orgqr¶
Generates the real orthogonal matrix \(Q\) of the QR factorization formed by geqrf.
Description
orgqr supports the following precisions.
T
float
double
The routine generates the whole or part of \(m \times m\) orthogonal matrix \(Q\) of the QR factorization formed by the routine geqrf.
Usually \(Q\) is determined from the QR factorization of an m
by p matrix \(A\) with \(m \ge p\). To compute the whole matrix
\(Q\), use:
oneapi::mkl::lapack::orgqr(queue, m, m, p, a, lda, tau, scratchpad, scratchpad_size)
To compute the leading \(p\) columns of \(Q\) (which form an orthonormal basis in the space spanned by the columns of \(A\)):
oneapi::mkl::lapack::orgqr(queue, m, p, p, a, lda, tau, scratchpad, scratchpad_size)
To compute the matrix \(Q^{k}\) of the QR factorization of leading \(k\) columns of the matrix \(A\):
oneapi::mkl::lapack::orgqr(queue, m, m, k, a, lda, tau, scratchpad, scratchpad_size)
To compute the leading \(k\) columns of \(Q^{k}\) (which form an orthonormal basis in the space spanned by leading \(k\) columns of the matrix \(A\)):
oneapi::mkl::lapack::orgqr(queue, m, k, k, a, lda, tau, scratchpad, scratchpad_size)
orgqr (Buffer Version)¶
Syntax
namespace oneapi::mkl::lapack {
void orgqr(sycl::queue &queue, std::int64_t m, std::int64_t n, std::int64_t k, sycl::buffer<T,1> &a, std::int64_t lda, sycl::buffer<T,1> &tau, sycl::buffer<T,1> &scratchpad, std::int64_t scratchpad_size)
}
Input Parameters
- queue
The queue where the routine should be executed.
- m
The number of rows in the matrix \(A\) (\(0 \le m\)).
- n
The number of columns in the matrix \(A\) (\(0 \le n\)).
- k
The number of elementary reflectors whose product defines the matrix \(Q\) (\(0 \le k \le n\)).
- a
The buffer
aas returned by geqrf.- lda
The leading dimension of
a(\(\text{lda} \le m\)).- tau
The buffer
tauas returned by geqrf.- 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 orgqr_scratchpad_size function.
Output Parameters
- a
Overwritten by \(n\) leading columns of the \(m \times m\) orthogonal matrix \(Q\).
- scratchpad
Buffer holding scratchpad memory to be used by routine for storing intermediate results.
orgqr (USM Version)¶
Syntax
namespace oneapi::mkl::lapack {
sycl::event orgqr(sycl::queue &queue, std::int64_t m, std::int64_t n, std::int64_t k, T *a, std::int64_t lda, T *tau, T *scratchpad, std::int64_t scratchpad_size, const std::vector<sycl::event> &events = {})
}
Input Parameters
- queue
The queue where the routine should be executed.
- m
The number of rows in the matrix \(A\) (\(0 \le m\)).
- n
The number of columns in the matrix \(A\) (\(0 \le n\)).
- k
The number of elementary reflectors whose product defines the matrix \(Q\) (\(0 \le k \le n\)).
- a
The pointer to
aas returned by geqrf.- lda
The leading dimension of
a(\(\text{lda} \le m\)).- tau
The pointer to
tauas returned by geqrf.- 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 orgqr_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
Overwritten by \(n\) leading columns of the \(m \times m\) orthogonal matrix \(Q\).
- scratchpad
Pointer to scratchpad memory to be used by routine for storing intermediate results.
Return Values
Output event to wait on to ensure computation is complete.
Parent topic: LAPACK Linear Equation Routines