rocsparse_sgtsv_no_pivot_strided_batch Interface Reference

rocsparse_sgtsv_no_pivot_strided_batch Interface Reference#

HIPFORT API Reference: hipfort_rocsparse::rocsparse_sgtsv_no_pivot_strided_batch Interface Reference

Strided Batch tridiagonal solver (no pivoting) More...

Public Member Functions
integer(kind(rocsparse_status_success)) function	rocsparse_sgtsv_no_pivot_strided_batch_ (handle, m, dl, d, du, x, batch_count, batch_stride, temp_buffer)

integer(kind(rocsparse_status_success)) function	rocsparse_sgtsv_no_pivot_strided_batch_rank_0 (handle, m, dl, d, du, x, batch_count, batch_stride, temp_buffer)

integer(kind(rocsparse_status_success)) function	rocsparse_sgtsv_no_pivot_strided_batch_rank_1 (handle, m, dl, d, du, x, batch_count, batch_stride, temp_buffer)

Detailed Description

Strided Batch tridiagonal solver (no pivoting)

rocsparse_gtsv_no_pivot_strided_batch solves a batched tridiagonal linear system

\[ T^{i}*x^{i} = x^{i} \]

where for each batch \(i=0\ldots\) batch_count, \(T^{i}\) is a sparse tridiagonal matrix and \(x^{i}\) is a dense right-hand side vector. All of the tridiagonal matrices, \(T^{i}\), are packed one after the other into three vectors: dl for the lower diagonals, d for the main diagonals, and du for the upper diagonals. See below for a description of what this strided memory pattern looks like.

Solving the batched tridiagonal system involves two steps. First, call rocsparse_Xgtsv_no_pivot_strided_batch_buffer_size() to determine the size of the required temporary storage buffer. After this is determined, allocate the buffer and pass it to rocsparse_Xgtsv_no_pivot_strided_batch() to perform the actual solve. The \(x^{i}\) vectors, which initially stores the right-hand side values, are overwritten with the solution after the call to rocsparse_Xgtsv_no_pivot_strided_batch().

The strided batch routines write each batch matrix one after the other in memory. For example, consider the following batch matrices:

\[ \begin{bmatrix} t^{0}_{00} & t^{0}_{01} & 0 \\% t^{0}_{10} & t^{0}_{11} & t^{0}_{12} \\% 0 & t^{0}_{21} & t^{0}_{22} \end{bmatrix} \begin{bmatrix} t^{1}_{00} & t^{1}_{01} & 0 \\% t^{1}_{10} & t^{1}_{11} & t^{1}_{12} \\% 0 & t^{1}_{21} & t^{1}_{22} \end{bmatrix} \begin{bmatrix} t^{2}_{00} & t^{2}_{01} & 0 \\% t^{2}_{10} & t^{2}_{11} & t^{2}_{12} \\% 0 & t^{2}_{21} & t^{2}_{22} \end{bmatrix} \]

In strided format, the upper, lower, and diagonal arrays would look like:

\[ \begin{align} \text{lower} &= \begin{bmatrix} 0 & t^{0}_{10} & t^{0}_{21} & 0 & t^{1}_{10} & t^{1}_{21} & 0 & t^{2}_{10} & t^{2}_{21} \end{bmatrix} \\% \text{diagonal} &= \begin{bmatrix} t^{0}_{00} & t^{0}_{11} & t^{0}_{22} & t^{1}_{00} & t^{1}_{11} & t^{1}_{22} & t^{2}_{00} & t^{2}_{11} & t^{2}_{22} \end{bmatrix} \\% \text{upper} &= \begin{bmatrix} t^{0}_{01} & t^{0}_{12} & 0 & t^{1}_{01} & t^{1}_{12} & 0 & t^{2}_{01} & t^{2}_{12} & 0 \end{bmatrix} \\% \end{align} \]

For the lower array, for each batch i, the i*batch_stride entries are zero, and for the upper array, the i*batch_stride+batch_stride-1 entries are zero.

Note: This function is non-blocking and executed asynchronously with respect to the host. It can return before the actual computation has finished.; This routine supports execution in a hipGraph context.

Parameters

[in]	handle	- handle to the rocSPARSE library context queue.
[in]	m	- size of the tri-diagonal linear system (must be >= 2).
[in]	dl	- lower diagonal of tri-diagonal system. The first entry must be zero.
[in]	d	- main diagonal of tri-diagonal system.
[in]	du	- upper diagonal of tri-diagonal system. The last entry must be zero.
[in,out]	x	- dense array of righthand-sides, where the ith right-hand side starts at `x+batch_stride*i`.
[in]	batch_count	- the number of systems to solve.
[in]	batch_stride	- the number of elements that separate each system. Must satisfy `batch_stride` >= `m`.
[in]	temp_buffer	- temporary storage buffer allocated by the user.

Return values

rocsparse_status_success	the operation completed successfully.
rocsparse_status_invalid_handle	the library context was not initialized.
rocsparse_status_invalid_size	`m`, `batch_count`, or `batch_stride` is invalid.
rocsparse_status_invalid_pointer	`dl`, `d`, `du`, `x`, or `temp_buffer` pointer is invalid.
rocsparse_status_internal_error	an internal error occurred.

Example

Member Function/Subroutine Documentation