orgqr (USM Version)¶

Generates the real orthogonal matrix Q of the QR factorization formed by the geqrf (USM Version) function. This routine belongs to the oneapi::mkl::lapack namespace.

Description ¶

The routine generates the whole or part of m-by-m orthogonal matrix Q of the QR factorization formed by the routine geqrf (USM Version) :ref:`geqrf-usm-version function.

Usually Q is determined from the QR factorization of an m by p matrix A with m≥p. To compute the whole matrix Q, use:

mkl::orgqr(queue, m, m, p, a, lda, tau, ...)

To compute the leading p columns of Q (which form an orthonormal basis in the space spanned by the columns of A):

mkl::orgqr(queue, m, p, p, a, lda, tau, ...)

To compute the matrix Q^k of the QR factorization of leading k columns of the matrix A:

mkl::orgqr(queue, m, m, k, a, lda, tau, ...)

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):

mkl::orgqr(queue, m, k, k, a, lda, tau, ...)

API ¶

Syntax¶

namespace oneapi::mkl::lapack {
  cl::sycl::event orgqr(cl::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<cl::sycl::event> &events = {})
}

orgqr (USM version) supports the following precisions and devices:

T	Devices supported
`float`	Host, CPU, and GPU
`double`	Host, CPU, and GPU

Input Parameters¶

queue: Device queue where calculations will be performed.
m: The number of rows in the matrix A (0≤m).
n: The number of columns in the matrix A (0≤n).
k: The number of elementary reflectors whose product defines the matrix Q (0≤k≤n).
a: Pointer to the result of geqrf (USM Version).
lda: The leading dimension of a (lda≤m).
tau: Pointer to the result of geqrf (USM Version).
scratchpad: Pointer to 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 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-by-m orthogonal matrix Q.

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`, d_ii is 0. The factorization has been completed, but `D` is exactly singular. Division by 0 will occur if you use `D` for solving a system of linear equations. 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.

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, d_ii is 0. The factorization has been completed, but D is exactly singular. Division by 0 will occur if you use D for solving a system of linear equations.

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

orgqr orgqr_batch (Buffer Strided Version)

oneAPI Math Kernel Library (oneMKL) documentation