# Multiple shooting and neural ode in Rc models

**URL:** <https://discourse.julialang.org/t/multiple-shooting-and-neural-ode-in-rc-models/104013>\
**Category:** New to Julia\
**Created:** [September 19, 2023, 7:36am UTC](https://discourse.julialang.org/t/multiple-shooting-and-neural-ode-in-rc-models/104013 "2023-09-19T07:36:31Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![Marco\_Nesta](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/marco_nesta/32/50318_2.png) [@Marco\_Nesta](https://discourse.julialang.org/u/Marco_Nesta)\
**Post date:** [September 19, 2023, 7:36am UTC](https://discourse.julialang.org/t/multiple-shooting-and-neural-ode-in-rc-models/104013/1 "2023-09-19T07:36:31Z")

</div>

Good morning everyone, I am working on using neural ode the optimization of RC models for house consumption.  
In the following code I have defined a first state where P and T are exogenous variables. could you give me advice on how to improve the learning? an alternative could be to use physics informed neural networks (NeuralPDE.jl) but for these odes I have not succeeded yet.

```julia
using DifferentialEquations, Plots, Flux,Optim, DiffEqFlux, DataInterpolations,Random, ComponentArrays, Lux
using Optimization, OptimizationOptimisers, OptimizationOptimJL,OptimizationNLopt
rng = Random.default_rng()
using CSV
using DataFrames
using Plots
using Flux
using Statistics: mean
using DiffEqFlux, Optimization, OptimizationOptimJL,Plots
using ComponentArrays, Lux, DiffEqFlux, Optimization, OptimizationPolyalgorithms, DifferentialEquations, Plots
using DiffEqFlux: group_ranges
# Load the data
df = CSV.read("/Users/marco/OneDrive/Desktop/Tesi/Julia_files/measured_data_ex_00.csv", DataFrame)
df=repeat(df, outer=10)

registered_gas_flow = df[:, :2]
Registered_Temperature = df[:, 3]
sec_Temp = [mean(Registered_Temperature[i:i+59]) for i in 1:60:length(Registered_Temperature)-59]
sec_gas = [mean(registered_gas_flow[i:i+59]) for i in 1:60:length(registered_gas_flow)-59]
#create a 3600 time vector
function RC!(du,u,p,t)
    Rv, Ci,Rv2,Ci2 = p
    Text = ext_Temp(t)
    P= ext_power(t)
    P2= ext_power2(t)
    
    du[1] = 1/(Rv*Ci) .* (Text .- u[1]) .+ P/Ci
    end

u0= [20.0]

tspan= (0.0f0,3000.0f0)
datasize = 6000
tsteps= range(tspan[1], tspan[2], length = datasize)
p= [10000, 10, 10000, 10]

Ext_temperature = LinearInterpolation(sec_Temp,tsteps);
power = LinearInterpolation(sec_gas,tsteps);
power2= LinearInterpolation(sec_gas,tsteps);
function ext_Temp(tsteps)
return Ext_temperature(tsteps)
end
    
function ext_power(tsteps)
return power(tsteps)
end   

function ext_power2(tsteps)
return power2(tsteps)
end

prob= ODEProblem(RC!, u0, tspan, p)
sol= solve(prob, Tsit5(), saveat=tsteps)[1,:]

# Verify ODE solution
ode_data =Array(solve(prob, Tsit5(), saveat=tsteps))

plot(tsteps, ode_data[1,:], label = "data")

#resize ode data 
ode_data=ode_data[:,1:20:3000]
tsteps=tsteps[1:20:3000]

plot(tsteps, ode_data[1,:], label = "data")

ode_data_train=ode_data[:,1:75]
ode_data_test=ode_data[:,76:150]
tspan= (0.0f0, 75.0f0)
tsteps= range(tspan[1], tspan[2], length = 75)
datasize=75

plot(ode_data[1,1:75], label = "datatrain")
plot!(ode_data[1,76:150], label = "datatest")

anim = Plots.Animation()

# Define the Neural Network
nn = Lux.Chain(
                Lux.Dense(1, 84, tanh),
                Lux.Dense(84, 84, tanh),
                Lux.Dense(84, 44, tanh),
                Lux.Dense(44,1))
p_init, st = Lux.setup(rng, nn)

neuralode = NeuralODE(nn, tspan, Tsit5(), saveat = tsteps)
prob_node = ODEProblem((u,p,t)->nn(u,p,st)[1], u0, tspan, ComponentArray(p_init))

function plot_multiple_shoot(plt, preds, group_size)
	step = group_size-1
	ranges = group_ranges(datasize, group_size)

	for (i, rg) in enumerate(ranges)
		plot!(plt, tsteps[rg], preds[i][1,:], markershape=:circle)
	end
end

# Animate training, cannot make animation on CI server
# anim = Plots.Animation()
iter = 0
callback = function (p, l, preds; doplot = true)
  display(l)
  global iter
  iter += 1
  if doplot && iter%1 == 0
    # plot the original data
    plt = scatter(tsteps, ode_data_train[1,:], label = "Data")

    # plot the different predictions for individual shoot
    plot_multiple_shoot(plt, preds, group_size)

    frame(anim)
    display(plot(plt))
  end
  return false
end

# Define parameters for Multiple Shooting
group_size = 3
continuity_term = 100

function loss_function(data, pred)
	return sum(abs2, data - pred)
end

function loss_multiple_shooting(p)
    return multiple_shoot(p, ode_data_train, tsteps, prob_node, loss_function, Tsit5(),
                          group_size; continuity_term)
end

adtype = Optimization.AutoZygote()
optf = Optimization.OptimizationFunction((x,p) -> loss_multiple_shooting(x), adtype)
optprob = Optimization.OptimizationProblem(optf, ComponentArray(p_init))
res_ms = Optimization.solve(optprob, PolyOpt(), callback = callback)

gif(anim, "multiple_shooting.gif", fps=15)

optimized_params= res_ms.u

u1 = Float32[ode_data_train[1,end]]
tspan1=(75.0f0, 150.0f0)
tsteps1=range(tspan1[1], tspan1[2], length = datasize)

prob_neuralode2 = NeuralODE(nn, tspan1,Tsit5(), saveat = tsteps1)

function predict_neuralode2(p)
  Array(prob_neuralode2(u1, p, st)[1])
end
prediction=predict_neuralode2(optimized_params)
tstepsfinal=range(0.0f0, 150.0f0, length = 150)

plot(tstepsfinal, ode_data[1,:], label = "data")
plot!(tsteps1,ode_data_test[1,:], label = "data to check prediction")
scatter!(tsteps1, prediction[1,:], label = "prediction to check prediction")

