# potrf_batch¶

Computes the LU factorizations of a batch of general matrices.

Description

potrf_batch supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## potrf_batch (Buffer Version)¶

Description

The buffer version of potrf_batch supports only the strided API.

Strided API

The routine forms the Cholesky factorizations of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices $$A_i$$, $$i \in \{1...batch\_size\}$$:
$$A_i = U_i^TU_i$$ 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.

Syntax

namespace oneapi::mkl::lapack {
void potrf_batch(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, cl::sycl::buffer<T> &a, std::int64_t lda, std::int64_t stride_a, 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 whether the upper or lower triangular part of $$A_i$$ is stored and how $$A_i$$ is factored:
If uplo = mkl::uplo::upper, the array a stores the upper triangular parts of the matrices $$A_i$$,
If uplo = mkl::uplo::lower, the array a stores the lower triangular parts of the matrices $$A_i$$.
n

Order of the matrices $$A_i$$, ($$0 \le n$$).

a

Array containing batch of input matrices $$A_i$$, each of $$A_i$$ being of size $$\text{lda} \cdot n$$ and holding either upper or lower triangular parts of the matrices $$A_i$$ (see uplo).

lda

Leading dimension of $$A_i$$.

stride_a

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

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 potrf_batch_scratchpad_size function.

Output Parameters

a

Cholesky factors $$U_i$$ or $$L_i$$, as specified by uplo.

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 the leading minors of some of matrices (and therefore some matrices $$A_i$$ themselves) are not positive-definite, and the factorizations could not be completed for these matrices from the batch. The indices of such matrices in the batch can be obtained with ids() method of the exception object. The orders of corresponding not positive-definite leading minors of these matrices can be obtained by exceptions() method of exception object.

## potrf_batch (USM Version)¶

Description

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

Group API

The routine forms the Cholesky factorizations of symmetric positive-definite or, for complex data, Hermitian positive-definite matrices $$A_i$$, $$i \in \{1...batch\_size\}$$:
$$A_i = U_i^TU_i$$ for real data ($$A_i = U_i^HU_i$$ for complex), if $$\text{uplo}_g$$ is mkl::uplo::upper,
$$A_i = L_iL_i^T$$ for real data ($$A_i = L_iL_i^H$$ for complex), if $$\text{uplo}_g$$ is mkl::uplo::lower,
where $$L_i$$ is a lower triangular matrix and $$U_i$$ is upper triangular, $$g$$ is an index of group of parameters corresponding to $$A_i$$, and 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 potrf_batch(cl::sycl::queue &queue, mkl::uplo *uplo, std::int64_t *n, T **a, std::int64_t *lda, 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 $$\text{uplo}_g$$ 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 $$g$$.

a

Array of batch_size pointers to input matrices $$A_i$$, each being of size $$\text{lda}_g \cdot n_g$$ ($$g$$ is an index of group to which $$A_i$$ belongs to) and holding either upper or lower triangular part as specified by $$\text{uplo}_g$$.

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 $$g$$.

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 potrf_batch_scratchpad_size function.

events

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

Output Parameters

a

Cholesky factors $$U_i$$ or $$L_i$$, as specified by $$\text{uplo}_g$$ from corresponding group of parameters.

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 the leading minors of some of the input matrices (and therefore some matrices themselves) are not positive-definite, and the factorizations could not be completed for these matrices from the batch. The indices of such matrices in the batch can be obtained with ids() method of the exception object. The orders of corresponding not positive-definite leading minors of these matrices can be obtained by exceptions() method of the exception object.

Strided API

The routine forms the Cholesky factorizations of a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices $$A_i$$, $$i \in \{1...batch\_size\}$$:
$$A_i = U_i^TU_i$$ 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.

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event potrf_batch(cl::sycl::queue &queue, mkl::uplo uplo, std::int64_t n, T *a, std::int64_t lda, std::int64_t stride_a, 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 whether the upper or lower triangular part of $$A_i$$ is stored and how $$A_i$$ is factored:
If uplo = mkl::uplo::upper, the array a stores the upper triangular parts of the matrices $$A_i$$,
If uplo = mkl::uplo::lower, the array a stores the lower triangular parts of the matrices $$A_i$$.
n

Order of the matrices $$A_i$$, ($$0 \le n$$).

a

Array containing batch of input matrices $$A_i$$, each of $$A_i$$ being of size $$\text{lda} \cdot n$$ and holding either upper or lower triangular parts of the matrices $$A_i$$ (see uplo).

lda

Leading dimension of $$A_i$$.

stride_a

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

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 potrf_batch_scratchpad_size function.

events

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

Output Parameters

a

Cholesky factors $$U_i$$ or $$L_i$$, as specified by uplo.

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 the leading minors of some of matrices (and therefore some matrices $$A_i$$ themselves) are not positive-definite, and the factorizations could not be completed for these matrices from the batch. The indices of such matrices in the batch can be obtained with ids() method of the exception object. The orders of corresponding not positive-definite leading minors of these matrices can be obtained by exceptions() method of exception object.

Parent topic: LAPACK-like Extensions Routines