Move Continuation{Solver,Solution} to top-level

Initially, I thought it's nice to have Bifurcations.Continuations usable
as a separate package since numerical continuation without (say)
stability analysis may be handy.  However, solution containers etc.
requires a tight coupling to the bifurcation problem (e.g., storing
Jacobian and its eigenproblem solutions).  I can probably define a very
general solution container but it's not a good idea to do at the moment
as I don't know what I need.  So, let's pull ContinuationSolution,
ContinuationSolver and other related stuff out of the sub-module
Bifurcations.Continuations.

src/Bifurcations.jl

@@ -2,15 +2,29 @@ module Bifurcations
 
 # Re-export methods from DifferentialEquations extended here:
 export init, solve, solve!, step!
-using DiffEqBase: init, solve, solve!, step!
-# see: continuations/interface.jl
+import DiffEqBase: init, solve, solve!, step!
+# see: solver.jl
 
 include("continuations/continuations.jl")
+
+# Continuation algorithm interface:
+using .Continuations: ContinuationCache, ContinuationOptions,
+    predictor_corrector_step!, new_branches!
+# TODO: Reconsider what/how `.Continuations` module "exposes"
+# continuation algorithm/method/solver interface.  For example, should
+# `predictor_corrector_step!` be renamed to `step!`?
+
+# Continuation problem interface:
 using .Continuations: AbstractContinuationProblem, AbstractProblemCache
 import .Continuations: get_prob_cache, get_u0, residual!, residual_jacobian!,
     residual, isindomain
 const _C = AbstractProblemCache
 
+include("utils.jl")
+
+include("solution.jl")
+include("solver.jl")
+
 include("fixedpoint.jl")
 include("diffeq.jl")
 include("examples/examples.jl")

src/continuations/branching.jl

@@ -95,7 +95,15 @@ function solve_simple_bifurcation!(cache, opts, u0, tJ, L, Q)
 end
 
 
-function new_branches!(cache, opts, sbint::SimpleBifurcationInterval)
+function new_branches!(
+        cache::ContinuationCache,
+        opts::ContinuationOptions,
+        sbint)
+    # TODO: `sbint` is expected to be a `SimpleBifurcationInterval`
+    # but it is defined in "down stream".  I should turn this into a
+    # function with "flat" arguments: `new_branches!(cache, opts, u0,
+    # u1, direction, h)`.
+
     u0, tJ, L, Q = find_simple_bifurcation!(cache, opts, sbint)
     # TODO: handle not-found case
 

src/continuations/continuations.jl

@@ -1,10 +1,7 @@
 module Continuations
-import DiffEqBase: solve, solve!, init, step!
 include("utils.jl")
 include("base.jl")
 include("euler_newton.jl")
-include("solution.jl")
-include("interface.jl")
 include("zero_point.jl")
 include("branching.jl")
 end

src/plotting.jl

@@ -1,7 +1,5 @@
 using RecipesBase
 
-using .Continuations: ContinuationSolution, sweeps_as_vectors
-
 @recipe function f(sol::ContinuationSolution; vars = (0, 1))
     ix, iy = vars
     xs = sweeps_as_vectors(sol, ix)

src/utils.jl

@@ -0,0 +1,2 @@
+using .Continuations: isalmostzero
+# [[./continuations/utils.jl]]

test/test_normal_form.jl

@@ -2,7 +2,7 @@ module TestNormalForm
 
 using Base.Test
 using Bifurcations
-using Bifurcations.Continuations: sweeps_as_vectors
+using Bifurcations: sweeps_as_vectors
 using Bifurcations.Examples: Pitchfork, Transcritical
 
 @testset "$normal" for normal in [Pitchfork, Transcritical]