```

![plot_rc](https://global.discourse-cdn.com/julialang/original/3X/7/c/7c59d47f062bc44adc4af3c57939c285defb01a0.png)  
 ![plot_rc2](https://global.discourse-cdn.com/julialang/original/3X/7/1/7185d149da3e10761bd65c5bd90e2f8b739e2e7e.png)

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [September 25, 2023, 12:06pm UTC](https://discourse.julialang.org/t/multiple-shooting-and-neural-ode-in-rc-models/104013/2 "2023-09-25T12:06:23Z")

</div>

I cannot run this, the measured data is not available.

---

<div class="post-metadata">

**Author:** ![Marco\_Nesta](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/marco_nesta/32/50318_2.png) [@Marco\_Nesta](https://discourse.julialang.org/u/Marco_Nesta)\
**Post date:** [September 25, 2023, 12:43pm UTC](https://discourse.julialang.org/t/multiple-shooting-and-neural-ode-in-rc-models/104013/3 "2023-09-25T12:43:23Z")

</div>

I can’t upload the csv file

---

<div class="post-metadata">

**Author:** ![Marco\_Nesta](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/marco_nesta/32/50318_2.png) [@Marco\_Nesta](https://discourse.julialang.org/u/Marco_Nesta)\
**Post date:** [September 25, 2023, 12:54pm UTC](https://discourse.julialang.org/t/multiple-shooting-and-neural-ode-in-rc-models/104013/4 "2023-09-25T12:54:27Z")

