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
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
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:
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]
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]
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
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
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.