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]) ans = -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 octave:5> A=toeplitz([-2,1,0,0,0,0,0]) A = -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 octave:6> whos Variables in the current scope: Attr Name Size Bytes Class ==== ==== ==== ===== ===== A 7x7 392 double ans 7x7 392 double Total is 98 elements using 784 bytes octave:7> B=sparse(A) B = Compressed Column Sparse (rows = 7, cols = 7, nnz = 19 [39%]) (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 octave:8> whos Variables in the current scope: Attr Name Size Bytes Class ==== ==== ==== ===== ===== A 7x7 392 double B 7x7 260 double ans 7x7 392 double Total is 117 elements using 1044 bytes octave:9> A=toeplitz(sparse([-2,1,0,0,0,0,0])) A = Compressed Column Sparse (rows = 7, cols = 7, nnz = 19 [39%]) (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 octave:10> sparse([1,1],[1,2],[-2,1],1,7) ans = Compressed Column Sparse (rows = 1, cols = 7, nnz = 2 [29%]) (1, 1) -> -2 (1, 2) -> 1 octave:11> toeplitz(sparse([1,1],[1,2],[-2,1],1,7)) ans = Compressed Column Sparse (rows = 7, cols = 7, nnz = 19 [39%]) (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 octave:12> full(toeplitz(sparse([1,1],[1,2],[-2,1],1,7))) ans = -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 1 0 0 0 0 0 1 -2 octave:13> edit catenaria octave:14> catenaria0 octave:15> x x = -1.000000 -0.979798 -0.959596 -0.939394 -0.919192 -0.898990 -0.878788 -0.858586 -0.838384 -0.818182 -0.797980 -0.777778 -0.757576 -0.737374 -0.717172 -0.696970 -0.676768 -0.656566 -0.636364 -0.616162 -0.595960 -0.575758 -0.555556 -0.535354 -0.515152 -0.494949 -0.474747 -0.454545 -0.434343 -0.414141 -0.393939 -0.373737 -0.353535 -0.333333 -0.313131 -0.292929 -0.272727 -0.252525 -0.232323 -0.212121 -0.191919 -0.171717 -0.151515 -0.131313 -0.111111 -0.090909 -0.070707 -0.050505 -0.030303 -0.010101 0.010101 0.030303 0.050505 0.070707 0.090909 0.111111 0.131313 0.151515 0.171717 0.191919 0.212121 0.232323 0.252525 0.272727 0.292929 0.313131 0.333333 0.353535 0.373737 0.393939 0.414141 0.434343 0.454545 0.474747 0.494949 0.515152 0.535354 0.555556 0.575758 0.595960 0.616162 0.636364 0.656566 0.676768 0.696970 0.717172 0.737374 0.757576 0.777778 0.797980 0.818182 0.838384 0.858586 0.878788 0.898990 0.919192 0.939394 0.959596 0.979798 1.000000 octave:16> catenaria0 parse error near line 6 of file /home/accounts/personale/clrmrc90/aa1819/equazioni_differenziali/catenaria0.m syntax error >>> D2 = toeplitz(sparse([1,1],[1,2],[-2,1]/h^2,1,m); ^ octave:16> catenaria0 ans = Columns 1 through 7: -40.50000 20.25000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 -40.50000 20.25000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 -40.50000 20.25000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 -40.50000 20.25000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 -40.50000 20.25000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 -40.50000 20.25000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 -40.50000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Columns 8 through 10: 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 20.25000 0.00000 0.00000 -40.50000 20.25000 0.00000 20.25000 -40.50000 20.25000 0.00000 20.25000 -40.50000 octave:17> catenaria0 ans = Columns 1 through 8: 0.00000 2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -2.