# Trying to translate Matlab code to Julia - need help #50640

**URL:** <https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111>\
**Category:** General Usage\
**Tags:** question, matlab, convert, julia\
**Created:** [July 26, 2023, 10:52am UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111 "2023-07-26T10:52:43Z")\
**Posts on this page:** 15\
**Page:** 1

<div class="post-metadata">

**Author:** ![manuelcaeiro](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/manuelcaeiro/32/51824_2.png) [@manuelcaeiro](https://discourse.julialang.org/u/manuelcaeiro)\
**Post date:** [July 26, 2023, 10:52am UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/1 "2023-07-26T10:52:43Z")

</div>

I’m trying to translate the following code in Matlab:

```julia
e = 1.05; %Eccentricity 
 a = -147562.72; %km
 b = abs(a)*sqrt(e.^2 -1); %Equation for Semi-Minor Axis, b

 x1 = linspace( a, 2*a, 1E3); %From 0 to a, Upper

 ytop = b*sqrt(x1.^2/a^2-1); %Upper Hyperbola Part
 ybot = -b*sqrt(x1.^2/a^2-1); %Lower Hyperbola Part

```

to Julia.

Everything seems to go well until `ytop`. Here’s my code up to that point:

```julia
 ecc=1.05; a=-14; b=abs(a)*sqrt(ecc.^2 -1)

x1=LinRange(a, 2*a, 100)
100-element LinRange{Float64, Int64}:
 -14.0,-14.1414,-14.2828,-14.4242,-14.5657,…,-27.5758,-27.7172,-27.8586,-28.0

```

but then:

```julia
 ytop=b*sqrt(x1.^2 / a^2 - 1)
 ERROR: MethodError: no method matching -(::Vector{Float64}, ::Int64)
 For element-wise subtraction, use broadcasting with dot syntax: array .- scalar
 Closest candidates are:
  -(::T, ::T) where T<:Union{Int128, Int16, Int32, Int64, Int8, UInt128, UInt16, UInt32, UInt64, UInt8} at ~/julia-1.7.1/share/julia base/int.jl:86
  -(::Rational, ::Integer) at ~/julia-1.7.1/share/julia/base/rational.jl:311
  -(::T, ::Integer) where T<:AbstractChar at ~/julia-1.7.1/share/julia/base/char.jl:227
  ...
Stacktrace:
 [1] top-level scope
   @ REPL[41]:1

```

I went through Julia and Matlab docs trying to understand the Error message (making several changes to the code, trying to match the types, for example), but I couldn’t do it.

Please forgive me my probable ignorance (both of Julia and Matlab), and be willing to help me please.

---

<div class="post-metadata">

**Author:** ![JM\_Beckers](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jm_beckers/32/22482_2.png) [@JM\_Beckers](https://discourse.julialang.org/u/JM_Beckers)\
**Post date:** [July 26, 2023, 11:06am UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/2 "2023-07-26T11:06:07Z")

</div>

> [@manuelcaeiro](#):
>
> `ytop=b*sqrt(x1.^2 / a^2 - 1)`

You need to broadcast the operations with a “.” as hinted to by the error message ` use broadcasting with dot syntax: array .- scalar`

```julia
ytop=b*sqrt.(x1.^2 / a^2 .- 1)

```

---

<div class="post-metadata">

**Author:** ![gustaphe](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gustaphe/32/18174_2.png) [@gustaphe](https://discourse.julialang.org/u/gustaphe)\
**Post date:** [July 26, 2023, 12:19pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/3 "2023-07-26T12:19:18Z")

</div>

In Matlab, a few operations have been identified as doing different things if applied as a scalar operation elementwise or as a matrix-matrix operation. In these cases you mark the difference with a period: `A * x` vs `A .* x`. In Julia, this distinction is applied consistently, and broadcasting (“elementwising”) can and is expected to be done for any function. For instance, if you define a function `f(x) = sin(x)*x^2`, you cannot now call `f` on a matrix `X`, but you _can_ broadcast it: `f.(X)`.

It takes a while to get used to, but it is really convenient, because you can easily do things like “sum every array in this array of arrays”, with quite intuitive syntax.

