def testOffsetSmall(self):
"""Test offset, angularSeparation and orientationTo for small offsets not too near the pole
In this regime delta-long = dist along long / cos(lat) is a reasonable approximation
but I have no simple way to compute toOrient, except if dist very small then toOrient = fromOrient
"""
for fromPolarAng in (-40.0, 0.43, 36.7):
cosPolarAng = cosd(fromPolarAng)
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-90, -72, -45.0, -30, 0.01, 12.5, 31, 47,
56, 68, 89):
cosFromOrient = cosd(fromOrient)
sinFromOrient = sind(fromOrient)
for dist in (0, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7,
1e-5, 0.001, 0.01, 0.13):
predEquatAng = fromEquatAng + (dist * cosFromOrient /
cosPolarAng)
predPolarAng = fromPolarAng + (dist * sinFromOrient)
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
if abs(dist) > 0.1:
places = 3
else:
places = 5
if abs(dist) < 0.0001:
orientPlaces = 4
else:
orientPlaces = 7
self.assertAlmostEqual(toEquatAng,
predEquatAng,
places=places)
self.assertAlmostEqual(toPolarAng,
predPolarAng,
places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(
dist, fromCoord.angularSeparation(toCoord))
predFromOrient = fromCoord.orientationTo(toCoord)
if numpy.isfinite(predFromOrient):
self.assertAlmostEqual(fromOrient,
predFromOrient,
places=orientPlaces)
self.assertAlmostEqual(
toOrient,
wrapNear(
180 + toCoord.orientationTo(fromCoord),
toOrient),
places=orientPlaces)
else:
self.assertLess(dist, 1e-7)
self.assertAlmostEqual(fromEquatAng, toEquatAng)
self.assertAlmostEqual(fromPolarAng, toPolarAng)
self.assertAlmostEqual(fromOrient, toOrient)
def testAtPole(self):
"""Test atPole computation
"""
for equatAng in (0, 33.6, -123.4):
for polarAng in (0, -89.999, 89.999, 89.9999999, -89.9999999):
coord = Coord(equatAng, polarAng)
vec = coord.getVecPos()
fracXYMag = math.hypot(vec[0], vec[1]) / coord.getDistance()
predAtPole = fracXYMag**2 < DoubleEpsilon
self.assertEqual(predAtPole, coord.atPole())
def testAtPole(self):
"""Test atPole computation
"""
for equatAng in (0, 33.6, -123.4):
for polarAng in (0, -89.999, 89.999, 89.9999999, -89.9999999):
coord = Coord(equatAng, polarAng)
vec = coord.getVecPos()
fracXYMag = math.hypot(vec[0], vec[1]) / coord.getDistance()
predAtPole = fracXYMag**2 < DoubleEpsilon
self.assertEqual(predAtPole, coord.atPole())
def testDist(self):
"""Test distance
"""
for parallax in (0, MinParallax / 0.899999999,
MinParallax / 0.900000001, MinParallax, 1, 3.4, 75.3):
adjParallax = max(parallax, MinParallax)
predDist = distanceFromParallax(adjParallax)
predAtInf = parallax < MinParallax / 0.9
for coord in ( # test one with space motion, one without
Coord(43, 23, parallax),
Coord(-32, 89.99, parallax, 3, 5, 2),
):
self.assertAlmostEqual(coord.getDistance(), predDist, 2)
self.assertEqual(predAtInf, coord.atInfinity())
def testOffset(self):
"""Test offset, angularSeparation and orientationTo for offsets over a wide range of angles
"""
for fromPolarAng in (-87.1, -25.5, 0.43, 36.7, 87.0):
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-89.9, -45.0, 0.01, 12.5, 89.0, 90.0):
for dist in (0.0001, 0.01, 0.13, 5.73):
sideA = 90.0 - fromPolarAng
angB = 90.0 - fromOrient
sideC = dist
unknownAng, angA, sideB, angC = angSideAng(sideA, angB, sideC)
self.assertFalse(unknownAng)
predEquatAng = fromEquatAng + angC
predPolarAng = 90 - sideB
predAng = angA - 90
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
places = 7
self.assertAlmostEqual(toEquatAng, predEquatAng, places=places)
self.assertAlmostEqual(toPolarAng, predPolarAng, places=places)
