def test_combinations():
# Test some particular combinations of coord sys transformations
# +90 around x, followed by shift to (1, 0, 0)
# equivalent to shift first, and then rotation +90 about x
# latter rotation can be either global or local, since origin is unaffected
# (1, 0, 0) -> (1, 0, 0)
# by convention for local rotation
# and by coincidence (origin is on xaxis) for global rotation
coordSys = batoid.CoordSys()
coordSys1 = coordSys.rotateGlobal(batoid.RotX(np.pi / 2)).shiftGlobal(
[1, 0, 0])
coordSys2 = coordSys.shiftGlobal([1, 0,
0]).rotateLocal(batoid.RotX(np.pi / 2))
coordSys3 = coordSys.shiftGlobal([1, 0,
0]).rotateGlobal(batoid.RotX(np.pi / 2))
np.testing.assert_allclose(coordSys1.origin, coordSys2.origin)
np.testing.assert_allclose(coordSys1.rot, coordSys2.rot)
np.testing.assert_allclose(coordSys1.origin, coordSys3.origin)
np.testing.assert_allclose(coordSys1.rot, coordSys3.rot)
# +45 around x, followed by sqrt(2) in new y direction, which is the (0, 1, 1)
# direction in global coords, followed by -45 about x.
# Should be parallel to global coords, but origin at (0, 1, 1)
coordSys1 = (batoid.CoordSys().rotateGlobal(batoid.RotX(
np.pi / 4)).shiftLocal([0, np.sqrt(2),
0]).rotateLocal(batoid.RotX(-np.pi / 4)))
coordSys2 = batoid.CoordSys().shiftLocal([0, 1, 1])
np.testing.assert_allclose(coordSys1.origin,
coordSys2.origin,
rtol=0,
atol=1e-15)
np.testing.assert_allclose(coordSys1.rot,
coordSys2.rot,
rtol=0,
atol=1e-15)
# rotate +90 around point (1, 0, 0) with rot axis parallel to y axis.
# moves origin from (0, 0, 0) to (1, 0, 1)
coordSys = batoid.CoordSys()
coordSys1 = coordSys.rotateGlobal(batoid.RotY(np.pi / 2), [1, 0, 0])
coordSys2 = coordSys.rotateGlobal(batoid.RotY(np.pi / 2)).shiftGlobal(
[1, 0, 1])
# local coords of global (1, 0, 1) are (-1, 0, 1)
coordSys3 = coordSys.rotateGlobal(batoid.RotY(np.pi / 2)).shiftLocal(
[-1, 0, 1])
np.testing.assert_allclose(coordSys1.origin, coordSys2.origin)
np.testing.assert_allclose(coordSys1.rot, coordSys2.rot)
np.testing.assert_allclose(coordSys1.origin, coordSys3.origin)
np.testing.assert_allclose(coordSys1.rot, coordSys3.rot)
def test_asphere_reflection_coordtransform():
import random
random.seed(5772156)
asphere = batoid.Asphere(23.0, -0.97, [1e-5, 1e-6])
for i in range(1000):
x = random.gauss(0, 1)
y = random.gauss(0, 1)
vx = random.gauss(0, 1e-1)
vy = random.gauss(0, 1e-1)
v = np.array([vx, vy, 1])
v /= np.linalg.norm(v)
ray = batoid.Ray([x, y, -0.1], v, 0)
ray2 = ray.copy()
cs = batoid.CoordSys(
[random.uniform(-0.01, 0.01),
random.uniform(-0.01, 0.01),
random.uniform(-0.01, 0.01)],
(batoid.RotX(random.uniform(-0.01, 0.01))
.dot(batoid.RotY(random.uniform(-0.01, 0.01)))
.dot(batoid.RotZ(random.uniform(-0.01, 0.01)))
)
)
rray = asphere.reflect(ray, coordSys=cs)
rray2 = asphere.reflect(ray2.toCoordSys(cs))
assert ray_isclose(rray, rray2)
def test_rotation():
try:
import galsim
except ImportError:
print("optic rotation test requires GalSim")
return
np.random.seed(57)
telescope = batoid.Optic.fromYaml("HSC.yaml")
rot = batoid.RotX(np.random.uniform(low=0.0, high=2*np.pi))
rot = rot.dot(batoid.RotY(np.random.uniform(low=0.0, high=2*np.pi)))
rot = rot.dot(batoid.RotZ(np.random.uniform(low=0.0, high=2*np.pi)))
rotInv = np.linalg.inv(rot)
