.. SPDX-FileCopyrightText: 2019-2020 Intel Corporation
..
.. SPDX-License-Identifier: CC-BY-4.0
.. _onemkl_lapack_potrs_batch:
potrs_batch
===========
Computes the LU factorizations of a batch of general matrices.
.. container:: section
.. rubric:: Description
``potrs_batch`` supports the following precisions.
.. list-table::
:header-rows: 1
* - T
* - ``float``
* - ``double``
* - ``std::complex``
* - ``std::complex``
.. _onemkl_lapack_potrs_batch_buffer:
potrs_batch (Buffer Version)
----------------------------
.. container:: section
.. rubric:: Description
The buffer version of ``potrs_batch`` supports only the strided API.
**Strided API**
| The routine solves for :math:`X_i` the systems of linear equations :math:`A_iX_i = B_i` with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices :math:`A_i`, given the Cholesky factorization of :math:`A_i`, :math:`i \in \{1...batch\_size\}`:
| :math:`A_i = U_i^TU_i` for real data, :math:`A_i = U_i^HU_i` for complex data if ``uplo = mkl::uplo::upper``,
| :math:`A_i = L_iL_i^T` for real data, :math:`A_i = L_iL_i^H` for complex data if ``uplo = mkl::uplo::lower``,
| where :math:`L_i` is a lower triangular matrix and :math:`U_i` is upper triangular.
| The systems are solved with multiple right-hand sides stored in the columns of the matrices :math:`B_i`.
| Before calling this routine, matrices :math:`A_i` should be factorized by call to the Strided API of the :ref:`onemkl_lapack_potrf_batch_buffer` function.
.. container:: section
.. rubric:: Syntax
.. code-block:: cpp
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 &a, std::int64_t lda, std::int64_t stride_a, cl::sycl::buffer &b, std::int64_t ldb, std::int64_t stride_b, std::int64_t batch_size, cl::sycl::buffer &scratchpad, std::int64_t scratchpad_size)
}
.. container:: section
.. rubric:: 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 :math:`U_i` of :math:`A_i` is stored, where :math:`A_i = U_i^TU_i` for real data, :math:`A_i = U_i^HU_i` for complex data.
| If ``uplo = mkl::uplo::lower``, the upper triangle :math:`L_i` of :math:`A_i` is stored, where :math:`A_i = L_iL_i^T` for real data, :math:`A_i = L_iL_i^H` for complex data.
n
The order of matrices :math:`A_i` (:math:`0 \le n`).
nrhs
The number of right-hand sides (:math:`0 \le \text{nrhs}`).
a
Array containing batch of factorizations of the matrices :math:`A_i`, as returned by the Strided API of the :ref:`onemkl_lapack_potrf_batch_buffer` function.
lda
Leading dimension of :math:`A_i`.
stride_a
Stride between the beginnings of matrices inside the batch array ``a``.
b
Array containing batch of matrices :math:`B_i` whose columns are the right-hand sides for the systems of equations.
ldb
Leading dimension of :math:`B_i`.
stride_b
Stride between the beginnings of matrices :math:`B_i` inside the batch array ``b``.
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 :ref:`onemkl_lapack_potrs_batch_scratchpad_size` function.
.. container:: section
.. rubric:: Output Parameters
b
Solution matrices :math:`X_i`.
.. container:: section
.. rubric:: 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.
:ref:`oneapi::mkl::lapack::batch_error`
:ref:`oneapi::mkl::unimplemented`
:ref:`oneapi::mkl::unsupported_device`
:ref:`oneapi::mkl::lapack::invalid_argument`
The ``info`` code of the problem can be obtained by `info()` method of exception object:
If ``info = -n``, the :math:`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.
.. _onemkl_lapack_potrs_batch_usm:
potrs_batch (USM Version)
-------------------------
.. container:: section
.. rubric:: Description
The USM version of ``potrs_batch`` supports the group API and strided API.
**Group API**
.. container:: section
.. rubric:: Syntax
.. code-block:: cpp
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 &events = {})
}
.. container:: section
.. rubric:: Input Parameters
queue
Device queue where calculations will be performed.
uplo
| Array of ``group_count`` :math:`\text{uplo}_g` parameters.
| Each of :math:`\text{uplo}_g` indicates whether the upper or lower triangular parts of the input matrices are provided:
| If :math:`\text{uplo}_g` is ``mkl::uplo::upper``, input matrices from array ``a`` belonging to group :math:`g` store the upper triangular parts,
| If :math:`\text{uplo}_g` is ``mkl::uplo::lower``, input matrices from array ``a`` belonging to group :math:`g` store the lower triangular parts.
n
| Array of ``group_count`` :math:`n_g` parameters.
