Q=randstocsym(4)
Q =
0.3748 0.3501 0.1750 0.1001
0.3501 0.2485 0.2985 0.1030
0.1750 0.2985 0.3185 0.2081
0.1001 0.1030 0.2081 0.5888
sum(Q)
ans =
1.0000 1.0000 1.0000 1.0000
sum(Q,2)
ans =
1.0000
1.0000
1.0000
1.0000
Q
Q =
0.3748 0.3501 0.1750 0.1001
0.3501 0.2485 0.2985 0.1030
0.1750 0.2985 0.3185 0.2081
0.1001 0.1030 0.2081 0.5888
Q=ones(4)/4
Q =
0.2500 0.2500 0.2500 0.2500
0.2500 0.2500 0.2500 0.2500
0.2500 0.2500 0.2500 0.2500
0.2500 0.2500 0.2500 0.2500
uiopen('/home/accounts/personale/clrmrc90/aa1112/sistemi_stocastici/metropolis.m', true);
v=rand(1,4)
v =
0.7689 0.1673 0.8620 0.9899
repmat(v,4,1)
ans =
0.7689 0.1673 0.8620 0.9899
0.7689 0.1673 0.8620 0.9899
0.7689 0.1673 0.8620 0.9899
0.7689 0.1673 0.8620 0.9899
V=repmat(v,4,1)
V =
0.7689 0.1673 0.8620 0.9899
0.7689 0.1673 0.8620 0.9899
0.7689 0.1673 0.8620 0.9899
0.7689 0.1673 0.8620 0.9899
W=repmat(v',1,4)
W =
0.7689 0.7689 0.7689 0.7689
0.1673 0.1673 0.1673 0.1673
0.8620 0.8620 0.8620 0.8620
0.9899 0.9899 0.9899 0.9899
find(V>=W)
ans =
1
2
6
9
10
11
13
14
15
16
v
v =
0.7689 0.1673 0.8620 0.9899
P=metropolis(v)
P =
0.5633 0.0898 0.2746 0.0723
0.4129 0.0866 0.1763 0.3243
0.2449 0.0342 0.4524 0.2685
0.0561 0.0548 0.2338 0.6552
sum(P,2)
ans =
1.0000
1.0000
1.0000
1.0000
ls
2011-10-21.txt metropolis.m
2011-11-04.txt randstoc.m
invariantPotenze.m randstocsym.m
invariantPotenze(P)
??? Input argument "tol" is undefined.
Error in ==> <a href="matlab: opentoline('/home/accounts/personale/clrmrc90/aa1112/sistemi_stocastici/invariantPotenze.m',17,0)">invariantPotenze at 17</a>
stimaerrore = tol+1;
invariantPotenze(P,1e-6,100)
ans =
0.2758 0.0600 0.3092 0.3551
v/sum(v)
ans =
0.2758 0.0600 0.3092 0.3551
H=[-1,1]
H =
-1 1
epsilon=1e-3;
v=exp(-H/epsilon)
v =
Inf 0
v=v/sum(v)
v =
NaN 0
repmat(H',1,2)-repmat(H,2,1)
ans =
0 -2
2 0
-(repmat(H',1,2)-repmat(H,2,1))/epsilon
ans =
0 2000
-2000 0
sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)).^(-1)
ans =
1 0
epsilon=1e-2
epsilon =
0.0100
sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)).^(-1)
ans =
1.0000 0.0000
format long e
sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)).^(-1)
ans =
Column 1
1.000000000000000e+00
Column 2
1.383896526736738e-87
epsilon=1e-1
epsilon =
1.000000000000000e-01
sum(exp(-(repmat(H',1,2)-repmat(H,2,1))/epsilon)).^(-1)
ans =
Column 1
9.999999979388463e-01
Column 2
2.061153618190204e-09
exp(-H/epsilon)
ans =
Column 1
2.202646579480672e+04
Column 2
4.539992976248485e-05
v=exp(-H/epsilon)
v =
Column 1
2.202646579480672e+04
Column 2
4.539992976248485e-05
v=v/sum(v)
v =
Column 1
9.999999979388463e-01
Column 2
2.061153618190203e-09
epsmet
epsilon =
10
ans =
Columns 1 through 3
2.8868e-01 6.6019e-03 5.1479e-02
8.4494e-03 1.6992e-01 8.6430e-02
1.3075e-01 1.7152e-01 2.0451e-01
8.6157e-02 1.2141e-01 4.3524e-02
4.7721e-02 5.1202e-02 1.6705e-02
1.0708e-01 1.0458e-01 5.5944e-02
8.9574e-02 9.5038e-02 8.8079e-02
1.2533e-01 1.5882e-01 1.8688e-02
6.2682e-03 1.6370e-03 1.8297e-03
1.5199e-01 9.8719e-02 6.3229e-03
Columns 4 through 6
6.7318e-02 1.4288e-01 8.3664e-02
