# Creating a sparse array with JuMP.QuadExpr elements

**URL:** <https://discourse.julialang.org/t/creating-a-sparse-array-with-jump-quadexpr-elements/103171>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [August 24, 2023, 9:07pm UTC](https://discourse.julialang.org/t/creating-a-sparse-array-with-jump-quadexpr-elements/103171 "2023-08-24T21:07:39Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![JPG](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jpg/32/52451_2.png) [@JPG](https://discourse.julialang.org/u/JPG)\
**Post date:** [August 24, 2023, 9:07pm UTC](https://discourse.julialang.org/t/creating-a-sparse-array-with-jump-quadexpr-elements/103171/1 "2023-08-24T21:07:39Z")

</div>

Hello all,

I’m very new to Julia and basically I want to define an empty sparse matrix of N x N and fill it up at certain points in the diagonal with just JuMP.QuadExpr elements.

I know I can do: A = spzeros(N, N) but trying to add a QuadExpr to an element results in the following error:

MethodError: Cannot `convert` an object of type GenericAffExpr{ComplexF64, VariableRef} to an object of type Float64

Any help is appreciated, thanks!

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [August 25, 2023, 2:58am UTC](https://discourse.julialang.org/t/creating-a-sparse-array-with-jump-quadexpr-elements/103171/2 "2023-08-25T02:58:00Z")

</div>

Hi @JPG, welcome to the forum.

You need to use the `spzeros(type, m, n)` method:

```plaintext
help?> SparseArrays.spzeros
  spzeros([type,]m[,n])

  Create a sparse vector of length m or sparse matrix of size m x n. This sparse array will not contain any nonzero
  values. No storage will be allocated for nonzero values during construction. The type defaults to Float64 if not
  specified.

  Examples
  ≡≡≡≡≡≡≡≡≡≡

  julia> spzeros(3, 3)
  3×3 SparseMatrixCSC{Float64, Int64} with 0 stored entries:
    ⋅ ⋅ ⋅
    ⋅ ⋅ ⋅
    ⋅ ⋅ ⋅
  
  julia> spzeros(Float32, 4)
  4-element SparseVector{Float32, Int64} with 0 stored entries

```

Here’s an example:

```julia
julia> Q = SparseArrays.spzeros(QuadExpr, 3, 3)
3×3 SparseArrays.SparseMatrixCSC{QuadExpr, Int64} with 0 stored entries:
 ⋅ ⋅ ⋅
 ⋅ ⋅ ⋅
 ⋅ ⋅ ⋅

julia> model = Model();

julia> @variable(model, x)
x

julia> Q[1, 1] = 2 * x^2 + 1
2 x² + 1

julia> Q
3×3 SparseArrays.SparseMatrixCSC{QuadExpr, Int64} with 1 stored entry:
 2 x² + 1 ⋅ ⋅
 ⋅ ⋅ ⋅
 ⋅ ⋅ ⋅

```

But it looks like you might have a complex-valued affine expression, not a quadratic expression?

In that case, you’d need

```julia
julia> Q = SparseArrays.spzeros(GenericAffExpr{ComplexF64, VariableRef}, 3, 3)
3×3 SparseArrays.SparseMatrixCSC{GenericAffExpr{ComplexF64, VariableRef}, Int64} with 0 stored entries:
 ⋅ ⋅ ⋅
 ⋅ ⋅ ⋅
 ⋅ ⋅ ⋅

julia> Q[1, 1] = (2.0 + 3.0im) * x
(2 + 3im) x

julia> Q
3×3 SparseArrays.SparseMatrixCSC{GenericAffExpr{ComplexF64, VariableRef}, Int64} with 1 stored entry:
 (2 + 3im) x ⋅ ⋅
 ⋅ ⋅ ⋅
 ⋅ ⋅ ⋅

```

---

<div class="post-metadata">

**Author:** ![JPG](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jpg/32/52451_2.png) [@JPG](https://discourse.julialang.org/u/JPG)\
**Post date:** [August 25, 2023, 3:58pm UTC](https://discourse.julialang.org/t/creating-a-sparse-array-with-jump-quadexpr-elements/103171/3 "2023-08-25T15:58:46Z")

</div>

Thank you very much, that worked perfectly!

As a side note, I do have complex-valued affine expressions and complex-value quadratic expressions, but your solution worked for both, I simply replaced the GenericAffExpr with GenericQuadExpr, for my other cases.