A Matrix-Type for Performance-Portability

We describe a datatype for (dense) matrices whose primitive operations are decomposition and composition (of submatrices), as opposed to indexed element access which is the primitive operation on conventional arrays. Using the composition and decomposition operations it is for example possible to express both recursive and traditional block matrix algorithms (e.g., Cholesky factorization, QR-factorization, etc.) as is illustrated by the following (pretty-printed and contracted) example: function cholesky: Matrix → Matrix is cholesky( [ a ] ) = [√ a ] .. cholesky( [ A B C D ] ) = let U = cholesky( A ) .. Z = zeros( C )