# Error with ForwardDiff no method matching Float64

**URL:** <https://discourse.julialang.org/t/error-with-forwarddiff-no-method-matching-float64/41905>\
**Category:** Numerics\
**Created:** [June 23, 2020, 1:40am UTC](https://discourse.julialang.org/t/error-with-forwarddiff-no-method-matching-float64/41905 "2020-06-23T01:40:51Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![smickus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/smickus/32/18002_2.png) [@smickus](https://discourse.julialang.org/u/smickus)\
**Post date:** [June 23, 2020, 1:40am UTC](https://discourse.julialang.org/t/error-with-forwarddiff-no-method-matching-float64/41905/1 "2020-06-23T01:40:51Z")

</div>

I am trying to use forwardDiff to compute the gradient of a function in which I am solving an ODE, but I am getting an error that there is no method matching Float64. I have been stumped with this error for awile and would greatly appreciate any assistance that could be provided.

```julia
using DifferentialEquations
using ForwardDiff

function CostFun(x)
    
    function SpringEqu!(du, u, x, t)
        du[1] = u[2]
        du[2] = -(x[1] / x[3]) * u[2] - (x[2] / x[3]) * u[1] + 50 / x[3]
    end
    
    u0 = [2.0, 0.0]
    tspan = (0.0, 1.0)
    prob = ODEProblem(SpringEqu!, u0, tspan, x)
    sol = solve(prob)

    Simpos = zeros(length(sol.t))
    Simvel = zeros(length(sol.t))
    tout = zeros(length(sol.t))
    for i = 1:length(sol.t)
        tout[i] = sol.t[i]
        Simpos[i] = sol[1, i]
        Simvel[i] = sol[2, i]
    end

    totalCost = sum(Simpos)
    return totalCost
end

xin = [2000.0, 20000.0, 80.0]

g = ForwardDiff.gradient(CostFun, xin)

```

The error from the function is the following:

```julia
LoadError: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3})
Closest candidates are:
  Float64(::Real, ::RoundingMode) where T<:AbstractFloat at rounding.jl:200
  Float64(::T) where T<:Number at boot.jl:715
  Float64(::Int8) at float.jl:60
  ...
Stacktrace:
 [1] convert(::Type{Float64}, ::ForwardDiff.Dual{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3}) 
at .\number.jl:7
 [2] setindex!(::Array{Float64,1}, ::ForwardDiff.Dual{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3}, ::Int64) at .\array.jl:826
 [3] CostFun(::Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3},1}) at C:\Users\spenc\github\MetaOpt\autodiffTest.jl:23
 [4] vector_mode_dual_eval at C:\Users\spenc\.juliapro\JuliaPro_v1.4.1-1\packages\ForwardDiff\cXTw0\src\apiutils.jl:37 [inlined]
 [5] vector_mode_gradient(::typeof(CostFun), ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3},1}}) at C:\Users\spenc\.juliapro\JuliaPro_v1.4.1-1\packages\ForwardDiff\cXTw0\src\gradient.jl:97
 [6] gradient(::Function, ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3},1}}, ::Val{true}) at C:\Users\spenc\.juliapro\JuliaPro_v1.4.1-1\packages\ForwardDiff\cXTw0\src\gradient.jl:17
 [7] gradient(::Function, ::Array{Float64,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3,Array{ForwardDiff.Dual{ForwardDiff.Tag{typeof(CostFun),Float64},Float64,3},1}}) at C:\Users\spenc\.juliapro\JuliaPro_v1.4.1-1\packages\ForwardDiff\cXTw0\src\gradient.jl:15 (repeats 2 times)
 [8] top-level scope at C:\Users\spenc\github\MetaOpt\autodiffTest.jl:34
in expression starting at C:\Users\spenc\github\MetaOpt\autodiffTest.jl:34

```

---

<div class="post-metadata">

**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [June 23, 2020, 3:40am UTC](https://discourse.julialang.org/t/error-with-forwarddiff-no-method-matching-float64/41905/2 "2020-06-23T03:40:57Z")

</div>

You need to allow numbers of type `ForwardDiff.Dual` to propagate through `CostFun`, something like this:

```julia
julia> function CostFun(x::AbstractVector{T}) where T
           
           function SpringEqu!(du, u, x, t)
               du[1] = u[2]
               du[2] = -(x[1] / x[3]) * u[2] - (x[2] / x[3]) * u[1] + 50 / x[3]
           end
           
           u0 = T[2.0, 0.0]
           tspan = (0.0, 1.0)
           prob = ODEProblem(SpringEqu!, u0, tspan, x)
           sol = solve(prob)

           Simpos = zeros(T, length(sol.t))
           Simvel = zeros(T, length(sol.t))
           tout = zeros(T, length(sol.t))
           for i = 1:length(sol.t)
               tout[i] = sol.t[i]
               Simpos[i] = sol[1, i]
               Simvel[i] = sol[2, i]
           end

           totalCost = sum(Simpos)
           return totalCost
       end
CostFun (generic function with 2 methods)

julia> g = ForwardDiff.gradient(CostFun, xin)
3-element Array{Float64,1}:
  0.0013186230010380866
 -0.00014123587229879185
  0.001994165580567926

```

---

<div class="post-metadata">

**Author:** ![smickus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/smickus/32/18002_2.png) [@smickus](https://discourse.julialang.org/u/smickus)\
**Post date:** [June 23, 2020, 5:44pm UTC](https://discourse.julialang.org/t/error-with-forwarddiff-no-method-matching-float64/41905/3 "2020-06-23T17:44:24Z")

</div>

Thanks for your help.

---

<div class="post-metadata">

**Author:** ![smickus](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/smickus/32/18002_2.png) [@smickus](https://discourse.julialang.org/u/smickus)\
**Post date:** [June 23, 2020, 7:15pm UTC](https://discourse.julialang.org/t/error-with-forwarddiff-no-method-matching-float64/41905/4 "2020-06-23T19:15:58Z")

</div>

Why did you make this change Simpos = zeros(T, length(sol.t))? I am having trouble figuring out why this was done.

---

<div class="post-metadata">

**Author:** ![mcabbott](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mcabbott/32/6603_2.png) [@mcabbott](https://discourse.julialang.org/u/mcabbott)\
**Post date:** [June 23, 2020, 8:07pm UTC](https://discourse.julialang.org/t/error-with-forwarddiff-no-method-matching-float64/41905/5 "2020-06-23T20:07:29Z")

</div>

It needs to be be able to fit the dual numbers, otherwise you’ll get the same error as before.

Perhaps clearer without `gradient`:

```julia
using ForwardDiff: Dual
xin = [2000.0 + Dual(0, (1,0,0)), 20000.0 + Dual(0, (0,1,0)), 80.0]
T = eltype(xin) # Dual{Nothing,Float64,3}
u0 = T[2.0, 0.0]
tspan = (0.0, 1.0)
prob = ODEProblem(SpringEqu!, u0, tspan, xin)
sol = solve(prob)

```

gives

```julia
julia> sol[1, :]
19-element Array{Dual{Nothing,Float64,3},1}:
  Dual{Nothing}(2.0,0.0,0.0,0.0)
  Dual{Nothing}(1.9999999989997657,8.341478310022593e-18,-5.0074311889727496e-14,0.0)
  Dual{Nothing}(1.9999999506887869,2.887412874324848e-15,-2.4686464570508713e-12,0.0)
...

```