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Docs for UnitUpperTriangular and UnitLowerTriangular #31247

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Docs for UnitUpperTriangular and UnitLowerTriangular #31247

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72 changes: 40 additions & 32 deletions stdlib/LinearAlgebra/docs/src/index.md
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Expand Up @@ -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:

Expand All @@ -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:

Expand Down Expand Up @@ -309,6 +315,8 @@ LinearAlgebra.Symmetric
LinearAlgebra.Hermitian
LinearAlgebra.LowerTriangular
LinearAlgebra.UpperTriangular
LinearAlgebra.UnitLowerTriangular
LinearAlgebra.UnitUpperTriangular
LinearAlgebra.UniformScaling
LinearAlgebra.lu
LinearAlgebra.lu!
Expand Down
4 changes: 2 additions & 2 deletions stdlib/LinearAlgebra/src/bunchkaufman.jl
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Expand Up @@ -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
Expand Down
46 changes: 46 additions & 0 deletions stdlib/LinearAlgebra/src/triangular.jl
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Expand Up @@ -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))
Expand Down