fix building of documentation

docs/make.jl

@@ -14,7 +14,8 @@ makedocs(
         "Library" => Any[
         "Types" => "lib/types.md",
         "Methods" => "lib/methods.md"],
-        "About" => "about.md"
+        "About" => "about.md",
+        "References" => "references.md"
     ],
     strict = true
 )

docs/src/index.md

@@ -89,12 +89,12 @@ julia> (-1.0..1.0) * A
 
 Or compute the square of $A$,
 ```jldoctest quickstart
-julia> A*A
+julia> square(A)
 2×2 IntervalMatrix{Float64, Interval{Float64}, Matrix{Interval{Float64}}}:
-    [2, 7]  [-8, 0]
- [-12, -1]  [6, 22]
+    [2, 7]  [-8, -1]
+ [-12, -2]   [6, 22]
 ```
-In these cases, the rules of interval arithmetic are used; see the wikipedia page
+In these cases, the rules of interval arithmetic are used; see the Wikipedia page
 on [interval arithmetic](https://en.wikipedia.org/wiki/Interval_arithmetic) for the
 relevant definitions and algebraic rules that apply.
 
@@ -107,14 +107,14 @@ $e^{At} - I$. Then, at $t = 1.0$,
 ```jldoctest quickstart
 julia> A + 1/2 * A^2
 2×2 IntervalMatrix{Float64, Interval{Float64}, Matrix{Interval{Float64}}}:
-  [1, 4.5]  [-3, 2]
- [-4, 2.5]  [-1, 9]
+  [0.5, 4.5]  [-3.25, 2.5]
+ [-4.25, 3]   [-2.25, 9]
 ```
 However, that result is not tight. The computation can be performed exactly via
 single-use expressions implemented in this library:
 
 ```jldoctest quickstart
-julia> quadratic_expansion(A, 1.0)
+julia> quadratic_expansion(A, 1.0, 0.5)
 2×2 IntervalMatrix{Float64, Interval{Float64}, Matrix{Interval{Float64}}}:
   [1, 4.5]  [-2, 1]
  [-3, 1.5]   [1, 7]

docs/src/lib/methods.md

@@ -18,15 +18,25 @@ inf
 sup
 mid
 diam
+radius
+midpoint_radius
 rand
 sample
-split
 ∈
+±
+⊆
+∩
+∪
+hull
+```
+
+## Arithmetic
+
+```@docs
 square
 scale
 scale!
-⊆
-∩
+set_multiplication_mode
 ```
 
 ## Matrix power

docs/src/references.md

@@ -0,0 +1,53 @@
+# References
+
+#### [RUM10]
+
+```@raw html
+<ul><li>
+```
+S.M. Rump, [*Verification methods: Rigorous results using floating-point arithmetic*](https://www.tuhh.de/ti3/paper/rump/Ru10.pdf), Acta Numerica, 19:287–449, 2010
+```@raw html
+<li style="list-style: none"><details>
+<summary>bibtex</summary>
+```
+```
+@article{rump2010verification,
+  title={Verification methods: Rigorous results using floating-point arithmetic},
+  author={Rump, Siegfried M},
+  journal={Acta Numerica},
+  volume={19},
+  pages={287--449},
+  year={2010},
+  publisher={Cambridge University Press}
+}
+```
+```@raw html
+</details></li></ul>
+```
+---
+
+#### [RUM99]
+
+```@raw html
+<ul><li>
+```
+Rump, Siegfried M. [*Fast and parallel interval arithmetic*](https://www.tuhh.de/ti3/paper/rump/Ru99b.pdf), BIT Numerical Mathematics 39.3, 534-554, 1999
+```@raw html
+<li style="list-style: none"><details>
+<summary>bibtex</summary>
+```
+```
+@article{rump1999fast,
+  title={Fast and parallel interval arithmetic},
+  author={Rump, Siegfried M},
+  journal={BIT Numerical Mathematics},
+  volume={39},
+  number={3},
+  pages={534--554},
+  year={1999},
+  publisher={Springer}
+}
+```
+```@raw html
+</details></li></ul>
+```

src/matrix.jl

@@ -135,7 +135,7 @@ i.e. `B[i, j] ≥ A[i, j]` for each `i` and `j`.
 ```jldoctest
 julia> IntervalMatrix([1 2; 3 4], [1 2; 4 5])
 2×2 IntervalMatrix{Float64, Interval{Float64}, Matrix{Interval{Float64}}}:
-  [1, 1]   [2, 2]
+ [1, 1]  [2, 2]
  [3, 4]  [4, 5]
 ```
 """
@@ -144,7 +144,7 @@ function IntervalMatrix(A::MT, B::MT) where {T, MT<:AbstractMatrix{T}}
                                 "matrices should match, but they are $(size(A)) " *
                                 "and $(size(B)) respectively"))
 
-    return map((x, y) -> Interval(x, y), A, B)
+    return IntervalMatrix(map((x, y) -> Interval(x, y), A, B))
 end
 
 """
@@ -182,5 +182,5 @@ function ±(C::MT, S::MT) where {T, MT<:AbstractMatrix{T}}
                                 "radii matrix should match, but they are $(size(C)) " *
                                 "and $(size(S)) respectively"))
 
-    return map((x, y) -> x ± y, C, S)
+    return IntervalMatrix(map((x, y) -> x ± y, C, S))
 end

src/operations/power.jl

@@ -33,8 +33,8 @@ julia> increment!(pow)
 
 julia> increment(pow)
 2×2 IntervalMatrix{Float64, Interval{Float64}, Matrix{Interval{Float64}}}:
- [8, 8]  [-1, 21]
- [0, 0]   [-1, 1]
+  [8, 8]  [-1, 21]
+ [-0, 0]   [-1, 1]
 
 julia> get(pow)
 2×2 IntervalMatrix{Float64, Interval{Float64}, Matrix{Interval{Float64}}}: