# How to compare vectors?
**URL:** https://discourse.julialang.org/t/how-to-compare-vectors/121295
**Category:** General Usage
**Tags:** question
**Created:** [October 14, 2024, 4:16pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295 "2024-10-14T16:16:31Z")
**Posts on this page:** 11
**Page:** 1
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [October 14, 2024, 4:16pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/1 "2024-10-14T16:16:31Z")
What is a good way to check if two vectors are approximately equal?
I have this check that fails:
```julia
using Test
a = [1,2,3]
b = [1,2,3.0000001]
@test a ≈ b
```
?
---
### Author:  [@DanielVandH](https://discourse.julialang.org/u/DanielVandH)
#### Post date: [October 14, 2024, 4:21pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/2 "2024-10-14T16:21:02Z")
Just pass the appropriate tolerances you want for your test. See `?@test`.
---
### Author:  [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)
#### Post date: [October 14, 2024, 4:28pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/3 "2024-10-14T16:28:18Z")
As an aside, I’m surprised you asked this question, as you’ve been here for a while and I’ve lost count of the number of times @stevengj has explained your question. 🙂
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [October 14, 2024, 4:39pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/4 "2024-10-14T16:39:19Z")
> [@DanielVandH](#):
>
> `?@test`.
Really helpful. Thank you!
For the record: This works:
```julia
using Test
a = [1,2,3]
b = [1,2,3.0000001]
@test a ≈ b atol=1e-5
```
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [October 14, 2024, 4:39pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/5 "2024-10-14T16:39:49Z")
> [@rafael.guerra](#):
>
> I’m surprised you asked this question
I am getting old. And it is not easy to find search terms that allow you to find the answer to this question online.
---
### Author:  [@\_bernhard](https://discourse.julialang.org/u/_bernhard)
#### Post date: [October 14, 2024, 4:57pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/6 "2024-10-14T16:57:02Z")
I think the point was rather, that
```julia
help?> @test
```
can be expected to be the first stop for getting help of anyone even just mildly familiar with julia.
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [October 14, 2024, 4:58pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/7 "2024-10-14T16:58:13Z")
Not really. How shall I know that the \approx operator is defined in the package Test? I did not expect that.
---
### Author:  [@nilshg](https://discourse.julialang.org/u/nilshg)
#### Post date: [October 14, 2024, 4:59pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/8 "2024-10-14T16:59:37Z")
See for one of the more recent ones:
> [@History of \`isapprox\` in languages](https://discourse.julialang.org/t/history-of-isapprox-in-languages/119347):
>
> Does anyone know why the de-facto standard definition of isapprox intentionally fails when one of the arguments is zero? isapprox(0.0, 0.0 + 1e-10) # false isapprox(1.0, 1.0 + 1e-10) # true It is clear from the formula why this is happening: ||x - y|| \le max(atol, rtol\*max(||x||, ||y||)) If we set y=0, we get: ||x|| \le max(atol, rtol\*||x||) The default atol = 0 then makes it: ||x|| \le rtol \* ||x|| and the default rtol = \sqrt\epsilon leads to: ||x|| \le \sqrt\epsilon ||x|| which…
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [October 14, 2024, 5:00pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/9 "2024-10-14T17:00:39Z")
That was one of the few threads I did not read because it is too long.
---
### Author:  [@\_bernhard](https://discourse.julialang.org/u/_bernhard)
#### Post date: [October 14, 2024, 5:08pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/10 "2024-10-14T17:08:32Z")
But you don’t need to know that for the above either, do you?
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [October 14, 2024, 5:32pm UTC](https://discourse.julialang.org/t/how-to-compare-vectors/121295/11 "2024-10-14T17:32:05Z")
> [@ufechner7](#):
>
> How shall I know that the \approx operator is defined in the package Test? I did not expect that.
It’s not, it’s defined in `Base`. See [`Base.isapprox`](https://docs.julialang.org/en/v1/base/math/#Base.isapprox) or type `≈` or `isapprox` at the `help?>` prompt.
What is specific to the `@test` macro is that it has its own convenience syntax for passing keyword arguments to infix operators, so that you can type:
```julia
@test x ≈ y rtol=1e-3
```
instead of
```julia
@test ≈(x,y, rtol=1e-3)
```
or
```julia
@test isapprox(x, y, rtol=1e-3)
```
though all three are equivalent. The `@test` keyword syntax isn’t actually specific to `≈`, but that is probably where it is most often used.