getrf_batch (USM Strided Version)¶

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

Description ¶

The routine computes the LU factorizations of a batch of general m-by-n matrices A_i, as

$A_i = P_i \times L_i \times U_i$

Where P_i is a permutation matrix, L_i is lower triangular with unit diagonal elements (lower trapezoidal if m > n) and U_i is upper triangular (upper trapezoidal if m < n). The routine uses partial pivoting with row interchanges.

API ¶

Syntax¶

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

Function supports the following precisions and devices.

T	Devices supported
`float`	Host, CPU, and GPU
`double`	Host, CPU, and GPU
`std::complex<float>`	Host, CPU, and GPU
`std::complex<double>`	Host, CPU, and GPU

Input Parameters¶

queue: Device queue where calculations will be performed.
m: The number of rows in the matrices A_i (0 ≤ m).
n: The number of columns in the matrices A_i (0 ≤ n).
a: Array holding input matrices A_i.
lda: The leading dimension of A_i .
stride_a: The stride between the beginnings of matrices A_i inside the batch array a.
stride_ipiv: The stride between the beginnings of arrays ipiv_i inside the array ipiv.
batch_size: Specifies the number of problems in a batch.
scratchpad: Scratchpad memory to be used by 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 getrf_batch_scratchpad_size (Strided Version).
events: List of events to wait for before starting computation. Defaults to empty list.

Output Parameters¶

a: Overwritten by L_i and U_i. The unit diagnonal elements of L_i are not stored.
ipiv: Array containing the batch of the pivot indices ipiv_i each of size at least max(1,min(m,n)); for 1 ≤ k ≤ min(m,n), row k of A_i was interchanged with row ipiv_i(k).

Exceptions¶

Exception	Description
`mkl::lapack::batch_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 = -n`, the `n`-th parameter had an illegal value. If `info` equals the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad is of insufficient size, and the required size should be not less then value returned by the detail() method of the exception object. If `info` is zero, then the diagonal element of some of `U`_i is zero, and the solve could not be completed. The indexes of such matrices in the batch can be obtained with the ids() method of the exception object. You can obtain the indexes of the first zero diagonal elements in these `U`_i matrices using the infos() method of the exception object.

Exception

Description

mkl::lapack::batch_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 = -n, the n-th parameter had an illegal value.

If info equals the value passed as scratchpad size, and detail() returns non-zero, then the passed scratchpad is of insufficient size, and the required size should be not less then value returned by the detail() method of the exception object.

If info is zero, then the diagonal element of some of U_i is zero, and the solve could not be completed. The indexes of such matrices in the batch can be obtained with the ids() method of the exception object. You can obtain the indexes of the first zero diagonal elements in these U_i matrices using the infos() method of the exception object.

Return Values¶

Output event to wait on to ensure computation is complete.

getrf_batch (Group Version) getrf_batch_scratchpad_size (Group Version)

oneAPI Math Kernel Library (oneMKL) documentation