her2k

Performs a Hermitian rank-2k update.

Syntax

void her2k(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_real beta, buffer<T, 1> &c, std::int64_t ldc)

her2k supports the following precisions and devices:

T

T_real

Devices Supported

std::complex<float>

float

Host, CPU, and GPU

std::complex<double>

double

Host, CPU, and GPU

Description

The her2k routines perform a rank-2k update of an n x n Hermitian matrix C by general matrices A and B. If trans = transpose::nontrans. The operation is defined as

C <- alpha*A*BH + conjg(alpha)B*AH + beta*C

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

If trans = transpose::conjtrans, the operation is defined as:

C <- alpha*AH*B + conjg(alpha)*BH*A + beta*C

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

In both cases:

alpha is a complex scalar and beta is a real scalar.

C is a Hermitian 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 A’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. Supported operations are transpose::nontrans and transpose::conjtrans.

n

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

k

The inner dimension of matrix multiplications. The value of k must be at least equal to zero.

alpha

Complex 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.

beta

Real scaling factor for matrix C.

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.

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.