# How to mutate values of matrix which by mutating its sub-matrix?

**URL:** <https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325>\
**Category:** General Usage\
**Tags:** question, arrays, views\
**Created:** [September 15, 2022, 6:14pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325 "2022-09-15T18:14:00Z")\
**Posts on this page:** 10\
**Page:** 1

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**Author:** ![Amro](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@Amro](https://discourse.julialang.org/u/Amro)\
**Post date:** [September 15, 2022, 6:14pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/1 "2022-09-15T18:14:00Z")

</div>

In the below, I building matrix `A` which consists of for sub-matrices `Y,A1,A2,A3`.I want the mutation on `A3` be applied automatically on `A` as well. How can I do that please?

```julia

using BenchmarkTools, StaticArrays, LinearAlgebra, SparseArrays, .Threads

Y = [1 2;3 4];
A1 = [5 6;7 8];
A2 = [11 22;33 44];
A3 = [0 0;0 0];

A = [Y A1; A2 A3]

A3 .= [1 1; 1 1]; # I want the change also be applied on A

A

```

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<div class="post-metadata">

**Author:** ![lmiq](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lmiq/32/18314_2.png) [@lmiq](https://discourse.julialang.org/u/lmiq)\
**Post date:** [September 15, 2022, 6:32pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/2 "2022-09-15T18:32:31Z")

</div>

You either want a vector of matrices, i. e.:

```julia
julia> A3 = [0 0;0 0];

julia> A = [Y,A1,A2,A3];

julia> A3 .= [1 1; 1 1]; # I want the change also be applied on A

julia> A
4-element Vector{Matrix{Int64}}:
 [1 2; 3 4]
 [5 6; 7 8]
 [11 22; 33 44]
 [1 1; 1 1]

```

Or you want to define the matrix and then its slices:

```julia
julia> A 
4×4 Matrix{Int64}:
  1 2 5 6
  3 4 7 8
 11 22 0 0
 33 44 0 0

julia> A3 = @view(A[3:4,3:4])
2×2 view(::Matrix{Int64}, 3:4, 3:4) with eltype Int64:
 0 0
 0 0

julia> A3 .= 1
2×2 view(::Matrix{Int64}, 3:4, 3:4) with eltype Int64:
 1 1
 1 1

julia> A
4×4 Matrix{Int64}:
  1 2 5 6
  3 4 7 8
 11 22 1 1
 33 44 1 1

```

---

<div class="post-metadata">

**Author:** ![Amro](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@Amro](https://discourse.julialang.org/u/Amro)\
**Post date:** [September 15, 2022, 6:57pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/3 "2022-09-15T18:57:46Z")

</div>

Thank you very much!  
If the first method is used, and I want to solve `x=A\b` I get the below error. Is there a way to solve it or just work with the second method you proposed?  
where,

```julia
Y = [1 2;3 4];
A1 = [5 6;7 8];
A2 = [11 22;33 44];
A3 = [5 5;5 5];
A = [Y,A1,A2,A3];
4-element Vector{Matrix{Int64}}:
 [1 2; 3 4]
 [5 6; 7 8]
 [11 22; 33 44]
 [5 5; 5 5]

julia> b=[1;1;1;1]
4-element Vector{Int64}:
 1
 1
 1
 1

julia> A\b
ERROR: MethodError: no method matching zero(::Type{Matrix{Int64}})

```

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<div class="post-metadata">

**Author:** ![lmiq](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lmiq/32/18314_2.png) [@lmiq](https://discourse.julialang.org/u/lmiq)\
**Post date:** [September 15, 2022, 7:15pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/4 "2022-09-15T19:15:22Z")

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Oh, yes, in the first one `A` is not a regular matrix, it is a vector of matrices, so `A\b` won’t work. I think you need something in the lines of the second case.

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<div class="post-metadata">

**Author:** ![sbuercklin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sbuercklin/32/15728_2.png) [@sbuercklin](https://discourse.julialang.org/u/sbuercklin)\
**Post date:** [September 15, 2022, 7:16pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/5 "2022-09-15T19:16:24Z")

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Edit- I see lmiq gave the `view` solution already, I missed the second half

I think what you want is a collection of `view`s into `A`.

