extension of symbols or probabilities

i am having this p=[ 0.3,0.25, 0.20, 0.10, 0.05, 0.04, 0.04, .02]; these are 8 symbols suppose A,B,C,D,E,F,G,H

now i want to extend these from 8 to 64

how to do that? using these above probabilities

[Azzi Abdelmalek]

extend these from 8 to 64

what do you mean?

[Walter Roberson]

Those probabilities add up to 1.0 exactly, so would the new 56 symbols each have probability 0 ?

[faraz.a]

i am having this p=[ 0.3,0.25, 0.20, 0.10, 0.05, 0.04, 0.04, .02]; these are 8 symbols suppose A,B,C,D,E,F,G,H now i want to extend these from 8 to 64

so 1-AA=0.3*0.3 
2-AB= 0.3*0.25 
3-AC=0.3*0.20 
4-AD-0.3*0.10 
5-AE 
6-AF 
7-AG 
8-AH 
9-BA 
10-BB 
11-BC 
12-BD 
...... son on till HH
same goes for 8 to 512 
8^3=512 
so 1-AAA 
2-AAB 
like wise till end HHH

[faraz.a]

it is very long i can't just find the probabilities and give it as input.. i want to do this calculation in matlab. i want to extend those 8 probabilities to 64 like i showed you in the above comment how to do that?

Answer 1

[Matt J]

 p64 = reshape(p.'*p,1,64);

Answer 2

[Walter Roberson]

My guess at what you want is

oldx = linspace(0,1,8);
newx = linspace(0,1,64);
newp = interp1(oldx, p, newx);

plot(oldx, p, 'b.', newx, newp, 'g')

The new entries will be linear interpolations of the old ones. You might prefer to use a non-linear interpolation.

[Walter Roberson]

ndim = 3;   %8 to the how many?
[t{1:ndim}] = ndgrid(p);
newp = prod(cat(ndim+1, t{:}), ndim+1);

The answers are now in the n-dimensional matrix newp; e.g., BDH is newp(2,4,8)

Answer 3

[Azzi Abdelmalek]

s='A':'H'
p=[ 0.3,0.25, 0.20, 0.10, 0.05, 0.04, 0.04, .02]
idx=arrangement(1:8,2)
new_s=s(idx)
new_p=prod(p(idx),2) 
out=[cellstr(new_s) num2cell(new_p)]

%-----------------------------------------------------------------
function y=arrangement(v,n)
 m=length(v);
 y=zeros(m^n,n);
 for k = 1:n
    y(:,k) = repmat(reshape(repmat(v,m^(n-k),1),m*m^(n-k),1),m^(k-1),1);
 end

[Walter Roberson]

This looks overly complicated.

[Azzi Abdelmalek]

Is there a built-in function that replace arrangement function?

[Walter Roberson]

The multinomial distribution ?

[Azzi Abdelmalek]

No, I can not find the name in english, in french it's arrangement

[Walter Roberson]

The A[sub n][super k] given in that article is the same as the P(n,k) in Permutations, and your formula looks to me like the probability mass function of the Multinomial Distribution

I haven't worked through to see if your formula is correct. Even if it is, I would think that the version I gave in my answer (starting with "ndim = 3" is a lot easier to understand. Yours might require a factor of ndim less memory, though.

Answer 4

[Image Analyst]

My guess at what he wants:

probabilityTable = p' * p

probabilityTable =
         0.09        0.075         0.06         0.03        0.015        0.012        0.012        0.006
        0.075       0.0625         0.05        0.025       0.0125         0.01         0.01        0.005
         0.06         0.05         0.04         0.02         0.01        0.008        0.008        0.004
         0.03        0.025         0.02         0.01        0.005        0.004        0.004        0.002
        0.015       0.0125         0.01        0.005       0.0025        0.002        0.002        0.001
        0.012         0.01        0.008        0.004        0.002       0.0016       0.0016       0.0008
        0.012         0.01        0.008        0.004        0.002       0.0016       0.0016       0.0008
        0.006        0.005        0.004        0.002        0.001       0.0008       0.0008       0.0004

It's a 2D table of the probability of that pair, so you just enter in the two letters as indexes. For example, probabilityTable(1,1) = 0.03 * 0.03 = 0.009 just like he wanted. Of course you could convert to a 1D table if you wanted:

probabilityTable = probabilityTable(:);

[Matt J]

That's a duplicate of my answer ( but I think you're right;) )

[Image Analyst]

You're right. I didn't notice at first because I saw the reshape(). I actually think it's more convenient to use the 2D version than the 1D version which he requested.