# Generate a numerical series

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Vittorio Faustinella on 28 Jan 2022
Edited: John D'Errico on 28 Jan 2022
Hi everyone, I want to generate this vector: 1e-8, 1e-9, 1e-10, 1e-11, 1e-12, 1e-13, 1e-14.
How can i do it?
Thanks
##### 1 CommentShowHide None
Torsten on 28 Jan 2022
v=10.^(-(8:14))

DGM on 28 Jan 2022
Edited: DGM on 28 Jan 2022
This is one way:
k = -8:-1:-14;
v = 10.^k
v = 1×7
1.0e+-8 * 1.0000 0.1000 0.0100 0.0010 0.0001 0.0000 0.0000
fprintf('%g\n',v.') % for sake of clarity
1e-08 1e-09 1e-10 1e-11 1e-12 1e-13 1e-14

### More Answers (1)

John D'Errico on 28 Jan 2022
Edited: John D'Errico on 28 Jan 2022
While @DGM is correct (+1 from me on that answer, please accept that answer, as it is the correct one), in that it is what I would do immediately, there are always many ways to do things like this. The alternative I can think of immediately is to use cumprod with repmat:
format long g
v = cumprod([1e-8,repmat(0.1,1,6)])
v = 1×7
1.0e+00 * 1e-08 1e-09 1e-10 1e-11 1e-12 1e-13 1e-14
fprintf('%g\n',v.') % for sake of clarity
1e-08 1e-09 1e-10 1e-11 1e-12 1e-13 1e-14
I could also have used cumprod, in conjunction with repelem instead of repmat. That would be slightly less kludgy looking.
cumprod([1e-8,repelem(0.1,6)])'
ans = 7×1
1.0e+00 * 1e-08 1e-09 1e-10 1e-11 1e-12 1e-13 1e-14
Then I think of logspace, which does work nicely. In fact, logspace is a pretty clean looking solution. Still not as obvious in my eyes as that which DGM proposed.
logspace(-8,-14,7).'
ans = 7×1
1.0e+00 * 1e-08 1e-09 1e-10 1e-11 1e-12 1e-13 1e-14
And of course, there is this devious solution:
exp((-8:-1:-14)*log(10)).'
ans = 7×1
1.0e+00 * 9.99999999999998e-09 9.99999999999997e-10 9.99999999999996e-11 9.99999999999998e-12 9.99999999999997e-13 9.99999999999996e-14 9.99999999999999e-15
which is technically correct, exceot that floating point trash appears in the least significant bits. But 9.99999999999999e-9 is technically 1e-8, exept for an error in the least significant bit of the result.
I can stop here, but with some effort, I'd bet there are more.

R2019b

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