broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>=-1, 'translated_east': d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': 2/(1+d['z']) if d['z']>-1 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>0, 'translated_east': d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': 2/(1+d['z']) if d['z']>-1 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

prompt:
The adapter reports an incorrect valid while other fields remain valid.

A supplied direction e,n,z is mapped by a stipulated stereographic sky chart with scale 2/(1+z), valid z>-1. Reference chart origin ox,oy is added only after projection. Exact antipode has no finite chart coordinate; inputs here have z>=-1. Output fields are defined by: plane_east = 2*d['e']/(1+d['z']) if d['z']>-1 else None; plane_north = 2*d['n']/(1+d['z']) if d['z']>-1 else None; valid = d['z']>-1; translated_east = d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None; translated_north = d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None; radial_scale = 2/(1+d['z']) if d['z']>-1 else None

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>-1, 'translated_east': 2*(d['ox']+d['e'])/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': 2/(1+d['z']) if d['z']>-1 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

meaning: Fixture-count band, not measured model difficulty

deps: stdlib

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>-1, 'translated_east': d['ox']+d['e']/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': 2/(1+d['z']) if d['z']>-1 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

prompt:
The adapter reports an incorrect translated east while other fields remain valid.

A supplied direction e,n,z is mapped by a stipulated stereographic sky chart with scale 2/(1+z), valid z>-1. Reference chart origin ox,oy is added only after projection. Exact antipode has no finite chart coordinate; inputs here have z>=-1. Output fields are defined by: plane_east = 2*d['e']/(1+d['z']) if d['z']>-1 else None; plane_north = 2*d['n']/(1+d['z']) if d['z']>-1 else None; valid = d['z']>-1; translated_east = d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None; translated_north = d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None; radial_scale = 2/(1+d['z']) if d['z']>-1 else None

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>-1, 'translated_east': d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['ox']+2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': 2/(1+d['z']) if d['z']>-1 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>-1, 'translated_east': d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['oy']-2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': 2/(1+d['z']) if d['z']>-1 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

prompt:
The adapter reports an incorrect translated north while other fields remain valid.

A supplied direction e,n,z is mapped by a stipulated stereographic sky chart with scale 2/(1+z), valid z>-1. Reference chart origin ox,oy is added only after projection. Exact antipode has no finite chart coordinate; inputs here have z>=-1. Output fields are defined by: plane_east = 2*d['e']/(1+d['z']) if d['z']>-1 else None; plane_north = 2*d['n']/(1+d['z']) if d['z']>-1 else None; valid = d['z']>-1; translated_east = d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None; translated_north = d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None; radial_scale = 2/(1+d['z']) if d['z']>-1 else None

