How to extract leading non-zero digit?

Question

John Booker 2011-1-4

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https://ww2.mathworks.cn/matlabcentral/answers/16-how-to-extract-leading-non-zero-digit

评论： Asif Newaz 2019-11-22

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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Answer 1

Walter Roberson 2011-1-20

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https://ww2.mathworks.cn/matlabcentral/answers/16-how-to-extract-leading-non-zero-digit#answer_162

在 MATLAB Online 中打开

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))));

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Jan 2012-6-28

I suggest to accept this one.

John Booker 2013-8-1

Sorry it took me so long to accept. I stole this question from Ned before Answers launched and forgot about it =).

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Answer 2

Ned Gulley 2011-1-11

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https://ww2.mathworks.cn/matlabcentral/answers/16-how-to-extract-leading-non-zero-digit#answer_24

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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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Answer 3

Daniel Shub 2012-6-28

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https://ww2.mathworks.cn/matlabcentral/answers/16-how-to-extract-leading-non-zero-digit#answer_52042

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 2012-6-28

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.

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