Once you combine `Y, A1, A2, A3` into `A`, `A` is now an entirely new `Matrix` without the references to `Y, A1, A2, A3`.

```julia
_Y = [1 2; 3 4];
_A1 = [5 6; 7 8];
_A2 = [11 22; 33 44];
_A3 = [0 0; 0 0];

A = [_Y _A1; _A2 _A3]
# 4×4 Matrix{Int64}:
# 1 2 5 6
# 3 4 7 8
# 11 22 0 0
# 33 44 0 0

Y = view(A, 1:2, 1:2)
A1 = view(A, 1:2, 3:4)
A2 = view(A, 3:4, 1:2)
A3 = view(A, 3:4, 3:4)

A3 .= 1

A
# 4x4 Matrix{Int64}:
# 1 2 5 6
# 3 4 7 8
# 11 22 1 1
# 33 44 1 1

```

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<div class="post-metadata">

**Author:** ![Amro](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@Amro](https://discourse.julialang.org/u/Amro)\
**Post date:** [September 15, 2022, 9:30pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/7 "2022-09-15T21:30:47Z")

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@lmiq @sbuercklin  
Thank you very much!

I tried to implement your feedbacks on building a left-shifted matrix `A_shiftl` of `A`. So, when I mutate `A`, the `A_shiftl` will be mutated as well. However, I could not do that. Any help please here?  
I have and I have which it elements

```julia
A = [1.0 5 0 0 0;0 1 0 0 0;0 0 1 0 0 ;0 0 0 1 0;0 0 0 0 1];
A_shiftl = [@view(A[:,2:end]) zeros(size(A,1))]
A[3,3] =5;
julia> A
5×5 Matrix{Float64}:
 1.0 5.0 0.0 0.0 0.0
 0.0 1.0 0.0 0.0 0.0
 0.0 0.0 5.0 0.0 0.0
 0.0 0.0 0.0 1.0 0.0
 0.0 0.0 0.0 0.0 1.0

julia> A_shiftl # It did not follow the change in A
5×5 Matrix{Float64}:
 5.0 0.0 0.0 0.0 0.0
 1.0 0.0 0.0 0.0 0.0
 0.0 1.0 0.0 0.0 0.0
 0.0 0.0 1.0 0.0 0.0
 0.0 0.0 0.0 1.0 0.0

```

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<div class="post-metadata">

**Author:** ![lmiq](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lmiq/32/18314_2.png) [@lmiq](https://discourse.julialang.org/u/lmiq)\
**Post date:** [September 15, 2022, 9:45pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/8 "2022-09-15T21:45:04Z")

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No, that won’t work like that in general. It is better of you write functions that operate on the matrices as you want, given ranges and values.

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<div class="post-metadata">

**Author:** ![Amro](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@Amro](https://discourse.julialang.org/u/Amro)\
**Post date:** [September 15, 2022, 10:13pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/10 "2022-09-15T22:13:13Z")

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@lmiq @sbuercklin  
When I am using @view with sparsematrix, the resulting one is not sparse like `Asp_r ` below. Any way to keep it sparse?

```julia
Asp = spzeros(5,6);
Asp[1,1] = 1.0;
Asp[1,2] = 5.0; 
Asp[2,2] = 1.0; 
Asp[3,3] = 1.0; 
Asp[4,4] = 1.0; 
Asp[5,5] = 1.0; 
julia> Asp_r =@view(Asp[:,1:end-1])
5×5 view(::SparseMatrixCSC{Float64, Int64}, :, 1:5) with eltype Float64:
 1.0 5.0 0.0 0.0 0.0
 0.0 1.0 0.0 0.0 0.0
 0.0 0.0 1.0 0.0 0.0
 0.0 0.0 0.0 1.0 0.0
 0.0 0.0 0.0 0.0 1.0

```

---

<div class="post-metadata">

**Author:** ![sbuercklin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sbuercklin/32/15728_2.png) [@sbuercklin](https://discourse.julialang.org/u/sbuercklin)\
**Post date:** [September 16, 2022, 12:00am UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/11 "2022-09-16T00:00:17Z")

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It looks sparse to me, it just prints a `0.0` instead of `.` for the empty entries because of how `view`s print. You can check sparsity using `issparse`:

```julia
julia> issparse(Asp_r)
true

```

I recommend looking at the `Views` section of the Julia manual [here](https://docs.julialang.org/en/v1/base/arrays/#Views-(SubArrays-and-other-view-types))

---

<div class="post-metadata">

**Author:** ![Amro](https://avatars.discourse-cdn.com/v4/letter/a/4491bb/32.png) [@Amro](https://discourse.julialang.org/u/Amro)\
**Post date:** [September 16, 2022, 2:36pm UTC](https://discourse.julialang.org/t/how-to-mutate-values-of-matrix-which-by-mutating-its-sub-matrix/87325/12 "2022-09-16T14:36:31Z")

</div>

Thanks for your feedback.