30-Oct-2013


1> % risolvere il sistema lineare x + 2y = 1, x + 2 y = 5


1> A = [1 2; 1 2]
A =

   1   2
   1   2



2> b = [1; 5]
b =

   1
   5



3> x = A\b
x =

   0.60000
   1.20000



4> inv(A)
ans =

   Inf   Inf
   Inf   Inf



5> % Octave: minimizza |A*x-b|


5> x = linspace(-1,2);


6> y1 = -x/2 + 1/2;


7> y2 = -x/2 + 5/2;


8> plot(x,y1, x,y2,'g')


9> grid on; axis equal


10> hold on


11> plot(x,2*x,'r')


12> replot


13> % calcolare l'angolo in radianti e in gradi


13> % compreso tra i vettori (1,1,1) e (1,1,0)


13> % serve il prodotto scalare


13> a = [1,1,1]
a =

   1   1   1



14> b =[1 1 0]
b =

   1   1   0



15> p = a * b'
p =  2


16> dot(a,b)
ans =  2


17> a * b
error: operator *: nonconformant arguments (op1 is 1x3, op2 is 1x3)


17> norm(a)
ans =  1.7321


18> ans^2
ans =  3.0000


19> sqrt(dot(a,a))
ans =  1.7321


20> % angolo in radianti


20> acos(dot(a,b)/(norm(a) * norm(b)))
ans =  0.61548


21> % angoli in gradi


21> ans * 180/pi
ans =  35.264


22> hold off


23> quiver3(0,0,0,1,1,1)


24> h = quiver3(0,0,0,1,1,1)
h = -18.129


25> set(h, 'color', 'r')


26> set (h,'MaxHeadSize',0.02,'AutoScale','off');


27> set (h,'MaxHeadSize',0.2,'AutoScale','off');


28> hold on


29> g = quiver3(0,0,0,1,1,0)
g = -23.352


30> set (g, 'color', 'g');


31> axis equal


32> quit