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Columns 9 and 10: 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2.25000 0.00000 0.00000 2.25000 -2.25000 0.00000 octave:18> catenaria0 octave:19> full(b) ans = 19.25000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 19.25000 octave:20> catenaria0 octave:21> catenaria0 ans = 11.15192 26.86559 -24.01582 12.34439 -9.13215 10.74820 -13.19863 3.73386 0.79908 1.51441 ans = 11.15192 26.86560 -24.01577 12.34440 -9.13215 10.74820 -13.19863 3.73387 0.79912 1.51441 octave:22> catenaria0 octave:23> catenaria0 octave:24> norm(F(u),inf) ans = 5.1781e-13 octave:25> norm(F(uesatta),inf) ans = 3.4005e-05 octave:26> catenaria0 ans = 0.042929 ans = 1.3613e-04 ans = 9.7231e-10 octave:27> catenaria0 ans = 0.048494 ans = 0.0060049 ans = 6.2473e-04 ans = 5.1645e-05 ans = 3.5842e-06 octave:28> catenaria0 octave:29> 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:30> catenaria0 ans = 1.5441e-05 octave:31> catenaria0 ans = 3.8217e-06 octave:32> 1.5441e-05/4 ans = 3.8603e-06 octave:33> catenaria0 ans = 1.1056e-04 octave:34> catenaria0 ans = 3.8792e-05 octave:35> 1.1056e-04/4 ans = 2.7640e-05 octave:36> catenaria0 ans = 0.49995 ans = 0.042929 ans = 1.3613e-04 ans = 9.7231e-10 ans = 1.5441e-05 octave:37> catenaria0 ans = 0.49995 ans = 0.042929 ans = 1.3613e-04 ans = 9.7231e-10 octave:38> catenaria0in ans = 0.49995 ans = 0.038304 ans = 0.0043252 ans = 4.0280e-04 ans = 3.1209e-05 ans = 2.0623e-06 octave:39> catenaria0in ans = 0.49995 ans = 0.038304 ans = 0.0043252 ans = 4.0280e-04 ans = 3.1209e-05 ans = 2.0623e-06 octave:40> tic,catenaria0,toc ans = 0.49995 ans = 0.042929 ans = 1.3613e-04 ans = 9.7231e-10 Elapsed time is 0.103309 seconds. octave:41> tic,catenaria0,toc ans = 0.49995 ans = 0.042929 ans = 1.3613e-04 ans = 9.7231e-10 Elapsed time is 0.106109 seconds. octave:42> tic,catenaria0in,toc ans = 0.49995 ans = 0.038304 ans = 0.0043252 ans = 4.0280e-04 ans = 3.1209e-05 ans = 2.0623e-06 Elapsed time is 0.101831 seconds. octave:43> tic,catenaria0in,toc ans = 0.49995 ans = 0.038304 ans = 0.0043252 ans = 4.0280e-04 ans = 3.1209e-05 ans = 2.0623e-06 Elapsed time is 0.105664 seconds. octave:44> tic,catenaria0,toc ans = 0.50000 ans = 0.042944 ans = 1.3616e-04 ans = 9.7148e-10 Elapsed time is 0.101085 seconds. octave:45> tic,catenaria0,toc ans = 0.50000 ans = 0.042944 ans = 1.3616e-04 ans = 9.7148e-10 Elapsed time is 0.100039 seconds. octave:46> tic,catenaria0in,toc ans = 0.50000 ans = 0.038317 ans = 0.0043267 ans = 4.0270e-04 ans = 3.1156e-05 ans = 2.0533e-06 ans = 1.1771e-07 Elapsed time is 0.112169 seconds. octave:47> tic,catenaria0in,toc ans = 0.50000 ans = 0.038317 ans = 0.0043267 ans = 4.0270e-04 ans = 3.1156e-05 ans = 2.0533e-06 ans = 1.1771e-07 Elapsed time is 0.101863 seconds. octave:48> tic,catenaria0in,toc ans = 0.50000 ans = 0.038317 ans = 0.0043267 ans = 4.0270e-04 ans = 3.1156e-05 ans = 2.0533e-06 ans = 1.1771e-07 Elapsed time is 0.106518 seconds. octave:49> tic,catenaria0in,toc ans = 0.50000 ans = 0.038317 ans = 0.0043267 ans = 4.0270e-04 ans = 3.1156e-05 ans = 2.0533e-06 ans = 1.1771e-07 Elapsed time is 0.103703 seconds. octave:50> quit