getrf¶
Computes the LU factorization of a general \(m \times n\) matrix.
Description
getrf supports the following precisions.
T
float
double
std::complex<float>
std::complex<double>
The routine computes the LU factorization of a general \(m \times n\) matrix \(A\) as \(A = PLU\),
where \(P\) is a permutation matrix, \(L\) is lower triangular with unit diagonal elements (lower trapezoidal if \(m > n\)) and \(U\) is upper triangular (upper trapezoidal if \(m < n\)). The routine uses partial pivoting, with row interchanges.
getrf (BUFFER Version)¶
Syntax
namespace oneapi::mkl::lapack {
void getrf(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, cl::sycl::buffer<T,1> &a, std::int64_t lda, cl::sycl::buffer<std::int64_t,1> &ipiv, cl::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 \(A\) (\(0 \le n\)).
- a
Buffer holding input matrix \(A\). The buffer a contains the matrix \(A\). The second dimension of a must be at least \(\max(1, n)\).
- lda
The leading dimension of
a.- 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 getrf_scratchpad_size function.
Output Parameters
- a
Overwritten by \(L\) and \(U\). The unit diagonal elements of \(L\) are not stored.
- ipiv
Array, size at least \(\max(1,\min(m, n))\). Contains the pivot indices; for \(1 \le i \le \min(m, n)\), row \(i\) was interchanged with row \(\text{ipiv}(i)\).
- scratchpad
Buffer holding scratchpad memory to be used by routine for storing intermediate results.
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 \(\text{info}=-i\), the \(i\)-th parameter had an illegal value.
If \(\text{info}=i\), \(u_{ii}\) is 0. The factorization has been completed, but \(U\) is exactly singular. Division by 0 will occur if you use the factor \(U\) for solving a system of linear equations.
If \(\text{info}\) equals 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.
getrf (USM Version)¶
Syntax
namespace oneapi::mkl::lapack {
cl::sycl::event getrf(cl::sycl::queue &queue, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, std::int64_t *ipiv, T *scratchpad, std::int64_t scratchpad_size, const std::vector<cl::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 \(A\) (\(0 \le n\)).
- a
Pointer to array holding input matrix \(A\). The second dimension of
amust be at least \(\max(1, n)\).- lda
The leading dimension of
a.- 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 getrf_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
Overwritten by \(L\) and \(U\). The unit diagonal elements of \(L\) are not stored.
- ipiv
Array, size at least \(\max(1,\min(m, n))\). Contains the pivot indices; for \(1 \le i \le \min(m, n)\), row \(i\) was interchanged with row \(\text{ipiv}(i)\).
- scratchpad
Pointer to scratchpad memory to be used by routine for storing intermediate results.
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 \(\text{info}=-i\), the \(i\)-th parameter had an illegal value.
If \(\text{info}=i\), \(u_{ii}\) is 0. The factorization has been completed, but \(U\) is exactly singular. Division by 0 will occur if you use the factor \(U\) for solving a system of linear equations.
If \(\text{info}\) equals 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