# getrs_batch#

Solves a system of linear equations with a batch of LU-factored square coefficient matrices, with multiple right-hand sides.

Description

getrs_batch supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## getrs_batch (Buffer Version)#

Description

The buffer version of getrs_batch supports only the strided API.

Strided API

The routine solves for the following systems of linear equations $$X_i$$:
$$A_iX_i = B_i$$, if trans=mkl::transpose::nontrans
$$A_i^TX_i = B_i$$, if trans=mkl::transpose::trans
$$A_i^HX_i = B_i$$, if trans=mkl::transpose::conjtrans
Before calling this routine, the Strided API of the getrf_batch (Buffer Version) function should be called to compute the LU factorizations of $$A_i$$.

Syntax

namespace oneapi::mkl::lapack {
void getrs_batch(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 stride_a, cl::sycl::buffer<std::int64_t> &ipiv, std::int64_t stride_ipiv, cl::sycl::buffer<T> &b, std::int64_t ldb, std::int64_t stride_b, std::int64_t batch_size, cl::sycl::buffer<T> &scratchpad, std::int64_t scratchpad_size)
}


Input Parameters

queue

Device queue where calculations will be performed.

trans
Form of the equations:
If trans = mkl::transpose::nontrans, then $$A_iX_i = B_i$$ is solved for $$Xi$$.
If trans = mkl::transpose::trans, then $$A_i^TX_i = B_i$$ is solved for $$X_i$$.
If trans = mkl::transpose::conjtrans, then $$A_i^HX_i = B_i$$ is solved for $$X_i$$.
n

Order of the matrices $$A_i$$ and the number of rows in matrices $$B_i$$ ($$0 \le n$$).

nrhs

Number of right-hand sides ($$0 \le \text{nrhs}$$).

a

Array containing the factorizations of the matrices $$A_i$$, as returned the Strided API of the getrf_batch (Buffer Version) function.

lda

Leading dimension of $$A_i$$.

stride_a

Stride between the beginnings of matrices $$A_i$$ inside the batch array a.

ipiv

ipiv array, as returned by the Strided API of the getrf_batch (Buffer Version) function.

stride_ipiv

Stride between the beginnings of arrays $$\text{ipiv}_i$$ inside the array ipiv.

b

Array containing the matrices $$B_i$$ whose columns are the right-hand sides for the systems of equations.

ldb

Leading dimension of $$B_i$$.

stride_b

Stride between the beginnings of matrices $$B_i$$ inside the batch array b.

batch_size

Specifies the number of problems in a batch.

Scratchpad memory to be used by routine for storing intermediate results.

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by the Strided API of the getrs_batch_scratchpad_size function.

Output Parameters

b

Solution matrices $$X_i$$.

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::mkl::lapack::batch_error

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

The info code of the problem can be obtained by info() method of exception object:

If info = -n, the $$n$$-th parameter had an illegal value.

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

If info is not zero and detail() returns zero, then there were some errors for some of the problems in the supplied batch and info code contains the number of failed calculations in a batch.

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

## getrs_batch (USM Version)#

Description

The USM version of getrs_batch supports the group API and strided API.

Group API

The routine solves the following systems of linear equations for $$X_i$$ ($$i \in \{1...batch\_size\}$$):
$$A_iX_i = B_i$$, if trans=mkl::transpose::nontrans
$$A_i^TX_i = B_i$$, if trans=mkl::transpose::trans
$$A_i^HX_i = B_i$$, if trans=mkl::transpose::conjtrans
Before calling this routine, call the Group API of the getrf_batch (USM Version) function to compute the LU factorizations of $$A_i$$.
Total number of problems to solve, batch_size, is a sum of sizes of all of the groups of parameters as provided by group_sizes array.

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event getrs_batch(cl::sycl::queue &queue, mkl::transpose *trans, std::int64_t *n, std::int64_t *nrhs, T **a, std::int64_t *lda, std::int64_t **ipiv, T **b, std::int64_t *ldb, std::int64_t group_count, std::int64_t *group_sizes, T *scratchpad, std::int64_t scratchpad_size, const std::vector<cl::sycl::event> &events = {})
}


Input Parameters

queue

Device queue where calculations will be performed.

trans
Array of group_count parameters $$trans_g$$ indicating the form of the equations for the group $$g$$:
If trans = mkl::transpose::nontrans, then $$A_iX_i = B_i$$ is solved for $$X_i$$.
If trans = mkl::transpose::trans, then $$A_i^TX_i = B_i$$ is solved for $$X_i$$.
If trans = mkl::transpose::conjtrans, then $$A_i^HX_i = B_i$$ is solved for $$X_i$$.
n