# It's hard to test the two telescopes for equality due to rounding errors, so we test by
# comparing zernikes
rotTel = telescope.withLocalRotation(rot).withLocalRotation(rotInv)
theta_x = np.random.uniform(-0.005, 0.005)
theta_y = np.random.uniform(-0.005, 0.005)
wavelength = 750e-9
np.testing.assert_allclose(
batoid.psf.zernike(telescope, theta_x, theta_y, wavelength),
batoid.psf.zernike(rotTel, theta_x, theta_y, wavelength),
atol=1e-5
)
for item in telescope.itemDict:
rotTel = telescope.withLocallyRotatedOptic(item, rot)
rotTel = rotTel.withLocallyRotatedOptic(item, rotInv)
rotTel2 = telescope.withLocallyRotatedOptic(item, np.eye(3))
theta_x = np.random.uniform(-0.005, 0.005)
theta_y = np.random.uniform(-0.005, 0.005)
np.testing.assert_allclose(
batoid.psf.zernike(telescope, theta_x, theta_y, wavelength),
batoid.psf.zernike(rotTel, theta_x, theta_y, wavelength),
atol=1e-5
)
np.testing.assert_allclose(
batoid.psf.zernike(telescope, theta_x, theta_y, wavelength),
batoid.psf.zernike(rotTel2, theta_x, theta_y, wavelength),
atol=1e-5
)
# Test with non-fully-qualified name
rotTel = telescope.withLocallyRotatedOptic('G1', rot)
rotTel = rotTel.withLocallyRotatedOptic('G1', rotInv)
rotTel2 = rotTel.withLocallyRotatedOptic('G1', np.eye(3))
np.testing.assert_allclose(
batoid.psf.zernike(telescope, theta_x, theta_y, wavelength),
batoid.psf.zernike(rotTel, theta_x, theta_y, wavelength),
atol=1e-5
)
np.testing.assert_allclose(
batoid.psf.zernike(telescope, theta_x, theta_y, wavelength),
batoid.psf.zernike(rotTel2, theta_x, theta_y, wavelength),
atol=1e-5
)
def randomCoordSys():
import random
return batoid.CoordSys(
randomVec3(),
(batoid.RotX(random.uniform(0, 1))
.dot(batoid.RotY(random.uniform(0, 1)))
.dot(batoid.RotZ(random.uniform(0, 1))))
)
def test_simple_transform():
rng = np.random.default_rng(5)
size = 10_000
# Worked a few examples out manually
# Example 1
coordSys1 = batoid.CoordSys()
coordSys2 = batoid.CoordSys().shiftGlobal([0, 0, 1])
rv = randomRayVector(rng, size, coordSys1)
transform = batoid.CoordTransform(coordSys1, coordSys2)
rv2 = batoid.applyForwardTransform(transform, rv.copy())
np.testing.assert_allclose(rv.x, rv2.x)
np.testing.assert_allclose(rv.y, rv2.y)
np.testing.assert_allclose(rv.z - 1, rv2.z)
# Repeat using toCoordSys
rv3 = rv.copy().toCoordSys(coordSys2)
np.testing.assert_allclose(rv.x, rv3.x)
np.testing.assert_allclose(rv.y, rv3.y)
np.testing.assert_allclose(rv.z - 1, rv3.z)
# Transform of numpy array
x, y, z = transform.applyForwardArray(rv.x, rv.y, rv.z)
np.testing.assert_allclose(rv2.x, x)
np.testing.assert_allclose(rv2.y, y)
np.testing.assert_allclose(rv2.z, z)
# Example 2
# First for a single specific point I worked out
coordSys1 = batoid.CoordSys()
coordSys2 = batoid.CoordSys(origin=[1, 1, 1], rot=batoid.RotY(np.pi / 2))
x = y = z = np.array([2])
vx = vy = vz = np.array([0])
rv = batoid.RayVector(x, y, z, vx, vy, vz)
transform = batoid.CoordTransform(coordSys1, coordSys2)
rv2 = batoid.applyForwardTransform(transform, rv.copy())
np.testing.assert_allclose(rv2.r, [[-1, 1, 1]])
# Transform of numpy array
x, y, z = transform.applyForwardArray(rv.x, rv.y, rv.z)
np.testing.assert_allclose(rv2.x, x)
np.testing.assert_allclose(rv2.y, y)
np.testing.assert_allclose(rv2.z, z)
