Contents

# sygvd (USM Version)

Computes all eigenvalues and, optionally, eigenvectors of a real generalized symmetric definite eigenproblem using a divide and conquer method. This routine belongs to the
oneapi::mkl::lapack
namespace.

## Description

The routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form
A*x = λ*B*x
,
A*B*x = λ*x
, or
B*A*x = λ*x
.
Here
A
and
B
are assumed to be symmetric and
B
is also positive definite.
It uses a divide and conquer algorithm.

## API

Syntax
``````namespace oneapi::mkl::lapack {
cl::sycl::event sygvd(cl::sycl::queue &queue,
std::int64_t itype,
mkl::job jobz,
mkl::uplo uplo,
std::int64_t n,
T *a,
std::int64_t lda,
T *b,
std::int64_t ldb,
T *w,
const std::vector<cl::sycl::event> &events = {})
}``````
hegvd
(USM version) supports the following precision and devices.
T
Devices Supported
float
Host, CPU, GPU
double
Host, CPU, GPU
Input Parameters
queue
Device queue where calculations will be performed.
itype
Must be 1 or 2 or 3. Specifies the problem type to be solved:
if itype
= 1
, the problem type is
A*x = lambda*B*x;
if itype
= 2
, the problem type is
A*B*x = lambda*x;
if itype
= 3
, the problem type is
B*A*x = lambda*x
.
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
uplo = uplo::upper
, a and b store the upper triangular part of
A
and
B
.
If
uplo = uplo::lower
, a and b stores the lower triangular part of
A
and
B
.
n
The order of the matrices
A
and
B
(
0≤n
).
a
Pointer to the array of size
a(lda,*)
containing the upper or lower triangle of the symmetric matrix
A
, as specified by uplo.
The second dimension of a must be at least
max(1, n)
.
lda
The leading dimension of a; at least
max(1,n)
.
b
Pointer to the array of size
b(ldb,*)
containing the upper or lower triangle of the symmetric matrix
B
, as specified by uplo.
The second dimension of b must be at least
max(1, n)
.
ldb
The leading dimension of b; 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 sygvd_scratchpad_size function.
events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
a
On exit, if
jobz = job::vec
, then if
info = 0
, a contains the matrix
Z
of eigenvectors. The eigenvectors are normalized as follows:
if itype
= 1
or
2
,
Z
T
*B*Z = I
;
if itype
= 3
,
Z
T
*
inv(B)*Z = I
;
If
jobz = job::novec
, then on exit the upper triangle (if
uplo = uplo::upper
) or the lower triangle (if
uplo = uplo::lower
) of
A
, including the diagonal, is destroyed.
b
On exit, if
info≤n
, the part of b containing the matrix is overwritten by the triangular factor
U
or
L
from the Cholesky factorization
B = U
T
*U
or
B
=
L
*
L
T
.
w
Pointer to the array of size at least n. If
info = 0
, contains the eigenvalues of the matrix
A
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. For
info ≤ n
: 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)
. For
info > n
: If
info = n + i
, for
1 ≤ i ≤ n
, then the leading minor of order
i
of
B
is not positive-definite. The factorization of
B
could not be completed and no eigenvalues or eigenvectors were computed.
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.