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>-1, 'translated_east': d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': (1+d['z'])/2}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'plane_east': 2*d['e']/(1+d['z']) if d['z']>-1 else None, 'plane_north': 2*d['n']/(1+d['z']) if d['z']>-1 else None, 'valid': d['z']>-1, 'translated_east': d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None, 'translated_north': d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None, 'radial_scale': 1/(1+d['z']) if d['z']>-1 else None}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'e': 2, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 12.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 2, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 2, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 2, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 2.6666666666666665, 'plane_north': 4.0, 'valid': True, 'translated_east': 12.666666666666666, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 2, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 2.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 2.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 2, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 2: [({'e': 3, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 13.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 3, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 3, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 3, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 3, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 3.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 3.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 3, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 3: [({'e': 4, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 14.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 4, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 4, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 4, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 5.333333333333333, 'plane_north': 4.0, 'valid': True, 'translated_east': 15.333333333333332, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 4, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 4.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 4.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 4, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 16.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 26.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 4: [({'e': 5, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 15.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 5, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 10.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 20.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 5, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 5, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 6.666666666666667, 'plane_north': 4.0, 'valid': True, 'translated_east': 16.666666666666668, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 5, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 5.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 5.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 5, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 20.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 30.0, 'translated_north': 12.0, 'radial_scale': 4.0})], 5: [({'e': 6, 'n': 3, 'z': 1, 'ox': 10, 'oy': 20}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 16.0, 'translated_north': 23.0, 'radial_scale': 1.0}), ({'e': 6, 'n': 3, 'z': 0, 'ox': 10, 'oy': 20}, {'plane_east': 12.0, 'plane_north': 6.0, 'valid': True, 'translated_east': 22.0, 'translated_north': 26.0, 'radial_scale': 2.0}), ({'e': 6, 'n': 3, 'z': -1, 'ox': 10, 'oy': 20}, {'plane_east': None, 'plane_north': None, 'valid': False, 'translated_east': None, 'translated_north': None, 'radial_scale': None}), ({'e': 6, 'n': 3, 'z': 0.5, 'ox': 10, 'oy': 20}, {'plane_east': 8.0, 'plane_north': 4.0, 'valid': True, 'translated_east': 18.0, 'translated_north': 24.0, 'radial_scale': 1.3333333333333333}), ({'e': 6, 'n': 3, 'z': 1, 'ox': 0, 'oy': 0}, {'plane_east': 6.0, 'plane_north': 3.0, 'valid': True, 'translated_east': 6.0, 'translated_north': 3.0, 'radial_scale': 1.0}), ({'e': 6, 'n': -2, 'z': -0.5, 'ox': 10, 'oy': 20}, {'plane_east': 24.0, 'plane_north': -8.0, 'valid': True, 'translated_east': 34.0, 'translated_north': 12.0, 'radial_scale': 4.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

prompt:
The adapter reports an incorrect radial scale while other fields remain valid.

A supplied direction e,n,z is mapped by a stipulated stereographic sky chart with scale 2/(1+z), valid z>-1. Reference chart origin ox,oy is added only after projection. Exact antipode has no finite chart coordinate; inputs here have z>=-1. Output fields are defined by: plane_east = 2*d['e']/(1+d['z']) if d['z']>-1 else None; plane_north = 2*d['n']/(1+d['z']) if d['z']>-1 else None; valid = d['z']>-1; translated_east = d['ox']+2*d['e']/(1+d['z']) if d['z']>-1 else None; translated_north = d['oy']+2*d['n']/(1+d['z']) if d['z']>-1 else None; radial_scale = 2/(1+d['z']) if d['z']>-1 else None

split: open-access


evaluation_group: astro-slit-sky-coordinate

prompt:
The adapter reports an incorrect along slit while other fields remain valid.

A spectrograph slit has supplied sine s and cosine c of position angle east of north. Sky offsets east E,north N map along slit E*s+N*c and across E*c-N*s. Slit scale a converts angle to detector pixels; spatial reference r and nod offset q are separate. Output fields are defined by: along_slit = d['E']*d['s']+d['N']*d['c']; across_slit = d['E']*d['c']-d['N']*d['s']; spatial_pixel = d['r']+(d['E']*d['s']+d['N']*d['c'])/d['a']; nodded_along = d['E']*d['s']+d['N']*d['c']-d['q']; nod_east = d['q']*d['s']; nod_north = d['q']*d['c']

split: open-access


evaluation_group: astro-slit-sky-coordinate

prompt:
The adapter reports an incorrect across slit while other fields remain valid.

A spectrograph slit has supplied sine s and cosine c of position angle east of north. Sky offsets east E,north N map along slit E*s+N*c and across E*c-N*s. Slit scale a converts angle to detector pixels; spatial reference r and nod offset q are separate. Output fields are defined by: along_slit = d['E']*d['s']+d['N']*d['c']; across_slit = d['E']*d['c']-d['N']*d['s']; spatial_pixel = d['r']+(d['E']*d['s']+d['N']*d['c'])/d['a']; nodded_along = d['E']*d['s']+d['N']*d['c']-d['q']; nod_east = d['q']*d['s']; nod_north = d['q']*d['c']

split: open-access


evaluation_group: astro-slit-sky-coordinate

prompt:
The adapter reports an incorrect spatial pixel while other fields remain valid.

