# Apply function to array in Julia

**URL:** <https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981>\
**Category:** New to Julia\
**Created:** [July 3, 2019, 12:28pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981 "2019-07-03T12:28:56Z")\
**Posts on this page:** 13\
**Page:** 1

<div class="post-metadata">

**Author:** ![Luigi\_Marongiu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/luigi_marongiu/32/7909_2.png) [@Luigi\_Marongiu](https://discourse.julialang.org/u/Luigi_Marongiu)\
**Post date:** [July 3, 2019, 12:28pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/1 "2019-07-03T12:28:56Z")

</div>

Dear all,  
I am reading a book on how to create a procedure for solving integrants using python. It is said to create an array and apply the function over an array in order to speed up the procedure. The code provided is:

```julia
from numpy import linspace, sum

def midpoint(f, a, b, n):
  h = float(b-a)/n
  x = linspace(a+h/2, b-h/2, n)
  return h*sum(f(x))

```

where f is the function to be integrated between the pioints a and b, and n is the number of iteractions.  
I converted this in Julia with:

```julia
function midpoint(f, a, b, n)
    h = (b-a)/n
    res = 0
    x = collect(range(z+h/2,stop=b-h/2,length=n) )
    res = sum(f(x))
    return res
end

```

x has been correctly generated: I set a=0, b=1, n=100 and:

```julia
julia> x
100-element Array{Float64,1}:
 0.005
 0.015
 0.025
 0.035
 ⋮
 0.965
 0.975
 0.985
 0.995

```

and I assigned a function to f:

```julia
julia> f=x->x^3+x^2
#11 (generic function with 1 method)

```

But when I try the apply it:

```julia
julia> res = sum(f(x))
ERROR: MethodError: no method matching ^(::Array{Float64,1}, ::Int64)
Closest candidates are:
  ^(::Float16, ::Integer) at math.jl:795
  ^(::Missing, ::Integer) at missing.jl:120
  ^(::Missing, ::Number) at missing.jl:93
  ...
Stacktrace:
 [1] macro expansion at ./none:0 [inlined]
 [2] literal_pow at ./none:0 [inlined]
 [3] (::getfield(Main, Symbol("##13#14")))(::Array{Float64,1}) at ./none:1
 [4] top-level scope at none:0

```

What am I missing? how can I apply a function to all elements of an array directly?

Thank you

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<div class="post-metadata">

**Author:** ![rveltz](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rveltz/32/2707_2.png) [@rveltz](https://discourse.julialang.org/u/rveltz)\
**Post date:** [July 3, 2019, 12:34pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/2 "2019-07-03T12:34:29Z")

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try `sum(f,x)` or `sum(f.(x))`

---

<div class="post-metadata">

**Author:** ![Luigi\_Marongiu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/luigi_marongiu/32/7909_2.png) [@Luigi\_Marongiu](https://discourse.julialang.org/u/Luigi_Marongiu)\
**Post date:** [July 3, 2019, 12:38pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/3 "2019-07-03T12:38:36Z")

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Thank you!

---

<div class="post-metadata">

**Author:** ![simeonschaub](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/simeonschaub/32/216566_2.png) [@simeonschaub](https://discourse.julialang.org/u/simeonschaub)\
**Post date:** [July 3, 2019, 12:39pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/4 "2019-07-03T12:39:29Z")

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You want to broadcast `f` over the array `x`, so you’re looking for `f.(x)`. Better still, you can avoid allocations by passing `f` directly to sum, i.e. `sum(f, x)`. You might also want to take a look at [https://docs.julialang.org/en/v1/manual/arrays/index.html#Array-and-Vectorized-Operators-and-Functions-1](https://docs.julialang.org/en/v1/manual/arrays/index.html#Array-and-Vectorized-Operators-and-Functions-1). Also note that the `collect` in the function above is unnecessary in most cases and you will get better performance by not collecting `x` into an array.

---

<div class="post-metadata">

**Author:** ![Luigi\_Marongiu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/luigi_marongiu/32/7909_2.png) [@Luigi\_Marongiu](https://discourse.julialang.org/u/Luigi_Marongiu)\
**Post date:** [July 3, 2019, 12:59pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/5 "2019-07-03T12:59:21Z")

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but if I don’t use collect I don’t get an array:

```julia
julia> range(Start+h/2,stop=End-h/2,length=Iter)
0.005:0.01:0.995
julia> collect(range(Start+h/2,stop=End-h/2,length=Iter))
100-element Array{Float64,1}:
 0.005
 0.015
 0.025
 0.035
 ⋮
 0.965
 0.975
 0.985
 0.995

```

---

<div class="post-metadata">

**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [July 3, 2019, 1:46pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/6 "2019-07-03T13:46:15Z")

</div>

Incidentally, there is no reason to pre-assign `res = 0`, or even to name it as a variable. Just `sum(f, x)` in the last line would be fine.

