# Stencil Computations (View Offsets)¶

Key RAJA features shown in the following example:

• RAJA::Kernel loop execution template
• RAJA kernel execution policies
• RAJA::View multi-dimensional data access
• RAJA:make_offset_layout method to apply index offsets

This example applies a five-cell stencil sum to the interior cells of a two-dimensional square lattice and stores the resulting sums in a second lattice of equal size. The five-cell stencil accumulates values from each interior cell and its four neighbors. We use RAJA::View and RAJA::Layout constructs to simplify the multi-dimensional indexing so that we can write the stencil operation as follows:

output(row, col) = input(row, col) +
input(row - 1, col) + input(row + 1, col) +
input(row, col - 1) + input(row, col + 1)


A lattice is assumed to have $$N_r \times N_c$$ interior cells with unit values surrounded by a halo of cells containing zero values for a total dimension of $$(N_r + 2) \times (N_c + 2)$$. For example, when $$N_r = N_c = 3$$, the input lattice and values are:

 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0

After applying the stencil, the output lattice and values are:

 0 0 0 0 0 0 3 4 3 0 0 4 5 4 0 0 3 4 3 0 0 0 0 0 0

For this $$(N_r + 2) \times (N_c + 2)$$ lattice case, here is our (row, col) indexing scheme.

 (-1, 3) (0, 3) (1, 3) (2, 3) (3, 3) (-1, 2) (0, 2) (1, 2) (2, 2) (3, 2) (-1, 1) (0, 1) (1, 1) (2, 1) (3, 1) (-1, 0) (0, 0) (1, 0) (2, 0) (3, 0) (-1, -1) (0, -1) (1, -1) (2, -1) (3, -1)

Notably $$[0, N_r) \times [0, N_c)$$ corresponds to the interior index range over which we apply the stencil, and $$[-1,N_r] \times [-1, N_c]$$ is the full lattice index range.

## RAJA Offset Layouts¶

We use the RAJA::make_offset_layout method to construct a RAJA::OffsetLayout object that defines our two-dimensional indexing scheme. Then, we create two RAJA::View objects for each of the input and output lattice arrays.

  const int DIM = 2;

RAJA::OffsetLayout<DIM> layout =
RAJA::make_offset_layout<DIM>({{-1, -1}}, {{N_r, N_c}});

RAJA::View<int, RAJA::OffsetLayout<DIM>> inputView(input, layout);
RAJA::View<int, RAJA::OffsetLayout<DIM>> outputView(output, layout);


Here, the row index range is $$[-1, N_r]$$, and the column index range is $$[-1, N_c]$$. The first argument to each call to the RAJA::View constructor is a pointer to an array that holds the data for the view; we assume the arrays are properly allocated before these calls.

The offset layout mechanics of RAJA allow us to write loops over data arrays using non-zero based indexing and without having to manually compute the proper offsets into the arrays. For more details on the RAJA::View and RAJA::Layout concepts we use in this example, please refer to View and Layout.

## RAJA Kernel Implementation¶

For the RAJA implementations of the example computation, we use two RAJA::RangeSegment objects to define the row and column iteration spaces for the interior cells:

  RAJA::RangeSegment col_range(0, N_r);
RAJA::RangeSegment row_range(0, N_c);


Here, is an implementation using RAJA::kernel multi-dimensional loop execution with a sequential execution policy.

  using NESTED_EXEC_POL1 =
RAJA::KernelPolicy<
RAJA::statement::For<1, RAJA::seq_exec,    // row
RAJA::statement::For<0, RAJA::seq_exec,  // col
RAJA::statement::Lambda<0>
>
>
>;

RAJA::kernel<NESTED_EXEC_POL1>(RAJA::make_tuple(col_range, row_range),
[=](int col, int row) {

outputView(row, col) =
inputView(row, col)
+ inputView(row - 1, col)
+ inputView(row + 1, col)
+ inputView(row, col - 1)
+ inputView(row, col + 1);
});


Since the stencil operation is data parallel, any parallel execution policy may be used. The file RAJA/examples/tut_offset-layout.cpp contains a complete working example code with various parallel implementations. For more information about using the RAJA::kernel interface, please see Complex Loops (RAJA::kernel).