rocsolver_sgelqf_batched Interface Reference

rocsolver_sgelqf_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgelqf_batched Interface Reference

GELQF_BATCHED computes the LQ factorization of a batch of general m-by-n matrices. More...

Public Member Functions
integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_batched_ (handle, m, n, A, lda, ipiv, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_batched_full_rank (handle, m, n, A, lda, ipiv, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_batched_rank_0 (handle, m, n, A, lda, ipiv, strideP, batch_count)

integer(kind(rocblas_status_success)) function	rocsolver_sgelqf_batched_rank_1 (handle, m, n, A, lda, ipiv, strideP, batch_count)

Detailed Description

GELQF_BATCHED computes the LQ factorization of a batch of general m-by-n matrices.

(This is the blocked version of the algorithm).

The factorization of matrix \(A_j\) in the batch has the form

\[ A_j = \left[\begin{array}{cc} L_j & 0 \end{array}\right] Q_j \]

where \(L_j\) is lower triangular (lower trapezoidal if m > n), and \(Q_j\) is a n-by-n orthogonal/unitary matrix represented as the product of Householder matrices

\[ Q_j = H_{j_k}'H_{j_{k-1}}' \cdots H_{j_1}', \quad \text{with} \: k = \text{min}(m,n). \]

Each Householder matrices \(H_{j_i}\) is given by

\[ H_{j_i} = I - \text{ipiv}_j[i] \cdot v_{j_i}' v_{j_i} \]

where the first i-1 elements of Householder vector \(v_{j_i}\) are zero, and \(v_{j_i}[i] = 1\).

Parameters

[in]	handle	rocblas_handle.
[in]	m	rocblas_int. m >= 0. The number of rows of all the matrices A_j in the batch.
[in]	n	rocblas_int. n >= 0. The number of columns of all the matrices A_j in the batch.
[in,out]	A	Array of pointers to type. Each pointer points to an array on the GPU of dimension lda*n. On entry, the m-by-n matrices A_j to be factored. On exit, the elements on and below the diagonal contain the factor L_j. The elements above the diagonal are the last n - i elements of Householder vector v_(j_i).
[in]	lda	rocblas_int. lda >= m. Specifies the leading dimension of matrices A_j.
[out]	ipiv	pointer to type. Array on the GPU (the size depends on the value of strideP). Contains the vectors ipiv_j of corresponding Householder scalars.
[in]	strideP	rocblas_stride. Stride from the start of one vector ipiv_j to the next one ipiv_(j+1). There is no restriction for the value of strideP. Normal use is strideP >= min(m,n).
[in]	batch_count	rocblas_int. batch_count >= 0. Number of matrices in the batch.

Member Function/Subroutine Documentation