trsm#

Solves a triangular matrix equation (forward or backward solve).

Description

The trsm routines solves a triangular matrix equations. There are two operations available, an in-place operation and an out-of-place operation. The in-place operation solves for X in:

\[op(A)*X = alpha*B\]

\[X*op(A) = alpha*B\]

The out-of-place operation solves for X and then adds that solution to a scaled matrix C:

\[op(A)*X = alpha*B, C \leftarrow X + beta*C\]

\[X*op(A) = alpha*B, C \leftarrow X + beta*C\]

where:

op(A) is one of op(A) = A, or op(A) = A^T, or op(A) = A^H,

alpha and beta are scalars,

A is a triangular matrix, and

B, X, and C are m x n general matrices.

A is either m x m or n x n, depending on whether it multiplies X on the left or right.

For the in-place operation, the matrix B is overwritten by the solution matrix X on return. 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

float

double

std::complex<float>

std::complex<double>

T
`float`
`double`
`std::complex<float>`
`std::complex<double>`

trsm (Buffer Version)#

In-place API#

Syntax

namespace oneapi::math::blas::column_major {
    void trsm(sycl::queue &queue,
              oneapi::math::side left_right,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose transa,
              oneapi::math::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)
}

namespace oneapi::math::blas::row_major {
    void trsm(sycl::queue &queue,
              oneapi::math::side left_right,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose transa,
              oneapi::math::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)
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether A multiplies X on the left (side::left) or on the right (side::right). See oneMath defined datatypes for more details.
upper_lower: Specifies whether the matrix A is upper or lower triangular. See oneMath defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to A. See oneMath defined datatypes for more details.
unit_diag: Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMath defined datatypes for more details.
m: Specifies the number of rows of B. The value of m must be at least zero.
n: Specifies the number of columns of B. The value of n must be at least zero.
alpha: Scaling factor for the solution.
a: Buffer holding input matrix A. Must have size at least lda*m if left_right = side::left, or lda*n if left_right = side::right. See Matrix Storage for more details.
lda: Leading dimension of A. Must be at least m if left_right = side::left, and at least n if left_right = side::right. Must be positive.
b: Buffer holding input/output matrix B. Must have size at least ldb*n if column major layout is used to store matrices or at least ldb*m if row major layout is used to store matrices. See Matrix Storage for more details.
ldb: Leading dimension of B. It must be positive and at least m if column major layout is used to store matrices or at least n if row major layout is used to store matrices.

Output Parameters

b: Output buffer. Overwritten by the solution matrix X.

Notes

If alpha = 0, matrix B is set to zero, and A and B do not need to be initialized at entry.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::math::invalid_argument

oneapi::math::unsupported_device

oneapi::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

Out-of-place API#

Syntax

namespace oneapi::math::blas::column_major {
    void trsm(sycl::queue &queue,
              oneapi::math::side left_right,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose trans,
              oneapi::math::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)
}

namespace oneapi::math::blas::row_major {
    void trsm(sycl::queue &queue,
              oneapi::math::side left_right,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose trans,
              oneapi::math::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)
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether A is on the left side of the matrix solve (side::left) or on the right side (side::right). See oneMath defined datatypes for more details.
upper_lower: Specifies whether the matrix A is upper or lower triangular. See oneMath defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to matrix A. See oneMath defined datatypes for more details.
unit_diag: Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMath defined datatypes for more details.
m: Specifices the number of rows of B. The value of m must be at least zero.
n: Specifies the Number of columns of B. The value of n must be at least zero.
alpha: Scaling factor for the solution.
a: Buffer holding input matrix A. Must have size at least lda*m if left_right = side::left or lda*n if left_right = side::right. See Matrix Storage for more details.
lda: Leading dimension of A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.
b: Buffer holding input matrix B. Must have size at least ldb*n if column major layout or at least ldb*m if row major layout is used. See Matrix Storage for more details.
ldb: Leading dimension of matrix B. It must be positive and at least m if column major layout or at least n if row major layout is used.
beta: Scaling factor for matrix C.
c: Buffer holding input/output matrix C. Size of the buffer must be at least ldc*n if column major layout or at least ldc*m if row major layout is used. See Matrix Storage for more details.
ldc: Leading dimension of matrix C. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.

Output Parameters

c: Output buffer overwritten by solution matrix X + beta*C.