</div>

,Registered Gas Flow,Registered Temperature  
0.0,1.7e-06,20.0  
0.1,1.5e-06,20.0  
0.2,2.2e-06,19.9  
0.3,2.2e-06,19.8  
0.4,2.6e-06,20.1  
0.5,1.9e-06,20.3  
0.6,2e-06,20.1  
0.7,2.4e-06,20.1  
0.8,1.4e-06,19.8  
0.9,1.5e-06,19.6  
1.0,2e-06,19.6  
1.1,2.2e-06,19.8  
1.2,1.5e-06,20.2  
1.3,1.9e-06,19.9  
1.4,1.5e-06,19.7  
1.5,2e-06,20.1  
1.6,2.3e-06,19.7  
1.7,2.2e-06,20.1  
1.8,2.6e-06,19.7  
1.9,2.5e-06,20.1  
2.0,2.1e-06,20.0  
2.1,1.6e-06,20.0  
2.2,2.2e-06,19.5  
2.3,2e-06,20.0  
2.4,2.3e-06,19.8  
2.5,2.6e-06,19.9  
2.6,2.4e-06,20.1  
2.7,1.8e-06,20.1  
2.8,1.5e-06,20.1  
2.9,2.4e-06,20.0  
3.0,1.9e-06,20.3  
3.1,2.2e-06,19.9  
3.2,2.4e-06,20.3  
3.3,2.7e-06,20.2  
3.4,1.9e-06,19.9  
3.5,1.8e-06,20.5  
3.6,2.7e-06,20.0  
3.7,2.3e-06,19.7  
3.8,2.4e-06,20.0  
3.9,2.3e-06,20.2  
4.0,1.6e-06,20.5  
4.1,2.3e-06,20.4  
4.2,2.6e-06,20.2  
4.3,1.8e-06,20.4  
4.4,2.1e-06,20.3  
4.5,2.5e-06,20.1  
4.6,2.1e-06,20.0  
4.7,1.8e-06,20.5  
4.8,1.9e-06,20.4  
4.9,2e-06,20.8  
5.0,1.7e-06,20.3  
5.1,2.1e-06,20.3  
5.2,2.7e-06,20.4  
5.3,2.7e-06,20.1  
5.4,1.6e-06,20.8  
5.5,2.7e-06,20.6  
5.6,2.2e-06,20.2  
5.7,2.2e-06,20.3  
5.8,1.9e-06,20.4  
5.9,2.9e-06,20.8  
6.0,2.2e-06,20.4  
6.1,1.8e-06,20.1  
6.2,1.7e-06,20.6  
6.3,2.8e-06,20.3  
6.4,1.6e-06,20.5  
6.5,2.2e-06,20.5  
6.6,2e-06,20.4  
6.7,1.9e-06,20.5  
6.8,2.8e-06,20.8  
6.9,2.2e-06,20.3  
7.0,2.2e-06,20.7  
7.1,2.8e-06,20.9  
7.2,1.6e-06,20.9  
7.3,2.6e-06,20.6  
7.4,2.6e-06,20.9  
7.5,2.7e-06,20.7  
7.6,1.7e-06,20.7  
7.7,1.6e-06,20.9  
7.8,2.5e-06,20.9  
7.9,2.8e-06,21.4  
8.0,2.4e-06,20.6  
8.1,2.6e-06,21.2  
8.2,2.6e-06,21.1  
8.3,2.9e-06,20.7  
8.4,2.8e-06,21.4  
8.5,1.9e-06,21.3  
8.6,2e-06,21.1  
8.7,2.1e-06,21.4  
8.8,2.3e-06,20.9  
8.9,2.4e-06,21.1  
9.0,2.7e-06,21.0  
9.1,2.2e-06,21.5  
9.2,2.7e-06,21.0  
9.3,2e-06,21.6  
9.4,2.2e-06,21.1  
9.5,2.3e-06,21.3  
9.6,2.2e-06,21.0  
9.7,2e-06,21.4  
9.8,1.9e-06,21.4  
9.9,1.8e-06,21.0  
10.0,2.4e-06,21.3  
10.1,2.7e-06,21.3  
10.2,1.7e-06,21.5  
10.3,2.4e-06,21.4  
10.4,2.3e-06,21.2  
10.5,2.9e-06,21.4  
10.6,2.6e-06,21.4  
10.7,2.4e-06,21.5  
10.8,2.9e-06,21.8  
10.9,2.5e-06,21.7  
11.0,2.8e-06,21.4  
11.1,1.8e-06,21.6  
11.2,1.9e-06,21.4  
11.3,2.6e-06,21.4  
11.4,1.8e-06,21.5  
11.5,1.8e-06,22.0  
11.6,2e-06,21.6  
11.7,1.6e-06,21.4  
11.8,2.2e-06,21.2  
11.9,1.7e-06,21.8  
12.0,2.6e-06,21.4  
12.1,2.9e-06,21.4  
12.2,1.9e-06,21.3  
12.3,1.9e-06,21.9  
12.4,2.1e-06,22.0  
12.5,2.9e-06,22.0  
12.6,2.6e-06,22.0  
12.7,1.8e-06,21.6  
12.8,2.6e-06,21.9  
12.9,2.2e-06,22.0  
13.0,2.2e-06,21.9  
13.1,2.4e-06,22.0  
13.2,1.9e-06,22.0  
13.3,2.5e-06,22.0  
13.4,2.9e-06,22.1  
13.5,2.5e-06,22.1  
13.6,3e-06,22.0  
13.7,2.5e-06,22.6  
13.8,1.8e-06,21.8  
13.9,3.1e-06,22.1  
14.0,2.3e-06,22.3  
14.1,1.9e-06,22.3  
14.2,2.5e-06,22.1  
14.3,2.1e-06,22.6  
14.4,2.4e-06,22.3  
14.5,2.4e-06,22.4  
14.6,3.1e-06,22.4  
14.7,1.9e-06,22.4  
14.8,2e-06,22.5  
14.9,2.1e-06,22.5  
15.0,2.6e-06,22.3  
15.1,1.9e-06,23.0  
15.2,2.6e-06,22.4  
15.3,2.6e-06,22.5  
15.4,2.8e-06,22.4  
15.5,2e-06,22.6  
15.6,2.4e-06,22.5  
15.7,2.2e-06,22.3  
15.8,2e-06,22.9  
15.9,1.7e-06,22.6  
16.0,3e-06,22.7  
16.1,2.3e-06,22.7  
16.2,1.9e-06,22.4  
16.3,3.1e-06,22.7  
16.4,2.3e-06,22.6  
16.5,1.9e-06,22.9  
16.6,3e-06,23.0  
16.7,1.9e-06,23.3  
16.8,2e-06,23.1  
