Simple mathematics giving unexpected outcome. Dividing data arrays/vectors

I am trying to do some calculations, but there are giving me really strange results. And I am not sure where to start looking for a solution.

I have a very simple calculation: Divide each element in the first row (or column) by the corresponding element in the second row (or column).

My input is attached;

bands 71X2 double

and I would like to get the 71 values that you get when you divide bands(:,1) by bands(2,:).

I tried this:

%original data, to ensure the right output, transpose the data:
spectralindex =  bands(:,1)' ./ bands(:,2)' ;

%Or transpose the data first:
bands2 = bands';
spectralindex2 =  bands2(1,:) ./ bands2(2,:) ;

%or create separate variables
band1 = bands(:,1)';
band2 = bands(:,2)';
spectralindex3 = band1 ./ band2;

Looking at the data:

bands(1,1) = 0.0709 & bands(1,2) = 0.0275. If I take a calculator and divide these, I get 0.0709 / 0.0275 = 2.578. This is the outcome I am expecting to get from matlab too. A regular division of value 1 by value 2.

However the matlab outcome shows 2.5803 as outcome.

There probably is something very logical about this, with me making a conceptual mistake on how these calculations are done. But.. I cannot figure out what. Slightly baffled. Does anyone have an idea of what is going on?

Answer 1

[Star Strider]

MATLAB maintains full internal precision in its calculations. Since 2.578 and 2.5803 are not significantly different, I suspect you are seeing the effect of the reduced precision of your hand calculations and MATLAB’s extended precision calculations.

Example —

d = rand(2,1)
Ratio_1 = d(1)/d(2)                             % Full Precision
Ratio_2 = round(d(1),4) / round(d(2),4)         % Limited Precision

d =
   0.712414805789522
   0.016674712940232

Ratio_1 =
  42.724262081335056

Ratio_2 =
  42.658682634730539

[Jelle]

{*} Stupid me.

Indeed. I was looking at data that was rounded in the viewer. In the source data, I have a much higher precision. 0.0709 is actually 0.070914537

Can't believe I wasted an hour of my life on this. Reminder to self. Check your input before you mistrust the software.

Thank You! I do not think I would have thought of this.

[Star Strider]

Not stupid at all!

It’s just one of those things we learn as we learn about floating-point computations. Note that these have their own limitations, most significantly summarized in Why is 0.3 - 0.2 - 0.1 (or similar) not equal to zero? (link) and How do I determine if the error in my answer is the result of round-off error or a bug? (link).

[Jelle]

Thx. that is very kind of you. But it is the sort of mistake I should not be making anymore after doing data processing for 2 decades. Guess that moving into a new processing tools got me off guard.