Huffman Dictionary, error with index exceed when i give specific probabilities.

조회 수: 2(최근 30일)
Rafael Nicolaou
Rafael Nicolaou 2022년 1월 6일
편집: David Goodmanson 2022년 1월 12일
When i change my probabilities numbers i receive an error.
Also if i change some of my probabilities im not getting the error.
Index exceeds the number of array elements. Index must not exceed 1.
Error in huffmandict (line 17)
min1 = sorted_p(2);
The probabilties are the frequencies of each english letter.
Input Data:
probabilities=[0.0698 0.0128 0.0238 0.0364 0.1086 ...
0.0190 0.0172 0.0521 0.0595 0.0013 ...
0.0066 0.0344 0.0206 0.0577 0.0642 ...
0.0165 0.0008 0.0512 0.0541 0.0774 ...
0.0236 0.0084 0.0202 0.0013 0.0169 0.0006 0.1453];
alphabet = {'a' 'b' 'c' 'd' 'e' 'f' ...
'g' 'h' 'i' 'j' 'k' 'l' ...
'm' 'n' 'o' 'p' 'q' 'r' ...
's' 't' 'u' 'v' 'w' 'x' 'y' 'z' '-'};
dict = huffmandict(alphabet, probabilities);
My huffman dictionary script
function dict = huffmandict(symbols, prob)
%Probability Length
probability_length = length(prob);
for i = 1:probability_length
code{i} = '';
symbol{i} = i;
while(prob ~= 1)
% Sorting probabilities
[~,sorted_p] = sort(prob);
% Indexes to be merged
min = sorted_p(1);
min1 = sorted_p(2);
min_set = symbol{min};
min1_set = symbol{min1};
% Get the sum of the probabilities
new_possibility = prob(min) + prob(min1);
merged_set = [min_set, min1_set];
% Probability updates
symbol(sorted_p(1:2)) = '';
symbol = [symbol merged_set];
prob(sorted_p(1:2)) = '';
prob = [prob new_possibility];
% Assigning 0 and 1 to symbols
for i = 1:length(min_set)
code{min_set(i)} = strcat('1',code{min_set(i)});
for i = 1:length(min1_set)
code{min1_set(i)} = strcat('0',code{min1_set(i)});
% Constructing the dictionary
dict = cell(probability_length,2);
for i=1:probability_length
dict{i,1} = symbols{i}(1);
dict{i,2} = code{i};

채택된 답변

David Goodmanson
David Goodmanson 2022년 1월 6일
편집: David Goodmanson 2022년 1월 6일
Hi Rafael,
ans = 1.0003
SInce the probabilities don't add up to 1, the code is going to have problems. I arbitrarily reduced the last probability by .0003, so now the last line is
0.0236 0.0084 0.0202 0.0013 0.0169 0.0006 0.1450]
ans = 1
and it works. However, you are using a check that reads
while(prob ~= 1)
and depends on the sum equaling 1 exactly. When adding floating point numbers this will only happen by luck. For example, suppose you change the last line to
0.0239 0.0081 0.0202 0.0013 0.0169 0.0006 0.1450]
This has increased the first element by .0003 and decreased the second element by .0003. The sum is still 1, but
ans = 2.2204e-16
so the exact 'while' check fails. That check needs to be changed to something like
while abs(prob-1)>tol
where tol is some suitable tolerance such as 1e-10.
  댓글 수: 4
David Goodmanson
David Goodmanson 2022년 1월 11일
Hi Rafael, If you have a list of probabilities and indend to use every one of them even if they don't add up to exactly 1, you could temporarily rescale them so that they do add up to 1, within something on the order of 10^-16. That doesn't change their relative sizes so the huffman code is unaffected.
probabilitiesnew = probabilities/sum(probabilities)
Then a tolerance of 1e-10 should work.

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추가 답변(1개)

Cris LaPierre
Cris LaPierre 2022년 1월 6일
The error is occuring the 27th time the while loop runs. prob only has a single value at this point, so sorted_p(2) does not exist.
% works
ans = 5
% Doesn't work
Index exceeds the number of array elements. Index must not exceed 1.

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