getrs¶

Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides. This routine belongs to the oneapi::mkl::lapack namespace.

Description ¶

The routine solves for X the following systems of linear equations:

Equation	Condition
`A*X = B`	if `trans`=`mkl::transpose::nontrans`
`AT*X = B`	if `trans`=`mkl::transpose::trans`
`AH*X = B`	if `trans`=`mkl::transpose::conjtrans`

Before calling this routine, you must call getrf to compute the LU factorization of A.

API ¶

Syntax¶

namespace oneapi::mkl::lapack {
  void getrs(cl::sycl::queue &queue,
  mkl::transpose trans,
  std::int64_t n,
  std::int64_t nrhs,
  cl::sycl::buffer<T> &a,
  std::int64_t lda,
  std::int64_t *ipiv,
  cl::sycl::buffer<T> &b,
  std::int64_t ldb,
  cl::sycl::buffer<T> &scratchpad,
  std::int64_t   scratchpad_size)
}

getrs 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.

trans

Indicates the form of the equations:

If trans=mkl::transpose::nontrans, then A*X = B is solved for X.

If trans=mkl::transpose::trans, then AT*X = B is solved for X.

If trans=mkl::transpose::conjtrans, then AH*X = B is solved for X.

n

The order of the matrix A and the number of rows in matrix B(0≤n).

nrhs

The number of right-hand sides (0≤nrhs).

a

Buffer holding the array containing the factorization of the matrix A, as returned by getrf. The second dimension of a must be at least max(1, n).

lda

The leading dimension of a.

ipiv

Array, size at least max(1, n). The ipiv array, as returned by getrf.

b

The array b contains the matrix B whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least max(1,nrhs).

ldb

The leading dimension of b.

scratchpad

Buffer holding 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 should not be less than the value returned by the getrs_scratchpad_size function.

Output Parameters¶

b: The buffer b is overwritten by the solution matrix X.

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`, the `i`-th diagonal element of `U` is zero, and the solve could not be completed. 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 should not be less than the value returned by the detail() method of the exception object.

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, the i-th diagonal element of U is zero, and the solve could not be completed.

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 should not be less than the value returned by the detail() method of the exception object.

Known Limitations¶

For GPU support, errors are reported through the info parameter, but computation does not halt for an algorithmic error.

getri_scratchpad_size getrs (USM Version)

oneAPI Math Kernel Library (oneMKL) documentation