uiopen('/home/accounts/personale/clrmrc90/aa1112/sistemi_stocastici/randstoc.m', true);
P=rand(4)

P =

    0.8147    0.6324    0.9575    0.9572
    0.9058    0.0975    0.9649    0.4854
    0.1270    0.2785    0.1576    0.8003
    0.9134    0.5469    0.9706    0.1419

sum(P)

ans =

    2.7609    1.5553    3.0506    2.3847

sum(P,2)

ans =

    3.3618
    2.4536
    1.3634
    2.5727

D=diag(1./sum(P,2))

D =

    0.2975         0         0         0
         0    0.4076         0         0
         0         0    0.7335         0
         0         0         0    0.3887

D*P

ans =

    0.2424    0.1881    0.2848    0.2847
    0.3692    0.0398    0.3933    0.1978
    0.0931    0.2043    0.1156    0.5870
    0.3550    0.2126    0.3773    0.0551

sum(D*P,2)

ans =

    1.0000
    1.0000
    1.0000
    1.0000

D=diag(sum(P,2))

D =

    3.3618         0         0         0
         0    2.4536         0         0
         0         0    1.3634         0
         0         0         0    2.5727

D\P

ans =

    0.2424    0.1881    0.2848    0.2847
    0.3692    0.0398    0.3933    0.1978
    0.0931    0.2043    0.1156    0.5870
    0.3550    0.2126    0.3773    0.0551

spdiags(sum(P,2),0,4,4)\P

ans =

    0.2424    0.1881    0.2848    0.2847
    0.3692    0.0398    0.3933    0.1978
    0.0931    0.2043    0.1156    0.5870
    0.3550    0.2126    0.3773    0.0551

P=randstoc(4)

P =

    0.1749    0.2719    0.2814    0.2718
    0.4870    0.0190    0.4030    0.0910
    0.2563    0.2748    0.2405    0.2285
    0.4140    0.4030    0.1692    0.0137

sum(P,2)

ans =

    1.0000
    1.0000
    1.0000
    1.0000

P=randstoc(4)

P =

    0.1734    0.4350    0.2747    0.1170
    0.0374    0.2568    0.3091    0.3967
    0.0430    0.4207    0.3390    0.1973
    0.3581    0.0150    0.3458    0.2811


[V,D]=eig(P')

V =

  Columns 1 through 2

   0.2758            -0.2864 + 0.4399i
   0.5257             0.6606          
   0.6253            -0.1087 + 0.0136i
   0.5065            -0.2655 - 0.4535i

  Columns 3 through 4

  -0.2864 - 0.4399i   0.6076          
   0.6606             0.2568          
  -0.1087 - 0.0136i  -0.7414          
  -0.2655 + 0.4535i  -0.1230          


D =

  Columns 1 through 2

   1.0000                  0          
        0            -0.0070 + 0.2880i
        0                  0          
        0                  0          

  Columns 3 through 4

        0                  0          
        0                  0          
  -0.0070 - 0.2880i        0          
        0             0.0642          

v=V(:,1)

v =

    0.2758
    0.5257
    0.6253
    0.5065

v*P
??? Error using ==> mtimes
Inner matrix dimensions must agree.

v'*P

ans =

    0.2758    0.5257    0.6253    0.5065

v'

ans =

    0.2758    0.5257    0.6253    0.5065

v=v'/sum(v)

v =

    0.1426    0.2719    0.3235    0.2620

sum(v)

ans =

     1

v*P

ans =

    0.1426    0.2719    0.3235    0.2620

v

v =

    0.1426    0.2719    0.3235    0.2620

invariantPotenze(P,1e-6,100)

ans =

    0.1426    0.2719    0.3235    0.2620

[v,iter]=invariantPotenze(P,1e-6,100)

v =

    0.1426    0.2719    0.3235    0.2620


iter =

    12

[P'-eye(4);ones(1,4)]\[zeros(4,1);1]

ans =

    0.1426
    0.2719
    0.3235
    0.2620

ans'

ans =

    0.1426    0.2719    0.3235    0.2620

[zeros(1,4),1]/[P-eye(4),ones(4,1)]

ans =

    0.1426    0.2719    0.3235    0.2620

diary off