$4$ Problem $2$: Matrix Diagonal Sums

$4\mathrm{.}1$ Overview

A problem that occasionally arises in numerical computing when working with Matrices $(2$D Arrays$)$ is to compute the sums of the Diagonals of a matrix. The main diagonal of a matrix is comprised of all elements at indices $(0,0),(1,1),(2,2),$ and so forth. There are several numbering schemes for diagonals but we will use the one represented in the following diagram which also shows the sums of the diagonals.

sumdiag.png

Figure $6$: $5$ by $5$ matrix with diagonals colored. The diagram shows our numbering scheme for diagonals and the corresponding diagonal sums. Diagonal numbers start at $0$ and progress counter$-$clockwise around the bottom and right of the matrix. For square matrices, the main diagonal is always numbered as the #rows$-1$ or #cols$-1$ which are equal.

A code is provided in the file sumdiag$\_$base.c which computes the sums of diagonals and stores them in a vector. The algorithm does so using the most "natural" approach of walking down each diagonal and totaling its elements then storing the result in the associated vector element. As you survey the code, note the use of various convenience functions such as mget$($mat$,$i$,$j$)$ and vset$($vec$,$i$,$x$)$ to interact with the matrix and vector types used.

int sumdiag$\_$BASE$\_$NORMAL$($matrix$\_$t mat, vector$\_$t vec$)\{$

if$($vec$.$len $!=($mat$.$rows $+$ mat.cols $-1))\{$

printf$("$sumdiag$\_$base: bad sizes

$")$;

return $1$;

$\}$

for$($int i$=0$; i