feat(matrices): add wilkinson

Author: AnzhiZhang

Diff for: src/matrices/index.jl

@@ -42,7 +42,8 @@ export
     Rosser,
     Sampling,
     Toeplitz,
-    Triw
+    Triw,
+    Wilkinson
 
 # include all matrices
 include("linearalgebra.jl")
@@ -85,6 +86,7 @@ include("rosser.jl")
 include("sampling.jl")
 include("toeplitz.jl")
 include("triw.jl")
+include("wilkinson.jl")
 
 # matrix groups
 const MATRIX_GROUPS = Dict{Group,Set{Type{<:AbstractMatrix}}}()
@@ -132,6 +134,7 @@ MATRIX_GROUPS[GROUP_BUILTIN] = Set([
     Sampling,
     Toeplitz,
     Triw,
+    Wilkinson
 ])
 MATRIX_GROUPS[GROUP_USER] = Set([])
 

Diff for: src/matrices/wilkinson.jl

@@ -0,0 +1,55 @@
+"""
+Wilkinson Matrix
+================
+The Wilkinson matrix is a symmetric tridiagonal matrix with pairs
+of nearly equal eigenvalues. The most frequently used case
+is `matrixdepot("wilkinson", 21)`. The result is of type `Tridiagonal`.
+
+*Input options:*
+
++ dim: the dimension of the matrix.
+
+*References:*
+
+**J. H. Wilkinson**, Error analysis of direct methods
+of matrix inversion, J. Assoc. Comput. Mach., 8 (1961),  pp. 281-330.
+"""
+struct Wilkinson{T<:Number} <: AbstractMatrix{T}
+    n::Integer
+
+    function Wilkinson{T}(n::Integer) where {T<:Number}
+        n >= 0 || throw(ArgumentError("$n < 0"))
+        return new{T}(n)
+    end
+end
+
+# constructors
+Wilkinson(n::Integer) = Wilkinson{Float64}(n)
+
+# metadata
+@properties Wilkinson [:symmetric, :eigen]
+
+# properties
+size(A::Wilkinson) = (A.n, A.n)
+LinearAlgebra.isdiag(A::Wilkinson) = A.n <= 1 ? true : false
+LinearAlgebra.issymmetric(::Wilkinson) = true
+
+# functions
+@inline Base.@propagate_inbounds function getindex(A::Wilkinson{T}, i::Integer, j::Integer) where {T}
+    @boundscheck checkbounds(A, i, j)
+    n = A.n
+    if n == 1
+        return one(T)
+    elseif i == j
+        m = (n - 1) / 2
+        return T(abs(m - (i - 1)))
+    elseif i == j + 1 || i == j - 1
+        return one(T)
+    else
+        return zero(T)
+    end
+end
+
+function Base.replace_in_print_matrix(A::Wilkinson, i::Integer, j::Integer, s::AbstractString)
+    i == j - 1 || i == j || i == j + 1 ? s : Base.replace_with_centered_mark(s)
+end