Merge pull request #107 from JuliaGNI/move_relevant_functions_to_utils

Moved write_ones kernel to utils.jl

src/arrays/skew_symmetric.jl

@@ -1,16 +1,12 @@
-"""
-A `SkewSymMatrix` is a matrix
-| 0 -S |
-| S  0 |
-
+@doc raw"""
+A `SkewSymMatrix` is a matrix ``A`` s.t. ``A^T = -A``.
 
-If the constructor is called with a matrix as input it returns a symmetric matrix via the projection 
-A ↦ .5*(A - Aᵀ). 
-This is a projection defined via the canonical metric (A,B) ↦ tr(AᵀB).
+If the constructor is called with a matrix as input it returns a symmetric matrix via the projection ``A \mapsto \frac{1}{2}(A - A^T)``. 
+This is a projection defined via the canonical metric ``\mathbb{R}^{n\times{}n}\times\mathbb{R}^{n\times{}n}\to\mathbb{R}, (A,B) \mapsto \mathrm{Tr}(A^TB)``.
 
 The first index is the row index, the second one the column index.
 
-TODO: Check how LinearAlgebra implements matrix multiplication!
+The struct two fields: `S` and `n`. The first stores all the entries of the matrix in a sparse fashion (in a vector) and the second is the dimension ``n`` for ``A\in\mathbb{R}^{n\times{}n}``.
 """
 
 mutable struct SkewSymMatrix{T, AT <: AbstractVector{T}} <: AbstractMatrix{T}
@@ -171,11 +167,6 @@ function Base.:*(A::SkewSymMatrix, b::AbstractVector{T}) where T
     A*reshape(b, size(b), 1)
 end
 
-@kernel function write_ones_kernel!(unit_matrix::AbstractMatrix{T}) where T
-    i = @index(Global)
-    unit_matrix[i, i] = one(T)
-end
-
 function Base.one(A::SkewSymMatrix{T}) where T
     backend = KernelAbstractions.get_backend(A.S)
     unit_matrix = KernelAbstractions.zeros(backend, T, A.n, A.n)

src/arrays/symmetric.jl

@@ -1,9 +1,5 @@
 @doc raw"""
-A `SymmetricMatrix` is a matrix
-| a  S |
-| S  b |
-
-The first index is the row index, the second one the column index.
+A `SymmetricMatrix` ``A`` is a matrix ``A^T = A``.
 
 If the constructor is called with a matrix as input it returns a symmetric matrix via the projection:
 ```math
@@ -17,7 +13,7 @@ Internally the `struct` saves a vector $S$ of size $n(n+1)\div2$. The conversion
                          S[( (j-1) j ) \div 2 + i] & \text{else}. \end{cases}
 ```
 
-So $S$ stores a string of vectors taken from $A$: $S = [\tilde{a}_1, \tilde{a}_2, \ldots, \tilde{a}_n]$ with $\tilde{a}_i = [[A]_{i1},[A]_{i2},\ldots,[A]_{ii}]$.
+So ``S`` stores a string of vectors taken from $A$: $S = [\tilde{a}_1, \tilde{a}_2, \ldots, \tilde{a}_n]$ with $\tilde{a}_i = [[A]_{i1},[A]_{i2},\ldots,[A]_{ii}]$.
 
 TODO: 
 - [x] Overload Adjoint operation for SymmetricMatrix!! (Aᵀ = A)

src/utils.jl

@@ -63,6 +63,13 @@ function Base.:+(a::Vector{Float64}, b::Tuple{Float64})
     return y+x
 end
 
+"""
+Kernel that is needed for functions relating to `SymmetricMatrix` and `SkewSymMatrix` 
+"""
+@kernel function write_ones_kernel!(unit_matrix::AbstractMatrix{T}) where T
+    i = @index(Global)
+    unit_matrix[i, i] = one(T)
+end
 
 # overloaded similar operation to work with NamedTuples
 _similar(x) = similar(x)
@@ -76,7 +83,6 @@ function _similar(x::NamedTuple)
 end
 
 # utils functions on string
-
 function type_without_brace(var)
     type_str = string(typeof(var))
     replace(type_str, r"\{.*\}"=>"")
@@ -91,8 +97,7 @@ function center_align_text(text,width)
 end
 
 
-#The following are fallback functions - maybe you want to put them into a separate file
-
+# The following are fallback functions - maybe you want to put them into a separate file
 function global_section(::AbstractVecOrMat)
     nothing
 end