rocsolver_cungbr Interface Reference

rocsolver_cungbr Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_cungbr Interface Reference

UNGBR generates an m-by-n complex Matrix Q with orthonormal rows or columns. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_cungbr_ (handle, storev, m, n, k, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_cungbr_full_rank (handle, storev, m, n, k, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_cungbr_rank_0 (handle, storev, m, n, k, A, lda, ipiv)

integer(kind(rocblas_status_success)) function	rocsolver_cungbr_rank_1 (handle, storev, m, n, k, A, lda, ipiv)

Detailed Description

UNGBR generates an m-by-n complex Matrix Q with orthonormal rows or columns.

If storev is column-wise, then the matrix Q has orthonormal columns. If m >= k, Q is defined as the first n columns of the product of k Householder reflectors of order m

\[ Q = H_1H_2\cdots H_k \]

If m < k, Q is defined as the product of Householder reflectors of order m

\[ Q = H_1H_2\cdots H_{m-1} \]

On the other hand, if storev is row-wise, then the matrix Q has orthonormal rows. If n > k, Q is defined as the first m rows of the product of k Householder reflectors of order n

\[ Q = H_kH_{k-1}\cdots H_1 \]

If n <= k, Q is defined as the product of Householder reflectors of order n

\[ Q = H_{n-1}H_{n-2}\cdots H_1 \]

The Householder matrices \(H_i\) are never stored, they are computed from its corresponding Householder vectors \(v_i\) and scalars \(\text{ipiv}[i]\), as returned by GEBRD in its arguments A and tauq or taup.

Parameters

[in]	handle	rocblas_handle.
[in]	storev	rocblas_storev. Specifies whether to work column-wise or row-wise.
[in]	m	rocblas_int. m >= 0. The number of rows of the matrix Q. If row-wise, then min(n,k) <= m <= n.
[in]	n	rocblas_int. n >= 0. The number of columns of the matrix Q. If column-wise, then min(m,k) <= n <= m.
[in]	k	rocblas_int. k >= 0. The number of columns (if storev is column-wise) or rows (if row-wise) of the original matrix reduced by GEBRD.
[in,out]	A	pointer to type. Array on the GPU of dimension lda*n. On entry, the Householder vectors as returned by GEBRD. On exit, the computed matrix Q.
[in]	lda	rocblas_int. lda >= m. Specifies the leading dimension of A.
[in]	ipiv	pointer to type. Array on the GPU of dimension min(m,k) if column-wise, or min(n,k) if row-wise. The Householder scalars as returned by GEBRD.

Member Function/Subroutine Documentation