Refactor and cleanup. Removes NewtonContractor (#55)

* Add interval and status functions for roots

* Bisect by default not exactly in centre

* Use broadcast for contains_zero

* Move contractors to contractors.jl

* Rename N -> 𝒩

* WIP refactor to remove NewtonContractor

* Refactoring to pass through tolerance. All except complex working

* Fix complex root finding

* bisect_place -> where_bisect

* Fix tests

* Changes from review

* More fixes

* Force bisection of infinite intervals in Newton

* Add tests with infinite intervals

* Remove old tests for the moment

* Split out Root object into new file, cleanup

* Fix failing Newton1D test

* Add missing source file

Author: dpsanders

src/IntervalRootFinding.jl

@@ -8,6 +8,9 @@ using IntervalArithmetic
 using ForwardDiff
 using StaticArrays
 
+
+import Base: ⊆, show, big
+
 import Polynomials: roots
 
 ## Root finding
@@ -17,26 +20,15 @@ export
     roots, find_roots,
     bisect, newton1d
 
-import Base: ⊆, show
-
-const Interval = IntervalArithmetic.Interval
+export isunique, root_status
 
-const derivative = ForwardDiff.derivative
-const D = derivative
 
-# Root object:
-immutable Root{T}
-    interval::T
-    status::Symbol
-end
+import IntervalArithmetic.interval
 
-show(io::IO, root::Root) = print(io, "Root($(root.interval), :$(root.status))")
 
-is_unique{T}(root::Root{T}) = root.status == :unique
-
-⊆(a::Interval, b::Root) = a ⊆ b.interval   # the Root object has the interval in the first entry
-⊆(a::Root, b::Root) = a.interval ⊆ b.interval
 
+const derivative = ForwardDiff.derivative
+const D = derivative
 
 # Common functionality:
 
@@ -56,12 +48,15 @@ function guarded_mid{T}(f::Function, x::Interval{T})
 end
 
 
+include("root_object.jl")
 include("bisect.jl")
-include("bisection.jl")
+
 include("newton.jl")
 include("krawczyk.jl")
+
 include("complex.jl")
-include("branch_and_prune.jl")
+include("contractors.jl")
+include("roots.jl")
 include("newton1d.jl")
 
 

src/bisect.jl

@@ -1,11 +1,13 @@
 
+const where_bisect = 0.49609375
+
 doc"""
     bisect(X::Interval, α=0.5)
 
 Split the interval `X` at position α; α=0.5 corresponds to the midpoint.
 Returns a tuple of the new intervals.
 """
-function bisect(X::Interval, α=0.5)
+function bisect(X::Interval, α=where_bisect)
     @assert 0 ≤ α ≤ 1
 
     m = mid(X, α)
@@ -18,7 +20,7 @@ doc"""
 
 Bisect the `IntervalBox` `X` at position α ∈ [0,1] along its longest side.
 """
-function bisect(X::IntervalBox, α=0.5)
+function bisect(X::IntervalBox, α=where_bisect)
     i = indmax(diam.(X))  # find longest side
 
     return bisect(X, i, α)
@@ -29,7 +31,7 @@ doc"""
 
 Bisect the `IntervalBox` in side number `i`.
 """
-function bisect(X::IntervalBox, i::Integer, α=0.5)
+function bisect(X::IntervalBox, i::Integer, α=where_bisect)
 
     x1, x2 = bisect(X[i], α)