How to implement Benford's law in MATLAB.

Question

I want to implement a version of Benford's law (http://en.wikipedia.org/wiki/Benford%27s_law) that basically asks for the first digit of a number to do analysis on the distribution.

1934---> 1
0.04 ---> 4
-56 ---> 5

How do you do this in MATLAB?

Answer 1

A few ways you can do this...

• Using REGEXP:

  wholeNumber = 1934;                      %# Your number
  numberString = num2str(wholeNumber,16);  %# Convert to a string
  matches = regexp(numberString,'[1-9]','match');  %# Find matches
  firstNumber = str2double(matches{1});  %# Convert the first match to a double
  

• Using ISMEMBER:

  wholeNumber = 0.04;                      %# Your number
  numberString = num2str(wholeNumber,16);  %# Convert to a string
  isInSet = ismember(numberString,'123456789');  %# Find numbers that are
                                                 %#  between 1 and 9
  numberIndex = find(isInSet,1);           %# Get the first number index
  firstNumber = str2double(numberString(numberIndex));  %# Convert to a double
  

EDIT:

Some discussion of this topic has arisen on one of the MathWorks blogs. Some interesting additional solutions are provided there. One issue that was brought up was having vectorized solutions, so here's one vectorized version I came up with:

numberVector = [1934 0.04 -56];
numberStrings = cellstr(num2str(numberVector(:),16));
firstIndices = regexp(numberStrings,'[1-9]','once');
firstNumbers = cellfun(@(s,i) s(i),numberStrings,firstIndices);

Answer 2

function res = first_digit(number)
    number = abs(number);
    res = floor(number / (10 ^ floor(log10(number))));
end

It works for all real numbers (see gnovice's comment for an extreme case)

Answer 3

Using log10 and floor built in functions,

floor(x./10.^floor(log10(x)))

returns the first digit of all elements in an array as well.