orgqr_batch¶
Generates the orthogonal/unitary matrix \(Q_i\) of the QR factorizations for a group of general matrices.
Description
orgqr_batch supports the following precisions.
T
float
double
orgqr_batch (Buffer Version)¶
Description
The buffer version of orgqr_batch supports only the strided API.
Strided API
The routine generates the wholes or parts of \(m \times n\) orthogonal matrices \(Q_i\) of the batch of QR factorizations formed by the Strided API of the geqrf_batch (Buffer Version) function.Usually \(Q_i\) is determined from the QR factorization of an \(m \times p\) matrix \(A_i\) with \(m \ge p\).To compute the whole matrices \(Q_i\), use:orgqr_batch(queue, m, m, p, a, ...)To compute the leading \(p\) columns of \(Q_i\) (which form an orthonormal basis in the space spanned by the columns of \(A_i\)):orgqr_batch(queue, m, p, p, a, ...)To compute the matrices \(Q_i^k\) of the QR factorizations of leading \(k\) columns of the matrices \(A_i\):orgqr_batch(queue, m, m, k, a, ...)To compute the leading \(k\) columns of \(Q_i^k\) (which form an orthonormal basis in the space spanned by leading \(k\) columns of the matrices \(A_i\)):orgqr_batch(queue, m, k, k, a, ...)
Syntax
namespace oneapi::mkl::lapack {
void orgqr_batch(sycl::queue &queue, std::int64_t m, std::int64_t n, std::int64_t k, sycl::buffer<T> &a, std::int64_t lda, std::int64_t stride_a, sycl::buffer<T> &tau, std::int64_t stride_tau, std::int64_t batch_size, sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)
}
Input Parameters
- queue
Device queue where calculations will be performed.
- m
Number of rows in the matrices \(A_i\) (\(0 \le m\)).
- n
Number of columns in the matrices \(A_i\) (\(0 \le n\)).
- k
Number of elementary reflectors whose product defines the matrices \(Q_i\) (\(0 \le k \le n\)).
- a
Array resulting after call to the Strided API of the geqrf_batch (Buffer Version) function.
- lda
Leading dimension of \(A_i\) (\(\text{lda} \le m\)).
- stride_a
The stride between the beginnings of matrices \(A_i\) inside the batch array
a.- tau
Array resulting from call to the Strided API of the geqrf_batch (Buffer Version) function.
- stride_tau
Stride between the beginnings of arrays \(\tau_i\) inside the array
tau.- batch_size
Specifies the number of problems in a batch.
- scratchpad
Scratchpad memory to be used by 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 then the value returned by the Strided API of the orgqr_batch_scratchpad_size function.
Output Parameters
- a
Batch of \(n\) leading columns of the \(m \times m\) orthogonal matrices \(Q_i\).
orgqr_batch (USM Version)¶
Description
The USM version of orgqr_batch supports the group API and strided API.
Group API
The routine generates the wholes or parts of \(m \times n\) orthogonal matrices \(Q_i\) of the batch of QR factorizations formed by the Group API of the onemkl_lapack_geqrf_batch_usm function.Usually \(Q_i\) is determined from the QR factorization of an \(m \times p\) matrix \(A_i\) with \(m \ge p\).To compute the whole matrices \(Q_i\), use:orgqr_batch(queue, m, m, p, a, ...)To compute the leading \(p\) columns of \(Q_i\) (which form an orthonormal basis in the space spanned by the columns of \(A_i\)):orgqr_batch(queue, m, p, p, a, ...)To compute the matrices \(Q_i^k\) of the QR factorizations of leading \(k\) columns of the matrices \(A_i\):orgqr_batch(queue, m, m, k, a, ...)To compute the leading \(k\) columns of \(Q_i^k\) (which form an orthonormal basis in the space spanned by leading \(k\) columns of the matrices \(A_i\)):orgqr_batch(queue, m, k, k, a, ...)
Syntax
namespace oneapi::mkl::lapack {
sycl::event orgqr_batch(sycl::queue &queue, std::int64_t *m, std::int64_t *n, std::int64_t *k, T **a, std::int64_t *lda, T **tau, std::int64_t group_count, std::int64_t *group_sizes, T *scratchpad, std::int64_t scratchpad_size, const std::vector<sycl::event> &events = {})
}
Input Parameters
- queue
Device queue where calculations will be performed.
