rocsolver_slabrd Interface Reference#
hipfort_rocsolver::rocsolver_slabrd Interface Reference
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Public Member Functions | |
| integer(kind(rocblas_status_success)) function | rocsolver_slabrd_full_rank (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy) |
| integer(kind(rocblas_status_success)) function | rocsolver_slabrd_orig (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy) |
| integer(kind(rocblas_status_success)) function | rocsolver_slabrd_rank_0 (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy) |
| integer(kind(rocblas_status_success)) function | rocsolver_slabrd_rank_1 (handle, m, n, k, A, lda, D, E, tauq, taup, X, ldx, Y, ldy) |
Detailed Description
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LABRD computes the bidiagonal form of the first k rows and columns of a general m-by-n matrix A, as well as the matrices X and Y needed to reduce the remaining part of A.
The bidiagonal form is given by:
B = Q' A P
where B is upper bidiagonal if m >= n and lower bidiagonal if m < n, and Q and P are orthogonalunitary matrices represented as the product of Householder matrices
Q = H(1) H(2) ... H(k) and P = G(1) G(2) ... G(k-1), if m >= n, or Q = H(1) H(2) ... H(k-1) and P = G(1) G(2) ... G(k), if m < n
Each Householder matrix H(i) and G(i) is given by
H(i) = I - tauq[i-1] v(i) v(i)', and G(i) = I - taup[i-1] u(i) u(i)'
If m >= n, the first i-1 elements of the Householder vector v(i) are zero, and v(i)[i] = 1; while the first i elements of the Householder vector u(i) are zero, and u(i)[i+1] = 1. If m < n, the first i elements of the Householder vector v(i) are zero, and v(i)[i+1] = 1; while the first i-1 elements of the Householder vector u(i) are zero, and u(i)[i] = 1.
The unreduced part of the matrix A can be updated using a block update:
A = A - V Y' - X U'
where V is an m-by-k matrix and U is an n-by-k formed using the vectors v and u.
- Parameters
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[in] handle rocblas_handle. [in] m rocblas_int. m >= 0.
The number of rows of the matrix A.[in] n rocblas_int. n >= 0.
The number of columns of the matrix A.[in] k rocblas_int. min(m,n) >= k >= 0.
The number of leading rows and columns of the matrix A to be reduced.[in,out] A pointer to type. Array on the GPU of dimension ldan.
On entry, the m-by-n matrix 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. If m >= n, the elements below the diagonal are the m - i elements of vector v(i) for i = 1,2,...,n, and the elements above the superdiagonal are the n - i - 1 elements of vector u(i) for i = 1,2,...,n-1. If m < n, the elements below the subdiagonal are the m - i - 1 elements of vector v(i) for i = 1,2,...,m-1, and the elements above the diagonal are the n - i elements of vector u(i) for i = 1,2,...,m.[in] lda rocblas_int. lda >= m.
specifies the leading dimension of A.[out] D pointer to real type. Array on the GPU of dimension k.
The diagonal elements of B.[out] E pointer to real type. Array on the GPU of dimension k.
The off-diagonal elements of B.[out] tauq pointer to type. Array on the GPU of dimension k.
The scalar factors of the Householder matrices H(i).[out] taup pointer to type. Array on the GPU of dimension k.
The scalar factors of the Householder matrices G(i).[out] X pointer to type. Array on the GPU of dimension ldxk.
The m-by-k matrix needed to reduce the unreduced part of A.[in] ldx rocblas_int. ldx >= m.
specifies the leading dimension of X.[out] Y pointer to type. Array on the GPU of dimension ldyk.
The n-by-k matrix needed to reduce the unreduced part of A.[in] ldy rocblas_int. ldy >= n.
specifies the leading dimension of Y.
Member Function/Subroutine Documentation
◆ rocsolver_slabrd_full_rank()
| integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_full_rank | ( | type(c_ptr), value | handle, |
| integer(c_int), value | m, | ||
| integer(c_int), value | n, | ||
| integer(c_int), value | k, | ||
| real(c_float), dimension(:,:), target | A, | ||
| integer(c_int), value | lda, | ||
| real(c_float), dimension(:), target | D, | ||
| real(c_float), dimension(:), target | E, | ||
| real(c_float), dimension(:), target | tauq, | ||
| real(c_float), dimension(:), target | taup, | ||
| real(c_float), dimension(:,:), target | X, | ||
| integer(c_int), value | ldx, | ||
| real(c_float), dimension(:,:), target | Y, | ||
| integer(c_int), value | ldy | ||
| ) |
◆ rocsolver_slabrd_orig()
| integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_orig | ( | type(c_ptr), value | handle, |
| integer(c_int), value | m, | ||
| integer(c_int), value | n, | ||
| integer(c_int), value | k, | ||
| type(c_ptr), value | A, | ||
| integer(c_int), value | lda, | ||
| type(c_ptr), value | D, | ||
| type(c_ptr), value | E, | ||
| type(c_ptr), value | tauq, | ||
| type(c_ptr), value | taup, | ||
| type(c_ptr), value | X, | ||
| integer(c_int), value | ldx, | ||
| type(c_ptr), value | Y, | ||
| integer(c_int), value | ldy | ||
| ) |
◆ rocsolver_slabrd_rank_0()
| integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_rank_0 | ( | type(c_ptr), value | handle, |
| integer(c_int), value | m, | ||
| integer(c_int), value | n, | ||
| integer(c_int), value | k, | ||
| real(c_float), target | A, | ||
| integer(c_int), value | lda, | ||
| real(c_float), target | D, | ||
| real(c_float), target | E, | ||
| real(c_float), target | tauq, | ||
| real(c_float), target | taup, | ||
| real(c_float), target | X, | ||
| integer(c_int), value | ldx, | ||
| real(c_float), target | Y, | ||
| integer(c_int), value | ldy | ||
| ) |
◆ rocsolver_slabrd_rank_1()
| integer(kind(rocblas_status_success)) function hipfort_rocsolver::rocsolver_slabrd::rocsolver_slabrd_rank_1 | ( | type(c_ptr), value | handle, |
| integer(c_int), value | m, | ||
| integer(c_int), value | n, | ||
| integer(c_int), value | k, | ||
| real(c_float), dimension(:), target | A, | ||
| integer(c_int), value | lda, | ||
| real(c_float), dimension(:), target | D, | ||
| real(c_float), dimension(:), target | E, | ||
| real(c_float), dimension(:), target | tauq, | ||
| real(c_float), dimension(:), target | taup, | ||
| real(c_float), dimension(:), target | X, | ||
| integer(c_int), value | ldx, | ||
| real(c_float), dimension(:), target | Y, | ||
| integer(c_int), value | ldy | ||
| ) |
The documentation for this interface was generated from the following file: