# getri_batch#

Computes the inverses of a batch of LU-factored matrices determined by getrf_batch.

Description

getri_batch supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

## getri_batch (Buffer Version)#

Description

The buffer version of getri_batch supports only the strided API.

Strided API

The routine computes the inverses $$A_i^{-1}$$ of general matrices $$A_i$$. Before calling this routine, call the Strided API of the getrf_batch (Buffer Version) function to factorize $$A_i$$.

Syntax

namespace oneapi::mkl::lapack {
void getri_batch(cl::sycl::queue &queue, std::int64_t n, 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, 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.

n

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

a

Result of the Strided API of the getrf_batch (Buffer Version) function.

lda

Leading dimension of $$A_i$$ ($$n\le \text{lda}$$).

stride_a

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

ipiv

Arrays 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.

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 than the value returned by the Strided API of the getri_batch_scratchpad_size function.

Output Parameters

a

Inverse $$n \times n$$ matrices $$A_i^{-1}$$.

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.

## getri_batch (USM Version)#

Description

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

Group API

The routine computes the inverses $$A_i^{-1}$$ of general matrices $$A_i$$, $$i \in \{1...batch\_size\}$$. Before calling this routine, call the Group API of the getrf_batch (USM Version) function to factorize $$A_i$$. 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 getri_batch(cl::sycl::queue &queue, 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 std::vector<cl::sycl::event> &events = {})
}


Input Parameters

queue

Device queue where calculations will be performed.

n

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

a

Result of the Group API of the getrf_batch (USM Version) function.

lda

Array of group_count $$\text{lda}_g$$ parameters specifying the leading dimensions of the matrices $$A_i$$ ($$n_g \le \text{lda}_g$$) belonging to group $$g$$.

ipiv

Arrays returned by the Group API of the getrf_batch (USM Version) function.

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 than the value returned by the Group API of the getri_batch_scratchpad_size function.

events

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

Output Parameters

a

Inverse $$n_g \times n_g$$ matrices $$A_i^{-1}$$.

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.

Strided API

The routine computes the inverses $$A_i^{-1}$$ of general matrices $$A_i$$. Before calling this routine, call the Strided API of the getrf_batch (USM Version) function to factorize $$A_i$$.

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event getri_batch(cl::sycl::queue &queue, std::int64_t n, T *a, std::int64_t lda, std::int64_t stride_a, std::int64_t *ipiv, std::int64_t stride_ipiv, 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.

n

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

a

Result of the Strided API of the getrf_batch (USM Version) function.

lda

Leading dimension of $$A_i$$ ($$n \le \text{lda}$$).

stride_a

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

ipiv

Arrays returned by the Strided API of the getrf_batch (USM Version) function.

stride_ipiv

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

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 than the value returned by the Strided API of the getri_batch_scratchpad_size function.

events

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

Output Parameters

a

Inverse $$n \times n$$ matrices $$A_i^{-1}$$.

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.

Parent topic: LAPACK-like Extensions Routines