Decomposition in any base Matlab

Hi, I would like to know if there was a Matlab builtin function that decompose any integer in a chosen base, it would be something like:

dec2base(52,4)

ans =

     0     1     3

I've write my own function, but it's pretty slow. Maybe you will detect an error in my code (nVariable is the length of the array I want my function to return):

function [digits] = LeftDecompose(number, base, nVariable)

% Decompose a number in any base.

quotient = floor(number/base^(nVariable-1));

remainder = number - quotient * base^(nVariable-1);

if remainder == 0

    digits = [zeros(1, nVariable-1) quotient];

else

    digits = [LeftDecompose(remainder, base, nVariable - 1) quotient];

end

end

Thank you in advance.

Answer 1

[David Sanchez]

I don't know whether you checked it out or not, but dec2base is a MATLAB built-in function. Type the following in the command window for all the details:

help dec2base
doc dec2base

[Martin]

Ok, I'm stupid then. Would you know another function / a very fast way to transform it directly to an array of number (faster than str2double for each character)? I'll have to handle each digit separately.

Thank you!

[Evan]

You could use arrayfun, but there are no guarantees it will be any faster than looping over every element with dec2base (because that's essentially what arrayfun does.

arrayfun(@(x)dec2base(x),my_array,'UniformOutput',0)

[Martin]

Thanks, I had troubles to use this command, could you please show me how to proceed? How should I initialize my_array? Say, for example, I want to decompose 54 in base 4.

[Cedric]

Here is an example .. say you want to convert integers from 50 to 56:

 >> my_array = 50:56
 my_array =
    50    51    52    53    54    55    56

 >> my_array_base4 = arrayfun(@(x)dec2base(x,4), my_array, 'UniformOutput', 0)
 my_array_base4 = 
    '302'    '303'    '310'    '311'    '312'    '313'    '320'

Now if you wanted to use an array of bases as well, you could do it as follows:

 >> values = [50, 100, 23, 78] ;
 >> bases  = [4, 7, 3, 10] ;
 >> valuesBases = arrayfun(@(x,b)dec2base(x,b), values, bases, ...
                           'UniformOutput', 0)
 valuesBases = 
    '302'    '202'    '212'    '78'

[Martin]

I don't understand, does it return an array of numbers instead of strings?

[Cedric]

It returns a cell array of strings, because DEC2BASE itself returns strings (more accurately char arrays):

 >> ret = dec2base(54, 4)
 ret =
 312

 >> class(ret)
 ans =
 char

ARRAYFUN itself does nothing else than to apply the function given as a first argument to values of arrays given as additional arguments, and output "some" array with the result. When the function (given as a 1st argument) outputs scalars, ARRAYFUN outputs a regular numeric array. When the function outputs arrays, we have to tell ARRAYFUN that it can generate a non uniform output (see last two args), which it does in a cell array.

You can then convert these strings to numbers using e.g. STR2DOUBLE on the whole cell array. To illustrate based on the first example above:

 >> class(my_array_base4)        % Check that output is a cell array.
 ans =
 cell

 >> class(my_array_base4{1})     % Check that cells content is char/string.
 ans =
 char

 >> values = str2double(my_array_base4)   % Convert to double.
 values =
     302   303   310   311   312   313   320

 >> class(values)                         % Check that it's double
 ans =
 double

BUT! these are base 10 numbers and there are not a lot of good reasons to convert back to double. In fact, DEC2BASE provides you with a representation of a decimal number into a certain base. The purpose is display or storage, for which strings are well adapted. MATLAB won't compute in base 4 for example and if you want to perform computations, you do it in base 10 first and you convert the result to a base 4 representation afterwards.