Array of group_count parameters $$n_g$$ specifying the order of the matrices $$A_i$$ and the number of rows in matrices $$B_i$$ ($$0 \le n_g$$) belonging to group $$g$$.

nrhs

Array of group_count parameters $$\text{nrhs}_g$$ specifying the number of right-hand sides ($$0 \le \text{nrhs}_g$$) for group $$g$$.

a

Array of batch_size pointers to factorizations of the matrices $$A_i$$, as returned by the Group API of the:ref:onemkl_lapack_getrf_batch_usm function.

lda

Array of group_count parameters $$\text{lda}_g$$ specifying the leading dimensions of $$A_i$$ from group $$g$$.

ipiv

ipiv array, as returned by the Group API of the getrf_batch (USM Version) function.

b

The array containing batch_size pointers to the matrices $$B_i$$ whose columns are the right-hand sides for the systems of equations.

ldb

Array of group_count parameters $$\text{ldb}_g$$ specifying the leading dimensions of $$B_i$$ in the 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 memory to be used by routine for storing intermediate results.

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by the Group API of the getrs_batch_scratchpad_size function.

events

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

Output Parameters

b

Solution matrices $$X_i$$.

Return Values

Output event to wait on to ensure computation is complete.

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::mkl::lapack::batch_error

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

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 info = -n, the $$n$$-th parameter had an illegal value.

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

If info is not zero and detail() returns zero, then there were some errors for some of the problems in the supplied batch and info code contains the number of failed calculations in a batch.

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

Strided API

The routine solves the following systems of linear equations for $$X_i$$:
$$A_iX_i = B_i$$, if trans=mkl::transpose::nontrans
$$A_i^TX_i = B_i$$, if trans=mkl::transpose::trans
$$A_i^HX_i = B_i$$, if trans=mkl::transpose::conjtrans
Before calling this routine, the Strided API of the getrf_batch function should be called to compute the LU factorizations of $$A_i$$.

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event getrs_batch(cl::sycl::queue &queue, mkl::transpose trans, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, std::int64_t stride_a, std::int64_t *ipiv, std::int64_t stride_ipiv, T *b, std::int64_t ldb, std::int64_t stride_b, std::int64_t batch_size, T *scratchpad, std::int64_t scratchpad_size, const std::vector<cl::sycl::event> &events = {})
};


Input Parameters

queue

Device queue where calculations will be performed.

trans
Form of the equations:
If trans = mkl::transpose::nontrans, then $$A_iX_i = B_i$$ is solved for $$X_i$$.
If trans = mkl::transpose::trans, then $$A_i^TX_i = B_i$$ is solved for $$X_i$$.
If trans = mkl::transpose::conjtrans, then $$A_i^HX_i = B_i$$ is solved for $$X_i$$.
n

Order of the matrices $$A_i$$ and the number of rows in matrices $$B_i$$ ($$0 \le n$$).

nrhs

Number of right-hand sides ($$0 \le \text{nrhs}$$).

a

Array containing the factorizations of the matrices $$A_i$$, as returned by the Strided API of the:ref:onemkl_lapack_getrf_batch_usm function.

lda

Leading dimension of $$A_i$$.

stride_a

Stride between the beginnings of matrices $$A_i$$ inside the batch array a.

ipiv

ipiv array, as returned by getrf_batch (USM) function.

stride_ipiv

Stride between the beginnings of arrays $$\text{ipiv}_i$$ inside the array ipiv.

b

Array containing the matrices $$B_i$$ whose columns are the right-hand sides for the systems of equations.

ldb

Leading dimensions of $$B_i$$.

stride_b

Stride between the beginnings of matrices $$B_i$$ inside the batch array b.

batch_size

Number of problems in a batch.

Scratchpad memory to be used by routine for storing intermediate results.

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less then the value returned by the Strided API of the getrs_batch_scratchpad_size function.

events

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

Output Parameters

b

Solution matrices $$X_i$$.

Return Values

Output event to wait on to ensure computation is complete.

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::mkl::lapack::batch_error

oneapi::mkl::unimplemented

oneapi::mkl::unsupported_device

oneapi::mkl::lapack::invalid_argument

The info code of the problem can be obtained by info() method of exception object:

If info = -n, the $$n$$-th parameter had an illegal value.

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

If info is not zero and detail() returns zero, then there were some errors for some of the problems in the supplied batch and info code contains the number of failed calculations in a batch.

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

Parent topic: LAPACK-like Extensions Routines