Developer Reference

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hetrd

Reduces a complex Hermitian matrix to tridiagonal form. This routine belongs to the
oneapi::mkl::lapack
namespace.

Description

The routine reduces a complex Hermitian matrix
A
to symmetric tridiagonal form
T
by a unitary similarity transformation:
A = Q*T*QH
. The unitary matrix
Q
is not formed explicitly but is represented as a product of
n
-1 elementary reflectors. Routines are provided to work with
Q
in this representation.

API

Syntax
namespace oneapi::mkl::lapack { cl::sycl::event hetrd(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &d, cl::sycl::buffer<T> &e, cl::sycl::buffer<T> &tau, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size) }
hetrd
supports the following precisions and devices:
T
Devices supported
std::complex<float>
Host, CPU, and GPU
std::complex<double>
Host, CPU, and GPU
Input Parameters
queue
The device queue where calculations will be performed.
uplo
Must be
uplo::upper
or
uplo::lower
.
If
uplo = uplo::upper
, a stores the upper triangular part of
A
.
If
uplo = uplo::lower
, a stores the lower triangular part of
A
.
n
The order of the matrices
A
(0≤n)
.
a
Buffer holding the matrix
A
, size
(lda,*)
. Contains the upper or lower triangle as specified by uplo.
lda
The leading dimension of a; at least
max(1, n)
scratchpad
Buffer holding scratchpad memory to be used by the routine for storing intermediate results.
scratchpad_size
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 hetrd_scratchpad_size function.
Output Parameters
a
On exit,
if
uplo = uplo::upper
, the diagonal and first superdiagonal of
A
are overwritten by the corresponding elements of the tridiagonal matrix
T
, and the elements above the first superdiagonal, with the buffer tau, represent the unitary matrix
Q
as a product of elementary reflectors;
if
uplo = uplo::lower
, the diagonal and first subdiagonal of
A
are overwritten by the corresponding elements of the tridiagonal matrix
T
, and the elements below the first subdiagonal, with the array tau, represent the unitary matrix
Q
as a product of elementary reflectors.
d
Buffer holding the diagonal elements of the matrix
T
. The dimension of d must be at least
max(1, n)
.
e
Buffer holding off diagonal elements of the matrix
T
. The dimension of e must be at least
max(1, n-1)
.
tau
Buffer holding array of size at least
max(1, n)
. Stores
(n-1)
scalars that define elementary reflectors in decomposition of the unitary matrix
Q
in a product of
n-1
elementary reflectors. tau
(n)
is used as workspace.
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
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.

Product and Performance Information

1

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