octave:3> A=rand(4)
A =

   0.23793   0.96505   0.24558   0.13013
   0.49199   0.44644   0.17120   0.22674
   0.41303   0.17793   0.36987   0.21160
   0.64432   0.26521   0.67999   0.84780

octave:4> tril(A)
ans =

   0.23793   0.00000   0.00000   0.00000
   0.49199   0.44644   0.00000   0.00000
   0.41303   0.17793   0.36987   0.00000
   0.64432   0.26521   0.67999   0.84780

octave:5> tril(A)-diag(diag(A))
ans =

   0.00000   0.00000   0.00000   0.00000
   0.49199   0.00000   0.00000   0.00000
   0.41303   0.17793   0.00000   0.00000
   0.64432   0.26521   0.67999   0.00000

octave:6> D=diag(diag(A))
D =

Diagonal Matrix

   0.23793         0         0         0
         0   0.44644         0         0
         0         0   0.36987         0
         0         0         0   0.84780

octave:7> inv(D)*A
ans =

   1.00000   4.05597   1.03214   0.54692
   1.10203   1.00000   0.38348   0.50788
   1.11668   0.48106   1.00000   0.57208
   0.76000   0.31283   0.80206   1.00000

octave:8> D\A
ans =

   1.00000   4.05597   1.03214   0.54692
   1.10203   1.00000   0.38348   0.50788
   1.11668   0.48106   1.00000   0.57208
   0.76000   0.31283   0.80206   1.00000

octave:9> ls
2017-10-16.txt	jacobi.m
octave:10> help jacobi
'jacobi' is a function from the file /home/accounts/personale/clrmrc90/aa1718/calcolo_numerico2/jacobi.m


 [x, its, norm_r] = jacobi (A, b, tol, max_its, x0)

 Compute the solution of A*x=b through the Jacobi method. tol is a
 vector of two components with the relative and the absolute
 tolerances (defaults [1e-6, 1e-6]). max_its is the maximum number of
 iterations (default 100) and x0 the initial solution (default zero).
 x is the computed solution, its the number of iterations and norm_r
 the norm of the final residual.

Additional help for built-in functions and operators is
available in the online version of the manual.  Use the command
'doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help@octave.org
mailing list.
octave:11> ls
2017-10-16.txt	jacobi.m
octave:12> A=rand(4)
A =

   0.2998528   0.0488113   0.1352657   0.8518925
   0.2255744   0.3702321   0.9409553   0.3118592
   0.4334212   0.9979016   0.4234071   0.4875793
   0.9388845   0.4415462   0.0070269   0.4623118

octave:13> b=rand(2,1)
b =

   0.632115
   0.013822

octave:14> jacobi(A,b)
error: jacobi: operator -: nonconformant arguments (op1 is 2x1, op2 is 4x1)
error: called from:
error:   /home/accounts/personale/clrmrc90/aa1718/calcolo_numerico2/jacobi.m at line 26, column 3
octave:14> 
octave:14> b=rand(4,1)
b =

   0.54162
   0.59886
   0.69480
   0.43986

octave:15> jacobi(A,b)
warning: Raggiunto il numero massimo di iterazioni
ans =

  -2.5796e+55
  -3.7703e+55
  -3.9535e+55
  -2.4520e+55

octave:16> jacobi(A,b,1e-4)
warning: Raggiunto il numero massimo di iterazioni
ans =

  -2.5796e+55
  -3.7703e+55
  -3.9535e+55
  -2.4520e+55

octave:17> jacobi(A,b,[],50)
warning: Raggiunto il numero massimo di iterazioni
ans =

  -2.6180e+27
  -3.8263e+27
  -4.0123e+27
  -2.4884e+27

octave:18> jacobi(A,b,[],50,[1;1;1;1])
warning: Raggiunto il numero massimo di iterazioni
ans =

   5.6930e+27
   8.3207e+27
   8.7251e+27
   5.4112e+27

octave:19> A = [2, 1, 0; 1, 2, 1; 0, 1, 2];
octave:20> A
A =

   2   1   0
   1   2   1
   0   1   2

octave:21> b = A * ones (3, 1);
octave:22> b
b =

   3
   4
   3

octave:23> x = jacobi (A, b, 1e-8);
octave:24> x
x =

   1.0000
   1.0000
   1.0000

octave:25> format long e
octave:26> x = jacobi (A, b, 1e-8);
octave:27> x
x =

   1.00000000745058e+00
   1.00000001490116e+00
   1.00000000745058e+00

octave:28> A = [1, 1, 1; 1, 2, 1; 0, 1, 1];
octave:29> b = A * ones (3, 1);
octave:30> [x, it] = jacobi (A, b, 1e-8);
warning: Impossibile raggiungere la tolleranza richiesta
octave:31> x
x =

  -5.98916301767963e+07
  -3.87977300743113e+07
  -3.25624208230304e+07

octave:32> it
it =    1.00000000000000e+02
octave:33> test jacobi
warning: Impossibile raggiungere la tolleranza richiesta
PASSES 2 out of 2 tests
octave:34> lu('ciao')
error: invalid conversion from string to real matrix
octave:34> jacobi(rand(4),2)
error: jacobi: A(I): index out of bounds; value 2 out of bound 1
error: called from:
error:   /home/accounts/personale/clrmrc90/aa1718/calcolo_numerico2/jacobi.m at line 32, column 10
octave:34> help gausssidel
'gausssidel' is a function from the file /home/accounts/personale/clrmrc90/aa1718/calcolo_numerico2/gausssidel.m


 [x, its, norm_r] = gausssidel (A, b, tol, max_its, x0)

 Compute the solution of A*x=b through the Gauss-Sidel method. tol is a
 vector of two components with the relative and the absolute
 tolerances (defaults [1e-6, 1e-6]). max_its is the maximum number of
 iterations (default 100) and x0 the initial solution (default zero).
 x is the computed solution, its the number of iterations and norm_r
 the norm of the final residual.

Additional help for built-in functions and operators is
available in the online version of the manual.  Use the command
'doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help@octave.org
mailing list.
octave:35> test gausssidel
PASSES 2 out of 2 tests
octave:36> A
A =

   1.00000000000000e+00   1.00000000000000e+00   1.00000000000000e+00
   1.00000000000000e+00   2.00000000000000e+00   1.00000000000000e+00
   0.00000000000000e+00   1.00000000000000e+00   1.00000000000000e+00

octave:37> format
octave:38> A
A =

   1   1   1
   1   2   1
   0   1   1

octave:39> A([3,1,2],:)
ans =

   0   1   1
   1   1   1
   1   2   1

octave:40> A=A([3,1,2],:)
A =

   0   1   1
   1   1   1
   1   2   1

octave:41> tril(A)'==triu(A)
ans =

   1   1   1
   1   1   0
   1   1   1

octave:42> A
A =

   0   1   1
   1   1   1
   1   2   1

octave:43> diary off