Basics of MATLAB and Beyond

first row of a by taking the columnar sum of the triangular matrix s:a(1,:) = sum(s)⎛⎞1 1 1 1 1 ···0 2 2 2 20 0 3 3 3= sum0 0 0 4 4⎜⎝0 0 0 0 5 ⎟⎠....We can generate the second row of a by taking the same columnar sumbut leaving out the first row of s:a(2,:) = sum(s(2:end,:))⎛⎞0 2 2 2 2 ···0 0 3 3 3= sum0 0 0 4 4⎜⎝0 0 0 0 5 ⎟⎠....In general, then, we can generate the ith row of a by taking the columnarsum of s leaving out its first i − 1 rows: a(i,:) = sum(s(i:end,:)).Our final code will consist of putting this statement inside a for loop(this will be a good use of a for loop—see the first paragraph in thissection). Before we do that, though, we still need to generate the utilitymatrix s; here we can use matrix multiplication. The matrix we wantcan be obtained by taking the upper triangular part of the product of acolumn vector and a row vector:⎛⎞ ⎡⎛⎞⎤1 1 1 1 1 ···10 2 2 2 220 0 3 3 330 0 0 4 4= triu4· ( 1 1 1 1 1··· )⎜⎝0 0 0 0 5 ⎟ ⎢⎜⎠ ⎣⎝5 ⎟⎥⎠⎦.... .So here we have the final code to generate the a matrix (for N = 200):N = 200;s = triu((1:N)’*ones(1,N));a = zeros(N,N);for i = 1:N-1a(i,:) = sum(s(i:end,:));enda(N,:) = s(N,:);..c○ 2000 by CRC Press LLC