1.2141e-01 1.9620e-01 1.0458e-01
8.6376e-02 1.2704e-01 1.1102e-01
2.3419e-01 8.9055e-02 9.8326e-02
2.3240e-02 6.8689e-01 2.2497e-02
9.8326e-02 8.6207e-02 2.7917e-01
1.2002e-01 2.5238e-03 4.5490e-02
1.3236e-01 1.7961e-02 1.1998e-01
3.7563e-03 1.7809e-02 4.9604e-03
7.8344e-02 7.1971e-02 6.9496e-03
Columns 7 through 9
7.5963e-03 9.7922e-02 1.3510e-01
1.0315e-02 1.5882e-01 4.5157e-02
1.8972e-02 3.7086e-02 1.0017e-01
1.3027e-02 1.3236e-01 1.0362e-01
7.1487e-05 4.6872e-03 1.2821e-01
4.9374e-03 1.1998e-01 1.3683e-01
2.2674e-01 1.3368e-01 1.8271e-02
1.4509e-02 2.3909e-01 6.4908e-02
7.1888e-05 2.3530e-03 9.5585e-01
1.9600e-02 1.0837e-01 1.5084e-01
Column 10
1.1876e-01
9.8719e-02
1.2548e-02
7.8344e-02
1.8782e-02
6.9496e-03
1.8058e-01
1.0837e-01
5.4683e-03
3.0689e-01
guarda P(5,5) e P(9,9)
epsilon =
1.0000e-01
ans =
Columns 1 through 3
7.2202e-01 1.6257e-13 4.3111e-42
8.4494e-03 2.6666e-01 2.9393e-31
1.3075e-01 1.7152e-01 2.2348e-01
8.6157e-02 1.2141e-01 1.4802e-31
3.3826e-49 8.9371e-60 9.9163e-90
1.0708e-01 1.0458e-01 1.9026e-31
8.9574e-02 9.5038e-02 8.8079e-02
1.2533e-01 1.5882e-01 6.3553e-32
6.0069e-135 3.8630e-146 1.4684e-175
1.5199e-01 9.8719e-02 2.1503e-32
Columns 4 through 6
1.6577e-12 1.4288e-01 2.0602e-12
1.2141e-01 1.9620e-01 1.0458e-01
8.6376e-02 1.2704e-01 1.1102e-01
2.9074e-01 8.9055e-02 9.8326e-02
4.0565e-60 8.7179e-01 3.9268e-60
9.8326e-02 8.6207e-02 3.4005e-01
1.2002e-01 2.5238e-03 4.5490e-02
1.3236e-01 1.7961e-02 1.1998e-01
8.8642e-146 2.4078e-87 1.1706e-145
7.8344e-02 7.1971e-02 6.9496e-03
Columns 7 through 9
6.2275e-109 2.4113e-12 1.3510e-01
3.4341e-98 1.5882e-01 4.5157e-02
1.8572e-68 3.7086e-02 1.0017e-01
4.3368e-98 1.3236e-01 1.0362e-01
4.1541e-158 8.1813e-61 1.2821e-01
1.6438e-98 1.1998e-01 1.3683e-01
2.2674e-01 1.3368e-01 1.8271e-02
4.8304e-98 2.7229e-01 6.4908e-02
5.6477e-243 5.5526e-146 1.0000e+00
6.5252e-98 1.0837e-01 1.5084e-01
Column 10
2.9244e-12
9.8719e-02
1.2548e-02
7.8344e-02
3.2783e-60
6.9496e-03
1.8058e-01
1.0837e-01
1.2904e-145
3.3281e-01
guarda P(5,5) e P(9,9)
epsilon =
1.0000e-02
ans =
Columns 1 through 3
7.2202e-01 5.8744e-110 0
8.4494e-03 2.6666e-01 3.7461e-299
1.3075e-01 1.7152e-01 2.2348e-01
8.6157e-02 1.2141e-01 1.8865e-299
0 0 0
1.0708e-01 1.0458e-01 2.4248e-299
8.9574e-02 9.5038e-02 8.8079e-02
1.2533e-01 1.5882e-01 8.0997e-300
0 0 0
1.5199e-01 9.8719e-02 2.7405e-300
Columns 4 through 6
5.9899e-109 1.4288e-01 7.4443e-109
1.2141e-01 1.9620e-01 1.0458e-01
8.6376e-02 1.2704e-01 1.1102e-01
2.9074e-01 8.9055e-02 9.8326e-02
0 8.7179e-01 0
9.8326e-02 8.6207e-02 3.4005e-01
1.2002e-01 2.5238e-03 4.5490e-02
1.3236e-01 1.7961e-02 1.1998e-01
0 0 0
7.8344e-02 7.1971e-02 6.9496e-03
Columns 7 through 9
0 8.7131e-109 1.3510e-01
0 1.5882e-01 4.5157e-02
0 3.7086e-02 1.0017e-01
0 1.3236e-01 1.0362e-01
0 0 1.2821e-01
0 1.1998e-01 1.3683e-01
2.2674e-01 1.3368e-01 1.8271e-02
0 2.7229e-01 6.4908e-02
0 0 1.0000e+00
0 1.0837e-01 1.5084e-01
Column 10
1.0567e-108
9.8719e-02
1.2548e-02
7.8344e-02
0
6.9496e-03
1.8058e-01
1.0837e-01
0
3.3281e-01
guarda P(5,5) e P(9,9)
diary 'off'