symm

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

Syntax

void symm(queue &exec_queue, side left_right, uplo upper_lower, std::int64_t m, std::int64_t n, T alpha, buffer<T, 1> &a, std::int64_t lda, buffer<T, 1> &b, std::int64_t ldb, T beta, buffer<T, 1> &c, std::int64_t ldc)

symm supports the following precisions and devices:

T

Devices Supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

std::complex<float>

Host, CPU, and GPU

std::complex<double>

Host, CPU, and GPU

Description

The symm routines compute a scalar-matrix-matrix product and add the result to a scalar-matrix product, where one of the matrices in the multiplication is symmetric. The argument left_right determines if the symmetric 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, the operation is defined as

C <- alpha*A*B + beta*C,

or

C <- alpha*B*A + beta*C,

where:

alpha and beta are scalars,

A is a symmetric matrix, either m-by-m or n-by-n,

B and C are m-by-n matrices.

Input Parameters

exec_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 Data Types for more details.

upper_lower

Specifies whether A’s data is stored in its upper or lower triangle. See Data Types for more details.

m

Number of rows of B and C. The value of m must be at least zero.

n

Number of columns of B and C. 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 A is on the left of the multiplication, or lda*n if A is on the right. See Matrix and Vector Storage for more details.

lda

Leading dimension of A. Must be at least m if A is on the left of the multiplication, or at least n if A is on the right. Must be positive.

b

Buffer holding input matrix B. It must have a size of 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 and Vector 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 column major layout is used to store matrices.

beta

Scaling factor for matrix C.

c

Buffer holding 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 and Vector Storage for more details.

ldc

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

Output buffer, overwritten by alpha*A*B + beta*C (left_right = side::left) or alpha*B*A + beta*C (left_right = side::right).

Notes

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