---

<div class="post-metadata">

**Author:** ![gdalle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gdalle/32/27854_2.png) [@gdalle](https://discourse.julialang.org/u/gdalle)\
**Post date:** [July 26, 2023, 12:39pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/4 "2023-07-26T12:39:17Z")

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> [@gustaphe](#):
>
> For instance, if you define a function `f(x) = sin(x)*x^2`, you cannot now call `f` on a matrix `X`, but you _can_ broadcast it: `f.(X)`.

Small correction: actually you can, but by default the `sin`, `*` and `^2` will be interpreted in a matrix-algebraic sense (i.e. `sin` is defined as the Taylor expansion). On the other hand, that function `f` wouldn’t work for vectors as is.

```julia
julia> f(x) = sin(x) * x^2
f (generic function with 1 method)

julia> A = rand(2, 2)
2×2 Matrix{Float64}:
 0.42875 0.743563
 0.466328 0.963168

julia> x = rand(2)
2-element Vector{Float64}:
 0.3776789845468388
 0.49083688309729057

julia> f(A)
2×2 Matrix{Float64}:
 0.515227 1.00944
 0.633075 1.24074

julia> f.(A)
2×2 Matrix{Float64}:
 0.0764227 0.374257
 0.0977732 0.761641

julia> f(x)
ERROR: MethodError: no method matching sin(::Vector{Float64})
...

julia> f.(x)
2-element Vector{Float64}:
 0.052601022788648956
 0.11356144554205107

```

Note how `f.(A)` is different from `f(A)`

---

<div class="post-metadata">

**Author:** ![gustaphe](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gustaphe/32/18174_2.png) [@gustaphe](https://discourse.julialang.org/u/gustaphe)\
**Post date:** [July 26, 2023, 2:21pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/5 "2023-07-26T14:21:06Z")

</div>

Ah, yes. You cannot call them on arbitrary matrices, only ones for which sine and square are defined.

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**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [July 26, 2023, 2:34pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/6 "2023-07-26T14:34:03Z")

</div>

> [@JM\_Beckers](#):
>
> `ytop=b*sqrt.(x1.^2 / a^2 .- 1)`

Add a few more dots:

```julia
ytop = b .* sqrt.(x1.^2 ./ a^2 .- 1)

```

This dots everything except `a^2`, which is a scalar-scalar operation.

---

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**Author:** ![stillyslalom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stillyslalom/32/45687_2.png) [@stillyslalom](https://discourse.julialang.org/u/stillyslalom)\
**Post date:** [July 26, 2023, 3:05pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/7 "2023-07-26T15:05:29Z")

</div>

And you can automatically broadcast everything in an expression with the `@.` macro:

```julia
ytop = @. b * sqrt(x1^2 / a^2 - 1)

```

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**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [July 26, 2023, 3:30pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/8 "2023-07-26T15:30:48Z")

</div>

Indeed, but for optimal performance, you would like to avoid dotting `a^2`.

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**Author:** ![frylock](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/frylock/32/50213_2.png) [@frylock](https://discourse.julialang.org/u/frylock)\
**Post date:** [July 26, 2023, 3:42pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/9 "2023-07-26T15:42:00Z")

</div>

I have not used this before, but this claims to be a [Matlab-to-Julia translator](https://lakras.github.io/matlab-to-julia/).  
If it works, I hope all Matlab users run this on their code and are happy with the results.

---

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**Author:** ![JM\_Beckers](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jm_beckers/32/22482_2.png) [@JM\_Beckers](https://discourse.julialang.org/u/JM_Beckers)\
**Post date:** [July 26, 2023, 5:57pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/10 "2023-07-26T17:57:45Z")

</div>

```julia
@btime ytop=b*sqrt.(x1.^2 / a^2 .- 1)
@btime ytop1=b.*sqrt.(x1.^2 ./ a^2 .- 1)
@btime ytop2= @. b*sqrt(x1^2 / a^2 - 1)

```

gives

1.930 μs (14 allocations: 3.84 KiB)  
2.756 μs (14 allocations: 1.66 KiB)  
3.200 μs (18 allocations: 1.86 KiB)

