Contents

# heevd (USM Version)

Computes all eigenvalues and, optionally, all eigenvectors of a complex Hermitian matrix using divide and conquer algorithm. This routine belongs to the
oneapi::mkl::lapack
namespace.

## Description

The routine computes all the eigenvalues, and optionally all the eigenvectors, of a complex Hermitian matrix
A
. In other words, it can compute the spectral factorization of
A
as:
A = Z*Λ*ZH
.
Here is a real diagonal matrix whose diagonal elements are the eigenvalues
i
, and
Z
is the orthogonal matrix whose columns are the eigenvectors
z
i
. Thus,
A*zi = λi*zi
for
i = 1, 2, ..., n
.
If the eigenvectors are requested, then this routine uses a divide and conquer algorithm to compute eigenvalues and eigenvectors. However, if only eigenvalues are required, then it uses the Pal-Walker-Kahan variant of the
QL
or
QR
algorithm.

## API

Syntax
``````namespace oneapi::mkl::lapack {
cl::sycl::event heevd(cl::sycl::queue &queue,
mkl::job jobz,
mkl::uplo uplo,
std::int64_t n,
T *a,
std::int64_t lda,
T *w,
const std::vector<cl::sycl::event> &events = {})
}``````
heevd
(USM version) supports the following precision and devices.
T
Devices Supported
std::complex<float>
Host, CPU, and GPU
std::complex<double>
Host, CPU, and GPU
Input Parameters
queue
Device queue where calculations will be performed.
jobz
Must be
job::novec
or
job::vec
.
If
jobz = job::novec
, then only eigenvalues are computed.
If
jobz = job::vec
, then eigenvalues and eigenvectors are computed.
uplo
Must be
uplo::upper
or
uplo::lower
.
If
upper_lower = job::upper
, a stores the upper triangular part of
A
.
If
upper_lower = job::lower
, a stores the lower triangular part of
A
.
n
The order of the matrix
A
(
0≤n
).
a
The pointer to the array containing
A
, size (
lda,*
). The second dimension of a must be at least
max(1, n)
.
lda
The leading dimension of a. Must be at least
max(1,n)
.
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 heevd_scratchpad_size function.
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
a
If
jobz = job::vec
, then on exit this is overwritten by the orthogonal matrix
Z
which contains the eigenvectors of
A
.
w
Pointer to array of size at least n. Contains the eigenvalues of the matrix
A
in ascending order.
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
, and
jobz = job::novec
, then the algorithm failed to converge;
i
indicates the number of off-diagonal elements of an intermediate tridiagonal form which did not converge to zero.
If
info = i
, and
jobz = job::vec
, then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns
info/(n+1)
through
mod(info,n+1)
.
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.