Fixed to allow using martices as scalar like entity

Fixes SciML#86

REQUIRE

@@ -1,3 +1,3 @@
-julia 0.3
+julia 0.4
 Polynomials
 Compat 0.4.1

src/ODE.jl

@@ -91,7 +91,7 @@ end
 
 # isoutofdomain takes the state and returns true if state is outside
 # of the allowed domain.  Used in adaptive step-control.
-isoutofdomain(x) = isnan(x)
+isoutofdomain(x) = any(isnan(x))
 
 function make_consistent_types(fn, y0, tspan, btab::Tableau)
     # There are a few types involved in a call to a ODE solver which

src/runge_kutta.jl

@@ -20,7 +20,7 @@ immutable TableauRKExplicit{Name, S, T} <: Tableau{Name, S, T}
         @assert istril(a)
         @assert S==length(c)==size(a,1)==size(a,2)==size(b,2)
         @assert size(b,1)==length(order)
-        @assert norm(sum(a,2)-c'',Inf)<1e-10 # consistency.  
+        @assert norm(sum(a,2)-c'',Inf)<1e-10 # consistency.
         new(order,a,b,c)
     end
 end
@@ -100,7 +100,7 @@ const bt_rk23 = TableauRKExplicit(:bogacki_shampine,(2,3), Rational{Int64},
                                    2/9       1/3     4/9     0],
                                   [7/24 1/4 1/3 1/8
                                    2/9 1/3 4/9 0],
-                                  [0, 1//2, 3//4, 1] 
+                                  [0, 1//2, 3//4, 1]
                          )
 
 # Fehlberg https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta%E2%80%93Fehlberg_method
@@ -163,17 +163,17 @@ ode2_heun(fn, y0, tspan) = oderk_fixed(fn, y0, tspan, bt_heun)
 ode4(fn, y0, tspan) = oderk_fixed(fn, y0, tspan, bt_rk4)
 
 function oderk_fixed(fn, y0, tspan, btab::TableauRKExplicit)
-    # Non-arrays y0 treat as scalar
-    fn_(t, y) = [fn(t, y[1])]
-    t,y = oderk_fixed(fn_, [y0], tspan, btab)
+    # For y0 which are scalar-like, wrap them in a vector:
+    fn_{T}(t, y::Vector{T}) = T[fn(t, y[1])]
+    t,y = oderk_fixed(fn_, typeof(y0)[y0], tspan, btab)
     return t, vcat_nosplat(y)
 end
 function oderk_fixed{N,S}(fn, y0::AbstractVector, tspan,
                           btab_::TableauRKExplicit{N,S})
     # TODO: instead of AbstractVector use a Holy-trait
 
     # Needed interface:
-    # On components: 
+    # On components:
     # On y0 container: length, deepcopy, similar, setindex!
     # On time container: getindex, convert. length
 
@@ -215,9 +215,9 @@ const ode45 = ode45_dp
 ode78(fn, y0, tspan; kwargs...) = oderk_adapt(fn, y0, tspan, bt_feh78; kwargs...)
 
 function oderk_adapt(fn, y0, tspan, btab::TableauRKExplicit; kwords...)
-    # For y0 which don't support indexing.
-    fn_ = (t, y) -> [fn(t, y[1])]
-    t,y = oderk_adapt(fn_, [y0], tspan, btab; kwords...)
+    # For y0 which are scalar-like, wrap them in a vector:
+    fn_{T}(t, y::Vector{T}) = T[fn(t, y[1])]
+    t,y = oderk_adapt(fn_, typeof(y0)[y0], tspan, btab; kwords...)
     return t, vcat_nosplat(y)
 end
 function oderk_adapt{N,S}(fn, y0::AbstractVector, tspan, btab_::TableauRKExplicit{N,S};
@@ -233,7 +233,7 @@ function oderk_adapt{N,S}(fn, y0::AbstractVector, tspan, btab_::TableauRKExplici
     #  - note that the type of the components might change!
     # On y0 container: length, similar, setindex!
     # On time container: getindex, convert, length
-    
+
     # For y0 which support indexing.  Currently y0<:AbstractVector but
     # that could be relaxed with a Holy-trait.
     !isadaptive(btab_) && error("Can only use this solver with an adaptive RK Butcher table")
@@ -254,11 +254,12 @@ function oderk_adapt{N,S}(fn, y0::AbstractVector, tspan, btab_::TableauRKExplici
     # work arrays:
     y      = similar(y0, Eyf, dof)      # y at time t
     y[:]   = y0
-    ytrial = similar(y0, Eyf, dof) # trial solution at time t+dt
-    yerr   = similar(y0, Eyf, dof) # error of trial solution
+    ytrial = similar(y, dof) # trial solution at time t+dt
+    zero!(ytrial, y[1])
+    yerr   = similar(y, dof) # error of trial solution
     ks = Array(Ty, S)
-    # allocate!(ks, y0, dof) # no need to allocate as fn is not in-place
-    ytmp   = similar(y0, Eyf, dof)
+    # allocate!(ks, y, dof) # no need to allocate as fn is not in-place
+    ytmp   = similar(y, dof)
 
