Unknown glitch when finding an exact array value

All,

I am experiencing a strange glitch within the following code. I understand this was probably not the best way to execute what i was looking to do, and have since re-worked the code to avoid this error.

In the following code, Matlab is failing to recognize t=0.3 within the t array. That is, T=find() skips over 0.3000 when the step size h is 0.05 or 0.025 in the t array. T=find() DOES correctly find 0.3000 in the t array when the step size h is <=0.01. I can also call for an indexing array:

a=t==0.3;

that fails to find the index of 0.3 within t, when the step size h is 0.05 or 0.025. Again, this indexing array works with step size h=0.01.

This has been verrified to happen on two machines running two different releases of Matlab. Mine is R2020a

clc
clear
h=0.05;%when h <=0.01, the error does not occur
t=0:h:2;
y=zeros(size(t));
y(1)=1;
n=numel(y);
%syms x real
%Y(x)=0.25*x-(3/16)+(19/16)*exp(4*x); %actual solution
for i=1:n-1
    f=1-t(i)+4.*y(i);
    y(i+1) = y(i)+h*f;
end

T=find(t==0.1 | t==0.2 | t==0.3 | t==0.4 | t==0.5 | t==1 | t==1.5 | t==2);

for j=1:numel(T)
    fprintf('y=%.6f\n',y(T(j)));
end
%plot(t,y,t,Y(t)); grid on 

The code following the first loop was re-written and will properly find t=0.3 with step size h=0.05:

inds = [0.1,0.2,0.3,0.4,0.5,1,1.5,2];
T=zeros(size(inds));

for i=1:length(inds)
   T(i)=find(t>=inds(i),1);
end

for j=1:length(T)
    fprintf('y=%.5f\n',y(T(j)));
end

Answer 1

[Star Strider]

That reflects the way the colon operator works to calculate the vector elements. See the documentation section on Floating-Point Numbers for an illustrative discussion.

Include a tolerance with find, as you did in the version that worked.

[Samuel Gaspar]

Thanks! Defining t using linspace also appears to fix it.

[Star Strider]

As always, my pleasure!

The linspace function produces more exact elements, however it requires a bit of forethought to produce exact integers with it.