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>`

trsm_batch (Buffer Version)¶

Buffer version of trsm_batch supports only strided API.

Strided API¶

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 == side::left) then
       compute X such that op(A) * X = alpha * B
    else
       compute X such that X * op(A) = alpha * B
    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 either m x m or n x n triangular matrix
B and X are m x n general matrices

On return, matrix B is overwritten by solution matrix X.

For strided API, a and b buffers contains all the input matrices. The stride between matrices is given by the stride parameters. Total number of matrices in a and b buffers is given by batch_size parameter.

Syntax¶

namespace oneapi::mkl::blas::column_major {
    void trsm_batch(sycl::queue &queue,
                    oneapi::mkl::side left_right,
                    oneapi::mkl::uplo upper_lower,
                    oneapi::mkl::transpose trans,
                    oneapi::mkl::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::mkl::blas::row_major {
    void trsm_batch(sycl::queue &queue,
                    oneapi::mkl::side left_right,
                    oneapi::mkl::uplo upper_lower,
                    oneapi::mkl::transpose trans,
                    oneapi::mkl::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 matrices A are on the left side or right side of the multiplication. See Data Types for more details.
upper_lower: Specifies whether matrices A are upper or lower triangular. See Data Types for more details.
trans: Specifies op(A), transposition operation applied to matrices A. See Data Types for more details.
unit_diag: Specifies whether matrices A are unit triangular or not. See Data Types for more details.
m: Number of rows of matrices B. Must be at least zero.
n: Number of columns of matrices B. Must be at least zero.
alpha: Scaling factor for the solution.
a: Buffer holding input matricees A. Size of the buffer must be at least stridea * batch_size.
lda: Leading dimension of matrices A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.
stridea: Stride between two consecutive A matrices.
b: Buffer holding input/output matrices B. Size of the buffer must be at least strideb * batch_size.
ldb: Leading dimension of matrices B. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.
strideb: Stride between two consecutive B matrices.
batch_size: Specifies number of triangular linear systems to solve.

Output Parameters¶

b: Output buffer overwritten by batch_size solution matrices X.

Note

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

trsm_batch (USM Version)¶

USM version of trsm_batch supports group API and strided API.

Group API¶

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 == 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

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 either m x m or n x n triangular matrix
B and X are m x n general matrices

On return, matrix B is overwritten by 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:

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

Syntax¶

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

namespace oneapi::mkl::blas::row_major {
    sycl::event trsm_batch(sycl::queue &queue,
                           oneapi::mkl::side *left_right,
                           oneapi::mkl::uplo *upper_lower,
                           oneapi::mkl::transpose *trans,
                           oneapi::mkl::diag *unit_diag,
                           std::int64_t *m,
                           std::int64_t *n,
                           T *alpha,
                           const T **a,
                           std::int64_t *lda,
                           T **b,
                           std::int64_t *ldb,
                           std::int64_t group_count,
                           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::mkl::side values. left_right[i] specifies whether matrices A are on the left side or right side of the multiplication in group i. See Data Types for more details.
upper_lower: Array of group_count oneapi::mkl::uplo values. upper_lower[i] specifies whether matrices A are upper or lower triangular in group i. See Data Types for more details.
trans: Array of group_count oneapi::mkl::transpose values. trans[i] specifies op(A), transposition operation applied to matrices A in each group i. See Data Types for more details.
unit_diag: Array of group_count oneapi::mkl::diag values. unit_diag[i] specifies whether matrices A are unit triangular or not. See Data Types for more details.
m: Array of group_count integers. m[i] specifies number of rows of matrices B in group i. All entries must be at least zero.
n: Array of group_count integers. n[i] specifies number of columns of matrices B in group i. All entries must be at least zero.
alpha: Array of group_count scalar elements. alpha[i] specifies scaling factors for the solutions in group i.
a: Array of total_batch_count pointers for input matrices A. See Matrix Storage for more details.
lda: Array of group_count integers. lda[i] specifies leading dimension of matrices A in group i. Must be at least m[i] if left_right[i] = side::left or at least n[i] if left_right[i] = side::right. All entries must be positive.
b: Array of total_batch_count pointers for input/output matrices B. See Matrix Storage for more details.
ldb: Array of group_count integers. ldb[i] specifies leading dimension of matrices B in group i. Must be at least m[i] if column major layout or at least n[i] if row major layout is used. All entries must be positive.
group_count: Number of groups. Must be at least zero.
group_size: Array of group_count integers. group_size[i] specifies the number of trsm operations in group i. Each element in group_size must be at least zero.
dependencies: List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters¶

b: Array of pointers to output matrices B overwritten by total_batch_count solution matrices X.

Note

If alpha = 0, matrices B are set to zero, and 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¶

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 == side::left) then
       compute X such that op(A) * X = alpha * B
    else
       compute X such that X * op(A) = alpha * B
    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 either m x m or n x n triangular matrix
B and X are m x n general matrices

On return, matrix B is overwritten by solution matrix X.

For strided API, a and b arrays contain all the input matrices. The stride between matrices is given by the stride parameters. Total number of matrices in a and b arrays is given by batch_size parameter.

Syntax¶

namespace oneapi::mkl::blas::column_major {
    sycl::event trsm_batch(sycl::queue &queue,
                           oneapi::mkl::side left_right,
                           oneapi::mkl::uplo upper_lower,
                           oneapi::mkl::transpose trans,
                           oneapi::mkl::diag unit_diag,
                           std::int64_t m,
                           std::int64_t n,
                           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::mkl::blas::row_major {
    sycl::event trsm_batch(sycl::queue &queue,
                           oneapi::mkl::side left_right,
                           oneapi::mkl::uplo upper_lower,
                           oneapi::mkl::transpose trans,
                           oneapi::mkl::diag unit_diag,
                           std::int64_t m,
                           std::int64_t n,
                           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 matrices A are on the left side or right side of the multiplication. See Data Types for more details.
upper_lower: Specifies whether matrices A are upper or lower triangular. See Data Types for more details.
trans: Specifies op(A), transposition operation applied to matrices A. See Data Types for more details.
unit_diag: Specifies whether matrices A are unit triangular or not. See Data Types for more details.
m: Number of rows of matrices B. Must be at least zero.
n: Number of columns of matrices B. Must be at least zero.
alpha: Scaling factor for the solution.
a: Pointer to input matricees A. Size of the array must be at least stridea * batch_size.
lda: Leading dimension of matrices A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.
stridea: Stride between two consecutive A matrices.
b: Pointer to input/output matrices B. Size of the array must be at least strideb * batch_size.
ldb: Leading dimension of matrices B. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.
strideb: Stride between two consecutive B matrices.
batch_size: Specifies number of triangular linear systems to solve.
dependencies: List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters¶

b: Pointer to output matrix B overwritten by batch_size solution matrices X.

Note

If alpha = 0, matrices B are set to zero, and 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.

syrk_batch omatcopy_batch

oneAPI Math Kernel Library (oneMKL) documentation

trsm_batch¶

Description¶

trsm_batch (Buffer Version)¶

Strided API¶

Syntax¶

Input Parameters¶

Output Parameters¶

trsm_batch (USM Version)¶

Group API¶

Syntax¶

Input Parameters¶

Output Parameters¶

Return Values¶

Strided API¶

Syntax¶

Input Parameters¶

Output Parameters¶

Return Values¶