# Here's the generalization
# Also using alternate syntax for applyForward here.
rv = randomRayVector(rng, size, coordSys1)
rv2 = transform.applyForward(rv.copy())
np.testing.assert_allclose(rv2.x, 1 - rv.z)
np.testing.assert_allclose(rv2.y, rv.y - 1)
np.testing.assert_allclose(rv2.z, rv.x - 1)
rv3 = rv.copy().toCoordSys(coordSys2)
np.testing.assert_allclose(rv3.x, 1 - rv.z)
np.testing.assert_allclose(rv3.y, rv.y - 1)
np.testing.assert_allclose(rv3.z, rv.x - 1)
# Transform of numpy array
x, y, z = transform.applyForwardArray(rv.x, rv.y, rv.z)
np.testing.assert_allclose(rv2.x, x)
np.testing.assert_allclose(rv2.y, y)
np.testing.assert_allclose(rv2.z, z)
def update(self, deltax):
"""
Updates the optic.
Parameters
----------
deltax: aos.state.State
The change in the optical state.
Notes
-----
Rotations only commute for small angles; otherwise order matters.
"""
camx, camy, camz, camrx, camry = deltax.camhex
self.optic = self.optic.withGloballyShiftedOptic('LSST.LSSTCamera', [camx, camy, camz])
camrot = np.dot(batoid.RotX(camrx), batoid.RotY(camry))
self.optic = self.optic.withLocallyRotatedOptic('LSST.LSSTCamera', camrot)
m2x, m2y, m2z, m2rx, m2ry = deltax.m2hex
self.optic = self.optic.withGloballyShiftedOptic('LSST.M2', [m2x, m2y, m2z])
m2rot = np.dot(batoid.RotX(m2rx), batoid.RotY(m2ry))
self.optic = self.optic.withLocallyRotatedOptic('LSST.M2', m2rot)
def test_rotation():
try:
import galsim
except ImportError:
print("optic rotation test requires GalSim")
return
np.random.seed(57)
fn = os.path.join(batoid.datadir, "HSC", "HSC.yaml")
config = yaml.load(open(fn))
telescope = batoid.parse.parse_optic(config['opticalSystem'])
rot = batoid.RotX(np.random.uniform(low=0.0, high=2 * np.pi))
rot = rot.dot(batoid.RotY(np.random.uniform(low=0.0, high=2 * np.pi)))
rot = rot.dot(batoid.RotZ(np.random.uniform(low=0.0, high=2 * np.pi)))
rotInv = np.linalg.inv(rot)
# It's hard to test the two telescopes for equality due to rounding errors, so we test by
# comparing zernikes
rotTel = telescope.withLocalRotation(rot).withLocalRotation(rotInv)
theta_x = np.random.uniform(-0.005, 0.005)
theta_y = np.random.uniform(-0.005, 0.005)
wavelength = 750e-9
np.testing.assert_allclose(batoid.psf.zernike(telescope, theta_x, theta_y,
wavelength),
batoid.psf.zernike(rotTel, theta_x, theta_y,
wavelength),
atol=1e-5)
for item in telescope.itemDict:
rotTel = telescope.withLocallyRotatedOptic(item, rot)
rotTel = rotTel.withLocallyRotatedOptic(item, rotInv)
rotTel2 = telescope.withLocallyRotatedOptic(item, np.eye(3))
theta_x = np.random.uniform(-0.005, 0.005)
theta_y = np.random.uniform(-0.005, 0.005)
np.testing.assert_allclose(batoid.psf.zernike(telescope, theta_x,
theta_y, wavelength),
batoid.psf.zernike(rotTel, theta_x, theta_y,
wavelength),
