trsm#
Solves a triangular matrix equation (forward or backward solve).
Description#
The trsm
routines solve triangular matrix equations where one of
the matrices in the multiplication is triangular. The argument
left_right
determines if the triangular matrix, A
, is on the
left of the multiplication (left_right
= side::left
) or on
the right (left_right
= side::right
). The operation is defined as:
There are two operations available, an in-place operation and an out-of-place operation. The in-place operation is defined as:
If (left_right
= side::left
),
If (left_right
= side::right
),
The out-of-place operation is defined as:
If (left_right
= side::left
),
If (left_right
= side::right
),
where:
op(
A
) is one of op(A
) =A
, or op(A
) =A
T, or op(A
) =A
Halpha
andbeta
are scalarsA
is eitherm
xm
orn
xn
triangular matrixB
,X
, andC
arem
xn
general matrices
For the in-place operation, the matrix B
is overwritten by solution matrix X
, while for the out-of-place operation, B
remains untouched and the solution is added to a scaled C
matrix.
trsm
supports the following precisions:
T |
---|
|
|
|
|
trsm (Buffer Version)#
In-place API#
Syntax#
namespace oneapi::mkl::blas::column_major {
void trsm(sycl::queue &queue,
oneapi::mkl::side left_right,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose transa,
oneapi::mkl::diag unit_diag,
std::int64_t m,
std::int64_t n,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &b,
std::int64_t ldb,
compute_mode mode = compute_mode::unset)
}
namespace oneapi::mkl::blas::row_major {
void trsm(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,
sycl::buffer<T,1> &b,
std::int64_t ldb,
compute_mode mode = compute_mode::unset)
}
Input Parameters#
- queue
The queue where the routine will be executed.
- left_right
Specifies whether matrix
A
is on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
A
is upper or lower triangular. See Data Types for more details.- trans
Specifies op(
A
), the transposition operation applied to matrixA
. See Data Types for more details.- unit_diag
Specifies whether matrix
A
is unit triangular or not. See Data Types for more details.- m
Number of rows of matrix
B
. Must be at least zero.- n
Number of columns of matrix
B
. Must be at least zero.- alpha
Scaling factor for the solution.
- a
Buffer holding input matrix
A
. Size of the buffer must be at leastlda
*m
ifleft_right
=side::left
orlda
*n
ifleft_right
=side::right
. See Matrix Storage for more details.- lda
Leading dimension of matrix
A
. Must be at leastm
ifleft_right
=side::left
or at leastn
ifleft_right
=side::right
. Must be positive.- b
Buffer holding input matrix
B
. Size of the buffer must be at leastldb
*n
if column major layout or at leastldb
*m
if row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B
. Must be at leastm
if column major layout or at leastn
if row major layout is used. Must be positive.- mode
Optional. Compute mode settings. See Compute Modes for more details.
Output Parameters#
- b
Output buffer overwritten by solution matrix
X
.
Note
If alpha
= 0, matrix B
is set to zero, and A
and B
do not need to be initialized before calling trsm
.
Out-of-place API#
Syntax#
namespace oneapi::mkl::blas::column_major {
void trsm(sycl::queue &queue,
oneapi::mkl::side left_right,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose transa,
oneapi::mkl::diag unit_diag,
std::int64_t m,
std::int64_t n,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &b,
std::int64_t ldb,
T beta,
sycl::buffer<T,1> &c,
std::int64_t ldc,
compute_mode mode = compute_mode::unset)
}
namespace oneapi::mkl::blas::row_major {
void trsm(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,
sycl::buffer<T,1> &b,
std::int64_t ldb,
T beta,
sycl::buffer<T,1> &c,
std::int64_t ldc,
compute_mode mode = compute_mode::unset)
}
Input Parameters#
- queue
The queue where the routine will be executed.
- left_right
Specifies whether matrix
A
is on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
A
is upper or lower triangular. See Data Types for more details.- trans
Specifies op(
A
), the transposition operation applied to matrixA
. See Data Types for more details.- unit_diag
Specifies whether matrix
A
is unit triangular or not. See Data Types for more details.- m
Number of rows of matrix
B
. Must be at least zero.- n
Number of columns of matrix
B
. Must be at least zero.- alpha
Scaling factor for the solution.
- a
Buffer holding input matrix
A
. Size of the buffer must be at leastlda
*m
ifleft_right
=side::left
orlda
*n
ifleft_right
=side::right
. See Matrix Storage for more details.- lda
Leading dimension of matrix
A
. Must be at leastm
ifleft_right
=side::left
or at leastn
ifleft_right
=side::right
. Must be positive.- b
Buffer holding input matrix
B
. Size of the buffer must be at leastldb
*n
if column major layout or at leastldb
*m
if row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B
. Must be at leastm
if column major layout or at leastn
if row major layout is used. Must be positive.- beta
Scaling factor for matrix
C
.- c
Buffer holding input/output matrix
C
. Size of the buffer must be at leastldc
*n
if column major layout or at leastldc
*m
if row major layout is used. See Matrix Storage for more details.- ldc
Leading dimension of matrix
C
. Must be at leastm
if column major layout or at leastn
if row major layout is used. Must be positive.- mode
Optional. Compute mode settings. See Compute Modes for more details.
