take sum log of probability matrix

I have data

m= 1 8 3 3 3 8 4 1 8 4 1 6 7 10 10 8 6 8 6 8 6 3 3 8 3 9......2000

with sequence length 2000. with this data I made transition probability matrix p

          1         2         3         4         5         6         7         8         9        10
   1   0.0781    0.1317    0.0489    0.0652    0.1222    0.0713    0.1371    0.2077    0.0339    0.1039
   2   0.0681    0.1482    0.1012    0.0669    0.0319    0.0783    0.0892    0.1163    0.1398    0.1602
   3   0.0421    0.1672    0.1125    0.0798    0.0679    0.0805    0.0773    0.1898    0.0974    0.0855
   4   0.1421    0.1099    0.0465    0.0661    0.0357    0.0420    0.1528    0.1698    0.1939    0.0411
   5   0.1809    0.1485    0.0477    0.0486    0.0837    0.0594    0.1206    0.1773    0.0774    0.0558
   6   0.0545    0.0881    0.1186    0.0401    0.1154    0.1202    0.2588    0.0777    0.0897    0.0369
   7   0.1935    0.0494    0.0445    0.1698    0.0327    0.1044    0.0661    0.1079    0.0445    0.1872
   8   0.0612    0.0564    0.1830    0.0858    0.0828    0.2106    0.0390    0.0318    0.0828    0.1668
   9   0.2055    0.0522    0.3804    0.0449    0.0353    0.0449    0.0955    0.0385    0.0425    0.0602
  10   0.0781    0.2253    0.0525    0.1133    0.1824    0.0456    0.0394    0.0871    0.0961    0.0802

and initial probability matrix r

      1         2         3         4         5         6         7         8         9        10
   0.1052    0.1186    0.1136    0.0799    0.0794    0.0892    0.1026    0.1191    0.0890    0.1034

now I want to select data with window size 10, so 10 elements of m i.e. 1 8 3 3 3 8 4 1 8 4 are selected. I want to take sum of log of transition probability and initial probability of corresponding selected elements of m. i.e. 1 8 3 3 3 8 4 1 8 4 are selected so

log(r1)+log(r3)+log(r4)+log(r8)+log(p11)+log(p13)+log(14)+log(18)+log(31)+log(33)+log(34)+log(38)+log(41)+log(43)+log(44)+log(48)+log(81)+log(83)+log(84)+log(88)

in above r1,r3,r4,r8 are initial probability and p11,p13... are transition probability. so above result would be one single value, now same above thing I want to do with sliding window by 1 position to next i.e. skipping previous element and adding next element so selected elements of m will be 8 3 3 3 8 4 1 8 4 1. how to do this for sliding window upto end. each window operation give one value so window operation value should be accumulate in one variable. how to do this.

Answer 1

[Guillaume]

This function will calculate the probability for a window:

function lp = logprobability(window, p, r)
   uv = unique(window);  %get unique values in window
   [row, col] = ndgrid(uv);  %generate all combinations of unique values
   lp = sum(log(r(uv))) + sum(log(p(sub2ind(size(p), row(:), col(:)))));
end

To apply that to consecutive windows of size 10 of m:

windowsize = 10;
assert(mod(numel(m) / windowsize), 1) == 0, 'number of elements of m not a multiple of window size')
lps = cellfun(@(w) logprobability(w, p, r), mat2cell(m, 1, ones(1, numel(m)/windowsize) * windowsize));