## Issue

I have simulation program written in Julia that does something equivalent to this as a part of its main loop:

```
# Some fake data
M = [randn(100,100) for m=1:100, n=1:100]
W = randn(100,100)
work = zip(W,M)
result = mapreduce(x -> x[1]*x[2], +,work)
```

In other words, a simple sum of weighted matrices. Timing the above code yields

```
0.691084 seconds (79.03 k allocations: 1.493 GiB, 70.59% gc time, 2.79% compilation time)
```

I am surprised about the large number of memory allocations, as this problem should be possible to do in-place. To see if it was my use of mapreduce that was wrong I also tested the following equivalent implementation:

```
@time begin
res = zeros(100,100)
for m=1:100
for n=1:100
res += W[m,n] * M[m,n]
end
end
end
```

which gave

```
0.442521 seconds (50.00 k allocations: 1.491 GiB, 70.81% gc time)
```

So, if I wrote this in C++ or Fortran it would be simple to do all of this in-place. Is this impossible in Julia? Or am I missing something here…?

## Solution

It is possible to do it in place like this:

```
function ws(W, M)
res = zeros(100,100)
for m=1:100
for n=1:100
@. res += W[m,n] * M[m, n]
end
end
return res
end
```

and the timing is:

```
julia> @time ws(W, M);
0.100328 seconds (2 allocations: 78.172 KiB)
```

Note that in order to perform this operation in-place I used broadcasting (I could also use loops, but it would be the same).

The problem with your code is that in line:

```
res += W[m,n] * M[m,n]
```

You get two allocations:

- When you do multiplication
`W[m,n] * M[m,n]`

a new matrix is allocated. - When you do addition
`res += ...`

again a matrix is allocated

By using broadcasting with `@.`

you perform an in-place operation, see https://docs.julialang.org/en/v1/manual/mathematical-operations/#man-dot-operators for more explanations.

Additionally note that I have wrapped the code inside a function. If you do not do it then access both `W`

and `M`

is type unstable which also causes allocations, see https://docs.julialang.org/en/v1/manual/performance-tips/#Avoid-global-variables.

Answered By – Bogumił Kamiński

Answer Checked By – Clifford M. (BugsFixing Volunteer)