This is a duplicate of https://groups.google.com/forum/#!topic/julia-users/u9Tjpg19e9k . I decided to move the conversation to discourse because it allows for formatting of code.

I am encountering an unexpected amount of storage allocation in the `cfactor!{A::HBlkDiag)`

method in the `MixedModels`

package. See

https://github.com/dmbates/MixedModels.jl/blob/master/src/cfactor.jl for the code.

An `HBlkDiag`

matrix is a homogeneous block diagonal matrix where “homogeneous” refers to the fact that all the diagonal blocks are square and of the same size. Because of this homogeneity the blocks can be stored in an `r x r x k`

array where `r`

is the size of each of the square block and `k`

is the number of such blocks.

On entry to this method the blocks are symmetric, positive semi-definite. I want to overwrite the upper triangle of each of these blocks with its Cholesky factor. I call `LAPACK.potrf!`

directly because I don’t want `cholfact!`

to throw a non-positive-definite error. The strange thing to me is that when I monitor the storage allocation, I get a huge amount of storage being allocated in the line with that call. This may be because `LAPACK.potrf!`

returns a tuple of the original matrix and an Int (the `info`

code) but I’m not sure.

To see an example of this unusual amount of allocation try the following code with julia --track-allocation=user

```
using Feather, MixedModels
cd(Pkg.dir("MixedModels", "test", "data"))
sleepstudy = Feather.read("sleepstudy.feather", nullable=false)
fm1 = fit!(lmm(Reaction ~ 1 + Days + (1 + Days | Subject), sleepstudy))
Profile.clear_malloc_data()
devs, vars, betas, thetas = bootstrap(10_000, fm1)
```

I get

```
- function cfactor!{T}(A::HBlkDiag{T})
- Aa = A.arr
0 r, s, t = size(Aa)
0 if r ≠ s
0 throw(ArgumentError("HBlkDiag matrix A must be square"))
- end
94428000 scm = Array(T, (r, r))
0 for k in 1 : t # FIXME: Lots of allocations in this loop
0 for j in 1 : r, i in 1 : j
0 scm[i, j] = Aa[i, j, k]
- end
566568000 LAPACK.potrf!('U', scm)
0 for j in 1 : r, i in 1 : j
0 Aa[i, j, k] = scm[i, j]
- end
- end
10492000 UpperTriangular(A)
- end
```

In this case the `HBlkDiag`

matrix being decomposed is 36 by 36 consisting of 18 2 by 2 diagonal blocks. `scm`

is a scratch 2 by 2 matrix that is overwritten in sequence by the upper triangle of each of the original 2 by 2 blocks and passed to `LAPACK.potrf!`