16.9,1.8e-06,23.2  
17.0,2.2e-06,22.3  
17.1,2.1e-06,22.8  
17.2,1.9e-06,23.0  
17.3,2.9e-06,22.9  
17.4,2.4e-06,22.7  
17.5,2.3e-06,23.2  
17.6,2.4e-06,22.8  
17.7,2.9e-06,22.9  
17.8,3.1e-06,22.8  
17.9,2.7e-06,23.4  
18.0,2.1e-06,23.3  
18.1,2.7e-06,23.3  
18.2,3.1e-06,23.4  
18.3,2.1e-06,23.3  
18.4,3e-06,23.2  
18.5,2.5e-06,23.9  
18.6,2.5e-06,23.5  
18.7,2.7e-06,23.9  
18.8,2.9e-06,23.4  
18.9,2.8e-06,23.3  
19.0,2.5e-06,24.1  
19.1,3.2e-06,23.7  
19.2,2.7e-06,23.6  
19.3,2.4e-06,23.7  
19.4,3e-06,24.2  
19.5,2.8e-06,24.2  
19.6,2.8e-06,23.9  
19.7,3.3e-06,24.2  
19.8,3.2e-06,24.3  
19.9,3e-06,23.8  
20.0,2.2e-06,24.0  
20.1,2.5e-06,24.1  
20.2,2.6e-06,24.8  
20.3,1.9e-06,24.0  
20.4,2.4e-06,24.6  
20.5,2.6e-06,24.3  
20.6,3.1e-06,24.5  
20.7,2.4e-06,24.3  
20.8,2.9e-06,24.7  
20.9,3.1e-06,24.4  
21.0,2.8e-06,24.4  
21.1,3e-06,24.9  
21.2,2.8e-06,24.9  
21.3,2.9e-06,25.0  
21.4,1.8e-06,25.0  
21.5,3.1e-06,24.8  
21.6,2.6e-06,25.5  
21.7,2.5e-06,25.2  
21.8,1.9e-06,24.8  
21.9,2.9e-06,25.0  
22.0,2.5e-06,25.2  
22.1,2.8e-06,24.7  
22.2,2.8e-06,25.1  
22.3,2.1e-06,25.0  
22.4,3.1e-06,24.9  
22.5,3.1e-06,25.2  
22.6,3.1e-06,25.3  
22.7,2.6e-06,25.7  
22.8,2e-06,25.2  
22.9,2.5e-06,25.5  
23.0,3.3e-06,25.3  
23.1,2.1e-06,25.8  
23.2,2.5e-06,25.6  
23.3,2.2e-06,25.2  
23.4,2.6e-06,25.4  
23.5,3.1e-06,25.5  
23.6,2.4e-06,25.3  
23.7,2.6e-06,26.4  
23.8,3.1e-06,26.4  
23.9,2.4e-06,25.9  
24.0,2.1e-06,26.0  
24.1,3.3e-06,25.9  
24.2,2.1e-06,26.4  
24.3,2.8e-06,26.3  
24.4,2.8e-06,26.3  
24.5,1.8e-06,26.0  
24.6,1.8e-06,26.3  
24.7,3e-06,25.8  
24.8,3e-06,26.5  
24.9,2.3e-06,26.0  
25.0,2.5e-06,26.6  
25.1,2.9e-06,26.5  
25.2,2.9e-06,26.5  
25.3,2.2e-06,26.6  
25.4,3.2e-06,26.8  
25.5,2.9e-06,26.6  
25.6,3.1e-06,26.4  
25.7,2e-06,26.6  
25.8,1.9e-06,26.6  
25.9,3e-06,26.5  
26.0,2.8e-06,26.6  
26.1,2.1e-06,26.5  
26.2,2.2e-06,26.7  
26.3,2e-06,27.2  
26.4,2.5e-06,27.4  
26.5,3.4e-06,27.0  
26.6,3.3e-06,26.8  
26.7,2.5e-06,27.2  
26.8,2.3e-06,27.0  
26.9,2.9e-06,26.9  
27.0,2.3e-06,27.0  
27.1,3e-06,26.9  
27.2,3.1e-06,27.8  
27.3,2.5e-06,27.2  
27.4,2.3e-06,27.4  
27.5,2.2e-06,27.4  
27.6,1.9e-06,27.6  
27.7,2.2e-06,27.7  
27.8,3.4e-06,27.2  
27.9,2.2e-06,27.2  
28.0,3.1e-06,27.2  
28.1,2.1e-06,28.0  
28.2,2.5e-06,27.3  
28.3,2.8e-06,27.7  
28.4,2.2e-06,28.0  
28.5,3.2e-06,27.4  
28.6,2.1e-06,28.1  
28.7,3.5e-06,28.1  
28.8,2.3e-06,27.6  
28.9,2.2e-06,28.0  
29.0,2e-06,28.0  
29.1,2.2e-06,27.8  
29.2,2.9e-06,27.9  
29.3,3.1e-06,28.6  
29.4,3.2e-06,28.4  
29.5,3e-06,28.2  
29.6,3.1e-06,28.5  
29.7,3e-06,28.4  
29.8,2.9e-06,28.4  
29.9,2e-06,28.2  
30.0,2.8e-06,28.0  
30.1,2.3e-06,28.7  
30.2,2.4e-06,28.8  
30.3,3e-06,28.4  
30.4,2.1e-06,28.2  
30.5,3.2e-06,29.0  
30.6,2.7e-06,28.5  
30.7,2.8e-06,28.5  
30.8,2.9e-06,29.1  
30.9,2.4e-06,29.0  
31.0,3e-06,28.9  
31.1,2.1e-06,29.0  
31.2,2.1e-06,28.6  
31.3,2.7e-06,28.8  
31.4,3.4e-06,29.5  
31.5,3.2e-06,28.7  
31.6,2.8e-06,29.0  
31.7,3.1e-06,28.8  
31.8,2.4e-06,29.4  
31.9,2.1e-06,29.1  
32.0,2.8e-06,29.2  
32.1,2.4e-06,29.3  
32.2,2.8e-06,29.1  
32.3,2.8e-06,29.4  
32.4,2.6e-06,29.7  
32.5,2.4e-06,29.8  
32.6,2.5e-06,29.6  
32.7,2.6e-06,30.3  
32.8,2.6e-06,29.4  
32.9,2.7e-06,29.8  
33.0,2.5e-06,29.5  
33.1,2.3e-06,29.3  
33.2,2.1e-06,29.9  
33.3,2.6e-06,30.0  
33.4,2.4e-06,30.5  
