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>

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::math::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::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

oneapi::math::unsupported_device

oneapi::math::lapack::invalid_argument

oneapi::math::lapack::computation_error

Exception is thrown in case of problems during calculations. The info code 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)#