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.

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 cl::sycl::vector_class<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 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.

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.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: LAPACK Linear Equation Routines