getrf (USM Version)#

Computes the LU factorization of a general m-by-n matrix. This routine belongs to the oneapi::mkl::lapack namespace.

Description#

The routine computes the LU factorization of a general m-by-n matrix A as

\[A = P*L*U,\]

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.

API#

Syntax#

namespace oneapi::mkl::lapack {
  sycl::event getrf(sycl::queue &queue,
  int64_t m,
  int64_t n,
  T *a,
  int64_t lda,
  int64_t *ipiv,
  T *scratchpad,
  int64_t scratchpad_size,
  const std::vector<sycl::event> &events = {})
}

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

T

Devices supported

float

CPU, GPU*

double

CPU, GPU*

std::complex<float>

CPU, GPU*

std::complex<double>

CPU, GPU*

*Hybrid support; some computations are performed on the CPU.

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).

a

Pointer to the array holding input matrix A. The array must be of size at least lda * max(1, n).

lda

The leading dimension of a (ldamax(1, m)).

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 must not be less than the value returned by the 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 i min(m,n), row i was interchanged with row ipiv(i).

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, uii 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 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 must 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.