From 163c031d84003b055a4c541338e98f61741098ad Mon Sep 17 00:00:00 2001
From: Anton Khirnov <anton@khirnov.net>
Date: Mon, 15 Aug 2022 16:21:08 +0200
Subject: doublenull: switch from odeint to newer solve_ivp

Use its events feature to terminate integration on grid boundaries.
---
 doublenull.py | 57 +++++++++++++++++++++++++++++++++------------------------
 1 file changed, 33 insertions(+), 24 deletions(-)

diff --git a/doublenull.py b/doublenull.py
index 01264cf..a3f5caf 100644
--- a/doublenull.py
+++ b/doublenull.py
@@ -1,6 +1,6 @@
 import numpy as np
 import scipy.interpolate as interp
-from scipy.integrate import odeint
+from scipy.integrate import solve_ivp
 
 def calc_null_curves(times, spatial_coords, gXX, gXt, gtt):
     """
@@ -29,11 +29,24 @@ def calc_null_curves(times, spatial_coords, gXX, gXt, gtt):
     gXt_interp      = interp.RectBivariateSpline(times, spatial_coords, gXt)
     gtt_interp      = interp.RectBivariateSpline(times, spatial_coords, gtt)
 
-    def _dXdt(coord, t, sign,
-              coord_min = spatial_coords[0], coord_max = spatial_coords[-1],
-              gXX = gXX_interp, gtt = gtt_interp, gXt = gXt_interp):
-        if coord <= coord_min or coord >= coord_max:
-            return float('nan')
+
+    # terminate integration on reaching the outer boundaries
+    def event_x_bound_upper(t, x, sign):
+        return x[0] - spatial_coords[-1]
+    event_x_bound_upper.terminal  = True
+    event_x_bound_upper.direction = 1.0
+
+    def event_x_bound_lower(t, x, sign):
+        return x[0] - spatial_coords[0]
+    event_x_bound_lower.terminal  = True
+    event_x_bound_lower.direction = -1.0
+
+    events = [event_x_bound_upper, event_x_bound_lower]
+
+    # null geodesic equation RHS:
+    #    gXX dX^2 + 2 gXt dX dt - gtt dt^2 = 0
+    # => dx / dt = (-gXt ± √(gXt^2 - gXX gtt)) / gXX
+    def dXdt(t, coord, sign, gXX = gXX_interp, gtt = gtt_interp, gXt = gXt_interp):
         gXt_val = gXt(t, coord)
         gXX_val = gXX(t, coord)
         gtt_val = gtt(t, coord)
@@ -43,24 +56,20 @@ def calc_null_curves(times, spatial_coords, gXX, gXt, gtt):
     rays_neg = np.empty_like(rays_pos)
     for j, X0 in enumerate(spatial_coords):
         for tgt, sign in ((rays_pos, 1.0), (rays_neg, -1.0)):
-            ray = odeint(_dXdt, X0, times, (sign,))[:, 0]
-
-            # clip the rays to the integration area
-            k = 0
-            while np.isnan(ray[k]):
-                k += 1
-            while k > 0:
-                ray[k - 1] = ray[k]
-                k -= 1
-
-            k = ray.shape[0] - 1
-            while np.isnan(ray[k]):
-                k -= 1
-            while k < ray.shape[0] - 1:
-                ray[k + 1] = ray[k]
-                k += 1
-
-            tgt[j] = ray
+            ret = solve_ivp(dXdt, (times[0], times[-1]), (X0,),
+                            method = 'RK45', t_eval = times, args = (sign,),
+                            dense_output = True, events = events, rtol = 1e-6, atol = 1e-8)
+
+            t, x = ret.t, ret.y[0]
+
+            if len(t) < len(times):
+                x_ext = np.empty_like(times)
+                x_ext[:x.shape[0]] = x
+                x_ext[x.shape[0]:] = x[-1] + sign * (times[x.shape[0]:] - t[-1])
+
+                x = x_ext
+
+            tgt[j] = x
 
     return (rays_pos, rays_neg)
 
-- 
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