# gemm¶

Computes a matrix-matrix product with general matrices.

Description

The gemm routines compute a scalar-matrix-matrix product and add the result to a scalar-matrix product, with general matrices. The operation is defined as:

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

where:

op(X) is one of op(X) = X, or op(X) = XT, or op(X) = XH,

alpha and beta are scalars,

A, B and C are matrices,

op(A) is an m-by-k matrix,

op(B) is a k-by-n matrix,

C is an m-by-n matrix.

gemm supports the following precisions.

Ts

Ta

Tb

Tc

float

half

half

float

half

half

half

half

float

bfloat16

bfloat16

float

float

float

float

float

double

double

double

double

std::complex<float>

std::complex<float>

std::complex<float>

std::complex<float>

std::complex<double>

std::complex<double>

std::complex<double>

std::complex<double>

## gemm (Buffer Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
void gemm(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
Ts alpha,
sycl::buffer<Ta,1> &a,
std::int64_t lda,
sycl::buffer<Tb,1> &b,
std::int64_t ldb,
Ts beta,
sycl::buffer<Tc,1> &c,
std::int64_t ldc)
}

namespace oneapi::mkl::blas::row_major {
void gemm(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
Ts alpha,
sycl::buffer<Ta,1> &a,
std::int64_t lda,
sycl::buffer<Tb,1> &b,
std::int64_t ldb,
Ts beta,
sycl::buffer<Tc,1> &c,
std::int64_t ldc)
}


Input Parameters

queue

The queue where the routine should be executed.

transa

Specifies the form of op(A), the transposition operation applied to A.

transb

Specifies the form of op(B), the transposition operation applied to B.

m

Specifies the number of rows of the matrix op(A) and of the matrix C. The value of m must be at least zero.

n

Specifies the number of columns of the matrix op(B) and the number of columns of the matrix C. The value of n must be at least zero.

k

Specifies the number of columns of the matrix op(A) and the number of rows of the matrix op(B). The value of k must be at least zero.

alpha

Scaling factor for the matrix-matrix product.

a

The buffer holding the input matrix A.

A not transposed

A transposed

Column major

A is an m-by-k matrix so the array a must have size at least lda*k.

A is an k-by-m matrix so the array a must have size at least lda*m

Row major

A is an m-by-k matrix so the array a must have size at least lda*m.

A is an k-by-m matrix so the array a must have size at least lda*k

See Matrix Storage for more details.

lda

The leading dimension of A. It must be positive.

A not transposed

A transposed

Column major

lda must be at least m.

lda must be at least k.

Row major

lda must be at least k.

lda must be at least m.

b

The buffer holding the input matrix B.

B not transposed

B transposed

Column major

B is an k-by-n matrix so the array b must have size at least ldb*n.

B is an n-by-k matrix so the array b must have size at least ldb*k

Row major

B is an k-by-n matrix so the array b must have size at least ldb*k.

B is an n-by-k matrix so the array b must have size at least ldb*n

See Matrix Storage for more details.

ldb

The leading dimension of B. It must be positive.

B not transposed

B transposed

Column major

ldb must be at least k.

ldb must be at least n.

Row major

ldb must be at least n.

ldb must be at least k.

beta

Scaling factor for matrix C.

c

The buffer holding the input/output matrix C. It must have a size of at least ldc*n if column major layout is used to store matrices or at least ldc*m if row major layout is used to store matrices . See Matrix Storage for more details.

ldc

The leading dimension of C. It must be positive and at least m if column major layout is used to store matrices or at least n if column major layout is used to store matrices.

Output Parameters

c

The buffer, which is overwritten by alpha*op(A)*op(B) + beta*C.

Notes

If beta = 0, matrix C does not need to be initialized before calling gemm.

## gemm (USM Version)¶

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event gemm(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
Ts alpha,
const Ta *a,
std::int64_t lda,
const Tb *b,
std::int64_t ldb,
Ts beta,
Tc *c,
std::int64_t ldc,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event gemm(sycl::queue &queue,
onemkl::transpose transa,
onemkl::transpose transb,
std::int64_t m,
std::int64_t n,
std::int64_t k,
Ts alpha,
const Ta *a,
std::int64_t lda,
const Tb *b,
std::int64_t ldb,
Ts beta,
Tc *c,
std::int64_t ldc,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

transa

Specifies the form of op(A), the transposition operation applied to A.

transb

Specifies the form of op(B), the transposition operation applied to B.

m

Specifies the number of rows of the matrix op(A) and of the matrix C. The value of m must be at least zero.

n

Specifies the number of columns of the matrix op(B) and the number of columns of the matrix C. The value of n must be at least zero.

k

Specifies the number of columns of the matrix op(A) and the number of rows of the matrix op(B). The value of k must be at least zero.

alpha

Scaling factor for the matrix-matrix product.

a

Pointer to input matrix A.

A not transposed

A transposed

Column major

A is an m-by-k matrix so the array a must have size at least lda*k.

A is an k-by-m matrix so the array a must have size at least lda*m

Row major

A is an m-by-k matrix so the array a must have size at least lda*m.

A is an k-by-m matrix so the array a must have size at least lda*k

See Matrix Storage for more details.

lda

The leading dimension of A. It must be positive.

A not transposed

A transposed

Column major

lda must be at least m.

lda must be at least k.

Row major

lda must be at least k.

lda must be at least m.

b

Pointer to input matrix B.

B not transposed

B transposed

Column major

B is an k-by-n matrix so the array b must have size at least ldb*n.

B is an n-by-k matrix so the array b must have size at least ldb*k

Row major

B is an k-by-n matrix so the array b must have size at least ldb*k.

B is an n-by-k matrix so the array b must have size at least ldb*n

See Matrix Storage for more details.

ldb

The leading dimension of B. It must be positive.

B not transposed

B transposed

Column major

ldb must be at least k.

ldb must be at least n.

Row major

ldb must be at least n.

ldb must be at least k.

beta

Scaling factor for matrix C.

c

The pointer to input/output matrix C. It must have a size of at least ldc*n if column major layout is used to store matrices or at least ldc*m if row major layout is used to store matrices . See Matrix Storage for more details.

ldc

The leading dimension of C. It must be positive and at least m if column major layout is used to store matrices or at least n if column 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

c

Pointer to the output matrix, overwritten by alpha*op(A)*op(B) + beta*C.

Notes

If beta = 0, matrix C does not need to be initialized before calling gemm.

Return Values

Output event to wait on to ensure computation is complete.

Parent topic: BLAS Level 3 Routines