# Linear Algebra

User Q-functions often perform small (1x1, 2x2, or 3x3) linear algebra
operations (determinant, matrix-vector product, etc.) at every Q-point. For good
performance, it is important to use specialized versions of these operations for
the given size.

If the matrix or vector is given in a statically sized container (e.g. using
[StaticArrays.jl](https://github.com/JuliaArrays/StaticArrays.jl/)) then this
happens automatically. However, if the matrix is not statically sized, and
instead is given as, for example, a view into a larger array, then LibCEED.jl
provides some convenient specialized functions.

In order to allow for generic code, the [`CeedDim`](@ref) struct is used for
dispatch. An object `D = CeedDim(dim)` can be created, and passed as a second
argument to functions like `det` to choose the specialized implementations. In
this case, `dim` should be known as a compile-time constant, otherwise it will
result in a type instability, and give poor performance.

For example:
```@repl
using LibCEED, LinearAlgebra

dim = 3;
J = rand(dim, dim);

det(J) # Slow!
det(J, CeedDim(dim)) # Fast!
```

```@docs
CeedDim
det(J, ::CeedDim{1})
setvoigt
getvoigt
```