How to to report row at which the difference reaches below a threshold?

For example, if I have this matrix, transposed:

a = [10 7 5 2 1 0.5 0.4 0.3 0.3 ...]

i.e. it is getting smaller at a decreasing rate.

And I want to report the row in which the difference gets sufficiently small, or almost at steady state. I would want it to report the row of 0.4 or the 1st 0.3.

How can I do this?

Answer 1

[the cyclist]

Probably the hardest part will be defining the exact rule for "sufficiently small difference". After that, I think something like

threshold = 0.11;
find(diff(-a) < threshold,1);

will find what you want. Note that diff(a) is one element shorter than a, so be careful with indexing.

Also, it is a bit trickier if you need to define a relatively small difference (compared to earlier differences), rather than an absolute difference (as I did here with 0.11 threshold).

[the cyclist]

Oh, another cautionary note: Be wary of checking an exact threshold value. Because some decimal numbers cannot be represented exactly, you need to be careful of floating point error in calculations like

>> (0.5-0.4)-0.1

ans =

    -2.775557561562891e-17