Searching vector for precision values

There are many times where I have found myself searching a time vector for a specific time to offset data. Typically I use find(t == d) where d is a specific value which is known to be in t and t is a vector with length > 2000. However, for specific values of d (which I cannot understand) the boolean statement returns a zero vector (d not detected). For Example.

t = 1:1/400:10;

c = 5.465;

d = 5.565;

e = 5.665;

n = find(t == c);

m = find(t == d);

p = find(t == e);

produces n = 1787, m = null double vector, p = 1867.

and t(1827) = 5.5650

Answer 1

[Dave B]

This is a common error with floating point precision, the numbers are not actually the same:

t = 1:1/400:10;
d = 5.565;
m = find(t == d)

m =

  1×0 empty double row vector

[~,nearest]=min(abs(t-d));
t(nearest) % looks the same?

ans = 5.5650

d==t(nearest) % but it isn't equal

ans = logical
   0

d-t(nearest) % the values are ever so slightly different

ans = 8.8818e-16

% Here's the common workaround:
tol = 1e-10; %whatever is appropriate for your data
find(abs(t-d)<tol)

ans = 1827

Here's a wikipedia about floating point error mitigation: https://en.wikipedia.org/wiki/Floating-point_error_mitigation

Here's a nice description about floating point from Cleve: https://blogs.mathworks.com/cleve/2014/07/07/floating-point-numbers/

If you search for "floating point error", or "floating point error matlab" you'll find lots more resources.

Note that there are a few functions in MATLAB that take a tolerance, like ismembertol but there's no isequaltol