trmm

Computes a matrix-matrix product where one input matrix is triangular and one input matrix is general.

Description

The trmm routines compute a scalar-matrix-matrix product 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). Depending on left_right.

There are two operations available, an in-place operation and an out-of-place operation. The in-place operation is defined as:

\[B \leftarrow alpha*op(A)*B\]

or

\[B \leftarrow alpha*B*op(A)\]

The out-of-place operation is defined as:

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

or

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

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 and C are general matrices.

Here B and C are m x n and A is either m x m or n x n, depending on left_right.

trmm supports the following precisions.

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

trmm (Buffer Version)

In-place API

Syntax

namespace oneapi::mkl::blas::column_major {
    void trmm(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)
}

namespace oneapi::mkl::blas::row_major {
    void trmm(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)
}

Input Parameters

queue

The queue where the routine should be executed.

left_right

Specifies whether A is on the left side of the multiplication (side::left) or on the right side (side::right). See oneMKL defined datatypes for more details.

upper_lower

Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.

trans

Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

unit_diag

Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMKL 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 matrix-matrix product.

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 alpha*op(A)*B or alpha*B*op(A).

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::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::host_bad_alloc

oneapi::mkl::device_bad_alloc

oneapi::mkl::unimplemented

Out-of-place API

Syntax

namespace oneapi::mkl::blas::column_major {
    void trmm(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)
}

namespace oneapi::mkl::blas::row_major {
    void trmm(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)
}

Input Parameters

queue

The queue where the routine should be executed.

left_right

Specifies whether A is on the left side of the multiplication (side::left) or on the right side (side::right). See oneMKL defined datatypes for more details.

upper_lower

Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.

trans

Specifies op(A), the transposition operation applied to matrix A. See oneMKL defined datatypes for more details.

unit_diag

Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMKL 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 matrix-matrix product.

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 alpha*op(A)*B + beta*C if left_right = side::left or alpha*B*op(A) + beta*C if left_right = side::right.

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::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::host_bad_alloc

oneapi::mkl::device_bad_alloc

oneapi::mkl::unimplemented

trmm (USM Version)

In-place API

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event trmm(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,
                     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::mkl::blas::row_major {
    sycl::event trmm(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,
                     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 is on the left side of the multiplication (side::left) or on the right side (side::right). See oneMKL defined datatypes for more details.

upper_lower

Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.

trans

Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details.

unit_diag

Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMKL 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 matrix-matrix product. 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 alpha*op(A)*B or alpha*B*op(A).

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

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::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::host_bad_alloc

oneapi::mkl::device_bad_alloc

oneapi::mkl::unimplemented

Out-of-place API

Syntax

namespace oneapi::mkl::blas::column_major {
    void trmm(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,
              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::mkl::blas::row_major {
    void trmm(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,
              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 multiplication (side::left) or on the right side (side::right). See oneMKL defined datatypes for more details.

upper_lower

Specifies whether the matrix A is upper or lower triangular. See oneMKL defined datatypes for more details.

trans

Specifies op(A), the transposition operation applied to matrix A. See oneMKL defined datatypes for more details.

unit_diag

Specifies whether A is assumed to be unit triangular (all diagonal elements are 1). See oneMKL 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 matrix-matrix product. 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.

Output Parameters

c

Pointer to the output matrix, overwritten by alpha*op(A)*B + beta*C if left_right = side::left or alpha*B*op(A) + beta*C if left_right = side::right.

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::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::host_bad_alloc

oneapi::mkl::device_bad_alloc

oneapi::mkl::unimplemented

Parent topic: BLAS Level 3 Routines