A spectrograph slit has supplied sine s and cosine c of position angle east of north. Sky offsets east E,north N map along slit E*s+N*c and across E*c-N*s. Slit scale a converts angle to detector pixels; spatial reference r and nod offset q are separate. Output fields are defined by: along_slit = d['E']*d['s']+d['N']*d['c']; across_slit = d['E']*d['c']-d['N']*d['s']; spatial_pixel = d['r']+(d['E']*d['s']+d['N']*d['c'])/d['a']; nodded_along = d['E']*d['s']+d['N']*d['c']-d['q']; nod_east = d['q']*d['s']; nod_north = d['q']*d['c']

split: open-access


evaluation_group: astro-slit-sky-coordinate

prompt:
The adapter reports an incorrect nodded along while other fields remain valid.

A spectrograph slit has supplied sine s and cosine c of position angle east of north. Sky offsets east E,north N map along slit E*s+N*c and across E*c-N*s. Slit scale a converts angle to detector pixels; spatial reference r and nod offset q are separate. Output fields are defined by: along_slit = d['E']*d['s']+d['N']*d['c']; across_slit = d['E']*d['c']-d['N']*d['s']; spatial_pixel = d['r']+(d['E']*d['s']+d['N']*d['c'])/d['a']; nodded_along = d['E']*d['s']+d['N']*d['c']-d['q']; nod_east = d['q']*d['s']; nod_north = d['q']*d['c']

split: open-access


evaluation_group: astro-slit-sky-coordinate

prompt:
The adapter reports an incorrect nod east while other fields remain valid.

A spectrograph slit has supplied sine s and cosine c of position angle east of north. Sky offsets east E,north N map along slit E*s+N*c and across E*c-N*s. Slit scale a converts angle to detector pixels; spatial reference r and nod offset q are separate. Output fields are defined by: along_slit = d['E']*d['s']+d['N']*d['c']; across_slit = d['E']*d['c']-d['N']*d['s']; spatial_pixel = d['r']+(d['E']*d['s']+d['N']*d['c'])/d['a']; nodded_along = d['E']*d['s']+d['N']*d['c']-d['q']; nod_east = d['q']*d['s']; nod_north = d['q']*d['c']

split: open-access


evaluation_group: astro-slit-sky-coordinate

prompt:
The adapter reports an incorrect nod north while other fields remain valid.

A spectrograph slit has supplied sine s and cosine c of position angle east of north. Sky offsets east E,north N map along slit E*s+N*c and across E*c-N*s. Slit scale a converts angle to detector pixels; spatial reference r and nod offset q are separate. Output fields are defined by: along_slit = d['E']*d['s']+d['N']*d['c']; across_slit = d['E']*d['c']-d['N']*d['s']; spatial_pixel = d['r']+(d['E']*d['s']+d['N']*d['c'])/d['a']; nodded_along = d['E']*d['s']+d['N']*d['c']-d['q']; nod_east = d['q']*d['s']; nod_north = d['q']*d['c']

split: open-access


evaluation_group: astro-polarization-sky-position-angle

prompt:
The adapter reports an incorrect sky q while other fields remain valid.

Stokes Q,U rotate from instrument to sky with supplied c=cos(2theta),s=sin(2theta), so Qsky=cQ-sU and Usky=sQ+cU. Instrument mirror reverses U and V; I stays invariant. This model accepts exact supplied trigonometric values and does not infer astronomical angle zero points. Output fields are defined by: sky_q = d['c']*d['Q']-d['s']*d['U']; sky_u = d['s']*d['Q']+d['c']*d['U']; mirror_u = -d['U'] if d['mirror'] else d['U']; mirror_v = -d['V'] if d['mirror'] else d['V']; linear_power = d['Q']**2+d['U']**2; inverse_q = d['c']*d['Q']+d['s']*d['U']

split: open-access


evaluation_group: astro-polarization-sky-position-angle

prompt:
The adapter reports an incorrect sky u while other fields remain valid.

