syr2k

Performs a symmetric rank-2k update.

Syntax

void syr2k(queue &exec_queue, uplo upper_lower, transpose trans, std::int64_t n, std::int64_t k, 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)

syr2k 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 syr2k routines perform a rank-2k update of an n x n symmetric matrix C by general matrices A and B. If trans = transpose::nontrans, the operation is defined as:

C <- alpha*(A*BT + B*AT) + beta*C

where A is n x k and B is k x n.

If trans = transpose::trans, the operationis defined as:

C <- alpha*(AT*B + BT*A) + beta*C

where A is k x n and B is n x k.

In both cases:

alpha and beta are scalars,

C is a symmetric matrix and A,B are general matrices,

The inner dimension of both matrix multiplications is k.

Input Parameters

exec_queue

The queue where the routine should be executed.

upper_lower

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

trans

Specifies the operation to apply, as described above. Conjugation is never performed, even if trans = transpose::conjtrans.

n

Number of rows and columns in C.The value of n must be at least zero.

k

Inner dimension of matrix multiplications.The value of k must be at least zero.

alpha

Scaling factor for the rank-2k update.

a

Buffer holding input matrix A. If trans = transpose::nontrans, A is an n-by-k matrix so the array a must have size at least lda*k (respectively, lda*n) if column (respectively, row) major layout is used to store matrices. Otherwise, A is an k-by-n matrix so the array a must have size at least lda*n (respectively, lda*k) if column (respectively, row) major layout is used to store matrices. See Matrix and Vector Storage for more details.

lda

Leading dimension of A. If matrices are stored using column major layout, lda must be at least n if trans=transpose::nontrans, and at least k otherwise. If matrices are stored using row major layout, lda must be at least k if trans=transpose::nontrans, and at least n otherwise. Must be positive.

b

Buffer holding input matrix B. If trans = transpose::nontrans, B is an k-by-n matrix so the array b must have size at least ldb*n (respectively, ldb*k) if column (respectively, row) major layout is used to store matrices. Otherwise, B is an n-by-k matrix so the array b must have size at least ldb*k (respectively, ldb*n) if column (respectively, row) major layout is used to store matrices. See Matrix and Vector Storage for more details.

ldb

Leading dimension of B. If matrices are stored using column major layout, ldb must be at least k if trans = transpose::nontrans, and at least n otherwise. If matrices are stored using row major layout, ldb must be at least n if trans = transpose::nontrans, and at least k otherwise. Must be positive.

beta

Scaling factor for matrix C.

c

Buffer holding input/output matrix C. Must have size at least ldc*n. See Matrix and Vector Storage for more details

ldc

Leading dimension of C. Must be positive and at least n.

Output Parameters

c

Output buffer, overwritten by the updated C matrix.