getrf_batch

Computes the LU factorizations of a batch of general matrices.

Description

getrf_batch supports the following precisions.

T
float
double
std::complex<float>
std::complex<double>

getrf_batch (Buffer Version)

Description

The buffer version of getrf_batch supports only the strided API.

Strided API

The routine computes the LU factorizations of general \(m \times n\) matrices \(A_i\) as \(A_i = P_iL_iU_i\), where \(P_i\) is a permutation matrix, \(L_i\) is lower triangular with unit diagonal elements (lower trapezoidal if \(m > n\)) and \(U_i\) is upper triangular (upper trapezoidal if \(m < n\)). The routine uses partial pivoting, with row interchanges.

Syntax

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

m

Number of rows in matrices \(A_i\) (\(0 \le m\)).

n

Number of columns in matrices \(A_i\) (\(0 \le n\)).

a

Array holding input matrices \(A_i\).

lda

Leading dimension of matrices \(A_i\).

stride_a

Stride between the beginnings of matrices \(A_i\) inside the batch array a.

stride_ipiv

Stride between the beginnings of arrays \(ipiv_i\) inside the array ipiv.

batch_size

Number of problems in a batch.

scratchpad

Scratchpad memory to be used by 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 Strided API of the getrf_batch_scratchpad_size function.

Output Parameters

a

\(L_i\) and \(U_i\). The unit diagonal elements of \(L_i\) are not stored.

ipiv

Array containing batch of the pivot indices \(\text{ipiv}_i\) each of size at least \(\max(1,\min(m,n))\); for \(1 \le k \le \min(m,n)\), where row \(k\) of \(A_i\) was interchanged with row \(\text{ipiv}_i(k)\).

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 positive, then the factorization has been completed, but some of \(U_i\) are exactly singular. Division by 0 will occur if you use the factor \(U_i\) for solving a system of linear equations.

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.

getrf_batch (USM Version)

Description

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

Group API

The routine computes the batch of LU factorizations of general \(m \times n\) matrices \(A_i\) (\(i \in \{1...batch\_size\}\)) as \(A_i = P_iL_iU_i\), where \(P_i\) is a permutation matrix, \(L_i\) is lower triangular with unit diagonal elements (lower trapezoidal if \(m > n\)) and \(U_i\) is upper triangular (upper trapezoidal if \(m < n\)). The routine uses partial pivoting, with row interchanges. 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 getrf_batch(cl::sycl::queue &queue, std::int64_t *m, 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.

m

Array of group_count parameters \(m_g\) specifying the number of rows in matrices \(A_i\) (\(0 \le m_g\)) belonging to group \(g\).

n

Array of group_count parameters \(n_g\) specifying the number of columns in matrices \(A_i\) (\(0 \le n_g\)) belonging to group \(g\).

a

Array holding batch_size pointers to input matrices \(A_i\).

lda

Array of group_count parameters \(lda_g\) specifying the leading dimensions of \(A_i\) 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

Scratchpad memory to be used by 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 then the value returned by the Group API of the getrf_batch_scratchpad_size function.

events

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

Output Parameters

a

\(L_i\) and \(U_i\). The unit diagonal elements of \(L_i\) are not stored.

ipiv

Arrays of batch_size pointers to arrays containing pivot indices \(\text{ipiv}_i\) each of size at least \(\max(1,\min(m_g,n_g))\); for \(1 \le k \le \min(m_g,n_g)\), where row \(k\) of \(A_i\) was interchanged with row \(\text{ipiv}_i(k)\).

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 positive, then the factorization has been completed, but some of \(U_i\) are exactly singular. Division by 0 will occur if you use the factor \(U_i\) for solving a system of linear equations.

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 computes the LU factorizations of general \(m \times n\) matrices \(A_i\) as \(A_i = P_iL_iU_i\), where \(P_i\) is a permutation matrix, \(L_i\) is lower triangular with unit diagonal elements (lower trapezoidal if \(m > n\)) and \(U_i\) is upper triangular (upper trapezoidal if \(m < n\)). The routine uses partial pivoting, with row interchanges.

Syntax

namespace oneapi::mkl::lapack {
  cl::sycl::event getrf_batch(cl::sycl::queue &queue, std::int64_t m, 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.

m

Number of rows in matrices \(A_i\) (\(0 \le m\)).

n

Number of columns in matrices \(A_i\) (\(0 \le n\)).

a

Array holding input matrices \(A_i\).

lda

Leading dimension of matrices \(A_i\).

stride_a

Stride between the beginnings of matrices \(A_i\) inside the batch array a.

stride_ipiv

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

batch_size

Number of problems in a batch.

scratchpad

Scratchpad memory to be used by 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 then the value returned by the Strided API of the getrf_batch_scratchpad_size function.

events

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

Output Parameters

a

\(L_i\) and \(U_i\). The unit diagonal elements of \(L_i\) are not stored.

ipiv

Array containing batch of the pivot indices \(\text{ipiv}_i\) each of size at least \(\max(1,\min(m,n))\); for \(1 \le k \le \min(m,n)\), where row \(k\) of \(A_i\) was interchanged with row \(\text{ipiv}_i(k)\).

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 positive, then the factorization has been completed, but some of \(U_i\) are exactly singular. Division by 0 will occur if you use the factor \(U_i\) for solving a system of linear equations.

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