| Each :math:`n_g` specifies the order of the input matrices from array ``a`` belonging to group :math:`g`.
nrhs
| Array of ``group_count`` :math:`\text{nrhs}_g` parameters.
| Each :math:`\text{nrhs}_g` specifies the number of right-hand sides supplied for group :math:`g` in corresponding part of array ``b``.
a
Array of ``batch_size`` pointers to Cholesky factored matrices :math:`A_i` as returned by the Group API of the :ref:`onemkl_lapack_potrf_batch_usm` function.
lda
| Array of ``group_count`` :math:`\text{lda}_g` parameters.
| Each :math:`\text{lda}_g` specifies the leading dimensions of the matrices from ``a`` belonging to group :math:`g`.
b
Array of ``batch_size`` pointers to right-hand side matrices :math:`B_i`, each of size :math:`\text{ldb}_g \cdot \text{nrhs}_g`, where :math:`g` is an index of group corresponding to :math:`B_i`.
ldb
| Array of ``group_count`` :math:`\text{ldb}_g` parameters.
| Each :math:`\text{ldb}_g` specifies the leading dimensions of the matrices from ``b`` belonging to group :math:`g`.
group_count
Number of groups of parameters. Must be at least 0.
group_sizes
Array of ``group_count`` integers. Array element with index :math:`g` specifies the number of problems to solve for each of the groups of parameters :math:`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 :ref:`onemkl_lapack_potrs_batch_scratchpad_size` function.
events
List of events to wait for before starting computation. Defaults to empty list.
.. container:: section
.. rubric:: Output Parameters
b
Solution matrices :math:`X_i`.
.. container:: section
.. rubric:: Return Values
Output event to wait on to ensure computation is complete.
.. container:: section
.. rubric:: 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.
:ref:`oneapi::mkl::lapack::batch_error`
:ref:`oneapi::mkl::unimplemented`
:ref:`oneapi::mkl::unsupported_device`
:ref:`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 :math:`X_i` the systems of linear equations :math:`A_iX_i = B_i` with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrices :math:`A_i`, given the Cholesky factorization of :math:`A_i`, :math:`i \in \{1...batch\_size\}`:
| :math:`A_i = U_i^TU_i` for real data, :math:`A_i = U_i^HU_i` for complex data if ``uplo = mkl::uplo::upper``,
| :math:`A_i = L_iL_i^T` for real data, :math:`A_i = L_iL_i^H` for complex data if ``uplo = mkl::uplo::lower``,
| where :math:`L_i` is a lower triangular matrix and :math:`U_i` is upper triangular.
| The systems are solved with multiple right-hand sides stored in the columns of the matrices :math:`B_i`.
| Before calling this routine, matrices :math:`A_i` should be factorized by call to the Strided API of the :ref:`onemkl_lapack_potrf_batch_usm` function.
.. container:: section
.. rubric:: Syntax
.. code-block:: cpp
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 &events = {})
};
.. container:: section
.. rubric:: 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 :math:`U_i` of :math:`A_i` is stored, where :math:`A_i = U_i^TU_i` for real data, :math:`A_i = U_i^HU_i` for complex data.
| If ``uplo = mkl::uplo::lower``, the upper triangle :math:`L_i` of :math:`A_i` is stored, where :math:`A_i = L_iL_i^T` for real data, :math:`A_i = L_iL_i^H` for complex data.
n
The order of matrices :math:`A_i` (:math:`0 \le n`).
nrhs
The number of right-hand sides (:math:`0 \le nrhs`).
a
Array containing batch of factorizations of the matrices :math:`A_i`, as returned by the Strided API of the :ref:`onemkl_lapack_potrf_batch_usm` function.
lda
Leading dimension of :math:`A_i`.
stride_a
Stride between the beginnings of matrices inside the batch array ``a``.
b
Array containing batch of matrices :math:`B_i` whose columns are the right-hand sides for the systems of equations.
ldb
Leading dimension of :math:`B_i`.
stride_b
Stride between the beginnings of matrices :math:`B_i` inside the batch array ``b``.
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 :ref:`onemkl_lapack_potrs_batch_scratchpad_size` function.
events
List of events to wait for before starting computation. Defaults to empty list.
.. container:: section
.. rubric:: Output Parameters
b
Solution matrices :math:`X_i`.
.. container:: section
.. rubric:: Return Values
Output event to wait on to ensure computation is complete.
.. container:: section
.. rubric:: 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.
:ref:`oneapi::mkl::lapack::batch_error`
:ref:`oneapi::mkl::unimplemented`
:ref:`oneapi::mkl::unsupported_device`
:ref:`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 :math:`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:** :ref:`onemkl_lapack-like-extensions-routines`