Docs for UnitUpperTriangular and UnitLowerTriangular

inkydragon · Mar 4, 2019 · 2fffe9f · 2fffe9f
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diff --git a/stdlib/LinearAlgebra/docs/src/index.md b/stdlib/LinearAlgebra/docs/src/index.md
@@ -162,31 +162,35 @@ specialized routines that are specially developed for particular matrix types.
 The following tables summarize the types of special matrices that have been implemented in Julia,
 as well as whether hooks to various optimized methods for them in LAPACK are available.
 
-| Type | Description |
-|:------------------------- |:-------------------------------------------------------------------------------- |
-| [`Symmetric`](@ref) | [Symmetric matrix](https://en.wikipedia.org/wiki/Symmetric_matrix) |
-| [`Hermitian`](@ref) | [Hermitian matrix](https://en.wikipedia.org/wiki/Hermitian_matrix) |
-| [`UpperTriangular`](@ref) | Upper [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
-| [`LowerTriangular`](@ref) | Lower [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
-| [`Tridiagonal`](@ref) | [Tridiagonal matrix](https://en.wikipedia.org/wiki/Tridiagonal_matrix) |
-| [`SymTridiagonal`](@ref) | Symmetric tridiagonal matrix |
-| [`Bidiagonal`](@ref) | Upper/lower [bidiagonal matrix](https://en.wikipedia.org/wiki/Bidiagonal_matrix) |
-| [`Diagonal`](@ref) | [Diagonal matrix](https://en.wikipedia.org/wiki/Diagonal_matrix) |
-| [`UniformScaling`](@ref) | [Uniform scaling operator](https://en.wikipedia.org/wiki/Uniform_scaling) |
+| Type | Description |
+|:----------------------------- |:--------------------------------------------------------------------------------------------- |
+| [`Symmetric`](@ref) | [Symmetric matrix](https://en.wikipedia.org/wiki/Symmetric_matrix) |
+| [`Hermitian`](@ref) | [Hermitian matrix](https://en.wikipedia.org/wiki/Hermitian_matrix) |
+| [`UpperTriangular`](@ref) | Upper [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
+| [`UnitUpperTriangular`](@ref) | Upper [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) with unit diagonal |
+| [`LowerTriangular`](@ref) | Lower [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
+| [`UnitLowerTriangular`](@ref) | Lower [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) with unit diagonal |
+| [`Tridiagonal`](@ref) | [Tridiagonal matrix](https://en.wikipedia.org/wiki/Tridiagonal_matrix) |
+| [`SymTridiagonal`](@ref) | Symmetric tridiagonal matrix |
+| [`Bidiagonal`](@ref) | Upper/lower [bidiagonal matrix](https://en.wikipedia.org/wiki/Bidiagonal_matrix) |
+| [`Diagonal`](@ref) | [Diagonal matrix](https://en.wikipedia.org/wiki/Diagonal_matrix) |
+| [`UniformScaling`](@ref) | [Uniform scaling operator](https://en.wikipedia.org/wiki/Uniform_scaling) |
 
 ### Elementary operations
 
-| Matrix type | `+` | `-` | `*` | `\` | Other functions with optimized methods |
-|:------------------------- |:--- |:--- |:--- |:--- |:----------------------------------------------------------- |
-| [`Symmetric`](@ref) | | | | MV | [`inv`](@ref), [`sqrt`](@ref), [`exp`](@ref) |
-| [`Hermitian`](@ref) | | | | MV | [`inv`](@ref), [`sqrt`](@ref), [`exp`](@ref) |
-| [`UpperTriangular`](@ref) | | | MV | MV | [`inv`](@ref), [`det`](@ref) |
-| [`LowerTriangular`](@ref) | | | MV | MV | [`inv`](@ref), [`det`](@ref) |
-| [`SymTridiagonal`](@ref) | M | M | MS | MV | [`eigmax`](@ref), [`eigmin`](@ref) |
-| [`Tridiagonal`](@ref) | M | M | MS | MV | |
-| [`Bidiagonal`](@ref) | M | M | MS | MV | |
-| [`Diagonal`](@ref) | M | M | MV | MV | [`inv`](@ref), [`det`](@ref), [`logdet`](@ref), [`/`](@ref) |
-| [`UniformScaling`](@ref) | M | M | MVS | MVS | [`/`](@ref) |
+| Matrix type | `+` | `-` | `*` | `\` | Other functions with optimized methods |
+|:----------------------------- |:--- |:--- |:--- |:--- |:----------------------------------------------------------- |
+| [`Symmetric`](@ref) | | | | MV | [`inv`](@ref), [`sqrt`](@ref), [`exp`](@ref) |
+| [`Hermitian`](@ref) | | | | MV | [`inv`](@ref), [`sqrt`](@ref), [`exp`](@ref) |
+| [`UpperTriangular`](@ref) | | | MV | MV | [`inv`](@ref), [`det`](@ref) |
+| [`UnitUpperTriangular`](@ref) | | | MV | MV | [`inv`](@ref), [`det`](@ref) |
+| [`LowerTriangular`](@ref) | | | MV | MV | [`inv`](@ref), [`det`](@ref) |
+| [`UnitLowerTriangular`](@ref) | | | MV | MV | [`inv`](@ref), [`det`](@ref) |
+| [`SymTridiagonal`](@ref) | M | M | MS | MV | [`eigmax`](@ref), [`eigmin`](@ref) |
+| [`Tridiagonal`](@ref) | M | M | MS | MV | |
+| [`Bidiagonal`](@ref) | M | M | MS | MV | |
+| [`Diagonal`](@ref) | M | M | MV | MV | [`inv`](@ref), [`det`](@ref), [`logdet`](@ref), [`/`](@ref) |
+| [`UniformScaling`](@ref) | M | M | MVS | MVS | [`/`](@ref) |
 
 Legend:
 
@@ -198,16 +202,18 @@ Legend:
 
 ### Matrix factorizations
 
-| Matrix type | LAPACK | [`eigen`](@ref) | [`eigvals`](@ref) | [`eigvecs`](@ref) | [`svd`](@ref) | [`svdvals`](@ref) |
-|:------------------------- |:------ |:------------- |:----------------- |:----------------- |:------------- |:----------------- |
-| [`Symmetric`](@ref) | SY | | ARI | | | |
-| [`Hermitian`](@ref) | HE | | ARI | | | |
-| [`UpperTriangular`](@ref) | TR | A | A | A | | |
-| [`LowerTriangular`](@ref) | TR | A | A | A | | |
-| [`SymTridiagonal`](@ref) | ST | A | ARI | AV | | |
-| [`Tridiagonal`](@ref) | GT | | | | | |
-| [`Bidiagonal`](@ref) | BD | | | | A | A |
-| [`Diagonal`](@ref) | DI | | A | | | |
+| Matrix type | LAPACK | [`eigen`](@ref) | [`eigvals`](@ref) | [`eigvecs`](@ref) | [`svd`](@ref) | [`svdvals`](@ref) |
+|:----------------------------- |:------ |:------------- |:----------------- |:----------------- |:------------- |:----------------- |
+| [`Symmetric`](@ref) | SY | | ARI | | | |
+| [`Hermitian`](@ref) | HE | | ARI | | | |
+| [`UpperTriangular`](@ref) | TR | A | A | A | | |
+| [`UnitUpperTriangular`](@ref) | TR | A | A | A | | |
+| [`LowerTriangular`](@ref) | TR | A | A | A | | |
+| [`UnitLowerTriangular`](@ref) | TR | A | A | A | | |
+| [`SymTridiagonal`](@ref) | ST | A | ARI | AV | | |
+| [`Tridiagonal`](@ref) | GT | | | | | |
+| [`Bidiagonal`](@ref) | BD | | | | A | A |
+| [`Diagonal`](@ref) | DI | | A | | | |
 
 Legend:
 
@@ -309,6 +315,8 @@ LinearAlgebra.Symmetric
 LinearAlgebra.Hermitian
 LinearAlgebra.LowerTriangular
 LinearAlgebra.UpperTriangular
+LinearAlgebra.UnitLowerTriangular
+LinearAlgebra.UnitUpperTriangular
 LinearAlgebra.UniformScaling
 LinearAlgebra.lu
 LinearAlgebra.lu!

diff --git a/stdlib/LinearAlgebra/src/bunchkaufman.jl b/stdlib/LinearAlgebra/src/bunchkaufman.jl
@@ -154,8 +154,8 @@ end
 
 Extract the factors of the Bunch-Kaufman factorization `B`. The factorization can take the
 two forms `P'*L*D*L'*P` or `P'*U*D*U'*P` (or `L*D*transpose(L)` in the complex symmetric case)
-where `P` is a (symmetric) permutation matrix, `L` is a `UnitLowerTriangular` matrix, `U` is a
-`UnitUpperTriangular`, and `D` is a block diagonal symmetric or Hermitian matrix with
+where `P` is a (symmetric) permutation matrix, `L` is a [`UnitLowerTriangular`](@ref) matrix, `U` is a
+[`UnitUpperTriangular`](@ref), and `D` is a block diagonal symmetric or Hermitian matrix with
 1x1 or 2x2 blocks. The argument `d` can be
 
 - `:D`: the block diagonal matrix

diff --git a/stdlib/LinearAlgebra/src/triangular.jl b/stdlib/LinearAlgebra/src/triangular.jl
@@ -97,6 +97,52 @@ julia> UpperTriangular(A)
 ```
 """
 UpperTriangular
+"""
+ UnitLowerTriangular(A::AbstractMatrix)
+
+Construct a `UnitLowerTriangular` view of the matrix `A`.
+Such a view has the [`oneunit`](@ref) of the [`eltype`](@ref)
+of `A` on its diagonal.
+
+# Examples
+```jldoctest
+julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
+3×3 Array{Float64,2}:
+ 1.0 2.0 3.0
+ 4.0 5.0 6.0
+ 7.0 8.0 9.0
+
+julia> UnitLowerTriangular(A)
+3×3 UnitLowerTriangular{Float64,Array{Float64,2}}:
+ 1.0 ⋅ ⋅
+ 4.0 1.0 ⋅
+ 7.0 8.0 1.0
+```
+"""
+UnitLowerTriangular
+"""
+ UnitUpperTriangular(A::AbstractMatrix)
+
+Construct an `UnitUpperTriangular` view of the matrix `A`.
+Such a view has the [`oneunit`](@ref) of the [`eltype`](@ref)
+of `A` on its diagonal.
+
+# Examples
+```jldoctest
+julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
+3×3 Array{Float64,2}:
+ 1.0 2.0 3.0
+ 4.0 5.0 6.0
+ 7.0 8.0 9.0
+
+julia> UnitUpperTriangular(A)
+3×3 UnitUpperTriangular{Float64,Array{Float64,2}}:
+ 1.0 2.0 3.0
+ ⋅ 1.0 6.0
+ ⋅ ⋅ 1.0
+```
+"""
+UnitUpperTriangular
 
 imag(A::UpperTriangular) = UpperTriangular(imag(A.data))
 imag(A::LowerTriangular) = LowerTriangular(imag(A.data))