33.5,3e-06,29.7  
33.6,3e-06,29.8  
33.7,2.8e-06,30.1  
33.8,3.1e-06,30.0  
33.9,3.1e-06,29.8  
34.0,3.5e-06,30.2  
34.1,2.7e-06,30.6  
34.2,3.5e-06,30.4  
34.3,2.5e-06,30.5  
34.4,2.7e-06,30.3  
34.5,2.8e-06,30.2  
34.6,3e-06,30.2  
34.7,2.6e-06,31.0  
34.8,3e-06,31.0  
34.9,3.6e-06,31.3  
35.0,2.2e-06,30.7  
35.1,3.1e-06,30.9  
35.2,2.5e-06,30.8  
35.3,2.8e-06,30.7  
35.4,2.8e-06,30.9  
35.5,3.3e-06,30.8  
35.6,2e-06,31.1  
35.7,2.4e-06,31.6  
35.8,3e-06,31.2  
35.9,2.9e-06,31.5  
36.0,3.5e-06,31.5  
36.1,2.4e-06,31.8  
36.2,3.6e-06,31.5  
36.3,2.4e-06,32.0  
36.4,3.4e-06,31.7  
36.5,3.1e-06,31.8  
36.6,2.8e-06,32.3  
36.7,3.3e-06,31.7  
36.8,2e-06,31.9  
36.9,2.2e-06,32.2  
37.0,3.1e-06,31.8  
37.1,3.2e-06,32.6  
37.2,2.7e-06,31.9  
37.3,2.9e-06,32.2  
37.4,3.2e-06,32.1  
37.5,3.6e-06,32.3  
37.6,3.1e-06,32.0  
37.7,2.4e-06,32.6  
37.8,3.3e-06,32.8  
37.9,2.2e-06,32.4  
38.0,2e-06,32.9  
38.1,2.8e-06,32.6  
38.2,2.1e-06,32.3  
38.3,2.2e-06,32.6  
38.4,3.5e-06,32.6  
38.5,3.3e-06,32.7  
38.6,3.3e-06,33.3  
38.7,2.7e-06,32.6  
38.8,2e-06,32.9  
38.9,3e-06,33.1  
39.0,2.8e-06,33.0  
39.1,2.1e-06,32.8  
39.2,2.9e-06,33.1  
39.3,2.6e-06,33.2  
39.4,2.3e-06,32.9  
39.5,2.6e-06,33.1  
39.6,3e-06,33.4  
39.7,3.1e-06,33.2  
39.8,3.1e-06,33.0  
39.9,2.9e-06,33.4  
40.0,2.4e-06,33.3  
40.1,3.4e-06,33.8  
40.2,2.6e-06,33.8  
40.3,3.1e-06,33.7  
40.4,2.5e-06,33.7  
40.5,2e-06,33.8  
40.6,2.1e-06,33.6  
40.7,2.8e-06,33.6  
40.8,3.3e-06,34.1  
40.9,2.3e-06,33.3  
41.0,2.1e-06,34.4  
41.1,2.1e-06,33.6  
41.2,2.2e-06,33.5  
41.3,3.2e-06,33.6  
41.4,2.5e-06,33.9  
41.5,2.1e-06,34.5  
41.6,2.8e-06,34.2  
41.7,2.8e-06,34.6  
41.8,2.9e-06,34.3  
41.9,2.7e-06,33.9  
42.0,2.2e-06,34.5  
42.1,2.5e-06,34.3  
42.2,3.4e-06,34.7  
42.3,3.1e-06,34.2  
42.4,3e-06,35.1  
42.5,3.1e-06,34.3  
42.6,2.5e-06,34.4  
42.7,2.1e-06,34.9  
42.8,3.6e-06,34.7  
42.9,2.9e-06,35.0  
43.0,2e-06,34.7  
43.1,3.4e-06,34.8  
43.2,2e-06,34.9  
43.3,2.6e-06,34.8  
43.4,2.8e-06,35.3  
43.5,2.9e-06,35.1  
43.6,3.2e-06,35.0  
43.7,3.1e-06,34.9  
43.8,2.8e-06,34.5  
43.9,2e-06,34.7  
44.0,2.2e-06,35.0  
44.1,3.6e-06,35.5  
44.2,2.3e-06,35.5  
44.3,2.5e-06,34.8  
44.4,2.9e-06,34.8  
44.5,3e-06,35.5  
44.6,2.1e-06,35.1  
44.7,2.8e-06,34.8  
44.8,3.5e-06,35.4  
44.9,2.5e-06,35.1  
45.0,3.3e-06,35.5  
45.1,3.6e-06,36.2  
45.2,2.4e-06,36.6  
45.3,2.4e-06,35.8  
45.4,2.7e-06,35.8  
45.5,3.3e-06,36.0  
45.6,3.5e-06,36.0  
45.7,2.3e-06,35.8  
45.8,3.3e-06,36.5  
45.9,3.2e-06,37.1  
46.0,2.7e-06,36.5  
46.1,2.4e-06,36.4  
46.2,3.1e-06,36.5  
46.3,2.1e-06,36.2  
46.4,2.3e-06,36.3  
46.5,2.1e-06,36.3  
46.6,2.9e-06,36.5  
46.7,1.9e-06,36.0  
46.8,2.2e-06,36.2  
46.9,3e-06,36.5  
47.0,2.7e-06,36.9  
47.1,2.1e-06,37.1  
47.2,3.1e-06,37.0  
47.3,2.6e-06,36.4  
47.4,3.3e-06,36.7  
47.5,2.2e-06,37.6  
47.6,3.6e-06,36.9  
47.7,2e-06,36.3  
47.8,2.1e-06,36.8  
47.9,2.8e-06,37.4  
48.0,3.3e-06,37.3  
48.1,3.5e-06,37.4  
48.2,2.4e-06,37.0  
48.3,2.5e-06,37.0  
48.4,3.2e-06,37.3  
48.5,2.8e-06,37.5  
48.6,3.2e-06,37.4  
48.7,3.1e-06,37.7  
48.8,3.1e-06,37.7  
48.9,3.2e-06,37.8  
49.0,2e-06,37.4  
49.1,2.3e-06,37.4  
49.2,2.3e-06,38.0  
49.3,2.9e-06,38.0  
49.4,3.1e-06,38.1  
49.5,3e-06,38.1  
49.6,2.5e-06,37.6  
49.7,2.3e-06,38.3  
49.8,2.4e-06,38.4  
49.9,3e-06,38.3  
50.0,2.2e-06,38.5  
50.1,3.1e-06,37.7  
