rocsolver_sormbr Interface Reference

rocsolver_sormbr Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sormbr Interface Reference

The ORMBR functions multiply a matrix Q with orthonormal rows or columns by a general m-by-n matrix C. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sormbr_ (handle, storev, side, trans, m, n, k, a, lda, ipiv, c, ldc)

integer(kind(rocblas_status_success)) function	rocsolver_sormbr_rank_0 (handle, storev, side, trans, m, n, k, a, lda, ipiv, c, ldc)

integer(kind(rocblas_status_success)) function	rocsolver_sormbr_rank_1 (handle, storev, side, trans, m, n, k, a, lda, ipiv, c, ldc)

integer(kind(rocblas_status_success)) function	rocsolver_sormbr_full_rank (handle, storev, side, trans, m, n, k, a, lda, ipiv, c, ldc)

Detailed Description

The ORMBR functions multiply a matrix Q with orthonormal rows or columns by a general m-by-n matrix C.

If storev is column-wise, then the matrix Q has orthonormal columns. If storev is row-wise, then the matrix Q has orthonormal rows. The matrix Q is applied in one of the following forms, depending on the values of side and trans:

\[ \begin{array}{cl} QC & \: \text{No transpose from the left,}\\% Q^TC & \: \text{Transpose from the left,}\\% CQ & \: \text{No transpose from the right, and}\\% CQ^T & \: \text{Transpose from the right.} \end{array} \]

The order q of the orthogonal matrix Q is q = m if applying from the left or q = n if applying from the right.

When storev is column-wise, if q >= k, then Q is defined as the product of k Householder reflectors

\[ Q = H(1)H(2)\cdots H(k), \]

and if q < k, then Q is defined as the product

\[ Q = H(1)H(2)\cdots H(q-1). \]

When storev is row-wise, if q > k, then Q is defined as the product of k Householder reflectors

\[ Q = H(1)H(2)\cdots H(k), \]

and if q <= k, Q is defined as the product

\[ Q = H(1)H(2)\cdots H(q-1). \]

The Householder matrices \(H(i)\) are never stored. They are computed from its corresponding Householder vectors and scalars 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]	side	- rocblas_side. Specifies from which side to apply Q.
[in]	trans	- rocblas_operation. Specifies whether the matrix Q or its transpose is to be applied.
[in]	m	- rocblas_int. m >= 0. Number of rows of matrix C.
[in]	n	- rocblas_int. n >= 0. Number of columns of matrix C.
[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]	A	- pointer to type. Array on the GPU of size ldamin(q,k) if column-wise, or ldaq if row-wise. The Householder vectors as returned by GEBRD.
[in]	lda	- rocblas_int. lda >= q if column-wise, or lda >= min(q,k) if row-wise. Leading dimension of A.
[in]	ipiv	- pointer to type. Array on the GPU of dimension at least min(q,k). The Householder scalars as returned by GEBRD.
[in,out]	C	- pointer to type. Array on the GPU of size ldc*n. On entry, the matrix C. On exit, it is overwritten with \(QC\), \(CQ\), \(Q^TC\), or \(CQ^T\).
[in]	ldc	- rocblas_int. ldc >= m. Leading dimension of C.

Member Function/Subroutine Documentation