Concept of Stencil Computation

Before using the SCA interface, it is necessary to understand some fundamental concepts of the stencil computation.

A stencil consists of stencil elements. Each stencil element has a relative location from the stencil center, a coefficient, and a reference to an input array. The mathematical expression of the stencil is shown below.

$Stencil(i_{\rm x},i_{\rm y},i_{\rm z},i_{\rm w}) = \sum_{k} c^{(k)} d^{(k)}[i_{\rm x}+l_{\rm x}^{(k)},i_{\rm y}+l_{\rm y}^{(k)},i_{\rm z}+l_{\rm z}^{(k)},i_{\rm w}+l_{\rm w}^{(k)}]$

Here, $(l_{\rm x}^{(k)},l_{\rm y}^{(k)},l_{\rm z}^{(k)},l_{\rm w}^{(k)})$ denotes the relative location of the kth stencil element, $c^{(k)}$ denotes the coefficient of the kth stencil element, and $d^{(k)}$ denotes the input array which the kth stencil element refers to.

In the SCA interface, you can specify either a scalar or an array as the coefficients $c^{(k)}$ .