MatlabNotes

15.6 Building MatricesIt is often convenient to build large matricesfrom smaller ones:>> C=[0 1; 3 -2; 4 2]; x=[8;-4;1];>> G = [C x]G =0 1 83 -2 -44 2 1>> A, B, H = [A; B]A =5 7 91 -3 -7B =-1 2 59 0 5H =5 7 91 -3 -7-1 2 59 0 5so we have added an extra column (x) toC inorder to form G and have stacked A and B ontop of each other to form H.>> J = [1:4; 5:8; 9:12; 20 0 5 4]J =1 2 3 45 6 7 89 10 11 1220 0 5 4>> K = [ diag(1:4) J; J’ zeros(4,4)]K =1 0 0 0 1 2 3 40 2 0 0 5 6 7 80 0 3 0 9 10 11 120 0 0 4 20 0 5 41 5 9 20 0 0 0 02 6 10 0 0 0 0 03 7 11 5 0 0 0 04 8 12 4 0 0 0 0The command spy(K) will produce a graphicaldisplay of the location of the nonzero entries inK (it will also give a value for nz—the numberof nonzero entries):>> spy(K), gridThe keyword end can also be used with multidimensionalarraysK(1:2,end-1:end)ans =3 47 815.7 Tabulating FunctionsThis has been addressed in earlier sections butwe are now in a position to produce a moresuitable table format.Example 15.1Tabulate the functions y = 4sin3x and u =3 sin 4x for x =0, 0.1, 0.2,...,0.5.>> x = 0:0.1:0.5;>> y = 4*sin(3*x); u = 3*sin(4*x);>> [ x’ y’ u’]ans =0 0 00.1000 1.1821 1.16830.2000 2.2586 2.15210.3000 3.1333 2.79610.4000 3.7282 2.99870.5000 3.9900 2.7279Note the use of transpose (’) to get columnvectors. (we could replace the last commandby [x; y; u;]’)We could also have done this more directly:>> x = (0:0.1:0.5)’;>> [x 4*sin(3*x) 3*sin(4*x)]15.8 Extracting Parts of MatricesWe may extract sections from a matrix in muchthe same way as for a vector (page 6).Each element of a matrix is indexed accordingto which row and column it belongs to. Theentry in the ith row and jth column is denotedmathematically by A i,j and, in Matlab,by A(i,j). So>> JJ =1 2 3 45 6 7 820