# Bug? isapprox different results elementwise (Julia 1.1.0)

**URL:** https://discourse.julialang.org/t/bug-isapprox-different-results-elementwise-julia-1-1-0/30271
**Category:** General Usage
**Tags:** bug
**Created:** [October 24, 2019, 3:29pm UTC](https://discourse.julialang.org/t/bug-isapprox-different-results-elementwise-julia-1-1-0/30271 "2019-10-24T15:29:09Z")
**Posts on this page:** 4
**Page:** 1

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### Author: ![dcastel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dcastel/32/10692_2.png) [@dcastel](https://discourse.julialang.org/u/dcastel)
#### Post date: [October 24, 2019, 3:29pm UTC](https://discourse.julialang.org/t/bug-isapprox-different-results-elementwise-julia-1-1-0/30271/1 "2019-10-24T15:29:09Z")

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I have this weird case where two tensors are element-wise and size-wise approx equal up to 3 digits but as a whole they aren’t. I’m still running Julia 1.1.0 though.

```julia
alldigits = cat([[0.375297 0.624703]; [0.39924 0.60076]], [[0.664557 0.335443]; [0.664557 0.335443]], dims=3)
2×2×2 Array{Float64,3}:
[:, :, 1] =
 0.375297 0.624703
 0.39924 0.60076 

[:, :, 2] =
 0.664557 0.335443
 0.664557 0.335443
julia> threedig = map(x -> round(x,digits=3), alldigits)
2×2×2 Array{Float64,3}:
[:, :, 1] =
 0.375 0.625
 0.399 0.601

[:, :, 2] =
 0.665 0.335
 0.665 0.335

julia> isapprox.(alldigits, threedig, atol=1e-3)
2×2×2 BitArray{3}:
[:, :, 1] =
 true true
 true true

[:, :, 2] =
 true true
 true true

julia> isapprox(alldigits, threedig, atol=1e-3)
false

julia> size(alldigits) == size(threedig)
true

```

I made a test script for it here:  
[https://gist.github.com/dietercastel/4ff276ad7d70ba91321a070de72b00f3](https://gist.github.com/dietercastel/4ff276ad7d70ba91321a070de72b00f3)

Anyone who knows why or how this happens?

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<div class="post-metadata">

### Author: ![dkarrasch](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dkarrasch/32/7410_2.png) [@dkarrasch](https://discourse.julialang.org/u/dkarrasch)
#### Post date: [October 24, 2019, 3:38pm UTC](https://discourse.julialang.org/t/bug-isapprox-different-results-elementwise-julia-1-1-0/30271/2 "2019-10-24T15:38:01Z")

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You’ll find the answer in the docstring of `isapprox` (`?isapprox`), given that

```julia
julia> norm(alldigits - threedig)
0.0010376001156515333

```

The norm computed is like an Euclidean norm of the difference, when viewing the 3D-tensors as if vectorized. But that Euclidean norm is something else than the maximum of the absolute value of the elementwise difference.

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<div class="post-metadata">

### Author: ![dcastel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dcastel/32/10692_2.png) [@dcastel](https://discourse.julialang.org/u/dcastel)
#### Post date: [October 24, 2019, 3:43pm UTC](https://discourse.julialang.org/t/bug-isapprox-different-results-elementwise-julia-1-1-0/30271/3 "2019-10-24T15:43:57Z")

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Oh, I see thanks. Should have read the manual better!

The element wise approx suffices for my use case. So not a bug, but what a response time!

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### Author: ![mbauman](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mbauman/32/31082_2.png) [@mbauman](https://discourse.julialang.org/u/mbauman)
#### Post date: [October 24, 2019, 4:06pm UTC](https://discourse.julialang.org/t/bug-isapprox-different-results-elementwise-julia-1-1-0/30271/4 "2019-10-24T16:06:07Z")

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Just a small addition to say that this is more general than just a quirk of `isapprox`. Julia treats matrices and arrays as real algebraic objects in their own right — they’re not “just” collections of numbers. You’ll see this distinction throughout: `*` vs `.*`, `exp(A)` vs. `exp.(A)`, etc, etc. Same deal here.