Matlab diary from CS 290H, Wednesday, April 02, 2014 This is /Users/gilbert/Documents/CS290hSpring2014/Matlab/startup.m Starting diary file diary-02-Apr-2014.txt > A = diag(ones(1,19),1); > A = A+A'; > L = laplacian(A) L = Columns 1 through 8 1 -1 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 -1 2 -1 0 ... > spy(L) > [W,D] = eig(L); > whos Name Size Bytes Class Attributes A 20x20 3200 double D 20x20 3200 double L 20x20 3200 double W 20x20 3200 double > l = diag(D) l = -0.0000 0.0246 0.0979 0.2180 0.3820 0.5858 0.8244 1.0920 1.3820 1.6871 2.0000 2.3129 2.6180 2.9080 3.1756 3.4142 3.6180 3.7820 3.9021 3.9754 > l(1) ans = -5.2834e-16 > W W = Columns 1 through 5 0.2236 -0.3153 0.3123 -0.3075 -0.3008 0.2236 -0.3075 0.2818 -0.2405 -0.1859 0.2236 -0.2922 0.2236 -0.1210 0.0000 0.2236 -0.2696 0.1436 0.0248 0.1859 0.2236 -0.2405 0.0495 0.1652 0.3008 0.2236 -0.2054 -0.0495 0.2696 0.3008 0.2236 -0.1652 -0.1436 0.3153 0.1859 0.2236 -0.1210 -0.2236 0.2922 -0.0000 0.2236 -0.0738 -0.2818 0.2054 -0.1859 0.2236 -0.0248 -0.3123 0.0738 -0.3008 0.2236 0.0248 -0.3123 -0.0738 -0.3008 0.2236 0.0738 -0.2818 -0.2054 -0.1859 0.2236 0.1210 -0.2236 -0.2922 0.0000 0.2236 0.1652 -0.1436 -0.3153 0.1859 0.2236 0.2054 -0.0495 -0.2696 0.3008 0.2236 0.2405 0.0495 -0.1652 0.3008 0.2236 0.2696 0.1436 -0.0248 0.1859 0.2236 0.2922 0.2236 0.1210 -0.0000 0.2236 0.3075 0.2818 0.2405 -0.1859 0.2236 0.3153 0.3123 0.3075 -0.3008 Columns 6 through 10 -0.2922 -0.2818 -0.2696 -0.2558 -0.2405 -0.1210 -0.0495 0.0248 0.0977 0.1652 0.1210 0.2236 0.2922 0.3162 0.2922 0.2922 0.3123 0.2405 0.0977 -0.0738 0.2922 0.1436 -0.0738 -0.2558 -0.3153 0.1210 -0.1436 -0.3075 -0.2558 -0.0248 -0.1210 -0.3123 -0.2054 0.0977 0.3075 -0.2922 -0.2236 0.1210 0.3162 0.1210 -0.2922 0.0495 0.3153 0.0977 -0.2696 -0.1210 0.2818 0.1652 -0.2558 -0.2054 0.1210 0.2818 -0.1652 -0.2558 0.2054 0.2922 0.0495 -0.3153 0.0977 0.2696 0.2922 -0.2236 -0.1210 0.3162 -0.1210 0.1210 -0.3123 0.2054 0.0977 -0.3075 -0.1210 -0.1436 0.3075 -0.2558 0.0248 -0.2922 0.1436 0.0738 -0.2558 0.3153 -0.2922 0.3123 -0.2405 0.0977 0.0738 -0.1210 0.2236 -0.2922 0.3162 -0.2922 0.1210 -0.0495 -0.0248 0.0977 -0.1652 0.2922 -0.2818 0.2696 -0.2558 0.2405 Columns 11 through 15 -0.2236 -0.2054 -0.1859 -0.1652 -0.1436 0.2236 0.2696 0.3008 0.3153 0.3123 0.2236 0.1210 -0.0000 -0.1210 -0.2236 -0.2236 -0.3075 -0.3008 -0.2054 -0.0495 -0.2236 -0.0248 0.1859 0.3075 0.2818 0.2236 0.3153 0.1859 -0.0738 -0.2818 0.2236 -0.0738 -0.3008 -0.2405 0.0495 -0.2236 -0.2922 0.0000 0.2922 0.2236 -0.2236 0.1652 0.3008 -0.0248 -0.3123 0.2236 0.2405 -0.1859 -0.2696 0.1436 0.2236 -0.2405 -0.1859 0.2696 0.1436 -0.2236 -0.1652 0.3008 0.0248 -0.3123 -0.2236 0.2922 0.0000 -0.2922 0.2236 0.2236 0.0738 -0.3008 0.2405 0.0495 0.2236 -0.3153 0.1859 0.0738 -0.2818 -0.2236 0.0248 0.1859 -0.3075 0.2818 -0.2236 0.3075 -0.3008 0.2054 -0.0495 0.2236 -0.1210 -0.0000 0.1210 -0.2236 0.2236 -0.2696 0.3008 -0.3153 0.3123 -0.2236 0.2054 -0.1859 0.1652 -0.1436 Columns 16 through 20 -0.1210 -0.0977 -0.0738 0.0495 -0.0248 0.2922 0.2558 0.2054 -0.1436 0.0738 -0.2922 -0.3162 -0.2922 0.2236 -0.1210 0.1210 0.2558 0.3153 -0.2818 0.1652 0.1210 -0.0977 -0.2696 0.3123 -0.2054 -0.2922 -0.0977 0.1652 -0.3123 0.2405 0.2922 0.2558 -0.0248 0.2818 -0.2696 -0.1210 -0.3162 -0.1210 -0.2236 0.2922 -0.1210 0.2558 0.2405 0.1436 -0.3075 0.2922 -0.0977 -0.3075 -0.0495 0.3153 -0.2922 -0.0977 0.3075 -0.0495 -0.3153 0.1210 0.2558 -0.2405 0.1436 0.3075 0.1210 -0.3162 0.1210 -0.2236 -0.2922 -0.2922 0.2558 0.0248 0.2818 0.2696 0.2922 -0.0977 -0.1652 -0.3123 -0.2405 -0.1210 -0.0977 0.2696 0.3123 0.2054 -0.1210 0.2558 -0.3153 -0.2818 -0.1652 0.2922 -0.3162 0.2922 0.2236 0.1210 -0.2922 0.2558 -0.2054 -0.1436 -0.0738 0.1210 -0.0977 0.0738 0.0495 0.0248 > norm(W' * W - eye(20)) ans = 3.1714e-15 > plot(W(:,1),'k-o') > hold on > plot(W(:,2),'r-o'); shg > plot(W(:,3),'b-o'); shg > plot(W(:,4),'g-o'); shg > clf > plot(W(:,20),'r-o'); shg