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
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[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.
Member Function/Subroutine Documentation
◆ 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: