Problems when creating matrix

Hello,

I am trying to create a matrix by several means, using linespace, using matrix notation and stating every element. For some reason the results obtained are not equal for some of the values in the matrix:

categ1=linspace(0.85,1.35, 51)

categ2=[0.85:0.01:1.35]

categ3=[0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.35]

categ1==categ2

categ2==categ3

Answer 1

[Daniel M]

The results are equal up to double precision. Look at this:

max(abs(categ1-categ2))
% ans =
%     2.22044604925031e-16
eps
% ans =
%     2.22044604925031e-16

So the values are equal up to the limit that the computer can differentiate between them.

It seems that linspace and colon have slightly different implementations. If you need something with higher precision, then look into John D'Errico's VPI toolbox.

https://www.mathworks.com/matlabcentral/fileexchange/22725-variable-precision-integer-arithmetic

[Juan Manuel Romero]

The problem is that when I create the matrix whit linspace and colon and later try to find the colation of the value equal to 1.2 get an empty matrix. Any idea of how can I solve that issue?

>> categ1=linspace(0.85,1.35, 51);
categ2=[0.85:0.01:1.35];
find(categ1==1.2)
find(categ2==1.2)
ans =
  1×0 empty double row vector
ans =
  1×0 empty double row vector

[Stephen23]

"Any idea of how can I solve that issue?"

Don't check for exact equality of floating point values.

Always check the absolute difference against a tolerance:

abs(A-B)<tol

The behaviors of floating point numbers are quite well documented, you need to learn how to write your code taking them into account. Start by reading these:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/41536-why-is-2-24-10-22-4-not-equal-to-0

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

etc.etc.

This is worth reading as well:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf