1*6f5dc8baSWill Pazner# Linear Algebra 2*6f5dc8baSWill Pazner 3*6f5dc8baSWill PaznerUser Q-functions often perform small (1x1, 2x2, or 3x3) linear algebra 4*6f5dc8baSWill Pazneroperations (determinant, matrix-vector product, etc.) at every Q-point. For good 5*6f5dc8baSWill Paznerperformance, it is important to use specialized versions of these operations for 6*6f5dc8baSWill Paznerthe given size. 7*6f5dc8baSWill Pazner 8*6f5dc8baSWill PaznerIf the matrix or vector is given in a statically sized container (e.g. using 9*6f5dc8baSWill Pazner[StaticArrays.jl](https://github.com/JuliaArrays/StaticArrays.jl/)) then this 10*6f5dc8baSWill Paznerhappens automatically. However, if the matrix is not statically sized, and 11*6f5dc8baSWill Paznerinstead is given as, for example, a view into a larger array, then LibCEED.jl 12*6f5dc8baSWill Paznerprovides some convenient specialized functions. 13*6f5dc8baSWill Pazner 14*6f5dc8baSWill PaznerIn order to allow for generic code, the [`CeedDim`](@ref) struct is used for 15*6f5dc8baSWill Paznerdispatch. An object `D = CeedDim(dim)` can be created, and passed as a second 16*6f5dc8baSWill Paznerargument to functions like `det` to choose the specialized implementations. In 17*6f5dc8baSWill Paznerthis case, `dim` should be known as a compile-time constant, otherwise it will 18*6f5dc8baSWill Paznerresult in a type instability, and give poor performance. 19*6f5dc8baSWill Pazner 20*6f5dc8baSWill PaznerFor example: 21*6f5dc8baSWill Pazner```@repl 22*6f5dc8baSWill Paznerusing LibCEED, LinearAlgebra 23*6f5dc8baSWill Pazner 24*6f5dc8baSWill Paznerdim = 3; 25*6f5dc8baSWill PaznerJ = rand(dim, dim); 26*6f5dc8baSWill Pazner 27*6f5dc8baSWill Paznerdet(J) # Slow! 28*6f5dc8baSWill Paznerdet(J, CeedDim(dim)) # Fast! 29*6f5dc8baSWill Pazner``` 30*6f5dc8baSWill Pazner 31*6f5dc8baSWill Pazner```@docs 32*6f5dc8baSWill PaznerCeedDim 33*6f5dc8baSWill Paznerdet(J, ::CeedDim{1}) 34*6f5dc8baSWill Paznersetvoigt 35*6f5dc8baSWill Paznergetvoigt 36*6f5dc8baSWill Pazner``` 37