# View of LowerMatrix is not working with ldiv! and mul!

**URL:** <https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046>\
**Category:** Numerics\
**Created:** [July 31, 2020, 3:48pm UTC](https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046 "2020-07-31T15:48:31Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![mleprovost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mleprovost/32/7166_2.png) [@mleprovost](https://discourse.julialang.org/u/mleprovost)\
**Post date:** [July 31, 2020, 3:48pm UTC](https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046/1 "2020-07-31T15:48:31Z")

</div>

Hello,

I am computed a large Cholesky factor L \in R^{N,N}, and I would like to multiply and divide an array of dimension n, M with n \leq N. I would like to use `view(L,1:n,1:n)` but `ldiv!`, `mul!` are not defined for views.

```julia
using LinearAlgebra
N = 50
M = 500

X = randn(N, M)

L = cholesky(X*X' + 1.0* I).L

n= 10

Y = randn(n, M)

ldiv!(view(L,1:n,1:n), Y) 

mul!(view(L,1:n,1:n), Y)

```

The error message for `mul!`:

```julia
 mul!(::AbstractArray, ::AbstractArray, !Matched::Number, !Matched::Number, !Matched::Number) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.4/LinearAlgebra/src/generic.jl:126
  mul!(::AbstractArray{T,2} where T, ::Union{DenseArray{T,2}, Base.ReinterpretArray{T,2,S,A} where S where A<:Union{SubArray{T,N,A,I,true} where I<:Union{Tuple{Vararg{Real,N} where N}, Tuple{AbstractUnitRange,Vararg{Any,N} where N}} where A<:DenseArray where N where T, DenseArray}, Base.ReshapedArray{T,2,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{Base.ReinterpretArray{T,N,S,A} where S where A<:Union{SubArray{T,N,A,I,true} where I<:Union{Tuple{Vararg{Real,N} where N}, Tuple{AbstractUnitRange,Vararg{Any,N} where N}} where A<:DenseArray where N where T, DenseArray} where N where T, SubArray{T,N,A,I,true} where I<:Union{Tuple{Vararg{Real,N} where N}, Tuple{AbstractUnitRange,Vararg{Any,N} where N}} where A<:DenseArray where N where T, DenseArray}, SubArray{T,2,A,I,L} where L where I<:Tuple{Vararg{Union{Int64, AbstractRange{Int64}, Base.AbstractCartesianIndex},N} where N} where A<:Union{Base.ReinterpretArray{T,N,S,A} where S where A<:Union{SubArray{T,N,A,I,true} where I<:Union{Tuple{Vararg{Real,N} where N}, Tuple{AbstractUnitRange,Vararg{Any,N} where N}} where A<:DenseArray where N where T, DenseArray} where N where T, Base.ReshapedArray{T,N,A,MI} where MI<:Tuple{Vararg{Base.MultiplicativeInverses.SignedMultiplicativeInverse{Int64},N} where N} where A<:Union{Base.ReinterpretArray{T,N,S,A} where S where A<:Union{SubArray{T,N,A,I,true} where I<:Union{Tuple{Vararg{Real,N} where N}, Tuple{AbstractUnitRange,Vararg{Any,N} where N}} where A<:DenseArray where N where T, DenseArray} where N where T, SubArray{T,N,A,I,true} where I<:Union{Tuple{Vararg{Real,N} where N}, Tuple{AbstractUnitRange,Vararg{Any,N} where N}} where A<:DenseArray where N where T, DenseArray} where N where T, DenseArray}} where T, !Matched::Transpose{#s662,#s661} where #s661<:Diagonal where #s662, !Matched::Number, !Matched::Number) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.4/LinearAlgebra/src/diagonal.jl:341
  mul!(::AbstractArray{T,2} where T, ::Union{AbstractArray{T,1}, AbstractArray{T,2}} where T, !Matched::Transpose{#s662,#s661} where #s661<:(Union{AbstractArray{T,1}, AbstractArray{T,2}} where T) where #s662, !Matched::Number, !Matched::Number) at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.4/LinearAlgebra/src/matmul.jl:345

```

---

<div class="post-metadata">

**Author:** ![dlfivefifty](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dlfivefifty/32/1959_2.png) [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)\
**Post date:** [August 3, 2020, 9:29am UTC](https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046/2 "2020-08-03T09:29:26Z")

</div>

This problem is what ArrayLayouts.jl is designed to solve, but note that `view(L,1:n,1:n)` does not know from the type information that the view is lower triangular: this means its not clear that `ldiv!` can be overwrite the result. `view(L,Base.OneTo(n),Base.OneTo(n))` is a bit better though not yet supported, but would be easy to add a `LowerTrapezoidalLayout` for this case so that `ArrayLayouts.ldiv!(view(L,Base.OneTo(n),Base.OneTo(n)), Y)` works.

I don’t have time to do this myself but happy to walk you through it if you are willing to make a PR.

---

<div class="post-metadata">

**Author:** ![mleprovost](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mleprovost/32/7166_2.png) [@mleprovost](https://discourse.julialang.org/u/mleprovost)\
**Post date:** [August 3, 2020, 4:18pm UTC](https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046/3 "2020-08-03T16:18:52Z")

</div>

> [@dlfivefifty](#):
>
> ArrayLayouts.jl

Thank you @dlfivefifty. Yes, I will be happy to work on `LowerTrapezoidalLayout`. How can I start?

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<div class="post-metadata">

**Author:** ![dlfivefifty](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dlfivefifty/32/1959_2.png) [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)\
**Post date:** [August 3, 2020, 4:21pm UTC](https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046/4 "2020-08-03T16:21:47Z")

</div>

Look at `TriangularLayout ` in ArrayLayouts.jl/src/memorylayouts.jl and triangular.jl

Probably should have said `TrapezoidalLayout` as the upper/lower is determined by a character.

---

<div class="post-metadata">

**Author:** ![dlfivefifty](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dlfivefifty/32/1959_2.png) [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)\
**Post date:** [August 3, 2020, 4:22pm UTC](https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046/5 "2020-08-03T16:22:23Z")

</div>

(Please file an issue on github to discuss further questions)

---

<div class="post-metadata">

**Author:** ![andreasnoack](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andreasnoack/32/27_2.png) [@andreasnoack](https://discourse.julialang.org/u/andreasnoack)\
**Post date:** [August 6, 2020, 7:44am UTC](https://discourse.julialang.org/t/view-of-lowermatrix-is-not-working-with-ldiv-and-mul/44046/6 "2020-08-06T07:44:32Z")

</div>

As a short term work around, you can reverse the view and the `LowerTriangular` wrapping, i.e. something like

```julia
julia> L = LowerTriangular(randn(4,4));

julia> ldiv!(LowerTriangular(parent(L)[1:3, 1:3]), ones(3))
3-element Array{Float64,1}:
 -0.748637727829292
  4.553737980760209
 -8.60259724047278

```