Stokes Q,U rotate from instrument to sky with supplied c=cos(2theta),s=sin(2theta), so Qsky=cQ-sU and Usky=sQ+cU. Instrument mirror reverses U and V; I stays invariant. This model accepts exact supplied trigonometric values and does not infer astronomical angle zero points. Output fields are defined by: sky_q = d['c']*d['Q']-d['s']*d['U']; sky_u = d['s']*d['Q']+d['c']*d['U']; mirror_u = -d['U'] if d['mirror'] else d['U']; mirror_v = -d['V'] if d['mirror'] else d['V']; linear_power = d['Q']**2+d['U']**2; inverse_q = d['c']*d['Q']+d['s']*d['U']

split: open-access


evaluation_group: astro-polarization-sky-position-angle

prompt:
The adapter reports an incorrect mirror u while other fields remain valid.

Stokes Q,U rotate from instrument to sky with supplied c=cos(2theta),s=sin(2theta), so Qsky=cQ-sU and Usky=sQ+cU. Instrument mirror reverses U and V; I stays invariant. This model accepts exact supplied trigonometric values and does not infer astronomical angle zero points. Output fields are defined by: sky_q = d['c']*d['Q']-d['s']*d['U']; sky_u = d['s']*d['Q']+d['c']*d['U']; mirror_u = -d['U'] if d['mirror'] else d['U']; mirror_v = -d['V'] if d['mirror'] else d['V']; linear_power = d['Q']**2+d['U']**2; inverse_q = d['c']*d['Q']+d['s']*d['U']

split: open-access


evaluation_group: astro-polarization-sky-position-angle

prompt:
The adapter reports an incorrect mirror v while other fields remain valid.

Stokes Q,U rotate from instrument to sky with supplied c=cos(2theta),s=sin(2theta), so Qsky=cQ-sU and Usky=sQ+cU. Instrument mirror reverses U and V; I stays invariant. This model accepts exact supplied trigonometric values and does not infer astronomical angle zero points. Output fields are defined by: sky_q = d['c']*d['Q']-d['s']*d['U']; sky_u = d['s']*d['Q']+d['c']*d['U']; mirror_u = -d['U'] if d['mirror'] else d['U']; mirror_v = -d['V'] if d['mirror'] else d['V']; linear_power = d['Q']**2+d['U']**2; inverse_q = d['c']*d['Q']+d['s']*d['U']

split: open-access


evaluation_group: astro-polarization-sky-position-angle

prompt:
The adapter reports an incorrect linear power while other fields remain valid.

Stokes Q,U rotate from instrument to sky with supplied c=cos(2theta),s=sin(2theta), so Qsky=cQ-sU and Usky=sQ+cU. Instrument mirror reverses U and V; I stays invariant. This model accepts exact supplied trigonometric values and does not infer astronomical angle zero points. Output fields are defined by: sky_q = d['c']*d['Q']-d['s']*d['U']; sky_u = d['s']*d['Q']+d['c']*d['U']; mirror_u = -d['U'] if d['mirror'] else d['U']; mirror_v = -d['V'] if d['mirror'] else d['V']; linear_power = d['Q']**2+d['U']**2; inverse_q = d['c']*d['Q']+d['s']*d['U']

split: open-access


evaluation_group: astro-polarization-sky-position-angle

prompt:
The adapter reports an incorrect inverse q while other fields remain valid.

Stokes Q,U rotate from instrument to sky with supplied c=cos(2theta),s=sin(2theta), so Qsky=cQ-sU and Usky=sQ+cU. Instrument mirror reverses U and V; I stays invariant. This model accepts exact supplied trigonometric values and does not infer astronomical angle zero points. Output fields are defined by: sky_q = d['c']*d['Q']-d['s']*d['U']; sky_u = d['s']*d['Q']+d['c']*d['U']; mirror_u = -d['U'] if d['mirror'] else d['U']; mirror_v = -d['V'] if d['mirror'] else d['V']; linear_power = d['Q']**2+d['U']**2; inverse_q = d['c']*d['Q']+d['s']*d['U']