self.assertAlmostEqual(toOrient, predAng, places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(dist, fromCoord.angularSeparation(toCoord))
self.assertAlmostEqual(fromOrient, fromCoord.orientationTo(toCoord))
self.assertAlmostEqual(toOrient, wrapNear(180 + toCoord.orientationTo(fromCoord), toOrient))
def coordIter():
for equatAng in (0, 71, -123.4):
for polarAng in (0, -75):
for parallax in (0, 0.1):
for equatPM in (0, -3):
for polarPM in (-7, 0):
for radVel in (0, -34):
yield Coord(equatAng, polarAng, parallax,
equatPM, polarPM, radVel)
def testOffset(self):
"""Test offset, angularSeparation and orientationTo for offsets over a wide range of angles
"""
for fromPolarAng in (-87.1, -25.5, 0.43, 36.7, 87.0):
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-89.9, -45.0, 0.01, 12.5, 89.0, 90.0):
for dist in (0.0001, 0.01, 0.13, 5.73):
sideA = 90.0 - fromPolarAng
angB = 90.0 - fromOrient
sideC = dist
unknownAng, angA, sideB, angC = angSideAng(
sideA, angB, sideC)
self.assertFalse(unknownAng)
predEquatAng = fromEquatAng + angC
predPolarAng = 90 - sideB
predAng = angA - 90
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
places = 7
self.assertAlmostEqual(toEquatAng,
predEquatAng,
places=places)
self.assertAlmostEqual(toPolarAng,
predPolarAng,
places=places)
self.assertAlmostEqual(toOrient,
predAng,
places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(
dist, fromCoord.angularSeparation(toCoord))
self.assertAlmostEqual(
fromOrient, fromCoord.orientationTo(toCoord))
self.assertAlmostEqual(
toOrient,
wrapNear(180 + toCoord.orientationTo(fromCoord),
toOrient))
def testOffsetSmall(self):
"""Test offset, angularSeparation and orientationTo for small offsets not too near the pole
In this regime delta-long = dist along long / cos(lat) is a reasonable approximation
but I have no simple way to compute toOrient, except if dist very small then toOrient = fromOrient
"""
for fromPolarAng in (-40.0, 0.43, 36.7):
cosPolarAng = cosd(fromPolarAng)
for fromEquatAng in (0, 41.0): # should not matter
fromCoord = Coord(fromEquatAng, fromPolarAng)
for fromOrient in (-90, -72, -45.0, -30, 0.01, 12.5, 31, 47, 56, 68, 89):
cosFromOrient = cosd(fromOrient)
sinFromOrient = sind(fromOrient)
for dist in (0, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-5, 0.001, 0.01, 0.13):
predEquatAng = fromEquatAng + (dist * cosFromOrient / cosPolarAng)
predPolarAng = fromPolarAng + (dist * sinFromOrient)
toCoord, toOrient = fromCoord.offset(fromOrient, dist)
atPole, toEquatAng, toPolarAng = toCoord.getSphPos()
if abs(dist) > 0.1:
places = 3
else:
places = 5
if abs(dist) < 0.0001:
orientPlaces = 4
else:
orientPlaces = 7
self.assertAlmostEqual(toEquatAng, predEquatAng, places=places)
self.assertAlmostEqual(toPolarAng, predPolarAng, places=places)
fromCoord = Coord(fromEquatAng, fromPolarAng)
toCoord = Coord(toEquatAng, toPolarAng)
self.assertAlmostEqual(dist, fromCoord.angularSeparation(toCoord))
predFromOrient = fromCoord.orientationTo(toCoord)
if numpy.isfinite(predFromOrient):
self.assertAlmostEqual(fromOrient, predFromOrient, places=orientPlaces)
self.assertAlmostEqual(toOrient, wrapNear(180 + toCoord.orientationTo(fromCoord), toOrient), places=orientPlaces)
else:
self.assertLess(dist, 1e-7)
self.assertAlmostEqual(fromEquatAng, toEquatAng)
self.assertAlmostEqual(fromPolarAng, toPolarAng)
self.assertAlmostEqual(fromOrient, toOrient)
def testBasics(self):
"""Check sph -> vec and back again for points not at the pole
The round trip test relies on the fact that the internal representation of a coord is vector,
so simply retrieving the sph info again suffices to test a round trip.