Throws

oneapi::math::invalid_argument

oneapi::math::unsupported_device

oneapi::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

trsm (USM Version)#

In-place API#

Syntax

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

namespace oneapi::math::blas::row_major {
    sycl::event trsm(sycl::queue &queue,
                     oneapi::math::side left_right,
                     oneapi::math::uplo upper_lower,
                     oneapi::math::transpose transa,
                     oneapi::math::diag unit_diag,
                     std::int64_t m,
                     std::int64_t n,
                     value_or_pointer<T> alpha,
                     const T *a,
                     std::int64_t lda,
                     T *b,
                     std::int64_t ldb,
                     const std::vector<sycl::event> &dependencies = {})
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether A multiplies X on the left (side::left) or on the right (side::right). See oneMath defined datatypes for more details.
upper_lower: Specifies whether the matrix A is upper or lower triangular. See oneMath defined datatypes for more details.
transa: Specifies op(A), the transposition operation applied to A. See oneMath defined datatypes for more details.
unit_diag: Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMath defined datatypes for more details.
m: Specifies the number of rows of B. The value of m must be at least zero.
n: Specifies the number of columns of B. The value of n must be at least zero.
alpha: Scaling factor for the solution. See Scalar Arguments in BLAS for more details.
a: Pointer to input matrix A. Must have size at least lda*m if left_right = side::left, or lda*n if left_right = side::right. See Matrix Storage for more details.
lda: Leading dimension of A. Must be at least m if left_right = side::left, and at least n if left_right = side::right. Must be positive.
b: Pointer to input/output matrix B. Must have size at least ldb*n if column major layout is used to store matrices or at least ldb*m if row major layout is used to store matrices. See Matrix Storage for more details.
ldb: Leading dimension of B. It must be positive and at least m if column major layout is used to store matrices or at least n if row major layout is used to store matrices.
dependencies: List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters

b: Pointer to the output matrix. Overwritten by the solution matrix X.

Notes

If alpha = 0, matrix B is set to zero, and A and B do not need to be initialized at entry.

Return Values

Output event to wait on to ensure computation is complete.

Throws

oneapi::math::invalid_argument

oneapi::math::unsupported_device

oneapi::math::host_bad_alloc

oneapi::math::device_bad_alloc

oneapi::math::unimplemented

Out-of-place API#

Syntax

namespace oneapi::math::blas::column_major {
    void trsm(sycl::queue &queue,
              oneapi::math::side left_right,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose trans,
              oneapi::math::diag unit_diag,
              std::int64_t m,
              std::int64_t n,
              value_or_pointer<T> alpha,
              const T *a,
              std::int64_t lda,
              const T *b,
              std::int64_t ldb,
              value_or_pointer<T> beta,
              T *c,
              std::int64_t ldc,
              const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::math::blas::row_major {
    void trsm(sycl::queue &queue,
              oneapi::math::side left_right,
              oneapi::math::uplo upper_lower,
              oneapi::math::transpose trans,
              oneapi::math::diag unit_diag,
              std::int64_t m,
              std::int64_t n,
              value_or_pointer<T> alpha,
              const T *a,
              std::int64_t lda,
              const T *b,
              std::int64_t ldb,
              value_or_pointer<T> beta,
              T *c,
              std::int64_t ldc,
              const std::vector<sycl::event> &dependencies = {})
}

Input Parameters

queue: The queue where the routine should be executed.
left_right: Specifies whether A is on the left side of the matrix solve (side::left) or on the right side (side::right). See oneMath defined datatypes for more details.
upper_lower: Specifies whether the matrix A is upper or lower triangular. See oneMath defined datatypes for more details.
trans: Specifies op(A), the transposition operation applied to matrix A. See oneMath defined datatypes for more details.
unit_diag: Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMath defined datatypes for more details.
m: Specifices the number of rows of B. The value of m must be at least zero.
n: Specifies the Number of columns of B. The value of n must be at least zero.
alpha: Scaling factor for the solution. See Scalar Arguments in BLAS for more details.
a: Pointer to input matrix A. Must have size at least lda*m if left_right = side::left or lda*n if left_right = side::right. See Matrix Storage for more details.
lda: Leading dimension of A. Must be at least m if left_right = side::left or at least n if left_right = side::right. Must be positive.
b: Pointer to input matrix B. Must have size at least ldb*n if column major layout or at least ldb*m if row major layout is used. See Matrix Storage for more details.
ldb: Leading dimension of matrix B. It must be positive and at least m if column major layout or at least n if row major layout is used.
beta: Scaling factor for matrix C. See Scalar Arguments in BLAS for more details.
c: Pointer to input/output matrix C. Must have size at least ldc*n if column major layout or at least ldc*m if row major layout is used. See Matrix Storage for more details.
ldc: Leading dimension of matrix C. Must be at least m if column major layout or at least n if row major layout is used. Must be positive.
dependencies: List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.