trsm_batch#

Computes a group of trsm operations.

Description

The trsm_batch routines are batched versions of trsm, performing multiple trsm operations in a single call. Each trsm solves an equation of the form op(A) * X = alpha * B or X * op(A) = alpha * B.

trsm_batch supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

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

trsm_batch (Buffer Version)#

Description

The buffer version of trsm_batch supports only the strided API.

The strided API operation is defined as:

for i = 0 … batch_size – 1
    A and B are matrices at offset i * stridea and i * strideb in a and b.
    if (left_right == oneapi::math::side::left) then
        compute X such that op(A) * X = alpha * B
    else
        compute X such that X * op(A) = alpha * B
    end if
    B := X
end for

where:

op(A) is one of op(A) = A, or op(A) = A^T, or op(A) = A^H,

alpha is a scalar,

A is a triangular matrix,

B and X are m x n general matrices,

A is either m x m or n x n,depending on whether it multiplies X on the left or right. On return, the matrix B is overwritten by the solution matrix X.

The a and b buffers contain all the input matrices. The stride between matrices is given by the stride parameter. The total number of matrices in a and b buffers are given by the batch_size parameter.

Strided API

Syntax

namespace oneapi::math::blas::column_major {
    void trsm_batch(sycl::queue &queue,
                    oneapi::math::side left_right,
                    oneapi::math::uplo upper_lower,
                    oneapi::math::transpose trans,
                    oneapi::math::diag unit_diag,
                    std::int64_t m,
                    std::int64_t n,
                    T alpha,
                    sycl::buffer<T,1> &a,
                    std::int64_t lda,
                    std::int64_t stridea,
                    sycl::buffer<T,1> &b,
                    std::int64_t ldb,
                    std::int64_t strideb,
                    std::int64_t batch_size)
}

namespace oneapi::math::blas::row_major {
    void trsm_batch(sycl::queue &queue,
                    oneapi::math::side left_right,
                    oneapi::math::uplo upper_lower,
                    oneapi::math::transpose trans,
                    oneapi::math::diag unit_diag,
                    std::int64_t m,
                    std::int64_t n,
                    T alpha,
                    sycl::buffer<T,1> &a,
                    std::int64_t lda,
                    std::int64_t stridea,
                    sycl::buffer<T,1> &b,
                    std::int64_t ldb,
                    std::int64_t strideb,
                    std::int64_t batch_size)
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether the matrices A multiply X on the left (side::left) or on the right (side::right). See oneMath defined datatypes for more details.
upper_lower: Specifies whether the matrices A are upper or lower triangular. See oneMath defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to the matrices A. See oneMath defined datatypes for more details.
unit_diag: Specifies whether the matrices A are assumed to be unit triangular (all diagonal elements are 1). See oneMath defined datatypes for more details.
m: Number of rows of the B matrices. Must be at least zero.
n: Number of columns of the B matrices. Must be at least zero.
alpha: Scaling factor for the solutions.
a: Buffer holding the input matrices A with size stridea * batch_size.
lda: Leading dimension of the matrices A. Must be at least m if left_right = side::left, and at least n if left_right = side::right. Must be positive.
stridea: Stride between different A matrices.
b: Buffer holding the input matrices B with size strideb * batch_size.
ldb: Leading dimension of the matrices B. It must be positive and at least m if column major layout is used to store matrices or at least n if row major layout is used to store matrices.
strideb: Stride between different B matrices.
batch_size: Specifies the number of triangular linear systems to solve.

Output Parameters

b: Output buffer, overwritten by batch_size solution matrices X.

Notes

If alpha = 0, matrix B is set to zero and the matrices A and B do not need to be initialized before calling trsm_batch.

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::math::invalid_argument

oneapi::math::unsupported_device

oneapi::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

trsm_batch (USM Version)#

Description

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

The group API operation is defined as:

idx = 0
for i = 0 … group_count – 1
    for j = 0 … group_size – 1
        A and B are matrices in a[idx] and b[idx]
        if (left_right == oneapi::math::side::left) then
            compute X such that op(A) * X = alpha[i] * B
        else
            compute X such that X * op(A) = alpha[i] * B
        end if
        B := X
        idx = idx + 1
    end for
end for

The strided API operation is defined as:

for i = 0 … batch_size – 1
    A and B are matrices at offset i * stridea and i * strideb in a and b.
    if (left_right == oneapi::math::side::left) then
        compute X such that op(A) * X = alpha * B
    else
        compute X such that X * op(A) = alpha * B
    end if
    B := X
end for

where:

op(A) is one of op(A) = A, or op(A) = A^T, or op(A) = A^H,

alpha is a scalar,

A is a triangular matrix,

B and X are m x n general matrices,

A is either m x m or n x n,depending on whether it multiplies X on the left or right. On return, the matrix B is overwritten by the solution matrix X.

For group API, a and b arrays contain the pointers for all the input matrices. The total number of matrices in a and b are given by:

\[total\_batch\_count = \sum_{i=0}^{group\_count-1}group\_size[i]\]

For strided API, a and b arrays contain all the input matrices. The total number of matrices in a and b are given by the batch_size parameter.

