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Order of magnitude of number

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Returns the order of magnitude of one or more numbers.



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Returns the order of magnitude of one or more numbers. Works on arrays. You can also specify the number base.

order( 1.2e-5 ) %returns -5
order(1) = 0
order( 1.12344e8 ) %returns 8
%Specify base 2:
order(1.2*2^5,2) %returns 5

Comments and Ratings (11)


Robert (view profile)

If you input at the command line:

log(1000)./log(10) - 3

you will see why the original fails at this value. It also fails and a number of other (positive) powers of 10 as shown by the following:

b = -100:100
for q = 1:length(b)
a(q) = order(10^b(q));
plot(b, a, 'kx', b, b, 'ro')
grid on

If the black 'x' is not inside a red 'o' then it's a failure.
No failures of negative powers in this range.


Ben (view profile)

Now tested with vector:

>> floor(single(log([1000 100 1000 10000 100])./log(10)))

ans =

3 2 3 4 2

Joel, I seem to experience the same problem when the input is an exact integer value. I think this will be a problem when the input is a whole power of the base. I am not sure yet how this shuold be solved, one would have to do a test on the input to detect if it is a whole power of the base within numerical precision


Joel (view profile)

I seem to experience a severe precision error using this function. I get order(1000) = 2. order(1000.000000000001) gives me the correct value of 3.

Irem Altan


Carlos (view profile)




John (view profile)

I see what you're doing and it makes sense, thanks for the reply!

Thanks John. But I think one should leave the order of magnitude of 0 to be minus infinity, that`s just what it is. If you set it to zero, consider this:
o = order(x);
x2 and x should then be the same, but they won`t be if you set the order to 0. x2 would then be 1.


John (view profile)

added the following to the bottom:

% If the value is zero then the order is set to zero
n(isinf(n)) = 0;


John (view profile)

works great!



Added possibility to specify base.

MATLAB Release
MATLAB 7.14 (R2012a)

Inspired by: logb

Inspired: SEROUND: Round value and standard error

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