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'radial_distance': d['r'], 'tangential_displacement': d['u']*d['t'], 'direction_tangent': d['x']+d['u']*d['t']/(d['r']+d['v']*d['t']), 'angular_rate': d['u']*d['r']/(d['r']+d['v']*d['t'])**2, 'radial_fraction': d['v']*d['t']/d['r'], 'initial_angular_acceleration': -2*d['u']*d['v']/d['r']**2}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'r': 20, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.10416666666666667, 'radial_fraction': 0.2, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 20, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': -3, 'direction_tangent': 4.833333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': 6, 'direction_tangent': 5.333333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': 0.015}), ({'r': 20, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.2, 'initial_angular_acceleration': 0.0})], 2: [({'r': 21, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 25, 'tangential_displacement': 6, 'direction_tangent': 5.24, 'angular_rate': 0.1008, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 21, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': -3, 'direction_tangent': 4.842105263157895, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': 6, 'direction_tangent': 5.315789473684211, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': 0.013605442176870748}), ({'r': 21, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 25, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': 0.0})], 3: [({'r': 22, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 26, 'tangential_displacement': 6, 'direction_tangent': 5.230769230769231, 'angular_rate': 0.09763313609467456, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 22, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': -3, 'direction_tangent': 4.85, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': 0.012396694214876033}), ({'r': 22, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 26, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': 0.0})], 4: [({'r': 23, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 27, 'tangential_displacement': 6, 'direction_tangent': 5.222222222222222, 'angular_rate': 0.09465020576131687, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 6, 'direction_tangent': 5.260869565217392, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 23, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': -3, 'direction_tangent': 4.857142857142857, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': 0.011342155009451797}), ({'r': 23, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 27, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': 0.0})], 5: [({'r': 24, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 28, 'tangential_displacement': 6, 'direction_tangent': 5.214285714285714, 'angular_rate': 0.09183673469387756, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 24, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': -3, 'direction_tangent': 4.863636363636363, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': 0.010416666666666666}), ({'r': 24, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 28, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': 0.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

evaluation_group: astro-astrometric-perspective-transport

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'radial_distance': d['r']-d['v']*d['t'], 'tangential_displacement': d['u']*d['t'], 'direction_tangent': d['x']+d['u']*d['t']/(d['r']+d['v']*d['t']), 'angular_rate': d['u']*d['r']/(d['r']+d['v']*d['t'])**2, 'radial_fraction': d['v']*d['t']/d['r'], 'initial_angular_acceleration': -2*d['u']*d['v']/d['r']**2}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'r': 20, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.10416666666666667, 'radial_fraction': 0.2, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 20, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': -3, 'direction_tangent': 4.833333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': 6, 'direction_tangent': 5.333333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': 0.015}), ({'r': 20, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.2, 'initial_angular_acceleration': 0.0})], 2: [({'r': 21, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 25, 'tangential_displacement': 6, 'direction_tangent': 5.24, 'angular_rate': 0.1008, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 21, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': -3, 'direction_tangent': 4.842105263157895, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': 6, 'direction_tangent': 5.315789473684211, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': 0.013605442176870748}), ({'r': 21, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 25, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': 0.0})], 3: [({'r': 22, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 26, 'tangential_displacement': 6, 'direction_tangent': 5.230769230769231, 'angular_rate': 0.09763313609467456, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 22, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': -3, 'direction_tangent': 4.85, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': 0.012396694214876033}), ({'r': 22, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 26, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': 0.0})], 4: [({'r': 23, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 27, 'tangential_displacement': 6, 'direction_tangent': 5.222222222222222, 'angular_rate': 0.09465020576131687, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 6, 'direction_tangent': 5.260869565217392, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 23, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': -3, 'direction_tangent': 4.857142857142857, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': 0.011342155009451797}), ({'r': 23, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 27, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': 0.0})], 5: [({'r': 24, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 28, 'tangential_displacement': 6, 'direction_tangent': 5.214285714285714, 'angular_rate': 0.09183673469387756, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 24, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': -3, 'direction_tangent': 4.863636363636363, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': 0.010416666666666666}), ({'r': 24, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 28, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': 0.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

prompt:
The adapter reports an incorrect radial distance while other fields remain valid.

A finite one-axis astrometric model has initial distance r>0, radial speed v, tangential speed u, elapsed t, and tangent origin x. New distance R=r+v*t remains positive for all fixtures. Direction tangent is x+u*t/R, and apparent angular rate is u*r/R**2; this is a rectilinear perspective model. Output fields are defined by: radial_distance = d['r']+d['v']*d['t']; tangential_displacement = d['u']*d['t']; direction_tangent = d['x']+d['u']*d['t']/(d['r']+d['v']*d['t']); angular_rate = d['u']*d['r']/(d['r']+d['v']*d['t'])**2; radial_fraction = d['v']*d['t']/d['r']; initial_angular_acceleration = -2*d['u']*d['v']/d['r']**2

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'radial_distance': d['r']+d['v']*d['t'], 'tangential_displacement': d['u']*d['t']/d['r'], 'direction_tangent': d['x']+d['u']*d['t']/(d['r']+d['v']*d['t']), 'angular_rate': d['u']*d['r']/(d['r']+d['v']*d['t'])**2, 'radial_fraction': d['v']*d['t']/d['r'], 'initial_angular_acceleration': -2*d['u']*d['v']/d['r']**2}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'r': 20, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.10416666666666667, 'radial_fraction': 0.2, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 20, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': -3, 'direction_tangent': 4.833333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': 6, 'direction_tangent': 5.333333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': 0.015}), ({'r': 20, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.2, 'initial_angular_acceleration': 0.0})], 2: [({'r': 21, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 25, 'tangential_displacement': 6, 'direction_tangent': 5.24, 'angular_rate': 0.1008, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 21, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': -3, 'direction_tangent': 4.842105263157895, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': 6, 'direction_tangent': 5.315789473684211, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': 0.013605442176870748}), ({'r': 21, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 25, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': 0.0})], 3: [({'r': 22, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 26, 'tangential_displacement': 6, 'direction_tangent': 5.230769230769231, 'angular_rate': 0.09763313609467456, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 22, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': -3, 'direction_tangent': 4.85, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': 0.012396694214876033}), ({'r': 22, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 26, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': 0.0})], 4: [({'r': 23, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 27, 'tangential_displacement': 6, 'direction_tangent': 5.222222222222222, 'angular_rate': 0.09465020576131687, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 6, 'direction_tangent': 5.260869565217392, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 23, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': -3, 'direction_tangent': 4.857142857142857, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': 0.011342155009451797}), ({'r': 23, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 27, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': 0.0})], 5: [({'r': 24, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 28, 'tangential_displacement': 6, 'direction_tangent': 5.214285714285714, 'angular_rate': 0.09183673469387756, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 24, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': -3, 'direction_tangent': 4.863636363636363, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': 0.010416666666666666}), ({'r': 24, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 28, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': 0.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

evaluation_group: astro-astrometric-perspective-transport

source:
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'radial_distance': d['r']+d['v']*d['t'], 'tangential_displacement': d['u'], 'direction_tangent': d['x']+d['u']*d['t']/(d['r']+d['v']*d['t']), 'angular_rate': d['u']*d['r']/(d['r']+d['v']*d['t'])**2, 'radial_fraction': d['v']*d['t']/d['r'], 'initial_angular_acceleration': -2*d['u']*d['v']/d['r']**2}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'r': 20, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.10416666666666667, 'radial_fraction': 0.2, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 20, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.15, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': -3, 'direction_tangent': 4.833333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': -0.03}), ({'r': 20, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 18, 'tangential_displacement': 6, 'direction_tangent': 5.333333333333333, 'angular_rate': 0.18518518518518517, 'radial_fraction': -0.1, 'initial_angular_acceleration': 0.015}), ({'r': 20, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.2, 'initial_angular_acceleration': 0.0})], 2: [({'r': 21, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 25, 'tangential_displacement': 6, 'direction_tangent': 5.24, 'angular_rate': 0.1008, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 21, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.14285714285714285, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': -3, 'direction_tangent': 4.842105263157895, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': -0.027210884353741496}), ({'r': 21, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 19, 'tangential_displacement': 6, 'direction_tangent': 5.315789473684211, 'angular_rate': 0.1745152354570637, 'radial_fraction': -0.09523809523809523, 'initial_angular_acceleration': 0.013605442176870748}), ({'r': 21, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 25, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.19047619047619047, 'initial_angular_acceleration': 0.0})], 3: [({'r': 22, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 26, 'tangential_displacement': 6, 'direction_tangent': 5.230769230769231, 'angular_rate': 0.09763313609467456, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 22, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13636363636363635, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': -3, 'direction_tangent': 4.85, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': -0.024793388429752067}), ({'r': 22, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 20, 'tangential_displacement': 6, 'direction_tangent': 5.3, 'angular_rate': 0.165, 'radial_fraction': -0.09090909090909091, 'initial_angular_acceleration': 0.012396694214876033}), ({'r': 22, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 26, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.18181818181818182, 'initial_angular_acceleration': 0.0})], 4: [({'r': 23, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 27, 'tangential_displacement': 6, 'direction_tangent': 5.222222222222222, 'angular_rate': 0.09465020576131687, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 6, 'direction_tangent': 5.260869565217392, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 23, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 23, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.13043478260869565, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': -3, 'direction_tangent': 4.857142857142857, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': -0.022684310018903593}), ({'r': 23, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 21, 'tangential_displacement': 6, 'direction_tangent': 5.285714285714286, 'angular_rate': 0.1564625850340136, 'radial_fraction': -0.08695652173913043, 'initial_angular_acceleration': 0.011342155009451797}), ({'r': 23, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 27, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.17391304347826086, 'initial_angular_acceleration': 0.0})], 5: [({'r': 24, 'v': 2, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 28, 'tangential_displacement': 6, 'direction_tangent': 5.214285714285714, 'angular_rate': 0.09183673469387756, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 0, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 6, 'direction_tangent': 5.25, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': 0.0}), ({'r': 24, 'v': 2, 'u': 3, 't': 0, 'x': 5}, {'radial_distance': 24, 'tangential_displacement': 0, 'direction_tangent': 5.0, 'angular_rate': 0.125, 'radial_fraction': 0.0, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': 2, 'u': 3, 't': -1, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': -3, 'direction_tangent': 4.863636363636363, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': -0.020833333333333332}), ({'r': 24, 'v': -1, 'u': 3, 't': 2, 'x': 5}, {'radial_distance': 22, 'tangential_displacement': 6, 'direction_tangent': 5.2727272727272725, 'angular_rate': 0.1487603305785124, 'radial_fraction': -0.08333333333333333, 'initial_angular_acceleration': 0.010416666666666666}), ({'r': 24, 'v': 2, 'u': 0, 't': 2, 'x': 0}, {'radial_distance': 28, 'tangential_displacement': 0, 'direction_tangent': 0.0, 'angular_rate': 0.0, 'radial_fraction': 0.16666666666666666, 'initial_angular_acceleration': 0.0})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

prompt:
The adapter reports an incorrect tangential displacement while other fields remain valid.

A finite one-axis astrometric model has initial distance r>0, radial speed v, tangential speed u, elapsed t, and tangent origin x. New distance R=r+v*t remains positive for all fixtures. Direction tangent is x+u*t/R, and apparent angular rate is u*r/R**2; this is a rectilinear perspective model. Output fields are defined by: radial_distance = d['r']+d['v']*d['t']; tangential_displacement = d['u']*d['t']; direction_tangent = d['x']+d['u']*d['t']/(d['r']+d['v']*d['t']); angular_rate = d['u']*d['r']/(d['r']+d['v']*d['t'])**2; radial_fraction = d['v']*d['t']/d['r']; initial_angular_acceleration = -2*d['u']*d['v']/d['r']**2

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