getrf_batch (Group Version)

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

Syntax

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 **ipiv, std::int64_t group_count, std::int64_t *group_sizes, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<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

Description

The routine computes the LU factorizations of a batch of general m-by-n matrices Ai, (iϵ{1...batch_size}) as

image0

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

Total number of problems to solve, batch_size, is a sum of sizes of all of the groups of parameters as provided by group_sizesarray.

Input Parameters

queue

Device queue where calculations will be performed.

m

Array of group_count parameters mg specifying the number of rows in the matrices Ai (0 mg) belonging to group g.

n

Array of group_count parameters ng specifying the number of columns in the matrices Ai (0 ng) belonging to group g.

a

Array of batch_size pointers to input matricesAi.

lda

Array of group_count parameters ldag specifying the leading dimension of Ai belonging to group g.

group_count

Specifies the number of groups of parameters. Must be at least 0.

group_sizes

Array of group_count integers. Array element with index g specifies the number of problems to solve for each of the groups of parameters g. So the total number of problems to solve, batch_size, is a sum of all parameter group sizes.

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 then the value returned by getrf_batch_scratchpad_size.

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

a

Matrices pointed to by array a are overwritten by Li and Ui. The unit diagnonal elements of Li are not stored.

ipiv

Arrays of batch_size pointers to arrays containing pivot indices ipivi each of size at least max(1,min(mg,ng)); for 1 ≤ kmin(mg,ng), row k of Ai was interchanged with row ipivi(k).

Exceptions

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 Ui 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 Ui matrices using the infos() method of the exception object.

Return Values

Output event to wait on to ensure computation is complete.