code review

.github/workflows/CI.yml

@@ -20,7 +20,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "1.0"  # LTS
+          - "1.6"  # first supported version
           - "1"    # Latest Release
         os:
           - ubuntu-latest

Project.toml

@@ -7,10 +7,11 @@ version = "0.1.0"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
 [compat]
-julia = "1"
+julia = "1.6"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [targets]
-test = ["Test"]
+test = ["Test","Random"]

README.md

@@ -2,35 +2,43 @@
 
 WARNING: Package still in development!
 
-This package proposes specialized functions for dense real skew-symmetric matrices i.e $A=-A^T$.
-It provides the structure [`SkewSymmetric`](@ref) and the classical linear operations on such 
+This package provides specialized functions for dense real skew-symmetric matrices i.e $A=-A^T$.
+It provides the type [`SkewHermitian`](@ref) and the classical linear operations on such
 matrices. The package fits in the framework given by the LinearAlgebra package.
 
-In particular, the package provides de following functions for $A::$ [`SkewSymmetric`](@ref) :
+In particular, the package provides de following functions for $A::$ [`SkewHermitian`](@ref) :
 
 -Tridiagonal reduction: [`hessenberg`](@ref)\
 -Eigensolvers: [`eigen`](@ref), [`eigvals`](@ref),[`eigmax`](@ref),[`eigmin`](@ref)\
 -SVD: [`svd`](@ref), [`svdvals`](@ref)\
 -Trigonometric functions:[`exp`](@ref), [`cis`](@ref),[`cos`](@ref),[`sin`](@ref),[`tan`](@ref),[`sinh`](@ref),[`cosh`](@ref),[`tanh`](@ref)
 
-The SkewSymmetric type uses the complete matrix representation as data. It doesn't verify automatically that the given matrix input is skew-symmetric. In particular, in-place methods could destroy the skew-symmetry. The provided function [`isskewsymmetric(A)`](@ref) allows to verify that A is indeed skew-symmetric.
-Here is a basic example to initialize a [`SkewSymmetric`](@ref)
-```
+The `SkewHermitian(A)` wraps an existing matrix `A`, which *must* already be skew-Hermitian,
+in the `SkewHermitian` type, which supports fast specialized operations noted above.  You
+can use the function `isskewhermitian(A)` to check whether `A` is skew-Hermitian (`A == -A'`).
+
+Alternatively, you can use the funcition `skewhermitian(A)` to take the skew-Hermitian *part*
+of `A`, given by `(A - A')/2`, and wrap it in a `SkewHermitian` view.  Alternatively, the
+function `skewhermitian!(A)` does the same operation in-place on `A`.
+
+Here is a basic example to initialize a [`SkewHermitian`](@ref)
+```jl
 julia> A = [0 2 -7 4; -2 0 -8 3; 7 8 0 1;-4 -3 -1 0]
 3×3 Matrix{Int64}:
   0  2 -7  4
  -2  0 -8  3
   7  8  0  1
   -4 -3 -1 0
-julia> A = SkewSymmetric(A)
-4×4 Matrix{Int64}:
+
+julia> isskewhermitian(A)
+true
+
+julia> A = SkewHermitian(A)
+4×4 SkewHermitian{Int64, Matrix{Int64}}:
   0   2  -7  4
  -2   0  -8  3
   7   8   0  1
  -4  -3  -1  0
-
-julia> isskewsymmetric(A)
-true
 
 julia> tr(A)
 0
@@ -39,12 +47,12 @@ julia> det(A)
 81.0
 
 julia> inv(A)
-4×4 Matrix{Float64}:
- -0.0        0.111111  -0.333333     -0.888889
- -0.111111   0.0        0.444444      0.777778
-  0.333333  -0.444444   2.77556e-17   0.222222
-  0.888889  -0.777778  -0.222222      0.0
-  
+4×4 SkewHermitian{Float64, Matrix{Float64}}:
+  0.0        0.111111  -0.333333  -0.888889
+ -0.111111   0.0        0.444444   0.777778
+  0.333333  -0.444444   0.0        0.222222
+  0.888889  -0.777778  -0.222222   0.0
+
 julia> x=[1;2;3;4]
 4-element Vector{Int64}:
  1
@@ -59,7 +67,7 @@ julia> A\x
   0.3333333333333336
  -1.3333333333333333
   ```
-  
+
   The functions from the LinearAlgebra package can be used in the same fashion:
   ```
 julia> hessenberg(A)
@@ -68,22 +76,22 @@ julia> hessenberg(A)
  8.30662   0.0      -8.53382   ⋅
   ⋅        8.53382   0.0      1.08347
   ⋅         ⋅       -1.08347  0.0
-  
+
  julia> eigvals(A)
 4-element Vector{ComplexF64}:
   0.0 + 11.93445871397423im
   0.0 + 0.7541188264752853im
  -0.0 - 0.7541188264752877im
  -0.0 - 11.934458713974225im
- 
+
  julia> eigmax(A)
 -0.0 - 11.934458713974223im
-  
+
   ```
   \usepackage{amsymb}\
  ## Hessenberg/tridiagonal reduction
 The hessenberg reduction performs a reduction $A=QHQ^T$ where $Q=\prod_i I-\tau_i v_iv_i^T$ is an orthonormal matrix.
-The [`hessenberg`](@ref) function returns a structure of type [`SkewHessenberg`](@ref) containing the [`Tridiagonal`](@ref) reduction $H\in \mathbb{R}^{n\times n}$, the householder reflectors $v_i$ in a  [`UnitLowerTriangular`](@ref) $V\in \mathbb{R}^{n-1\times n-1}$  and the $n-2$ scalars $\tau_i$ associated to the reflectors. A function [`getQ`](@ref) is provided to retrieve the orthogonal transformation Q. 
+The [`hessenberg`](@ref) function returns a structure of type [`SkewHessenberg`](@ref) containing the [`Tridiagonal`](@ref) reduction $H\in \mathbb{R}^{n\times n}$, the householder reflectors $v_i$ in a  [`UnitLowerTriangular`](@ref) $V\in \mathbb{R}^{n-1\times n-1}$  and the $n-2$ scalars $\tau_i$ associated to the reflectors. A function [`getQ`](@ref) is provided to retrieve the orthogonal transformation Q.
 
   ```
   julia> H=hessenberg(A)
@@ -93,31 +101,31 @@ The [`hessenberg`](@ref) function returns a structure of type [`SkewHessenberg`]
   ⋅        8.53382   0.0      1.08347
   ⋅         ⋅       -1.08347  0.0
 3×3 UnitLowerTriangular{Float64, SubArray{Float64, 2, Matrix{Float64}, Tuple{UnitRange{Int64}, UnitRange{Int64}}, false}}:
-  1.0         ⋅         ⋅ 
+  1.0         ⋅         ⋅
  -0.679175   1.0        ⋅
   0.3881    -0.185238  1.0
 2-element Vector{Float64}:
  1.2407717061715382
  1.9336503566410876
- 
+
  julia> Q=getQ(H)
 4×4 Matrix{Float64}:
  1.0   0.0        0.0         0.0
  0.0  -0.240772  -0.95927    -0.14775
  0.0   0.842701  -0.282138    0.458534
  0.0  -0.481543  -0.0141069   0.876309
- 
+
  ```
 \usepackage{hyperref}
 
  ## Eigenvalues and eigenvectors
- 
- The package also provides eigensolvers for  [`SkewSymmetric`](@ref) matrices. The method to solve the eigenvalue problem is issued from: \url{C.Penke,A.Marek,C.Vorwerk,C.Draxl,P.Benner, \textit{ High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving Bethe-Salpeter Eigenvalue Problem}, 2020.}
- 
+
+ The package also provides eigensolvers for  [`SkewHermitian`](@ref) matrices. The method to solve the eigenvalue problem is issued from: \url{C.Penke,A.Marek,C.Vorwerk,C.Draxl,P.Benner, \textit{ High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving Bethe-Salpeter Eigenvalue Problem}, 2020.}
+
   The function [`eigen`](@ref) returns the eigenvalues plus the real part of the eigenvectors and the imaginary part separeted.
  ```
   julia> val,Qr,Qim=eigen(A)
- 
+
   julia> val
 4-element Vector{ComplexF64}:
   0.0 + 11.934458713974193im
@@ -138,7 +146,7 @@ julia> Qim
  -0.176712   0.0931315   0.0931315  -0.176712
   0.615785  -0.284619   -0.284619    0.615785
  -0.299303  -0.640561   -0.640561   -0.299303
- 
+
  ```
  The function [`eigvals`](@ref) provides de eigenvalues of $A$. The eigenvalues can be sorted and found partially with imaginary part in some given real range or by order.
  ```
@@ -153,18 +161,18 @@ julia> eigvals(A,0,15)
 2-element Vector{ComplexF64}:
  0.0 + 11.93445871397414im
  0.0 + 0.7541188264752858im
- 
+
 julia> eigvals(A,1:3)
 3-element Vector{ComplexF64}:
   0.0 + 11.93445871397423im
   0.0 + 0.7541188264752989im
  -0.0 - 0.7541188264752758im
  ```
  ## SVD
- 
+
  Specialized SVD using the eigenvalue decomposition is implemented for [`SkewSymmetric`](@ref) type.
  These functions can be used using the LinearAlgebra syntax.
- 
+
  ```
  julia> svd(A)
 SVD{ComplexF64, Float64, Matrix{ComplexF64}}
@@ -186,17 +194,17 @@ Vt factor:
  0.0-0.49111im    -0.176712-0.488014im   0.615785-0.143534im  -0.299303-0.00717668im
  0.0-0.508735im  -0.0931315+0.471107im   0.284619+0.138561im   0.640561+0.00692804im
  0.0-0.508735im   0.0931315+0.471107im  -0.284619+0.138561im  -0.640561+0.00692804im
- 
+
  julia> svdvals(A)
 4-element Vector{Float64}:
  11.93445871397423
  11.934458713974225
   0.7541188264752877
   0.7541188264752853
- 
+
  ```
  ## Trigonometric functions
- 
+
  The package implements special versions of the trigonometric functions using the eigenvalue decomposition. The provided functions are [`exp`](@ref), [`cis`](@ref),[`cos`](@ref),[`sin`](@ref),[`tan`](@ref),[`sinh`](@ref),[`cosh`](@ref),[`tanh`](@ref).
  ```
  julia> exp(A)
@@ -205,7 +213,7 @@ Vt factor:
  -0.697298   0.140338     0.677464   0.187414
   0.578289  -0.00844255   0.40033    0.710807
   0.279941  -0.559925     0.555524  -0.547275
-  
+
  julia> cis(A)
 4×4 Matrix{ComplexF64}:
    5.95183+0.0im       3.21734+1.80074im     -0.658082-3.53498im      -1.4454+5.61775im
@@ -226,9 +234,9 @@ julia> cosh(A)
  -0.756913   0.140338  0.334511  -0.186256
   0.154821   0.334511  0.40033    0.633165
   0.340045  -0.186256  0.633165  -0.547275
- 
+
  ```
- 
-  
-  
-  
+
+
+
+