# For loop with decimal increment not seen as integer or logical value

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Commented: Walter Roberson on 23 Jan 2020
Goal:
1. Have for loop repeatedly create matrices of random integers
2. Create new matrix where columns = variance for each row of random integer matrices
3. Compare variance to increment ranging from 0:0.01:4 (0-4 in increments of 0.01) and retain each matrix of 0s and 1s generated this way
The following code produces the desired results when the increment = 1 (not 0.01)
T = 10;
W = zeros(3,10);
for trial = 1:T
mtest = randi([1,5],3,4)
W(:,trial) = var(mtest,0,2);
end
minc = zeros(3,10,5);
for mindex = 0:1:4
minc(:,:,mindex+1) = W >= mindex
end
Problem 1: The same code does not work when the increment is set to 0.01:
linc = zeros(3,10,401);
for lindex = 0:0.01:4
linc(:,:,lindex+1) = W >= lindex
end
Error = Index in position 3 is invalid. Array indices must be positive integers or logical values.
Problem 2: After much reading, I think the problem is that "lindex+1" produces indices of 1.01, 1.02...etc. Yet both of the below solutions produce the same error.
Solution 1: Add 1 to remove 0 from index; multiply by 100 such that index should proceed as 100, 101, 102...etc.
linc = zeros(3,10,401);
for lindex = 0:0.01:4
linc(:,:,(lindex+1)*100) = W >= lindex
end
Solution 2: Start index at 0.01 instead of 0 and multiply by 100 such that index should proceed as 100, 101, 102...etc.
linc = zeros(3,10,401);
for lindex = 0.01:0.01:4
linc(:,:,lindex*100) = W >= lindex
end
Why does the code work if increment = 1 but not 0.01? How can I fix this? Thank you in advance, this is a wonderful community.
I should add for anyone else who comes across this thread...this link posted in another thread by Image Analyst also really helped me. At least, I was able to identify how my index was a non-integer after reading this. There's a section toward the end that addresses this exact error message.

KSSV on 23 Jan 2020
Edited: KSSV on 23 Jan 2020
lindex = 0:0.01:4 ;
linc = zeros(3,10,401);
for i = 1:length(lindex)
linc(:,:,i) = W >= lindex(i) ;
end
Please note that, your indices should not be zero, or fractions or negative. In your original code in problem 1, you have used fractions, zero as indices, therefore you gor errors.
Walter Roberson on 23 Jan 2020
If you take values constructed with the : operator with increment 0.01 and you multiply the values by 100, then roughly 1/10th of the results will not be integers.
MATLAB does not represent numbers in decimal: it represents them in binary. In binary, 1/100 requires an infinite repeating number to represent exactly, for precisely the same reason that in decimal, 1/7 needs an infinite repeating number to exactly represent. Therefore any finite binary truncation of a multiple of 1/100 will not exactly represent the fraction, and when you multiply the inexact representation by 100 you will not always get out an integer.