Output Parameters#
- c
Output buffer overwritten by solution matrix
X
+beta
*C
.
trsm (USM Version)#
In-place API#
Syntax#
namespace oneapi::mkl::blas::column_major {
sycl::event trsm(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,
oneapi::mkl::value_or_pointer<T> alpha,
const T *a,
std::int64_t lda,
T *b,
std::int64_t ldb,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
namespace oneapi::mkl::blas::row_major {
sycl::event trsm(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,
oneapi::mkl::value_or_pointer<T> alpha,
const T *a,
std::int64_t lda,
T *b,
std::int64_t ldb,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
Input Parameters#
- queue
The queue where the routine will be executed.
- left_right
Specifies whether matrix
A
is on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
A
is upper or lower triangular. See Data Types for more details.- trans
Specifies op(
A
), the transposition operation applied to matrixA
. See Data Types for more details.- unit_diag
Specifies whether matrix
A
is unit triangular or not. See Data Types for more details.- m
Number of rows of matrix
B
. Must be at least zero.- n
Number of columns of matrix
B
. Must be at least zero.- alpha
Scaling factor for the solution. See Scalar Arguments for more information on the
value_or_pointer
data type.- a
Pointer to input matrix
A
. Size of the array must be at leastlda
*m
ifleft_right
=side::left
orlda
*n
ifleft_right
=side::right
. See Matrix Storage for more details.- lda
Leading dimension of matrix
A
. Must be at leastm
ifleft_right
=side::left
or at leastn
ifleft_right
=side::right
. Must be positive.- b
Pointer to input matrix
B
. Size of the array must be at leastldb
*n
if column major layout or at leastldb
*m
if row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B
. Must be at leastm
if column major layout or at leastn
if row major layout is used. Must be positive.- mode
Optional. Compute mode settings. See Compute Modes for more details.
- dependencies
Optional. List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.
mode
anddependencies
may be omitted independently; it is not necessary to specifymode
in order to provide dependencies.
Output Parameters#
- b
Pointer to output matrix overwritten by solution matrix
X
.
Note
If alpha
= 0, matrix B
is set to zero, and A
and B
do not need to be initialized before calling trsm
.
Return Values#
Output event to wait on to ensure computation is complete.
Out-of-place API#
Syntax#
namespace oneapi::mkl::blas::column_major {
sycl::event trsm(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,
oneapi::mkl::value_or_pointer<T> alpha,
const T *a,
std::int64_t lda,
const T *b,
std::int64_t ldb,
oneapi::mkl::value_or_pointer<T> beta,
T *c,
std::int64_t ldc,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
namespace oneapi::mkl::blas::row_major {
sycl::event trsm(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,
oneapi::mkl::value_or_pointer<T> alpha,
const T *a,
std::int64_t lda,
const T *b,
std::int64_t ldb,
oneapi::mkl::value_or_pointer<T> beta,
T *c,
std::int64_t ldc,
compute_mode mode = compute_mode::unset,
const std::vector<sycl::event> &dependencies = {})
}
Input Parameters#
- queue
The queue where the routine will be executed.
- left_right
Specifies whether matrix
A
is on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
A
is upper or lower triangular. See Data Types for more details.- trans
Specifies op(
A
), the transposition operation applied to matrixA
. See Data Types for more details.- unit_diag
Specifies whether matrix
A
is unit triangular or not. See Data Types for more details.- m
Number of rows of matrix
B
. Must be at least zero.- n
Number of columns of matrix
B
. Must be at least zero.- alpha
Scaling factor for the solution. See Scalar Arguments for more information on the
value_or_pointer
data type.- a
Pointer to input matrix
A
. Size of the array must be at leastlda
*m
ifleft_right
=side::left
orlda
*n
ifleft_right
=side::right
. See Matrix Storage for more details.- lda
Leading dimension of matrix
A
. Must be at leastm
ifleft_right
=side::left
or at leastn
ifleft_right
=side::right
. Must be positive.- b
Pointer to input matrix
B
. Size of the array must be at leastldb
*n
if column major layout or at leastldb
*m
if row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B
. Must be at leastm
if column major layout or at leastn
if row major layout is used. Must be positive.- beta
Scaling factor for matrix
C
. See Scalar Arguments for more information on thevalue_or_pointer
data type.- c
Pointer to input/output matrix
C
. Size of the array must be at leastldc
*n
if column major layout or at leastldc
*m
if row major layout is used. See Matrix Storage for more details.- ldc
Leading dimension of matrix
C
. Must be at leastm
if column major layout or at leastn
if row major layout is used. Must be positive.- mode
Optional. Compute mode settings. See Compute Modes for more details.
- dependencies
Optional. List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.
mode
anddependencies
may be omitted independently; it is not necessary to specifymode
in order to provide dependencies.
Output Parameters#
- c
Pointer to output matrix overwritten by solution matrix
X
+beta
*C
.
Return Values#
Output event to wait on to ensure computation is complete.