- m
Array of
group_count\(m_g\) parameters as previously supplied to group version of geqrf_batch function.- n
Array of
group_count\(n_g\) parameters as previously supplied to group version of geqrf_batch function.- k
Array of
group_count\(k_g\) parameters as previously supplied to the Group API of the onemkl_lapack_geqrf_batch_usm function. The number of elementary reflectors whose product defines the matrices \(Q_i\) (\(0 \le k_g \le n_g\)).- a
Array resulting after call to the Group API of the onemkl_lapack_geqrf_batch_usm function.
- lda
Array of leading dimensions of \(A_i\) as previously supplied to the Group API of the onemkl_lapack_geqrf_batch_usm function.
- tau
Array resulting after call to the Group API of the onemkl_lapack_geqrf_batch_usm function.
- group_count
Number of groups of parameters. Must be at least 0.
- group_sizes
Array of
group_countintegers. Array element with index \(g\) specifies the number of problems to solve for each of the groups of parameters \(g\). So the total number of problems to solve,batch_size, is a sum of all parameter group sizes.- scratchpad
Scratchpad memory to be used by 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 then the value returned by Group API of the orgqr_batch_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
\(n_g\) leading columns of the \(m_g \times m_g\) orthogonal matrices \(Q_i\), where \(g\) is an index of group of parameters corresponding to \(Q_i\).
Return Values
Output event to wait on to ensure computation is complete.
Strided API
The routine generates the wholes or parts of \(m \times n\) orthogonal matrices \(Q_i\) of the batch of QR factorizations formed by the Strided API of the onemkl_lapack_geqrf_batch_usm function.Usually \(Q_i\) is determined from the QR factorization of an \(m \times p\) matrix \(A_i\) with \(m \ge p\).To compute the whole matrices \(Q_i\), use:orgqr_batch(queue, m, m, p, a, ...)To compute the leading \(p\) columns of \(Q_i\) (which form an orthonormal basis in the space spanned by the columns of \(A_i\)):orgqr_batch(queue, m, p, p, a, ...)To compute the matrices \(Q_i^k\) of the QR factorizations of leading \(k\) columns of the matrices \(A_i\):orgqr_batch(queue, m, m, k, a, ...)To compute the leading \(k\) columns of \(Q_i^k\) (which form an orthonormal basis in the space spanned by leading \(k\) columns of the matrices \(A_i\)):orgqr_batch(queue, m, k, k, a, ...)
Syntax
namespace oneapi::mkl::lapack {
sycl::event orgqr_batch(sycl::queue &queue, std::int64_t m, std::int64_t n, std::int64_t k, T *a, std::int64_t lda, std::int64_t stride_a, T *tau, std::int64_t stride_tau, std::int64_t batch_size, T *scratchpad, std::int64_t scratchpad_size, const std::vector<sycl::event> &events = {})
};
Input Parameters
- queue
Device queue where calculations will be performed.
- m
Number of rows in the matrices \(A_i\) (\(0 \le m\)).
- n
Number of columns in the matrices \(A_i\) (\(0 \le n\)).
- k
Number of elementary reflectors whose product defines the matrices \(Q_i\) (\(0 \le k \le n\)).
- a
Array resulting after call to the Strided API of the onemkl_lapack_geqrf_batch_usm function.
- lda
Leading dimension of \(A_i\) (\(\text{lda} \le m\)).
- stride_a
The stride between the beginnings of matrices \(A_i\) inside the batch array
a.- tau
Array resulting from call to the Strided API of the onemkl_lapack_geqrf_batch_usm function.
- stride_tau
Stride between the beginnings of arrays \(\tau_i\) inside the array
tau.- batch_size
Specifies the number of problems in a batch.
- scratchpad
Scratchpad memory to be used by 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 then the value returned by the Strided API of the orgqr_batch_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
Batch of \(n\) leading columns of the \(m \times m\) orthogonal matrices \(Q_i\).
Return Values
Output event to wait on to ensure computation is complete.
Parent topic: LAPACK-like Extensions Routines