# rocsolver_sgebrd_batched Interface Reference#

HIPFORT API Reference: hipfort_rocsolver::rocsolver_sgebrd_batched Interface Reference
hipfort_rocsolver::rocsolver_sgebrd_batched Interface Reference

GEBRD_BATCHED computes the bidiagonal form of a batch of general m-by-n matrices. More...

## Public Member Functions

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_batched_ (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_batched_full_rank (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_batched_rank_0 (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

integer(kind(rocblas_status_success)) function rocsolver_sgebrd_batched_rank_1 (handle, m, n, A, lda, D, strideD, E, strideE, tauq, strideQ, taup, strideP, batch_count)

## Detailed Description

GEBRD_BATCHED computes the bidiagonal form of a batch of general m-by-n matrices.

(This is the blocked version of the algorithm).

For each instance in the batch, the bidiagonal form is given by:

$B_j = Q_j' A_j P_j$

where $$B_j$$ is upper bidiagonal if m >= n and lower bidiagonal if m < n, and $$Q_j$$ and $$P_j$$ are orthogonal/unitary matrices represented as the product of Householder matrices

$\begin{array}{cl} Q_j = H_{j_1}H_{j_2}\cdots H_{j_n}\: \text{and} \: P_j = G_{j_1}G_{j_2}\cdots G_{j_{n-1}}, & \: \text{if}\: m >= n, \:\text{or}\newline Q_j = H_{j_1}H_{j_2}\cdots H_{j_{m-1}}\: \text{and} \: P_j = G_{j_1}G_{j_2}\cdots G_{j_m}, & \: \text{if}\: m < n. \end{array}$

Each Householder matrix $$H_{j_i}$$ and $$G_{j_i}$$ is given by

$\begin{array}{cl} H_{j_i} = I - \text{tauq}_j[i] \cdot v_{j_i} v_{j_i}', & \: \text{and}\newline G_{j_i} = I - \text{taup}_j[i] \cdot u_{j_i}' u_{j_i}. \end{array}$

If m >= n, the first i-1 elements of the Householder vector $$v_{j_i}$$ are zero, and $$v_{j_i}[i] = 1$$; while the first i elements of the Householder vector $$u_{j_i}$$ are zero, and $$u_{j_i}[i+1] = 1$$. If m < n, the first i elements of the Householder vector $$v_{j_i}$$ are zero, and $$v_{j_i}[i+1] = 1$$; while the first i-1 elements of the Householder vector $$u_{j_i}$$ are zero, and $$u_{j_i}[i] = 1$$.

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 the diagonal and superdiagonal (if m >= n), or subdiagonal (if m < n) contain the bidiagonal form B_j. If m >= n, the elements below the diagonal are the last m - i elements of Householder vector v_(j_i), and the elements above the superdiagonal are the last n - i - 1 elements of Householder vector u_(j_i). If m < n, the elements below the subdiagonal are the last m - i - 1 elements of Householder vector v_(j_i), and the elements above the diagonal are the last n - i elements of Householder vector u_(j_i). [in] lda rocblas_int. lda >= m. Specifies the leading dimension of matrices A_j. [out] D pointer to real type. Array on the GPU (the size depends on the value of strideD). The diagonal elements of B_j. [in] strideD rocblas_stride. Stride from the start of one vector D_j to the next one D_(j+1). There is no restriction for the value of strideD. Normal use case is strideD >= min(m,n). [out] E pointer to real type. Array on the GPU (the size depends on the value of strideE). The off-diagonal elements of B_j. [in] strideE rocblas_stride. Stride from the start of one vector E_j to the next one E_(j+1). There is no restriction for the value of strideE. Normal use case is strideE >= min(m,n)-1. [out] tauq pointer to type. Array on the GPU (the size depends on the value of strideQ). Contains the vectors tauq_j of Householder scalars associated with matrices Q_j. [in] strideQ rocblas_stride. Stride from the start of one vector tauq_j to the next one tauq_(j+1). There is no restriction for the value of strideQ. Normal use is strideQ >= min(m,n). [out] taup pointer to type. Array on the GPU (the size depends on the value of strideP). Contains the vectors taup_j of Householder scalars associated with matrices P_j. [in] strideP rocblas_stride. Stride from the start of one vector taup_j to the next one taup_(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.

## ◆ rocsolver_sgebrd_batched_()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd_batched::rocsolver_sgebrd_batched_ ( type(c_ptr), value handle, integer(c_int), value m, integer(c_int), value n, type(c_ptr) A, integer(c_int), value lda, type(c_ptr), value D, integer(c_int64_t), value strideD, type(c_ptr), value E, integer(c_int64_t), value strideE, type(c_ptr), value tauq, integer(c_int64_t), value strideQ, type(c_ptr), value taup, integer(c_int64_t), value strideP, integer(c_int), value batch_count )

## ◆ rocsolver_sgebrd_batched_full_rank()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd_batched::rocsolver_sgebrd_batched_full_rank ( type(c_ptr) handle, integer(c_int) m, integer(c_int) n, real(c_float), dimension(:,:,:), target A, integer(c_int) lda, real(c_float), dimension(:), target D, integer(c_int64_t) strideD, real(c_float), dimension(:), target E, integer(c_int64_t) strideE, real(c_float), dimension(:), target tauq, integer(c_int64_t) strideQ, real(c_float), dimension(:), target taup, integer(c_int64_t) strideP, integer(c_int) batch_count )

## ◆ rocsolver_sgebrd_batched_rank_0()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd_batched::rocsolver_sgebrd_batched_rank_0 ( type(c_ptr) handle, integer(c_int) m, integer(c_int) n, real(c_float), target A, integer(c_int) lda, real(c_float), target D, integer(c_int64_t) strideD, real(c_float), target E, integer(c_int64_t) strideE, real(c_float), target tauq, integer(c_int64_t) strideQ, real(c_float), target taup, integer(c_int64_t) strideP, integer(c_int) batch_count )

## ◆ rocsolver_sgebrd_batched_rank_1()

 integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_sgebrd_batched::rocsolver_sgebrd_batched_rank_1 ( type(c_ptr) handle, integer(c_int) m, integer(c_int) n, real(c_float), dimension(:), target A, integer(c_int) lda, real(c_float), dimension(:), target D, integer(c_int64_t) strideD, real(c_float), dimension(:), target E, integer(c_int64_t) strideE, real(c_float), dimension(:), target tauq, integer(c_int64_t) strideQ, real(c_float), dimension(:), target taup, integer(c_int64_t) strideP, integer(c_int) batch_count )

The documentation for this interface was generated from the following file: