How to extract leading non-zero digit?
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I'm working on a research problem related to Benford's Law which states that the distribution of leading digits is not random. This is probably because many things grow logarithmically. I am trying to extract the leading digit from these vectors below:
10 --> 1
13 --> 1
0.3 --> 3
-4 --> 4
-5 --> 5
-0.006 --> 6
Input will be a vector
x = [1 0.3 -2 0.001 -0.0006, 582398, 3020];
Output should be
y = [1 3 2 1 6 5 3];
Any help?
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Walter Roberson
2011년 1월 20일
The answer is complicated because numbers such as 0.0006 have no exact representation in binary floating point number, and the closest number that can be represented might not have the same leading binary digit.
If one does NOT take that factor in to account, then:
y = floor(abs(x) ./ 10.^floor(log10(abs(x))));
추가 답변 (3개)
Ned Gulley
2011년 1월 11일
You'll probably need to do some kind of textual manipulation. Here's one way to do it.
function y = leadingDigit(x)
s = sprintf('%1.2e\n',abs(x));
y = s(1:(length(s)/length(x)):end)-48;
end
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Daniel Shub
2012년 6월 28일
Is this really the first question on Answers? I was going to use our new magic power and start accepting answers. The only problem is I think there is now a better answer to this question on Loren's blog.
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Jan
2012년 6월 28일
I thought of accepting this answer, because it contains a link to good solutions. But actually the method shown by Walter hits the point (and is found in this blog also). Ned's method is more efficient than STR2DOUBLE, but a clean numerical approach is moire direct for a numerical question.
Oleg Komarov
2012년 9월 5일
regexp(num2str(x), '(?<=(^|\s+)[\-\.0]*)[1-9](?=[\d\.]*)', 'match')
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Asif Newaz
2019년 11월 22일
can u explain the 'expression'... i've found regexp quite complicated but very useful
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