---

<div class="post-metadata">

**Author:** ![kristoffer.carlsson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kristoffer.carlsson/32/22_2.png) [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)\
**Post date:** [July 3, 2019, 2:24pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/7 "2019-07-03T14:24:55Z")

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> [@Luigi\_Marongiu](#):
>
> but if I don’t use collect I don’t get an array:

Why do you want an array specifically? The range contains the same information, only more efficiently.

---

<div class="post-metadata">

**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 3, 2019, 3:06pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/8 "2019-07-03T15:06:10Z")

</div>

> [@Luigi\_Marongiu](#):
>
> but if I don’t use collect I don’t get an array:

A range is an array, it just isn’t an `Array`. Specifically, it’s a `StepRangeLen` which is a type of `AbstractArray`.

You should _definitely not_ use `collect` here, in fact, you should almost _never_ collect ranges. The whole point of ranges is that they are smarter and faster and lighter than a full `Array`. Using `collect` just ruins that.

You should write

```julia
x = range(z+h/2, b-h/2, length=n)
res = sum(f, x)

```

Not `sum(f.(x))`. This is the best and fastest way.

---

<div class="post-metadata">

**Author:** ![Luigi\_Marongiu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/luigi_marongiu/32/7909_2.png) [@Luigi\_Marongiu](https://discourse.julialang.org/u/Luigi_Marongiu)\
**Post date:** [July 3, 2019, 6:25pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/9 "2019-07-03T18:25:36Z")

</div>

I will be happy NOT to use collect, but so why the difference in output that I have shown?

> 0.005:0.01:0.995

vs

> 100-element Array{Float64,1}:

In fact, following the [manual](https://en.wikibooks.org/wiki/Introducing_Julia/Arrays_and_tuples#Creating_arrays_using_range_objects):

```julia
julia> x = range(1, stop=100, step=10)
1:10:91

julia> println(x)
1:10:91

julia> x = collect(range(1, stop=100, step=10))
10-element Array{Int64,1}:
  1
 11
 21
 31
 41
 51
 61
 71
 81
 91

julia> println(x)
[1, 11, 21, 31, 41, 51, 61, 71, 81, 91]

```

And the manual also added:

> If you really want it in array form, you can use the range object to build an array:
> 
> `julia> collect(range(1, length=12, stop=100))`

I don’t need an `Array`, and I can see that range is an array:

```julia
julia> x = range(1, stop=100, step=10)
1:10:91

julia> typeof(x)
StepRange{Int64,Int64}

```

but I do I use `range` then? for iteractions, for instance:

```julia
julia> for i in x

           println(x)

       end
1:10:91
1:10:91
1:10:91
1:10:91
1:10:91
1:10:91
1:10:91
1:10:91
1:10:91
1:10:91

```

---

<div class="post-metadata">

**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 3, 2019, 6:30pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/10 "2019-07-03T18:30:28Z")

</div>

Well, of course they print differently, otherwise how could you tell that one is a smart compact array, and the other a dumb big one? 🙂

> [@Luigi\_Marongiu](#):
>
> ```julia
> for i in x 
> println(x)
> end
> 
> ```

Presumably, you mean

```julia
for i in x 
    println(i)
end

```

?

BTW, for integer ranges it is more convenient to write `1:10:100` rather than `range(1, stop=100, step=10)`.

---

<div class="post-metadata">

**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 3, 2019, 6:37pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/11 "2019-07-03T18:37:54Z")

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The `StepRange` prints differently than an `Array`, because it is a different kind of object, but it does ~~everything~~ almost everything an `Array` can do, for instance indexing,

```julia
julia> x[3]
21

julia> collect(x)[3]
21

```

scalar multiplication,

```julia
julia> 3.14159 * x
3.14159:31.4159:285.88469 # note the result is another StepRange

```

and matrix-array multiplication:

```julia
julia> M = randn(10, 10);
julia> M * x # "just works"

```

**Edit** But not mutation:

```julia
julia> x[3] = 22
ERROR: setindex! not defined for StepRange{Int64,Int64}

```

because `StepRanges` are immutable, and, more fundamentally, because the value at `x[3]` isn’t actually stored anywhere: it’s calculated on-demand when you ask for it.

---

<div class="post-metadata">

**Author:** ![Luigi\_Marongiu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/luigi_marongiu/32/7909_2.png) [@Luigi\_Marongiu](https://discourse.julialang.org/u/Luigi_Marongiu)\
**Post date:** [July 3, 2019, 8:29pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/12 "2019-07-03T20:29:45Z")

</div>

> [@DNF](#):
>
> for i in x println(i) end

Ops! I see what you mean.

---

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**Author:** ![tomaklutfu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomaklutfu/32/2411_2.png) [@tomaklutfu](https://discourse.julialang.org/u/tomaklutfu)\
**Post date:** [July 3, 2019, 10:47pm UTC](https://discourse.julialang.org/t/apply-function-to-array-in-julia/25981/13 "2019-07-03T22:47:10Z")

</div>

Except being mutated