Logical Indexing With LinSpace Issues

Logical indexing is missing an equivalence in a linspace array. I have absolutely no idea why or how to fix this. I'm running MATALB R2022b on Windows 11.

Any ideas or help or explanation would be appreciated.

Here is how you can recreate my issue:

X = linspace(0.2,3,29); %Creates an array going from 0.2 -> 3 via steps of 0.1. So 1.3 is in it. 
disp(X(12))

    1.3000

flag = (X == 1.3);
any(flag) %Yet for some reason 1.3 isn't detected.

ans = logical
   0

%Just to be absolutely sure I'm not mad
disp(X(12))

    1.3000

X(12) == 1.3

ans = logical
   0

% Yet other non-integers still work! 
flag = (X == 1.1);
any(flag)

ans = logical
   1

[Stephen23]

"Any ideas or help or explanation would be appreciated."

This is a completely expected result with binary floating point numbers:

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/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

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

[Lucas Graham]

Thank you for these resources!

Answer 1

[Star Strider]

format long
X = linspace(0.2,3,29) %Creates an array going from 0.2 -> 3 via steps of 0.1. So 1.3 is in it. 

X = 1×29

0.200000000000000 0.300000000000000 0.400000000000000 0.500000000000000 0.600000000000000 0.700000000000000 0.800000000000000 0.900000000000000 1.000000000000000 1.100000000000000 1.200000000000000 1.300000000000000 1.400000000000000 1.500000000000000 1.600000000000000 1.700000000000000 1.800000000000000 1.900000000000000 2.000000000000000 2.100000000000000 2.200000000000000 2.300000000000000 2.400000000000000 2.500000000000000 2.600000000000000 2.700000000000000 2.800000000000000 2.900000000000000 3.000000000000000

disp(X(12))

   1.300000000000000

flag = (X == 1.3);
any(flag) %Yet for some reason 1.3 isn't detected.

ans = logical
   0

Check_Equality = 1.3 - X(12)

Check_Equality = 
     2.220446049250313e-16

%Just to be absolutely sure I'm not mad
disp(X(12))

   1.300000000000000

X(12) == 1.3

ans = logical
   0

% Yet other non-integers still work! 
flag = (X == 1.1);
any(flag)

ans = logical
   1

The‘Check_Equality’ assignment demonstrates that the two numbers are actually not equal.

You’re not mad! You just haven’t been introduced to the subtle mysteries of floating-point numeric repreesentation.

See Floating-Point Numbers and Accuracy of Floating-Point Data for an extensive discussion.

.

[Lucas Graham]

Thank you!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

Answer 2

[Chris]

This looks like a problem of computer precision. Double-precision floating point numbers in matlab (and floating-point numbers in general) a̶r̶e̶ ̶n̶o̶t̶ ̶e̶x̶a̶c̶t̶ (edit: are a finite set of discrete values, so they are usually unlikely to exactly match the value we see displayed)

X = linspace(0.2,3,29);
Y = 0.2:0.1:3;

% X(11)==1.2 because the result of the linspace division 
% is the same as the double representation for 1.2
sprintf('%.60f\n%.60f',X(11),Y(11))

ans = 
    '1.199999999999999955591079014993738383054733276367187500000000
     1.199999999999999955591079014993738383054733276367187500000000'

% X(12) doesn't equal the double for 1.3.
sprintf('%.60f\n%.60f',X(12),Y(12))

ans = 
    '1.299999999999999822364316059974953532218933105468750000000000
     1.300000000000000044408920985006261616945266723632812500000000'

You can use other comparison operators to test rough equivalence, e.g., (X(12)-1.3) < 1e-14

Here's a bit more information, if you're interested.

https://www.geeksforgeeks.org/ieee-standard-754-floating-point-numbers/

[Lucas Graham]

Thank you! I'll stick to using colon notation for simple ranges like mine.

[Walter Roberson]

Well, in a sense, double precision is exact... but only for a subset of rationals, some of the rationals that have powers of two as the denominator (not all of those). It is however not exact for powers of 10 in the denominator (just like finite decimal is not exact for powers of 3 or 7 in the denominator)

[Lucas Graham]

My intuition is that using MATLAB's colon operator to build arrays is less likely to run into float point errors because it probably uses addition instead of division, is that correct?

For example, using like you did 0.2:0.1:3 vs. linspace(0.2,3,29).

[Walter Roberson]

No, the opposite. Each time you add two floating point numbers, the round-off error can increase (unless the sequence of operations has been carefully chosen.) The error for 0.1, 0.1+0.1, 0.1+0.1+0.1 is greater than for (1:3)/10