Light travel time can be almost unchanged; see #526

The light travel time routine can survive almost unchanged if instead of
expecting NumPy broadcasting to make up for extra missing dimensions, we
add an extra dimension to the observer’s position before calling, to
avoid NumPy needing to do its own back-to-front dimension matching.

Author: brandon-rhodes

design/broadcasting.py

@@ -8,6 +8,7 @@ def main():
 
     cfltt = _correct_for_light_travel_time   # the original
     #cfltt = _correct_for_light_travel_time2   # possible replacement
+    fcfltt = _correct_for_light_travel_time4   # possible replacement
 
     print('==== One time, one observer, one target ====')
 
@@ -42,15 +43,16 @@ def main():
         # Turn Earth into two observation positions.
         earth = planets['earth']
         earth._at = build_multi_at(earth._at)
+
     observer = earth.at(t)
     print('observer', observer.position.au.shape)
 
     target = planets['mars']
     target._at = build_multi_at(target._at)  # Turn Mars into 2 planets.
     print('target', target.at(t).position.au.shape)
 
-    t = ts.tt(t.tt[:,None])  # What if we add a dimension to t?
-    print('t', t.shape)
+    # t = ts.tt(t.tt[:,None])  # What if we add a dimension to t?
+    # print('t', t.shape)
 
     r, v, t2, light_time = _correct_for_light_travel_time2(observer, target)
     print(t.shape, observer.position.km.shape, '->', r.shape)
@@ -78,8 +80,8 @@ def main():
     target._at = build_multi_at(target._at)  # Turn Mars into 2 planets.
     print('target', target.at(t).position.au.shape)
 
-    t = ts.tt(t.tt[:,None])  # What if we add a dimension to t?
-    print('t', t.shape)
+    # t = ts.tt(t.tt[:,None])  # What if we add a dimension to t?
+    # print('t', t.shape)
 
     r, v, t2, light_time = _correct_for_light_travel_time3(observer, target)
     print(t.shape, observer.position.km.shape, '->', r.shape)
@@ -90,6 +92,52 @@ def main():
     print('Second planet:')
     print(r[:,:,1])
 
+    # Okay, so, the whole problem of broadcasting: is the only reason it
+    # comes up because we have more targets than observers?  What if we
+    # ask folks to expand the observers array dimensions as well, so
+    # that NumPy is never faced with arrays of different numbers of
+    # dimensions, which is what triggers its unfortunate decision to
+    # start matching at the ends of the arrays instead of their
+    # beginnings?
+
+    print('==== N times, one observers, M targets'
+          ' [TRY: EXTRA OBSERVER DIMENSION] ====')
+
+    # So: time has its usual extra dimension to accommodate 4 times.
+    t = ts.utc(2021, 2, 19, 13, [46, 47, 48, 49])
+    planets = load('de421.bsp')
+
+    earth = planets['earth']
+    observer = earth.at(t)
+    print('observer', observer.position.au.shape)
+    print('Supplementing dimensions')
+    observer.position.au = observer.position.au[:,:,None]
+    observer.velocity.au_per_d = observer.velocity.au_per_d[:,:,None]
+    print('observer', observer.position.au.shape)
+
+    target = planets['mars']
+    target._at = build_multi_at(target._at)  # Turn Mars into 2 planets.
+    print('target', target.at(t).position.au.shape)
+
+    # TODO: if we work out how we can expand the time's dimensions, as
+    # in the following line, before earth.at(t) without raising an
+    # exception, then the observer time would not be lacking a dimension
+    # that would need to be expanded in
+
+    t = ts.tt(t.tt[:,None])  # What if we add a dimension to t?
+    # print('t !!!!!!!!!!!!!!', t.shape)
+    # print('t !!!!!!!!!!!!!!', t.whole.shape)
+    # print('t !!!!!!!!!!!!!!', t.tdb_fraction.shape)
+
+    r, v, t2, light_time = _correct_for_light_travel_time4(observer, target)
+    print(t.shape, observer.position.au.shape, '->', r.shape)
+
+    print('Does it look like a second planet 1 AU away at the same 4 times?')
+    print('First planet:')
+    print(r[:,:,0])
+    print('Second planet:')
+    print(r[:,:,1])
+
 offset = array([0, 1])[None,None,:]  # Dimensions: [xyz, time, offset]
 
 def build_multi_at(_at):
@@ -262,6 +310,55 @@ def _correct_for_light_travel_time3(observer, target):
     tvelocity = tvelocity - cvelocity
     return tposition.T, tvelocity.T, t, light_time
 
+# What if the observer had an extra dimension so it matches too?
+
+def _correct_for_light_travel_time4(observer, target):
+    """Return a light-time corrected astrometric position and velocity.
+
+    Given an `observer` that is a `Barycentric` position somewhere in
+    the solar system, compute where in the sky they will see the body
+    `target`, by computing the light-time between them and figuring out
+    where `target` was back when the light was leaving it that is now
+    reaching the eyes or instruments of the `observer`.
+
+    """
+    t = observer.t
+    ts = t.ts
+    whole = t.whole
+    tdb_fraction = t.tdb_fraction
+
+    cposition = observer.position.au
+    cvelocity = observer.velocity.au_per_d
+
+    print('======', cposition.shape)
+    # ?
+    print('tdb_fraction before:', tdb_fraction.shape)
+    tdb_fraction = tdb_fraction[:,None]
+    print('tdb_fraction after:', tdb_fraction.shape)
+
+    tposition, tvelocity, gcrs_position, message = target._at(t)
+
+    distance = length_of(tposition - cposition)
+    light_time0 = 0.0
+    for i in range(10):
+        print('i =', i)
+        light_time = distance / C_AUDAY
+        delta = light_time - light_time0
+        if abs(max(delta)) < 1e-12:
+            break
+
+        # We assume a light travel time of at most a couple of days.  A
+        # longer light travel time would best be split into a whole and
+        # fraction, for adding to the whole and fraction of TDB.
+        t2 = ts.tdb_jd(whole, tdb_fraction - light_time)
+
+        tposition, tvelocity, gcrs_position, message = target._at(t2)
+        distance = length_of(tposition - cposition)
+        light_time0 = light_time
+    else:
+        raise ValueError('light-travel time failed to converge')
+    return tposition - cposition, tvelocity - cvelocity, t, light_time
+
 _reconcile  # So CI will think we used it, whether use above is commented or not
 
 if __name__ == '__main__':