Group API

Syntax

namespace oneapi::math::blas::column_major {
    sycl::event trsm_batch(sycl::queue &queue,
                           const oneapi::math::side *left_right,
                           const oneapi::math::uplo *upper_lower,
                           const oneapi::math::transpose *trans,
                           const oneapi::math::diag *unit_diag,
                           const std::int64_t *m,
                           const std::int64_t *n,
                           const T *alpha,
                           const T **a,
                           const std::int64_t *lda,
                           T **b,
                           const std::int64_t *ldb,
                           std::int64_t group_count,
                           const std::int64_t *group_size,
                           const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::math::blas::row_major {
    sycl::event trsm_batch(sycl::queue &queue,
                           const oneapi::math::side *left_right,
                           const oneapi::math::uplo *upper_lower,
                           const oneapi::math::transpose *trans,
                           const oneapi::math::diag *unit_diag,
                           const std::int64_t *m,
                           const std::int64_t *n,
                           const T *alpha,
                           const T **a,
                           const std::int64_t *lda,
                           T **b,
                           const std::int64_t *ldb,
                           std::int64_t group_count,
                           const std::int64_t *group_size,
                           const std::vector<sycl::event> &dependencies = {})
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Array of group_count oneapi::math::side values. left_right[i] specifies whether A multiplies X on the left (side::left) or on the right (side::right) for every trsm operation in group i. See oneMath defined datatypes for more details.
upper_lower: Array of group_count oneapi::math::uplo values. upper_lower[i] specifies whether A is upper or lower triangular for every matrix in group i. See oneMath defined datatypes for more details.
trans: Array of group_count oneapi::math::transpose values. trans[i] specifies the form of op(A) used for every trsm operation in group i. See oneMath defined datatypes for more details.
unit_diag: Array of group_count oneapi::math::diag values. unit_diag[i] specifies whether A is assumed to be unit triangular (all diagonal elements are 1) for every matrix in group i. See oneMath defined datatypes for more details.
m: Array of group_count integers. m[i] specifies the number of rows of B for every matrix in group i. All entries must be at least zero.
n: Array of group_count integers. n[i] specifies the number of columns of B for every matrix in group i. All entries must be at least zero.
alpha: Array of group_count scalar elements. alpha[i] specifies the scaling factor in group i.
a: Array of pointers to input matrices A with size total_batch_count. See Matrix Storage for more details.
lda: Array of group_count integers. lda[i] specifies the leading dimension of A for every matrix in group i. All entries must be at least m if left_right is side::left, and at least n if left_right is side::right. All entries must be positive.
b: Array of pointers to input matrices B with size total_batch_count. See Matrix Storage for more details.
ldb: Array of group_count integers. ldb[i] specifies the leading dimension of B for every matrix in group i. All entries must be positive and at least m and positive if column major layout is used to store matrices or at least n if row major layout is used to store matrices.
group_count: Specifies the number of groups. Must be at least 0.
group_size: Array of group_count integers. group_size[i] specifies the number of trsm operations in group i. All entries must be at least 0.
dependencies: List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters

b: Output buffer, overwritten by the total_batch_count solution matrices X.

Notes

If alpha = 0, matrix B is set to zero and the matrices A and B do not need to be initialized before calling trsm_batch.

Return Values

Output event to wait on to ensure computation is complete.

Strided API

Syntax

namespace oneapi::math::blas::column_major {
    sycl::event trsm_batch(sycl::queue &queue,
                           oneapi::math::side left_right,
                           oneapi::math::uplo upper_lower,
                           oneapi::math::transpose trans,
                           oneapi::math::diag unit_diag,
                           std::int64_t m,
                           std::int64_t n,
                           value_or_pointer<T> alpha,
                           const T *a,
                           std::int64_t lda,
                           std::int64_t stridea,
                           T *b,
                           std::int64_t ldb,
                           std::int64_t strideb,
                           std::int64_t batch_size,
                           const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::math::blas::row_major {
    sycl::event trsm_batch(sycl::queue &queue,
                           oneapi::math::side left_right,
                           oneapi::math::uplo upper_lower,
                           oneapi::math::transpose trans,
                           oneapi::math::diag unit_diag,
                           std::int64_t m,
                           std::int64_t n,
                           value_or_pointer<T> alpha,
                           const T *a,
                           std::int64_t lda,
                           std::int64_t stridea,
                           T *b,
                           std::int64_t ldb,
                           std::int64_t strideb,
                           std::int64_t batch_size,
                           const std::vector<sycl::event> &dependencies = {})
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether the matrices A multiply X on the left (side::left) or on the right (side::right). See oneMath defined datatypes for more details.
upper_lower: Specifies whether the matrices A are upper or lower triangular. See oneMath defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to the matrices A. See oneMath defined datatypes for more details.
unit_diag: Specifies whether the matrices A are assumed to be unit triangular (all diagonal elements are 1). See oneMath defined datatypes for more details.
m: Number of rows of the B matrices. Must be at least zero.
n: Number of columns of the B matrices. Must be at least zero.
alpha: Scaling factor for the solutions. See Scalar Arguments in BLAS for more details.
a: Pointer to input matrices A with size stridea * batch_size.
lda: Leading dimension of the matrices A. Must be at least m if left_right = side::left, and at least n if left_right = side::right. Must be positive.
stridea: Stride between different A matrices.
b: Pointer to input matrices B with size strideb * batch_size.
ldb: Leading dimension of the matrices B. It must be positive and at least m if column major layout is used to store matrices or at least n if row major layout is used to store matrices.
strideb: Stride between different B matrices.
batch_size: Specifies the number of triangular linear systems to solve.