50.2,2.3e-06,38.9  
50.3,2e-06,38.0  
50.4,3e-06,37.9  
50.5,2.1e-06,37.9  
50.6,3.5e-06,37.9  
50.7,2.7e-06,37.8  
50.8,3e-06,38.6  
50.9,3.5e-06,38.8  
51.0,1.9e-06,38.1  
51.1,2.9e-06,38.6  
51.2,3.1e-06,38.7  
51.3,2.8e-06,38.8  
51.4,2e-06,39.1  
51.5,2.6e-06,38.4  
51.6,2.8e-06,38.5  
51.7,3.2e-06,38.9  
51.8,2.1e-06,39.1  
51.9,2.6e-06,38.6  
52.0,3.5e-06,38.7  
52.1,2.7e-06,38.6  
52.2,2.4e-06,38.3  
52.3,2.7e-06,38.9  
52.4,3.1e-06,38.4  
52.5,2.3e-06,39.2  
52.6,2.2e-06,39.4  
52.7,2.6e-06,39.4  
52.8,3.4e-06,38.6  
52.9,3.5e-06,39.0  
53.0,2.3e-06,39.2  
53.1,2.1e-06,39.9  
53.2,2.1e-06,39.2  
53.3,2.8e-06,39.6  
53.4,2.2e-06,38.9  
53.5,2.8e-06,39.8  
53.6,2.1e-06,40.0  
53.7,3.3e-06,39.2  
53.8,2.5e-06,39.8  
53.9,2.6e-06,39.8  
54.0,2.5e-06,39.6  
54.1,3.1e-06,39.7  
54.2,2.9e-06,39.9  
54.3,3.4e-06,40.3  
54.4,3.1e-06,39.4  
54.5,3.3e-06,40.3  
54.6,3e-06,39.7  
54.7,2.6e-06,40.3  
54.8,3.5e-06,40.3  
54.9,2.9e-06,40.7  
55.0,2.5e-06,39.7  
55.1,2.8e-06,40.5  
55.2,2.6e-06,40.1  
55.3,2.6e-06,40.6  
55.4,2.3e-06,40.8  
55.5,2e-06,40.2  
55.6,2.6e-06,40.4  
55.7,2.7e-06,41.1  
55.8,2.4e-06,40.3  
55.9,2.1e-06,40.6  
56.0,2.3e-06,41.0  
56.1,3.3e-06,41.1  
56.2,2.8e-06,40.6  
56.3,3e-06,40.9  
56.4,3.3e-06,41.0  
56.5,2.3e-06,41.2  
56.6,3.1e-06,41.3  
56.7,2.3e-06,40.6  
56.8,2.5e-06,40.6  
56.9,2.1e-06,41.9  
57.0,2.7e-06,41.2  
57.1,2.3e-06,40.8  
57.2,3.2e-06,40.9  
57.3,2.7e-06,40.6  
57.4,1.9e-06,40.9  
57.5,2.3e-06,41.3  
57.6,3e-06,41.5  
57.7,2.6e-06,40.7  
57.8,2.2e-06,41.0  
57.9,3.5e-06,41.2  
58.0,2.1e-06,41.4  
58.1,3.2e-06,40.9  
58.2,3.4e-06,41.5  
58.3,2.2e-06,41.5  
58.4,2.9e-06,41.7  
58.5,2e-06,41.5  
58.6,2.5e-06,41.9  
58.7,2.4e-06,41.5  
58.8,2.7e-06,41.8  
58.9,3.3e-06,42.1  
59.0,3.2e-06,41.1  
59.1,3.1e-06,41.7  
59.2,2.4e-06,41.8  
59.3,3.2e-06,41.9  
59.4,2.9e-06,41.5  
59.5,2e-06,41.9  
59.6,2e-06,42.5  
59.7,2.1e-06,41.2  
59.8,3.2e-06,42.7  
59.9,2e-06,41.9  
60.0,2.7e-06,41.7  
60.1,3.4e-06,41.7  
60.2,2.2e-06,41.9  
60.3,2.2e-06,41.9  
60.4,2e-06,42.3  
60.5,3e-06,42.0  
60.6,3e-06,42.2  
60.7,2.7e-06,42.2  
60.8,2.3e-06,43.0  
60.9,3e-06,41.5  
61.0,2.5e-06,42.7  
61.1,2.2e-06,41.7  
61.2,2.3e-06,42.6  
61.3,2.6e-06,42.4  
61.4,2.7e-06,43.2  
61.5,3.3e-06,43.6  
61.6,3.4e-06,42.5  
61.7,2.6e-06,42.3  
61.8,1.9e-06,42.7  
61.9,2.7e-06,43.1  
62.0,1.9e-06,42.5  
62.1,3.1e-06,43.5  
62.2,2.8e-06,42.6  
62.3,3.2e-06,42.7  
62.4,2.4e-06,42.4  
62.5,2.3e-06,43.3  
62.6,2.8e-06,44.1  
62.7,2.5e-06,42.5  
62.8,2.5e-06,43.3  
62.9,3.4e-06,42.1  
63.0,3.4e-06,42.8  
63.1,3.2e-06,43.4  
63.2,3.3e-06,43.7  
63.3,2.4e-06,43.8  
63.4,2.1e-06,43.6  
63.5,3.4e-06,43.2  
63.6,2.9e-06,43.4  
63.7,2.6e-06,44.0  
63.8,3.3e-06,43.0  
63.9,3e-06,44.0  
64.0,3.1e-06,43.6  
64.1,2.7e-06,43.4  
64.2,2.7e-06,43.5  
64.3,2.1e-06,43.9  
64.4,3.4e-06,44.0  
64.5,3.1e-06,43.9  
64.6,2.1e-06,43.4  
64.7,1.9e-06,43.9  
64.8,2.4e-06,44.0  
64.9,2e-06,44.0  
65.0,2e-06,44.4  
65.1,2.6e-06,43.5  
65.2,1.8e-06,43.3  
65.3,2.7e-06,44.1  
65.4,3.2e-06,44.9  
65.5,2.7e-06,44.4  
65.6,2.9e-06,44.1  
65.7,3e-06,44.1  
65.8,2.9e-06,44.2  
65.9,1.9e-06,44.3  
66.0,2.1e-06,44.4  
66.1,2.8e-06,43.8  
66.2,2.4e-06,45.1  
66.3,1.9e-06,44.3  
66.4,2e-06,44.2  
66.5,3.2e-06,44.0  
66.6,2.2e-06,44.4  
66.7,2.4e-06,44.3  
66.8,2.7e-06,44.2  
