Add a new method for evaluate (for Taylor1 vectors) and evaluate!…

… and tests

docs/src/api.md

@@ -25,6 +25,7 @@ set_variables
 show_params_TaylorN
 get_coeff
 evaluate
+evaluate!
 derivative
 integrate
 gradient

src/Taylor1.jl

@@ -1049,6 +1049,39 @@ function evaluate{T<:Number,S<:Number}(a::Taylor1{T}, dx::S)
 end
 evaluate{T<:Number}(a::Taylor1{T}) = a.coeffs[1]
 
+doc"""
+    evaluate(x, δt)
+
+Evaluates each element of `x::Array{Taylor1{T},1}`, representing
+the dependent variables of an ODE, at *time* δt.
+"""
+function evaluate{T<:Number, S<:Number}(x::Array{Taylor1{T},1}, δt::S)
+    R = promote_type(T,S)
+    return evaluate(convert(Array{Taylor1{R},1},x), convert(R,δt))
+end
+function evaluate{T<:Number}(x::Array{Taylor1{T},1}, δt::T)
+    xnew = Array{T}( length(x) )
+    evaluate!(x, δt, xnew)
+    return xnew
+end
+evaluate{T<:Number}(a::Array{Taylor1{T},1}) = evaluate(a, zero(T))
+
+doc"""
+    evaluate!(x, δt, x0)
+
+Evaluates each element of `x::Array{Taylor1{T},1}`,
+representing the Taylor expansion for the dependent variables
+of an ODE at *time* δt. It updates the vector `x0` with the
+computed values.
+"""
+function evaluate!{T<:Number}(x::Array{Taylor1{T},1}, δt::T, x0::Array{T,1})
+    @assert length(x) == length(x0)
+    @inbounds for i in eachindex(x)
+        x0[i] = evaluate( x[i], δt )
+    end
+    nothing
+end
+
 
 """
     evaluate(a, x)

src/TaylorSeries.jl

@@ -24,11 +24,13 @@ import Base: zero, one, zeros, ones, isinf, isnan,
     convert, promote_rule, promote, eltype, length, show,
     real, imag, conj, ctranspose,
     rem, mod, mod2pi, abs, gradient,
-sqrt, exp, log, sin, cos, tan, asin, acos, atan, A_mul_B!
+    sqrt, exp, log, sin, cos, tan,
+    asin, acos, atan, A_mul_B!
 
 export Taylor1, TaylorN, HomogeneousPolynomial
 
-export get_coeff, derivative, integrate, evaluate,
+export get_coeff, derivative, integrate,
+    evaluate, evaluate!,
     show_params_TaylorN,
     get_order, get_numvars,
     set_variables, get_variables,

test/runtests.jl

@@ -101,10 +101,11 @@ facts("Tests for Taylor1 expansions") do
     @fact atan(tan(tsquare)) == tsquare --> true
     @fact asin(t) + acos(t) == pi/2 --> true
     @fact derivative(acos(t)) == - 1/sqrt(1-t^2) --> true
-    @fact_throws ArgumentError asin(ta(1.0))
-    @fact_throws ArgumentError acos(ta(big(1.0)))
-    @fact_throws ArgumentError atan(ta(1//1*im))
 
+    v = [sin(t), exp(-t)]
+    @fact evaluate(v) == [0.0, 1.0]  --> true
+    @fact evaluate(v, complex(0.0,0.2)) ==
+        [complex(0.0,sinh(0.2)),complex(cos(0.2),sin(-0.2))]  --> true
     @fact derivative(5, exp(ta(1.0))) == exp(1.0)  --> true
     @fact derivative(3, exp(ta(1.0pi))) == exp(1.0pi)  --> true
     @fact isapprox(derivative(10, exp(ta(1.0pi))) , exp(1.0pi) )  --> true