comp_t0 cubic fits

src/juobs_obs.jl

@@ -140,20 +140,21 @@ function comp_t0(Y::YData, plat::Vector{Int64}; L::Int64, pl::Bool=false, rw::Un
     xmax = size(Ysl, 2)
     nt0 = t0_guess(t, Ysl, plat, L)
     
-    Y_aux = Matrix{uwreal}(undef, xmax, 3)
+    Y_aux = Matrix{uwreal}(undef, xmax, 5)
     for i = 1:xmax
         k = 1
-        for j = nt0-1:nt0+1
+        for j = nt0-2:nt0+2
             Y_aux[i, k] = uwreal(Ysl[:, i, j], id)
             k = k + 1
         end
     end
-    x = t[nt0-1:nt0+1]
-    t2E = [plat_av(Y_aux[:, j], plat) for j=1:3] .* x.^2 / L^3
+    x = t[nt0-2:nt0+2]
+    t2E = [plat_av(Y_aux[:, j], plat) for j=1:5] .* x.^2 / L^3
     
-    par, chi2exp = lin_fit(x, t2E)
-
-    t0 = x_lin_fit(par, 0.3)
+    @. model(x, p) = p[1]*x^3 + p[2]*x^2 + p[3]*x + p[4]
+    par = fit_routine(model, x, t2E, 4)
+    fmin(x, p) = model(x, p) .- 0.3
+    t0 = root_error(fmin, t[nt0], par)
     if pl
         uwerr(t0)
         uwerr.(t2E)
@@ -169,9 +170,8 @@ function comp_t0(Y::YData, plat::Vector{Int64}; L::Int64, pl::Bool=false, rw::Un
         display(gcf())
 
         figure()
-        plot(collect(1:xmax), value.(Y_aux[:, 2]) * t[nt0]^2 / L^3, "x")
-        
-        fill_between(collect(plat[1]:plat[2]), v[2]+e[2], v[2]-e[2], alpha=0.75, color="green")
+        plot(collect(1:xmax), value.(Y_aux[:, 3]) * t[nt0]^2 / L^3, "x") 
+        fill_between(collect(plat[1]:plat[2]), v[3]+e[3], v[3]-e[3], alpha=0.75, color="green")
         ylabel(L"$t^2E(x0, t)$")
         xlabel(L"$x_0/a$")
         title(string(L"$t/a^2 = $", t[nt0]))
@@ -188,7 +188,6 @@ function comp_t0(Y::Vector{YData}, plat::Vector{Int64}; L::Int64, pl::Bool=false
     id = getfield.(Y, :id)
     vtr = getfield.(Y, :vtr)
     replica = length.(vtr)
-    
 
     if !all(id .== id[1])
         println("IDs are not equal")
@@ -196,25 +195,26 @@ function comp_t0(Y::Vector{YData}, plat::Vector{Int64}; L::Int64, pl::Bool=false
     end
 
     Ysl = isnothing(rw) ? Ysl : apply_rw.(Ysl, rw)
-
     tmp = Ysl[1]
     [tmp = cat(tmp, Ysl[k], dims=1) for k = 2:nr]
     nt0 = t0_guess(t, tmp, plat, L)
     xmax = size(tmp, 2)
 
-    Y_aux = Matrix{uwreal}(undef, xmax, 3)
+    Y_aux = Matrix{uwreal}(undef, xmax, 5)
     for i = 1:xmax
         k = 1
-        for j = nt0-1:nt0+1
+        for j = nt0-2:nt0+2
             Y_aux[i, k] = uwreal(tmp[:, i, j], id[1], replica)
             k = k + 1
         end
     end
-    x = t[nt0-1:nt0+1]
-    t2E = [plat_av(Y_aux[:, j], plat) for j=1:3] .* x.^2 / L^3
-    par, chi2exp = lin_fit(x, t2E)
+    x = t[nt0-2:nt0+2]
+    t2E = [plat_av(Y_aux[:, j], plat) for j=1:5] .* x.^2 / L^3
 
-    t0 = x_lin_fit(par, 0.3)
+    @. model(x, p) = p[1]*x^3 + p[2]*x^2 + p[3]*x + p[4]
+    par = fit_routine(model, x, t2E, 4)
+    fmin(x, p) = model(x, p) .- 0.3
+    t0 = root_error(fmin, t[nt0], par)
     if pl
         uwerr(t0)
         uwerr.(t2E)
@@ -230,8 +230,8 @@ function comp_t0(Y::Vector{YData}, plat::Vector{Int64}; L::Int64, pl::Bool=false
         display(gcf())
 
         figure()
-        plot(collect(1:xmax), value.(Y_aux[:, 2]) * t[nt0]^2 / L^3, "x")
-        fill_between(collect(plat[1]:plat[2]), v[2]+e[2], v[2]-e[2], alpha=0.75, color="green")
+        plot(collect(1:xmax), value.(Y_aux[:, 3]) * t[nt0]^2 / L^3, "x")
+        fill_between(collect(plat[1]:plat[2]), v[3]+e[3], v[3]-e[3], alpha=0.75, color="green")
         ylabel(L"$t^2E(x0, t)$")
         xlabel(L"$x_0/a$")
         title(string(L"$t/a^2 = $", t[nt0]))