Intel® oneAPI Math Kernel Library (oneMKL) - Data Parallel C++ Developer Reference

Developer Reference

Contents

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
.
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:
LaTex Math image.
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
.
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
.
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.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.