ensure computation is complete.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.