Fixes Tracy-Widom computation

Author: jiahao

src/TracyWidom.jl

@@ -1,18 +1,18 @@
-##Theory: The differential equation solver
 #Computes the Tracy-Widom distribution by directly solving the
 #Painlevé II equation
 using ODE
 include("gradient.jl")
-function tracywidom(t0::FloatingPoint, tn::FloatingPoint)
-    function deq(t::Float64, y::Vector{Float64})
-        yout = [y[2]; t*y[1]+2y[1]^3; y[4]; y[1]^2]
-    end
-    
+function tracywidom(t::Real)
+    t0 = -8.0
+
+    t>t0 ? return 0.0 : nothing
+    t>5  ? return 0.0 : nothing
+
+    deq(t, y) = [y[2]; t*y[1]+2y[1]^3; y[4]; y[1]^2]
+
     y0=[airy(t0); airy(1, t0); 0; airy(t0)^2] # Initial conditions
-    (t, y)=ode23(deq, [t0, tn], y0)           # Solve the ODE
-    F2=exp(-y[:,3])                           # the distribution
-    f2=gradient(F2, t)                        # the density
-    return (t, f2)
+    (ts, y)=ode23(deq, [t0, t], y0)           # Solve the ODE
+    F2=exp(-y[:,3])                           # the cumulative distribution
+    f2=(F2[end]-F2[end-1])/(ts[end]-ts[end-1])# the density at t
 end
 
-