Warning: the test of vector velocity is poor because the code is copied from the C++.
However, two other tests will help:
- Convert a coordinate system to itself with two different dates of observation
and check that the expected amount of spatial motion occurs
- Compare coordinate conversion results to the old TCC
"""
for equatAng in (0, 71, -123.4):
for polarAng in (0, -75, -89.999999, 89.999999):
for parallax in (0, MinParallax / 0.9000001, MinParallax / 0.8999999, 5):
for equatPM in (4,): # (0, 4):
for polarPM in (-7,): # (0, -7):
for radVel in (0, -34):
coord = Coord(equatAng, polarAng, parallax, equatPM, polarPM, radVel)
self.assertFalse(coord.atPole())
self.assertEqual(coord.atInfinity(), parallax < MinParallax / 0.9)
# check vector position
vecPos = coord.getVecPos()
dist = coord.getDistance()
self.assertAlmostEqual(numpy.linalg.norm(vecPos), dist, 2)
predVecPos = (
dist * cosd(polarAng) * cosd(equatAng),
dist * cosd(polarAng) * sind(equatAng),
dist * sind(polarAng),
)
self.assertTrue(numpy.allclose(predVecPos, vecPos))
# check vector proper motion
vecPM = coord.getVecPM()
RadPerYear_per_ArcsecPerCentury = RadPerDeg / (ArcsecPerDeg * 100.0)
SecPerYear = SecPerDay * DaysPerYear
AUPerYear_per_KmPerSec = SecPerYear / KmPerAU
sinEquat = sind(equatAng)
cosEquat = cosd(equatAng)
sinPolar = sind(polarAng)
cosPolar = cosd(polarAng)
# change units of proper motion from arcsec/century to au/year
pmAUPerYear1 = equatPM * dist * RadPerYear_per_ArcsecPerCentury
pmAUPerYear2 = polarPM * dist * RadPerYear_per_ArcsecPerCentury
# change units of radial velocity from km/sec to au/year
radVelAUPerYear = radVel * AUPerYear_per_KmPerSec
predVecPM = (
- (pmAUPerYear2 * sinPolar * cosEquat) - (pmAUPerYear1 * cosPolar * sinEquat) + (radVelAUPerYear * cosPolar * cosEquat),
- (pmAUPerYear2 * sinPolar * sinEquat) + (pmAUPerYear1 * cosPolar * cosEquat) + (radVelAUPerYear * cosPolar * sinEquat),
+ (pmAUPerYear2 * cosPolar) + (radVelAUPerYear * sinPolar),
)
self.assertTrue(numpy.allclose(predVecPM, vecPM))
# check round trip
atPole, destEquatAng, destPolarAng = coord.getSphPos()
self.assertAlmostEqual(wrapPos(equatAng), destEquatAng)
self.assertAlmostEqual(polarAng, destPolarAng)
destParallax = coord.getParallax()
predParallax = 0 if coord.atInfinity() else parallax
self.assertAlmostEqual(predParallax, destParallax)
atPole, destEquatPM, destPolarPM = coord.getPM()
self.assertAlmostEqual(equatPM, destEquatPM, 6)
self.assertAlmostEqual(polarPM, destPolarPM, 6)
destRadVel = coord.getRadVel()
self.assertAlmostEqual(radVel, destRadVel)
coordCopy = Coord(coord)
self.assertEqual(repr(coord), repr(coordCopy))
def testBasics(self):
"""Check sph -> vec and back again for points not at the pole
The round trip test relies on the fact that the internal representation of a coord is vector,
so simply retrieving the sph info again suffices to test a round trip.
