gerqf#
Computes the RQ factorization of a general \(m \times n\) matrix.
Description
gerqf supports the following precisions.
T
float
double
std::complex<float>
std::complex<double>
The routine forms the RQ factorization of a general \(m \times n\) matrix \(A\). No pivoting is performed. The routine does not form the matrix \(Q\) explicitly. Instead, \(Q\) is represented as a product of \(\min(m, n)\) elementary reflectors. Routines are provided to work with \(Q\) in this representation
gerqf (Buffer Version)#
Syntax
namespace oneapi::mkl::lapack {
void gerqf(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, cl::sycl::buffer<T> &tau, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)
}
Input Parameters
- queue
Device queue where calculations will be performed.
- m
The number of rows in the matrix \(A\) (\(0 \le m\)).
- n
The number of columns in the matrix \(A\) (\(0 \le n\)).
- a
Buffer holding input matrix \(A\). The second dimension of
amust be at least \(\max(1, n)\).- lda
The leading dimension of
a, at least \(\max(1, m)\).- 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 gerqf_scratchpad_size function.
Output Parameters
- a
Output buffer, overwritten by the factorization data as follows:
If \(m \le n\), the upper triangle of the subarray
a(1:m, n-m+1:n)contains the \(m \times m\) upper triangular matrix \(R\); if \(m \ge n\), the elements on and above the \((m-n)\)-th subdiagonal contain the \(m \times n\) upper trapezoidal matrix \(R\)In both cases, the remaining elements, with the array
tau, represent the orthogonal/unitary matrix \(Q\) as a product of \(\min(m,n)\) elementary reflectors.- tau
Array, size at least \(\min(m,n)\).
Contains scalars that define elementary reflectors for the matrix \(Q\) in its decomposition in a product of elementary reflectors.
Throws
This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.
oneapi::mkl::unsupported_device
oneapi::mkl::lapack::invalid_argument
oneapi::mkl::lapack::computation_error
Exception is thrown in case of problems during calculations. The
infocode of the problem can be obtained by info() method of exception object:If
info = -i, the \(i\)-th parameter had an illegal value.If
infoequals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object.
gerqf (USM Version)#
Syntax
namespace oneapi::mkl::lapack {
cl::sycl::event gerqf(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, T *tau, T *scratchpad, std::int64_t scratchpad_size, const std::vector<cl::sycl::event> &events = {})
}
Input Parameters
- queue
Device queue where calculations will be performed.
- m
The number of rows in the matrix \(A\) (\(0 \le m\)).
- n
The number of columns in the matrix \(A\) (\(0 \le n\)).
- a
Buffer holding input matrix \(A\). The second dimension of
amust be at least \(\max(1, n)\).- lda
The leading dimension of
a, at least \(\max(1, m)\).- 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 gerqf_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
Output buffer, overwritten by the factorization data as follows:
If \(m \le n\), the upper triangle of the subarray
a(1:m, n-m+1:n)contains the \(m \times m\) upper triangular matrix \(R\); if \(m \ge n\), the elements on and above the \((m-n)\)-th subdiagonal contain the \(m \times n\) upper trapezoidal matrix \(R\)In both cases, the remaining elements, with the array
tau, represent the orthogonal/unitary matrix \(Q\) as a product of \(\min(m,n)\) elementary reflectors.- tau
Array, size at least \(\min(m,n)\).
Contains scalars that define elementary reflectors for the matrix \(Q\) in its decomposition in a product of elementary reflectors.
Throws
This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.
oneapi::mkl::unsupported_device
oneapi::mkl::lapack::invalid_argument
oneapi::mkl::lapack::computation_error
Exception is thrown in case of problems during calculations. The
infocode of the problem can be obtained by info() method of exception object:If
info = -i, the \(i\)-th parameter had an illegal value.If
infoequals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object.
Return Values
Output event to wait on to ensure computation is complete.
Parent topic: LAPACK Linear Equation Routines