(Julia 1.8.5)

---

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**Author:** ![stillyslalom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stillyslalom/32/45687_2.png) [@stillyslalom](https://discourse.julialang.org/u/stillyslalom)\
**Post date:** [July 26, 2023, 6:39pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/11 "2023-07-26T18:39:59Z")

</div>

Always better to wrap your test articles in functions for benchmarking:

```julia
julia> f1(x1, a, b) = b .* sqrt.(x1.^2 ./ a^2 .- 1)
f1 (generic function with 1 method)

julia> f2(x1, a, b) = @. b * sqrt(x1^2 / a^2 - 1)
f2 (generic function with 1 method)

julia> @btime f1($x1, $a, $b);
  4.143 μs (1 allocation: 7.94 KiB)

julia> @btime f2($x1, $a, $b);
  4.143 μs (1 allocation: 7.94 KiB)

```

At least on Julia v1.9.2, the generated assembly is identical - the scalar doesn’t get broadcasted.

---

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**Author:** ![DNF](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dnf/32/10191_2.png) [@DNF](https://discourse.julialang.org/u/DNF)\
**Post date:** [July 26, 2023, 6:48pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/12 "2023-07-26T18:48:57Z")

</div>

Ah, it’s clever enough to avoid that extra operation, interesting.

---

<div class="post-metadata">

**Author:** ![manuelcaeiro](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/manuelcaeiro/32/51824_2.png) [@manuelcaeiro](https://discourse.julialang.org/u/manuelcaeiro)\
**Post date:** [July 27, 2023, 5:05pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/13 "2023-07-27T17:05:51Z")

</div>

Thank you all

The first solution was enough to solve my problem, but I will go through all the others (and even find a more elegant way to plot it).  
For now the plot is:

```julia
p = plot(x1,ytop); plot!(p,x1,ybot); plot!(p,-x1,ytop); plot!(p,-x1,ybot)

```

![Screenshot_2023-07-27_17-56-18](https://global.discourse-cdn.com/julialang/original/3X/6/c/6c55034c0aa3a78114bac50d4a529a326f6ab6b2.jpeg)

P.S.: I was pleasantly surprised to find such a lively community here. I guess I’ll have to take some time to understand better broadcasting process in Julia.

---

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**Author:** ![ElOceanografo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/eloceanografo/32/624_2.png) [@ElOceanografo](https://discourse.julialang.org/u/ElOceanografo)\
**Post date:** [July 27, 2023, 5:40pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/14 "2023-07-27T17:40:00Z")

</div>

This blog post from 2017 (when the dot-broadcasting syntax was first introduced in Julia v0.6) does a really nice job of explaining how/why it all works, if you’re interested in reading more:

> **[More Dots: Syntactic Loop Fusion in Julia](https://julialang.org/blog/2017/01/moredots/)**
>
> More Dots: Syntactic Loop Fusion in Julia | After a lengthy design process (https://github.com/JuliaLang/julia/issues/8450) and preliminary foundations in Julia 0.5 (/blog/2016-10-11-julia-0.5-highlights#vectorized\_function\_calls), Julia 0.6 includes...

---

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**Author:** ![GenerallyClueless](https://avatars.discourse-cdn.com/v4/letter/g/c37758/32.png) [@GenerallyClueless](https://discourse.julialang.org/u/GenerallyClueless)\
**Post date:** [July 27, 2023, 6:26pm UTC](https://discourse.julialang.org/t/trying-to-translate-matlab-code-to-julia-need-help-50640/102111/15 "2023-07-27T18:26:38Z")

</div>

JuliaAcademy is a great resource, even for experienced programmers. As a matter of fact, the Introduction to Julia (for programmers) course lesson on Functions discusses Map and Broadcast (very similar).

> **[Functions](https://juliaacademy.com/courses/375479/lectures/5871178)**
>
> Learn the language basics in this 10-part course.

The courses do help to explain differences Julia and other languages. It’s worth looking at in your spare time. 👍

I’d also like to give a shout out and THANK YOU 🥳 🎉 to all of the creators and maintainers for JuliaAcademy!!