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) =AT, or op(A) =AHalphaandbetaare scalarsAis eithermxmornxntriangular matrixB,X, andCaremxngeneral 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 |
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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
Ais on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
Ais 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
Ais 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*mifleft_right=side::leftorlda*nifleft_right=side::right. See Matrix Storage for more details.- lda
Leading dimension of matrix
A. Must be at leastmifleft_right=side::leftor at leastnifleft_right=side::right. Must be positive.- b
Buffer holding input matrix
B. Size of the buffer must be at leastldb*nif column major layout or at leastldb*mif row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B. Must be at leastmif column major layout or at leastnif 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
Ais on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
Ais 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
Ais 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*mifleft_right=side::leftorlda*nifleft_right=side::right. See Matrix Storage for more details.- lda
Leading dimension of matrix
A. Must be at leastmifleft_right=side::leftor at leastnifleft_right=side::right. Must be positive.- b
Buffer holding input matrix
B. Size of the buffer must be at leastldb*nif column major layout or at leastldb*mif row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B. Must be at leastmif column major layout or at leastnif 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*nif column major layout or at leastldc*mif row major layout is used. See Matrix Storage for more details.- ldc
Leading dimension of matrix
C. Must be at leastmif column major layout or at leastnif 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
Ais on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
Ais 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
Ais 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_pointerdata type.- a
Pointer to input matrix
A. Size of the array must be at leastlda*mifleft_right=side::leftorlda*nifleft_right=side::right. See Matrix Storage for more details.- lda
Leading dimension of matrix
A. Must be at leastmifleft_right=side::leftor at leastnifleft_right=side::right. Must be positive.- b
Pointer to input matrix
B. Size of the array must be at leastldb*nif column major layout or at leastldb*mif row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B. Must be at leastmif column major layout or at leastnif 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.
modeanddependenciesmay be omitted independently; it is not necessary to specifymodein 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
Ais on the left side or right side of the multiplication. See Data Types for more details.- upper_lower
Specifies whether matrix
Ais 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
Ais 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_pointerdata type.- a
Pointer to input matrix
A. Size of the array must be at leastlda*mifleft_right=side::leftorlda*nifleft_right=side::right. See Matrix Storage for more details.- lda
Leading dimension of matrix
A. Must be at leastmifleft_right=side::leftor at leastnifleft_right=side::right. Must be positive.- b
Pointer to input matrix
B. Size of the array must be at leastldb*nif column major layout or at leastldb*mif row major layout is used. See Matrix Storage for more details.- ldb
Leading dimension of matrix
B. Must be at leastmif column major layout or at leastnif row major layout is used. Must be positive.- beta
Scaling factor for matrix
C. See Scalar Arguments for more information on thevalue_or_pointerdata type.- c
Pointer to input/output matrix
C. Size of the array must be at leastldc*nif column major layout or at leastldc*mif row major layout is used. See Matrix Storage for more details.- ldc
Leading dimension of matrix
C. Must be at leastmif column major layout or at leastnif 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.
modeanddependenciesmay be omitted independently; it is not necessary to specifymodein 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.