  Matrices and more generally multidimensional arrays, form the backbone of
computational studies. In this paper we demonstrate increases in computational
efficiency by performing partial-tracing/tensor-contractions on sparse-arrays.
It was shown that sparse-arrays are really 3 dense-arrays (dense-shape,
index-array, and data-array). Dense-array manipulations of these constituent
arrays are used to determine the resulting partial-trace. Because computational
arrays are used in a verity of different studies, these methods are broadly
applicable.
