added missing functions (radius, issubset) and fixes in real-valued f…

…unctions (#170)

* added missing functions (radius, issubset) and fixes in real-valued functions

* added hull

* fix workflow

* removed strict subset and bumped patch version

.gitignore

@@ -5,3 +5,5 @@
 
 docs/build/
 docs/site/
+
+Manifest.toml

Project.toml

@@ -1,6 +1,6 @@
 name = "IntervalMatrices"
 uuid = "5c1f47dc-42dd-5697-8aaa-4d102d140ba9"
-version = "0.6.5"
+version = "0.6.6"
 
 [deps]
 IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"

src/matrix.jl

@@ -1,6 +1,6 @@
-import Base: similar, split, ∈, ⊆, ∩
+import Base: similar, split, ∈, ⊆, ∩, ∪
 import Random: rand
-import IntervalArithmetic: inf, sup, mid, diam
+import IntervalArithmetic: inf, sup, mid, diam, radius, hull
 
 """
     AbstractIntervalMatrix{IT} <: AbstractMatrix{IT}
@@ -227,7 +227,7 @@ element-wise infimum of `A`.
 A scalar matrix whose coefficients are the infima of each element in `A`.
 """
 function inf(A::IntervalMatrix{T}) where {T}
-    return map(inf, A)
+    return map(inf, A.mat)
 end
 
 """
@@ -245,7 +245,7 @@ element-wise supremum of `A`.
 A scalar matrix whose coefficients are the suprema of each element in `A`.
 """
 function sup(A::IntervalMatrix{T}) where {T}
-    return map(sup, A)
+    return map(sup, A.mat)
 end
 
 """
@@ -263,7 +263,25 @@ element-wise midpoint of `A`.
 A scalar matrix whose coefficients are the midpoints of each element in `A`.
 """
 function mid(A::IntervalMatrix{T}) where {T}
-    return map(mid, A)
+    return map(mid, A.mat)
+end
+
+"""
+    radius(A::IntervalMatrix{T}) where {T}
+
+Return the radius of an interval matrix `A`, which corresponds to taking the
+element-wise radius of `A`.
+
+### Input
+
+- `A` -- interval matrix
+
+### Output
+
+A scalar matrix whose coefficients are the radii of each element in `A`.
+"""
+function radius(A::IntervalMatrix{T}) where {T}
+    return map(radius, A.mat)
 end
 
 """
@@ -450,7 +468,7 @@ A matrix `B` of the same shape as `A` such that `B[i, j] == diam(A[i, j])` for
 each `i` and `j`.
 """
 function diam(A::IntervalMatrix{T}) where {T}
-    return map(diam, A)
+    return map(diam, A.mat)
 end
 
 """
@@ -519,13 +537,50 @@ function ∩(A::IntervalMatrix, B::IntervalMatrix)
     @assert size(A) == size(B) "incompatible matrix sizes (A: $(size(A)), B: " *
                                "$(size(B)))"
 
-    C = similar(A)
-    @inbounds for j in 1:n, i in 1:m
-        C[i, j] = A[i, j] ∩ B[i, j]
-    end
-    return C
+    return IntervalMatrix(map((x, y) -> x ∩ y, A, B))
 end
 
+
+"""
+    hull(A::IntervalMatrix, B::IntervalMatrix)
+
+Finds the interval hull of two interval matrices. This is equivalent to [`∪`](@ref).
+
+### Input
+
+- `A` -- interval matrix
+- `B` -- interval matrix (of the same shape as `A`)
+
+### Output
+
+A new matrix `C` of the same shape as `A` such that
+`C[i, j] = hull(A[i, j], B[i, j])` for each `i` and `j`.
+"""
+function hull(A::IntervalMatrix, B::IntervalMatrix)
+    @assert size(A) == size(B) "incompatible matrix sizes (A: $(size(A)), B: " *
+                               "$(size(B)))"
+
+    return IntervalMatrix(map((x, y) -> hull(x, y), A, B))
+end
+
+"""
+    ∪(A::IntervalMatrix, B::IntervalMatrix)
+
+Finds the interval union (hull) of two interval matrices.
+This is equivalent to [`hull`](@ref).
+
+### Input
+
+- `A` -- interval matrix
+- `B` -- interval matrix (of the same shape as `A`)
+
+### Output
+
+A new matrix `C` of the same shape as `A` such that
+`C[i, j] = A[i, j] ∪ B[i, j]` for each `i` and `j`.
+"""
+∪(A::IntervalMatrix, B::IntervalMatrix) = hull(A, B)
+
 """
     diam_norm(A::IntervalMatrix, p=Inf)
 

test/runtests.jl

@@ -69,10 +69,12 @@ end
     r = sup(m)
     c = mid(m)
     d = diam(m)
+    rad = radius(m)
     m2 = copy(m)
     @test m2 isa IntervalMatrix && m.mat == m2.mat
     @test l == inf.(m) && r == sup.(m) && c == mid.(m)
     @test d ≈ r - l
+    @test rad ≈ d/2
     sm = scale(m, 2.0)
     @test sm ==  2.0 .* m
     @test sm ≠ m
@@ -81,6 +83,7 @@ end
     m3 = IntervalMatrix([-2.0..2.0 -2.0..0.0; 0.0..2.0 -1.0..1.0])
     m4 = IntervalMatrix([-1.0..1.0 -1.0..1.0; -1.0..1.0 -2.0..2.0])
     @test m3 ∩ m4 == IntervalMatrix([-1.0..1.0 -1.0..0.0; 0.0..1.0 -1.0..1.0])
+    @test m3 ∪ m4 == IntervalMatrix([-2.0..2.0 -2.0..1.0; -1.0..2.0 -2.0..2.0])
     @test diam_norm(m3) ≈ 6.0 # default diameter p-norm is Inf
     @test diam_norm(m3, 1) ≈ 6.0
 end
@@ -122,6 +125,7 @@ end
     m1 = IntervalMatrix([-1.1..0.9 -4.1.. -3.9; 3.9..4.1 -1.1..0.9])
     m2 = IntervalMatrix([-1.2..1.0 -4.1.. -3.9; 3.9..4.2 -1.2..0.9])
     @test m1 ⊆ m2 && !(m2 ⊆ m1)
+
 end
 
 @testset "Interval matrix rand" begin