66.9,2.1e-06,45.1  
67.0,1.9e-06,44.3  
67.1,2.9e-06,44.3  
67.2,3e-06,45.0  
67.3,2.9e-06,44.5  
67.4,2e-06,45.3  
67.5,2.8e-06,45.8  
67.6,3.2e-06,44.6  
67.7,3.3e-06,45.1  
67.8,2.5e-06,45.1  
67.9,2.6e-06,44.9  
68.0,3.1e-06,44.8  
68.1,3.2e-06,44.5  
68.2,2.7e-06,44.7  
68.3,2.9e-06,44.8  
68.4,2.6e-06,45.9  
68.5,2.5e-06,44.1  
68.6,2e-06,43.9  
68.7,3.2e-06,44.5  
68.8,2.7e-06,45.2  
68.9,2.2e-06,45.8  
69.0,2.7e-06,46.2  
69.1,2.8e-06,45.2  
69.2,2.8e-06,45.0  
69.3,1.9e-06,45.4  
69.4,2.6e-06,45.0  
69.5,2.7e-06,45.8  
69.6,2.9e-06,46.6  
69.7,2.6e-06,45.8  
69.8,2.6e-06,44.9  
69.9,2.6e-06,45.1  
70.0,2.4e-06,45.6  
70.1,2e-06,45.4  
70.2,2.6e-06,46.4  
70.3,2.9e-06,45.5  
70.4,1.8e-06,46.1  
70.5,1.8e-06,45.4  
70.6,2.6e-06,45.9  
70.7,2.2e-06,45.6  
70.8,1.8e-06,45.2  
70.9,2.1e-06,45.7  
71.0,1.9e-06,44.5  
71.1,2.3e-06,45.3  
71.2,2.6e-06,45.2  
71.3,2.7e-06,45.8  
71.4,2.6e-06,45.4  
71.5,3.1e-06,44.9  
71.6,2.9e-06,46.1  
71.7,2.5e-06,46.5  
71.8,2.4e-06,45.2  
71.9,2.8e-06,46.9  
72.0,2.8e-06,46.6  
72.1,2.3e-06,45.8  
72.2,2.4e-06,45.6  
72.3,2.5e-06,46.4  
72.4,2.8e-06,45.7  
72.5,2.5e-06,46.3  
72.6,2.2e-06,46.5  
72.7,2.6e-06,46.5  
72.8,2.1e-06,45.6  
72.9,2.7e-06,45.5  
73.0,2.4e-06,45.0  
73.1,3.1e-06,46.1  
73.2,2.1e-06,46.6  
73.3,2.3e-06,46.1  
73.4,2.5e-06,45.4  
73.5,2.9e-06,46.9  
73.6,3.1e-06,46.9  
73.7,2.7e-06,46.9  
73.8,3e-06,47.6  
73.9,2.5e-06,47.0  
74.0,2e-06,46.7  
74.1,1.9e-06,46.2  
74.2,3e-06,46.3  
74.3,2.1e-06,46.5  
74.4,2.7e-06,47.1  
74.5,1.7e-06,46.1  
74.6,3e-06,45.8  
74.7,2.1e-06,47.1  
74.8,2.9e-06,46.9  
74.9,2.1e-06,46.3  
75.0,3e-06,46.3  
75.1,2.4e-06,46.5  
75.2,1.8e-06,46.3  
75.3,2.3e-06,46.7  
75.4,2.7e-06,47.1  
75.5,2.3e-06,47.3  
75.6,1.8e-06,46.5  
75.7,2.8e-06,46.5  
75.8,1.8e-06,47.2  
75.9,2.3e-06,46.8  
76.0,2.2e-06,46.8  
76.1,2.1e-06,46.9  
76.2,2.7e-06,46.4  
76.3,2.1e-06,46.7  
76.4,2.1e-06,47.1  
76.5,1.7e-06,46.0  
76.6,2.4e-06,46.3  
76.7,2.3e-06,46.5  
76.8,1.9e-06,46.6  
76.9,1.8e-06,46.3  
77.0,3e-06,46.6  
77.1,2.8e-06,46.6  
77.2,2.3e-06,46.3  
77.3,2.2e-06,47.2  
77.4,2.7e-06,46.2  
77.5,1.9e-06,46.7  
77.6,1.9e-06,46.9  
77.7,1.7e-06,46.7  
77.8,1.8e-06,46.5  
77.9,2.3e-06,46.6  
78.0,2.2e-06,47.2  
78.1,2.9e-06,46.9  
78.2,2.2e-06,46.1  
78.3,2.2e-06,47.3  
78.4,2.5e-06,46.7  
78.5,2e-06,46.7  
78.6,1.7e-06,46.7  
78.7,2.7e-06,45.8  
78.8,2.8e-06,46.6  
78.9,2.9e-06,46.8  
79.0,2.8e-06,46.4  
79.1,2.6e-06,45.8  
79.2,1.8e-06,47.0  
79.3,2.4e-06,46.7  
79.4,1.6e-06,46.7  
79.5,2.6e-06,46.2  
79.6,2.3e-06,47.0  
79.7,2.8e-06,47.6  
79.8,1.9e-06,46.7  
79.9,2.8e-06,47.7  
80.0,2.4e-06,46.8  
80.1,2.1e-06,47.0  
80.2,2.6e-06,46.5  
80.3,2.2e-06,45.9  
80.4,2.8e-06,46.1  
80.5,2.1e-06,46.3  
80.6,2.4e-06,47.5  
80.7,2.6e-06,47.1  
80.8,2.7e-06,47.1  
80.9,2e-06,46.7  
81.0,1.8e-06,47.5  
81.1,2.6e-06,47.5  
81.2,2.5e-06,47.5  
81.3,2.7e-06,47.0  
81.4,1.7e-06,47.4  
81.5,2.5e-06,46.7  
81.6,2.7e-06,47.1  
81.7,2.1e-06,48.3  
81.8,1.7e-06,46.9  
81.9,1.8e-06,48.2  
82.0,2.1e-06,47.4  
82.1,1.7e-06,46.7  
82.2,2.4e-06,46.6  
82.3,2.3e-06,46.8  
82.4,2.6e-06,47.1  
82.5,2.7e-06,46.8  
82.6,2.5e-06,46.8  
82.7,2.4e-06,48.3  
82.8,2.7e-06,47.4  
82.9,2.7e-06,47.3  
83.0,2.1e-06,47.1  
83.1,1.7e-06,47.8  
83.2,2e-06,46.5  
83.3,2e-06,47.9  
83.4,2.4e-06,47.6  
