From 479bc60e01ffc260bc66397931dd3973da1f03b0 Mon Sep 17 00:00:00 2001
From: Anton Khirnov <anton@khirnov.net>
Date: Fri, 17 Mar 2023 13:39:09 +0100
Subject: null: fix initial condition for non-zero shift

---
 null.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/null.py b/null.py
index 407987f..c0f08ee 100644
--- a/null.py
+++ b/null.py
@@ -89,8 +89,10 @@ def _null_geodesic_kernel(times, t0, events, pu_t_0,
                           gtX,     gtX_dX,   gtX_dt):
     gtt_0   = gtt(t0, 0.0).flatten()[0]
     gXX_0   = gXX(t0, 0.0).flatten()[0]
+    gtX_0   = gtX(t0, 0.0).flatten()[0]
 
-    pu_X_0 = np.sqrt(-gtt_0 / gXX_0) * pu_t_0
+    term_t = gtX_0 * pu_t_0
+    pu_X_0 = (-term_t + np.sqrt(term_t * term_t - gtt_0 * gXX_0 * pu_t_0 * pu_t_0)) / gXX_0
 
     args = {
         # workaround for older versions of scipy not supporting args for fun
-- 
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