Warning: the test of vector velocity is poor because the code is copied from the C++.
However, two other tests will help:
- Convert a coordinate system to itself with two different dates of observation
and check that the expected amount of spatial motion occurs
- Compare coordinate conversion results to the old TCC
"""
for equatAng in (0, 71, -123.4):
for polarAng in (0, -75, -89.999999, 89.999999):
for parallax in (0, MinParallax / 0.9000001,
MinParallax / 0.8999999, 5):
for equatPM in (4, ): # (0, 4):
for polarPM in (-7, ): # (0, -7):
for radVel in (0, -34):
coord = Coord(equatAng, polarAng, parallax,
equatPM, polarPM, radVel)
self.assertFalse(coord.atPole())
self.assertEqual(coord.atInfinity(),
parallax < MinParallax / 0.9)
# check vector position
vecPos = coord.getVecPos()
dist = coord.getDistance()
self.assertAlmostEqual(
numpy.linalg.norm(vecPos), dist, 2)
predVecPos = (
dist * cosd(polarAng) * cosd(equatAng),
dist * cosd(polarAng) * sind(equatAng),
dist * sind(polarAng),
)
self.assertTrue(
numpy.allclose(predVecPos, vecPos))
# check vector proper motion
vecPM = coord.getVecPM()
RadPerYear_per_ArcsecPerCentury = RadPerDeg / (
ArcsecPerDeg * 100.0)
SecPerYear = SecPerDay * DaysPerYear
AUPerYear_per_KmPerSec = SecPerYear / KmPerAU
sinEquat = sind(equatAng)
cosEquat = cosd(equatAng)
sinPolar = sind(polarAng)
cosPolar = cosd(polarAng)
# change units of proper motion from arcsec/century to au/year
pmAUPerYear1 = equatPM * dist * RadPerYear_per_ArcsecPerCentury
pmAUPerYear2 = polarPM * dist * RadPerYear_per_ArcsecPerCentury
# change units of radial velocity from km/sec to au/year
radVelAUPerYear = radVel * AUPerYear_per_KmPerSec
predVecPM = (
-(pmAUPerYear2 * sinPolar * cosEquat) -
(pmAUPerYear1 * cosPolar * sinEquat) +
(radVelAUPerYear * cosPolar * cosEquat),
-(pmAUPerYear2 * sinPolar * sinEquat) +
(pmAUPerYear1 * cosPolar * cosEquat) +
(radVelAUPerYear * cosPolar * sinEquat),
+(pmAUPerYear2 * cosPolar) +
(radVelAUPerYear * sinPolar),
)
self.assertTrue(
numpy.allclose(predVecPM, vecPM))
# check round trip
atPole, destEquatAng, destPolarAng = coord.getSphPos(
)
self.assertAlmostEqual(wrapPos(equatAng),
destEquatAng)
self.assertAlmostEqual(polarAng, destPolarAng)
destParallax = coord.getParallax()
predParallax = 0 if coord.atInfinity(
) else parallax
self.assertAlmostEqual(predParallax,
destParallax)
atPole, destEquatPM, destPolarPM = coord.getPM(
)
self.assertAlmostEqual(equatPM, destEquatPM, 6)
self.assertAlmostEqual(polarPM, destPolarPM, 6)
destRadVel = coord.getRadVel()
self.assertAlmostEqual(radVel, destRadVel)
coordCopy = Coord(coord)
self.assertEqual(repr(coord), repr(coordCopy))