sytrd#
Reduces a real symmetric matrix to tridiagonal form. This routine
belongs to the oneapi::mkl::lapack namespace.
Description#
The routine reduces a real symmetric matrix A to symmetric
tridiagonal form T by an orthogonal similarity transformation:
A = Q*T*QT. The orthogonal matrix Q is not formed explicitly
but is represented as a product of n-1 elementary reflectors.
Routines are provided for working with Q in this representation .
API#
Syntax#
namespace oneapi::mkl::lapack {
void sytrd(sycl::queue &queue,
mkl::uplo uplo,
int64_t n,
sycl::buffer<T> &a,
int64_t lda,
sycl::buffer<T> &d,
sycl::buffer<T> &e,
sycl::buffer<T> &tau,
sycl::buffer<T> &scratchpad,
int64_t scratchpad_size)
}
sytrd supports the following precisions and devices:
T |
Devices supported |
|---|---|
|
CPU and GPU* |
|
CPU and GPU* |
*Interface support only; all computations are performed on the CPU.
Input Parameters#
- queue
Device queue where calculations will be performed.
- uplo
Must be
uplo::upperoruplo::lower.If
uplo = uplo::upper,astores the upper triangular part ofA.If
uplo = uplo::lower,astores the lower triangular part ofA.- n
The order of the matrices
A(0 ≤ n).- a
Buffer holding 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 sytrd_scratchpad_size function.
Output Parameters#
- a
On exit,
if
uplo = uplo::upper, the diagonal and first superdiagonal ofAare overwritten by the corresponding elements of the tridiagonal matrixT, and the elements above the first superdiagonal, with the buffer tau, represent the orthogonal matrixQas a product of elementary reflectors;if
uplo = uplo::lower, the diagonal and first subdiagonal ofAare overwritten by the corresponding elements of the tridiagonal matrixT, and the elements below the first subdiagonal, with the buffer tau, represent the orthogonal matrixQas a product of elementary reflectors.- d
Buffer holding the diagonal elements of the matrix
T. The dimension of d must be at leastmax(1, n).- e
Buffer holding the off diagonal elements of the matrix
T. The dimension of e must be at leastmax(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 matrixQin a product ofn-1elementary reflectors. tau(n)is used as workspace.
Exceptions#
Exception |
Description |
|---|---|
|
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 If |