# The SUNLinSol_cuSolverSp_batchQR Module¶

The SUNLinearSolver_cuSolverSp_batchQR implementation of the SUNLinearSolver API is designed to be used with the SUNMATRIX_CUSPARSE matrix, and the NVECTOR_CUDA vector. The header file to include when using this module is sunlinsol/sunlinsol_cusolversp_batchqr.h. The installed library to link to is libsundials_sunlinsolcusolversp.lib where .lib is typically .so for shared libraries and .a for static libraries.

The SUNLinearSolver_cuSolverSp_batchQR module is experimental and subject to change.

## SUNLinSol_cuSolverSp_batchQR description¶

The SUNLinearSolver_cuSolverSp_batchQR implementation provides an interface to the batched sparse QR factorization method provided by the NVIDIA cuSOLVER library ([cuSOLVER]). The module is designed for solving block diagonal linear systems of the form

$\begin{split}\begin{bmatrix} \mathbf{A_1} & 0 & \cdots & 0\\ 0 & \mathbf{A_2} & \cdots & 0\\ \vdots & \vdots & \ddots & \vdots\\ 0 & 0 & \cdots & \mathbf{A_n}\\ \end{bmatrix} x_j = b_j\end{split}$

where all block matrices $$\mathbf{A_j}$$ share the same sparsisty pattern. The matrix must be the The SUNMATRIX_CUSPARSE Module.

## SUNLinSol_cuSolverSp_batchQR functions¶

The SUNLinearSolver_cuSolverSp_batchQR module defines implementations of all “direct” linear solver operations listed in The SUNLinearSolver API:

• SUNLinSolGetType_cuSolverSp_batchQR
• SUNLinSolInitialize_cuSolverSp_batchQR – this sets the first_factorize flag to 1
• SUNLinSolSetup_cuSolverSp_batchQR – this always copies the relevant SUNMATRIX_SPARSE data to the GPU; if this is the first setup it will perform symbolic analysis on the system
• SUNLinSolSolve_cuSolverSp_batchQR – this calls the cusolverSpXcsrqrsvBatched routine to perform factorization
• SUNLinSolLastFlag_cuSolverSp_batchQR
• SUNLinSolFree_cuSolverSp_batchQR

In addition, the module provides the following user-callable routines:

SUNLinearSolver SUNLinSol_cuSolverSp_batchQR(N_Vector y, SUNMatrix A, cusolverHandle_t cusol)

The function SUNLinSol_cuSolverSp_batchQR creates and allocates memory for a SUNLinearSolver object.

This returns a SUNLinearSolver object. If either A or y are incompatible then this routine will return NULL.

This routine analyzes the input matrix and vector to determine the linear system size and to assess compatibility with the solver.

This routine will perform consistency checks to ensure that it is called with consistent N_Vector and SUNMatrix implementations. These are currently limited to the SUNMATRIX_CUSPARSE matrix type and the NVECTOR_CUDA vector type. Since the SUNMATRIX_CUSPARSE matrix type is only compatible with the NVECTOR_CUDA the restriction is also in place for the linear solver. As additional compatible matrix and vector implementations are added to SUNDIALS, these will be included within this compatibility check.

void SUNLinSol_cuSolverSp_batchQR_GetDescription(SUNLinearSolver LS, char **desc)

The function SUNLinSol_cuSolverSp_batchQR_GetDescription accesses the string description of the object (empty by default).

void SUNLinSol_cuSolverSp_batchQR_SetDescription(SUNLinearSolver LS, const char *desc)

The function SUNLinSol_cuSolverSp_batchQR_SetDescription sets the string description of the object (empty by default).

void SUNLinSol_cuSolverSp_batchQR_GetDeviceSpace(SUNLinearSolver S, size_t* cuSolverInternal, size_t* cuSolverWorkspace)

The function SUNLinSol_cuSolverSp_batchQR_GetDeviceSpace returns the cuSOLVER batch QR method internal buffer size, in bytes, in the argument cuSolverInternal and the cuSOLVER batch QR workspace buffer size, in bytes, in the agrument cuSolverWorkspace. The size of the internal buffer is proportional to the number of matrix blocks while the size of the workspace is almost independent of the number of blocks.

## SUNLinSol_cuSolverSp_batchQR content¶

The SUNLinSol_cuSolverSp_batchQR module defines the content field of a SUNLinearSolver to be the following structure:

struct _SUNLinearSolverContent_cuSolverSp_batchQR {
int                last_flag;       /* last return flag                          */
booleantype        first_factorize; /* is this the first factorization?          */
size_t             internal_size;   /* size of cusolver buffer for Q and R       */
size_t             workspace_size;  /* size of cusolver memory for factorization */
cusolverSpHandle_t cusolver_handle; /* cuSolverSp context                        */
csrqrInfo_t        info;            /* opaque cusolver data structure            */
void*              workspace;       /* memory block used by cusolver             */
const char*        desc;            /* description of this linear solver         */
};