     # output ys
     nsteps_fixed = length(tspan) # these are always output
@@ -366,8 +367,8 @@ function rk_embedded_step!{N,S}(ytrial, yerr, ks, ytmp, y, fn, t, dt, dof, btab:
     # On components: arithmetic, zero
     # On y0 container: fill!, setindex!, getindex
 
-    fill!(ytrial, zero(eltype(ytrial)) )
-    fill!(yerr, zero(eltype(ytrial)) )
+    fill!(ytrial, zero(ytrial[1]) )
+    fill!(yerr, zero(ytrial[1]) )
     for d=1:dof
         ytrial[d] += btab.b[1,1]*ks[1][d]
         yerr[d]   += btab.b[2,1]*ks[1][d]
@@ -441,10 +442,18 @@ end
 
 # Helper functions:
 function allocate!{T}(vec::Vector{T}, y0, dof)
-    # Allocates all vectors inside a Vector{Vector} using the same
-    # kind of container as y0 has and element type eltype(eltype(vec)).
+    # Allocates and zeros all vectors inside a Vector{Vector} using
+    # the same kind of container as y0 has and element type
+    # eltype(eltype(vec)).  Uses zero(y0[1]) to create zeros for each
+    # element.
     for s=1:length(vec)
         vec[s] = similar(y0, eltype(T), dof)
+        zero!(vec[s], y0[1])
+    end
+end
+function zero!(vec, zeroofthis)
+    for i in eachindex(vec)
+        vec[i] = zero(zeroofthis)
     end
 end
 function index_or_push!(vec, i, val)

test/interface-tests.jl

@@ -1,7 +1,9 @@
 # Here are tests which test what interface the solvers require.
 
+nonconforming_solvers = [ODE.ode23s, ODE.ode4s_s, ODE.ode4s_kr]
+
 ################################################################################
-# This is to test a scalar-like state variable
+# This is to test a scalar-like state variable which is encoded in a custom type
 # (due to @acroy: https://gist.github.com/acroy/28be4f2384d01f38e577)
 
 import Base: +, -, *, /, .+, .-, .*, ./
@@ -33,6 +35,7 @@ Base.norm(y::CompSol) = norm(y::CompSol, 2.0)
 ### new for PR #68
 Base.abs(y::CompSol) = norm(y, 2.) # TODO not needed anymore once https://github.com/JuliaLang/julia/pull/11043 is in current stable julia
 Base.zero(::Type{CompSol}) = CompSol(complex(zeros(2,2)), 0., 0.)
+Base.zero(::CompSol) = zero(CompSol)
 ODE.isoutofdomain(y::CompSol) = any(isnan, vcat(y.rho[:], y.x, y.p))
 
 # Because the new RK solvers wrap scalars in an array and because of
@@ -43,21 +46,18 @@ ODE.isoutofdomain(y::CompSol) = any(isnan, vcat(y.rho[:], y.x, y.p))
 .*(s::Real, y1::CompSol) = y1*s
 ./(y1::CompSol, s::Real) = CompSol(y1.rho/s, y1.x/s, y1.p/s)
 
-
-################################################################################
-
 # define RHSs of differential equations
 # delta, V and g are parameters
 function rhs(t, y, delta, V, g)
   H = [[-delta/2 V]; [V delta/2]]
- 
+
   rho_dot = -im*H*y.rho + im*y.rho*H
   x_dot = y.p
   p_dot = -y.x
- 
+
   return CompSol( rho_dot, x_dot, p_dot)
 end
- 
+
 # inital conditons
 rho0 = zeros(2,2);
 rho0[1,1]=1.;
@@ -70,13 +70,38 @@ t,y1 = ODE.ode45((t,y)->rhs(t, y, delta0, V0, g0), y0, [0., endt]) # used as ref
 print("Testing interface for scalar-like state... ")
 for solver in solvers
     # these only work with some Array-like interface defined:
-    if solver in [ODE.ode23s, ODE.ode4s_s, ODE.ode4s_kr]
+    if solver in nonconforming_solvers
         continue
     end
     t,y2 = solver((t,y)->rhs(t, y, delta0, V0, g0), y0, linspace(0., endt, 500))
     @test norm(y1[end]-y2[end])<0.1
 end
 println("ok.")
 
+################################################################################
+# Tests using a matrix as a scalar
+# test due to @gersonjferreira https://github.com/JuliaLang/ODE.jl/issues/86#issuecomment-224889775
+
+h = [5.0 1.0; -1.0 6.0]/10.0;
+tspan=linspace(0,1,30);
+dt=tspan[2]-tspan[1];
+
+y0 = [0.0 1.0; 1.0 1.0];
+
+function rhs(t, y)
+    return h*y
+end
+
+refsol = [ 0.173109  1.81331
+           1.81331   1.6402]
+solver = 1
+for solver in solvers
+    if solver in nonconforming_solvers
+        continue
+    end
+    t, y = solver(rhs, y0, tspan)
+    @test norm(y[end]-refsol) < 0.1
+end
+
 ################################################################################
 # TODO: test a vector-like state variable, i.e. one which can be indexed.