octave:2> toeplitz([-2,1,0,0]) ans = -2 1 0 0 1 -2 1 0 0 1 -2 1 0 0 1 -2 octave:3> toeplitz([0,-1,0,0],[0,1,0,0]) ans = 0 1 0 0 -1 0 1 0 0 -1 0 1 0 0 -1 0 octave:4> toeplitz([-2,1,0,0,0,0,0,0]) ans = -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 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 octave:5> sparse(toeplitz([-2,1,0,0,0,0,0,0])) ans = Compressed Column Sparse (rows = 8, cols = 8, nnz = 22 [34%]) (1, 1) -> -2 (2, 1) -> 1 (1, 2) -> 1 (2, 2) -> -2 (3, 2) -> 1 (2, 3) -> 1 (3, 3) -> -2 (4, 3) -> 1 (3, 4) -> 1 (4, 4) -> -2 (5, 4) -> 1 (4, 5) -> 1 (5, 5) -> -2 (6, 5) -> 1 (5, 6) -> 1 (6, 6) -> -2 (7, 6) -> 1 (6, 7) -> 1 (7, 7) -> -2 (8, 7) -> 1 (7, 8) -> 1 (8, 8) -> -2 octave:6> octave:6> octave:6> toeplitz(sparse([-2,1,0,0,0,0,0,0])) ans = Compressed Column Sparse (rows = 8, cols = 8, nnz = 22 [34%]) (1, 1) -> -2 (2, 1) -> 1 (1, 2) -> 1 (2, 2) -> -2 (3, 2) -> 1 (2, 3) -> 1 (3, 3) -> -2 (4, 3) -> 1 (3, 4) -> 1 (4, 4) -> -2 (5, 4) -> 1 (4, 5) -> 1 (5, 5) -> -2 (6, 5) -> 1 (5, 6) -> 1 (6, 6) -> -2 (7, 6) -> 1 (6, 7) -> 1 (7, 7) -> -2 (8, 7) -> 1 (7, 8) -> 1 (8, 8) -> -2 octave:7> octave:7> octave:7> octave:7> octave:7> octave:7> octave:7> octave:7> octave:7> octave:7> octave:7> sparse([1,1],[1,2],[-2,1],1,8) ans = Compressed Column Sparse (rows = 1, cols = 8, nnz = 2 [25%]) (1, 1) -> -2 (1, 2) -> 1 octave:8> toeplitz(sparse([1,1],[1,2],[-2,1],1,8)) ans = Compressed Column Sparse (rows = 8, cols = 8, nnz = 22 [34%]) (1, 1) -> -2 (2, 1) -> 1 (1, 2) -> 1 (2, 2) -> -2 (3, 2) -> 1 (2, 3) -> 1 (3, 3) -> -2 (4, 3) -> 1 (3, 4) -> 1 (4, 4) -> -2 (5, 4) -> 1 (4, 5) -> 1 (5, 5) -> -2 (6, 5) -> 1 (5, 6) -> 1 (6, 6) -> -2 (7, 6) -> 1 (6, 7) -> 1 (7, 7) -> -2 (8, 7) -> 1 (7, 8) -> 1 (8, 8) -> -2 octave:9> A=toeplitz(sparse([1,1],[1,2],[-2,1],1,8)) A = Compressed Column Sparse (rows = 8, cols = 8, nnz = 22 [34%]) (1, 1) -> -2 (2, 1) -> 1 (1, 2) -> 1 (2, 2) -> -2 (3, 2) -> 1 (2, 3) -> 1 (3, 3) -> -2 (4, 3) -> 1 (3, 4) -> 1 (4, 4) -> -2 (5, 4) -> 1 (4, 5) -> 1 (5, 5) -> -2 (6, 5) -> 1 (5, 6) -> 1 (6, 6) -> -2 (7, 6) -> 1 (6, 7) -> 1 (7, 7) -> -2 (8, 7) -> 1 (7, 8) -> 1 (8, 8) -> -2 octave:10> octave:10> full(A) ans = -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 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 octave:11> A=rand(4); octave:12> F=@(x) (A*x).^2; octave:13> JF=@(x) diag(2*A*x)*A; octave:14> u=rand(4,1); octave:15> v=rand(4,1); octave:16> epsilon=1e-4; octave:17> (F(u+epsilon*v)-F(u))/epsilon ans = 6.7597 4.1041 3.0125 1.8427 octave:18> JF(u)*v ans = 6.7593 4.1039 3.0124 1.8425 octave:19> catenaria parse error near line 11 of file /home/accounts/personale/clrmrc90/aa1718/equazioni_differenziali/catenaria.m syntax error >>> 1 / (2 * h), 1, m); ^ octave:19> catenaria octave:20> D2 D2 = Compressed Column Sparse (rows = 8, cols = 8, nnz = 22 [34%]) (1, 1) -> -24.500 (2, 1) -> 12.250 (1, 2) -> 12.250 (2, 2) -> -24.500 (3, 2) -> 12.250 (2, 3) -> 12.250 (3, 3) -> -24.500 (4, 3) -> 12.250 (3, 4) -> 12.250 (4, 4) -> -24.500 (5, 4) -> 12.250 (4, 5) -> 12.250 (5, 5) -> -24.500 (6, 5) -> 12.250 (5, 6) -> 12.250 (6, 6) -> -24.500 (7, 6) -> 12.250 (6, 7) -> 12.250 (7, 7) -> -24.500 (8, 7) -> 12.250 (7, 8) -> 12.250 (8, 8) -> -24.500 octave:21> full(D2) ans = Columns 1 through 6: -24.50000 12.25000 0.00000 0.00000 0.00000 0.00000 12.25000 -24.50000 12.25000 0.00000 0.00000 0.00000 0.00000 12.25000 -24.50000 12.25000 0.00000 0.00000 0.00000 0.00000 12.25000 -24.50000 12.25000 0.00000 0.00000 0.00000 0.00000 12.25000 -24.50000 12.25000 0.00000 0.00000 0.00000 0.00000 12.25000 -24.50000 0.00000 0.00000 0.00000 0.00000 0.00000 12.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Columns 7 and 8: 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 12.25000 0.00000 -24.50000 12.25000 12.25000 -24.50000 octave:22> full(D1) ans = Columns 1 through 7: 0.00000 1.75000 0.00000 0.00000 0.00000 0.00000 0.00000 -1.75000 0.00000 1.75000 0.00000 0.00000 0.00000 0.00000 0.00000 -1.75000 0.00000 1.75000 0.00000 0.00000 0.00000 0.00000 0.00000 -1.75000 0.00000 1.75000 0.00000 0.00000 0.00000 0.00000 0.00000 -1.75000 0.00000 1.75000 0.00000 0.00000 0.00000 0.00000 0.00000 -1.75000 0.00000 1.75000 0.00000 0.00000 0.00000 0.00000 0.00000 -1.75000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -1.75000 Column 8: 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.75000 0.00000 octave:23> catenaria octave:24> catenaria ans = 0.042929 ans = 1.3613e-04 ans = 9.7231e-10 octave:25> catenaria ans = 0.041808 ans = 0.0012317 ans = 2.5436e-05 ans = 4.3654e-07 octave:26> catenaria octave:27> catenaria octave:28> u u = NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN octave:29> catenaria ans = 1.0862 octave:30> catenaria ans = 1.5441e-05 octave:31> catenaria ans = 3.8217e-06 octave:32> ans*4 ans = 1.5287e-05 octave:33> catenaria ans = 1.1056e-04 octave:34> catenaria ans = 3.8792e-05 octave:35> ans*4 ans = 1.5517e-04 octave:36> catenaria ans = 1.3663e-05 octave:37> ans*4 ans = 5.4653e-05 octave:38> diary off