83.5,1.7e-06,47.6  
83.6,1.6e-06,47.7  
83.7,1.7e-06,47.4  
83.8,2.1e-06,47.6  
83.9,2.4e-06,46.4  
84.0,1.8e-06,47.3  
84.1,2e-06,47.2  
84.2,2.8e-06,47.3  
84.3,2.3e-06,46.7  
84.4,2.4e-06,47.0  
84.5,2.6e-06,46.6  
84.6,1.9e-06,46.6  
84.7,2.6e-06,47.8  
84.8,2.5e-06,46.9  
84.9,2.1e-06,47.9  
85.0,1.5e-06,46.1  
85.1,2.2e-06,47.9  
85.2,2.1e-06,47.2  
85.3,2e-06,46.7  
85.4,2.1e-06,46.9  
85.5,2.4e-06,46.7  
85.6,2.7e-06,47.7  
85.7,1.8e-06,47.0  
85.8,1.6e-06,47.0  
85.9,1.6e-06,46.9  
86.0,1.6e-06,47.0  
86.1,2.7e-06,47.3  
86.2,2e-06,48.2  
86.3,1.7e-06,46.7  
86.4,2.6e-06,46.5  
86.5,2.5e-06,46.6  
86.6,1.7e-06,47.6  
86.7,1.6e-06,47.2  
86.8,1.7e-06,47.3  
86.9,1.9e-06,46.8  
87.0,2.2e-06,46.9  
87.1,2e-06,47.3  
87.2,2.2e-06,46.6  
87.3,2e-06,46.8  
87.4,1.9e-06,47.0  
87.5,1.9e-06,47.3  
87.6,2.2e-06,46.6  
87.7,2e-06,46.6  
87.8,1.6e-06,46.3  
87.9,2.3e-06,47.1  
88.0,2.7e-06,47.9  
88.1,2.3e-06,46.9  
88.2,1.9e-06,46.9  
88.3,2.5e-06,46.9  
88.4,2.5e-06,47.5  
88.5,2.4e-06,46.7  
88.6,1.9e-06,46.7  
88.7,1.4e-06,46.7  
88.8,2e-06,47.3  
88.9,2.3e-06,48.1  
89.0,2.2e-06,47.4  
89.1,2.2e-06,46.1  
89.2,2.4e-06,46.6  
89.3,1.9e-06,46.5  
89.4,1.8e-06,46.9  
89.5,1.9e-06,46.5  
89.6,1.8e-06,47.2  
89.7,2.2e-06,46.2  
89.8,1.6e-06,46.9  
89.9,1.8e-06,47.3  
90.0,2.2e-06,46.5  
90.1,2.4e-06,46.8  
90.2,1.7e-06,46.0  
90.3,1.6e-06,46.3  
90.4,2.1e-06,47.2  
90.5,1.4e-06,46.2  
90.6,2.5e-06,46.8  
90.7,1.8e-06,46.1  
90.8,2e-06,46.7  
90.9,1.8e-06,46.6  
91.0,1.7e-06,45.7  
91.1,1.7e-06,46.4  
91.2,2.3e-06,45.0  
91.3,1.5e-06,46.3  
91.4,2.1e-06,46.7  
91.5,1.4e-06,46.7  
91.6,1.9e-06,45.9  
91.7,1.8e-06,46.5  
91.8,1.5e-06,45.0  
91.9,2.3e-06,46.5  
92.0,2.2e-06,46.3  
92.1,1.4e-06,45.8  
92.2,2.3e-06,45.9  
92.3,2e-06,45.5  
92.4,1.7e-06,46.1  
92.5,1.8e-06,46.1  
92.6,1.7e-06,46.1  
92.7,1.9e-06,45.9  
92.8,2.2e-06,46.1  
92.9,2.3e-06,45.6  
93.0,1.6e-06,46.0  
93.1,1.9e-06,45.7  
93.2,1.8e-06,45.9  
93.3,1.4e-06,46.7  
93.4,1.4e-06,46.1  
93.5,1.6e-06,45.8  
93.6,2e-06,46.2  
93.7,2.3e-06,45.7  
93.8,1.8e-06,46.3  
93.9,2.3e-06,45.4  
94.0,1.7e-06,46.1  
94.1,1.5e-06,46.0  
94.2,1.7e-06,45.3  
94.3,2.4e-06,46.6  
94.4,2e-06,45.1  
94.5,1.7e-06,45.2  
94.6,1.9e-06,46.0  
94.7,2.1e-06,46.3  
94.8,2.3e-06,44.9  
94.9,1.8e-06,45.6  
95.0,1.4e-06,45.5  
95.1,1.8e-06,45.6  
95.2,2e-06,46.2  
95.3,2.2e-06,45.8  
95.4,2.3e-06,46.1  
95.5,1.4e-06,45.2  
95.6,1.4e-06,45.6  
95.7,2e-06,44.9  
95.8,2.2e-06,45.1  
95.9,2e-06,45.7  
96.0,2e-06,45.4  
96.1,2.4e-06,45.3  
96.2,1.3e-06,44.9  
96.3,2.3e-06,45.2  
96.4,1.5e-06,45.1  
96.5,2.4e-06,45.5  
96.6,1.9e-06,45.7  
96.7,1.6e-06,45.5  
96.8,2.1e-06,45.4  
96.9,1.9e-06,45.3  
97.0,2.2e-06,45.5  
97.1,2.2e-06,45.5  
97.2,2e-06,44.9  
97.3,2.1e-06,44.9  
97.4,2e-06,45.8  
97.5,1.6e-06,44.7  
97.6,1.9e-06,45.2  
97.7,2e-06,45.1  
97.8,1.6e-06,44.4  
97.9,2.2e-06,44.8  
98.0,1.7e-06,45.1  
98.1,2.3e-06,45.7  
98.2,1.5e-06,44.8  
98.3,2.3e-06,44.8  
98.4,1.4e-06,44.2  
98.5,1.7e-06,44.2  
98.6,2.1e-06,44.2  
98.7,2.3e-06,44.5  
98.8,1.6e-06,45.3  
98.9,1.8e-06,45.1  
99.0,1.8e-06,45.7  
99.1,2.1e-06,44.0  
99.2,2.2e-06,44.7  
99.3,1.9e-06,45.0  
99.4,1.5e-06,44.5  
99.5,2.2e-06,44.8  
99.6,1.9e-06,44.7  
99.7,1.4e-06,45.0  
99.8,1.5e-06,44.7  
99.9,2.2e-06,44.8  
100.0,1.4e-06,45.0  
100.1,1.4e-06,44.6