# potrs_batch¶

Computes the LU factorizations of a batch of general matrices.

Description

potrs_batch supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## potrs_batch (Buffer Version)¶

Description

The buffer version of potrs_batch supports only the strided API.

Strided API

The routine solves for $$X_i$$ the systems of linear equations $$A_iX_i = B_i$$ with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices $$A_i$$, given the Cholesky factorization of $$A_i$$, $$i \in \{1...batch\_size\}$$:
$$A_i = U_i^TU_i$$ for real data, $$A_i = U_i^HU_i$$ for complex data if uplo = mkl::uplo::upper,
$$A_i = L_iL_i^T$$ for real data, $$A_i = L_iL_i^H$$ for complex data if uplo = mkl::uplo::lower,
where $$L_i$$ is a lower triangular matrix and $$U_i$$ is upper triangular.
The systems are solved with multiple right-hand sides stored in the columns of the matrices $$B_i$$.
Before calling this routine, matrices $$A_i$$ should be factorized by call to the Strided API of the potrf_batch (Buffer Version) function.

Syntax

namespace oneapi::mkl::lapack {
void potrs_batch(cl::sycl::queue &queue, mkl::uplo uplo, 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<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.

uplo
Indicates how the input matrices have been factored:
If uplo = mkl::uplo::upper, the upper triangle $$U_i$$ of $$A_i$$ is stored, where $$A_i = U_i^TU_i$$ for real data, $$A_i = U_i^HU_i$$ for complex data.
If uplo = mkl::uplo::lower, the upper triangle $$L_i$$ of $$A_i$$ is stored, where $$A_i = L_iL_i^T$$ for real data, $$A_i = L_iL_i^H$$ for complex data.
n

The order of matrices $$A_i$$ ($$0 \le n$$).

nrhs

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

a

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

lda

Leading dimension of $$A_i$$.

stride_a

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

b

Array containing batch of 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

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 potrs_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 for some of the matrices diagonal element of the Cholesky factor 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 matrices can be obtained by exceptions() method of exception object.

## potrs_batch (USM Version)¶

Description

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

Group API

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event potrs_batch(cl::sycl::queue &queue, mkl::uplo *uplo, std::int64_t *n, std::int64_t *nrhs, T **a, std::int64_t *lda, 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.

uplo
Array of group_count $$\text{uplo}_g$$ parameters.
Each of $$\text{uplo}_g$$ indicates whether the upper or lower triangular parts of the input matrices are provided:
If $$\text{uplo}_g$$ is mkl::uplo::upper, input matrices from array a belonging to group $$g$$ store the upper triangular parts,
If $$\text{uplo}_g$$ is mkl::uplo::lower, input matrices from array a belonging to group $$g$$ store the lower triangular parts.
n
Array of group_count $$n_g$$ parameters.
Each $$n_g$$ specifies the order of the input matrices from array a belonging to group $$g$$.
nrhs
Array of group_count $$\text{nrhs}_g$$ parameters.
Each $$\text{nrhs}_g$$ specifies the number of right-hand sides supplied for group $$g$$ in corresponding part of array b.
a

Array of batch_size pointers to Cholesky factored matrices $$A_i$$ as returned by the Group API of the potrf_batch (USM Version) function.

lda
Array of group_count $$\text{lda}_g$$ parameters.
Each $$\text{lda}_g$$ specifies the leading dimensions of the matrices from a belonging to group $$g$$.
b

Array of batch_size pointers to right-hand side matrices $$B_i$$, each of size $$\text{ldb}_g \cdot \text{nrhs}_g$$, where $$g$$ is an index of group corresponding to $$B_i$$.

ldb
Array of group_count $$\text{ldb}_g$$ parameters.
Each $$\text{ldb}_g$$ specifies the leading dimensions of the matrices from b belonging to group $$g$$.
group_count

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 potrs_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 for some of the matrices diagonal element of the Cholesky factor 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 matrices can be obtained by exceptions() method of exception object.

Strided API

The routine solves for $$X_i$$ the systems of linear equations $$A_iX_i = B_i$$ with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices $$A_i$$, given the Cholesky factorization of $$A_i$$, $$i \in \{1...batch\_size\}$$:
$$A_i = U_i^TU_i$$ for real data, $$A_i = U_i^HU_i$$ for complex data if uplo = mkl::uplo::upper,
$$A_i = L_iL_i^T$$ for real data, $$A_i = L_iL_i^H$$ for complex data if uplo = mkl::uplo::lower,
where $$L_i$$ is a lower triangular matrix and $$U_i$$ is upper triangular.
The systems are solved with multiple right-hand sides stored in the columns of the matrices $$B_i$$.
Before calling this routine, matrices $$A_i$$ should be factorized by call to the Strided API of the potrf_batch (USM Version) function.

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event potrs_batch(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, std::int64_t stride_a, 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.

uplo
Indicates how the input matrices have been factored:
If uplo = mkl::uplo::upper, the upper triangle $$U_i$$ of $$A_i$$ is stored, where $$A_i = U_i^TU_i$$ for real data, $$A_i = U_i^HU_i$$ for complex data.
If uplo = mkl::uplo::lower, the upper triangle $$L_i$$ of $$A_i$$ is stored, where $$A_i = L_iL_i^T$$ for real data, $$A_i = L_iL_i^H$$ for complex data.
n

The order of matrices $$A_i$$ ($$0 \le n$$).

nrhs

The number of right-hand sides ($$0 \le nrhs$$).

a

Array containing batch of factorizations of the matrices $$A_i$$, as returned by the Strided API of the potrf_batch (USM Version) function.

lda

Leading dimension of $$A_i$$.

stride_a

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

b

Array containing batch of 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

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 potrs_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 for some of the matrices diagonal element of the Cholesky factor 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 matrices can be obtained by exceptions() method of exception object.

Parent topic: LAPACK-like Extensions Routines