atol=1e-5)
np.testing.assert_allclose(batoid.psf.zernike(telescope, theta_x,
theta_y, wavelength),
batoid.psf.zernike(rotTel2, theta_x,
theta_y, wavelength),
atol=1e-5)
def test_properties():
rng = np.random.default_rng(5)
size = 10
for i in range(100):
x = rng.normal(size=size)
y = rng.normal(size=size)
z = rng.normal(size=size)
vx = rng.normal(size=size)
vy = rng.normal(size=size)
vz = rng.normal(size=size)
t = rng.normal(size=size)
w = rng.normal(size=size)
fx = rng.normal(size=size)
vig = rng.choice([True, False], size=size)
fa = rng.choice([True, False], size=size)
cs = batoid.CoordSys(
origin=rng.normal(size=3),
rot=batoid.RotX(rng.normal()) @ batoid.RotY(rng.normal()))
rv = batoid.RayVector(x, y, z, vx, vy, vz, t, w, fx, vig, fa, cs)
np.testing.assert_array_equal(rv.x, x)
np.testing.assert_array_equal(rv.y, y)
np.testing.assert_array_equal(rv.z, z)
np.testing.assert_array_equal(rv.r[:, 0], x)
np.testing.assert_array_equal(rv.r[:, 1], y)
np.testing.assert_array_equal(rv.r[:, 2], z)
np.testing.assert_array_equal(rv.vx, vx)
np.testing.assert_array_equal(rv.vy, vy)
np.testing.assert_array_equal(rv.vz, vz)
np.testing.assert_array_equal(rv.v[:, 0], vx)
np.testing.assert_array_equal(rv.v[:, 1], vy)
np.testing.assert_array_equal(rv.v[:, 2], vz)
np.testing.assert_array_equal(rv.k[:, 0], rv.kx)
np.testing.assert_array_equal(rv.k[:, 1], rv.ky)
np.testing.assert_array_equal(rv.k[:, 2], rv.kz)
np.testing.assert_array_equal(rv.t, t)
np.testing.assert_array_equal(rv.wavelength, w)
np.testing.assert_array_equal(rv.flux, fx)
np.testing.assert_array_equal(rv.vignetted, vig)
np.testing.assert_array_equal(rv.failed, fa)
assert rv.coordSys == cs
rv._syncToDevice()
do_pickle(rv)
def randomCoordSys(rng):
return batoid.CoordSys(
rng.uniform(size=3), (batoid.RotX(rng.uniform()).dot(
batoid.RotY(rng.uniform())).dot(batoid.RotZ(rng.uniform()))))
def test_rotation():
rng = np.random.default_rng(57)
telescope = batoid.Optic.fromYaml("HSC.yaml")
rot = batoid.RotX(rng.uniform(low=0.0, high=2 * np.pi))
rot = rot.dot(batoid.RotY(rng.uniform(low=0.0, high=2 * np.pi)))
rot = rot.dot(batoid.RotZ(rng.uniform(low=0.0, high=2 * np.pi)))
rotInv = np.linalg.inv(rot)
# It's hard to test the two telescopes for equality due to rounding errors,
# so we test by comparing zernikes
rotTel = telescope.withLocalRotation(rot).withLocalRotation(rotInv)
theta_x = rng.uniform(-0.005, 0.005)
theta_y = rng.uniform(-0.005, 0.005)
wavelength = 750e-9
for k in telescope.itemDict.keys():
np.testing.assert_allclose(telescope[k].coordSys.origin,
rotTel[k].coordSys.origin,
rtol=0,
atol=1e-14)
np.testing.assert_allclose(telescope[k].coordSys.rot,
rotTel[k].coordSys.rot,
rtol=0,
atol=1e-14)
np.testing.assert_allclose(batoid.zernikeGQ(telescope, theta_x, theta_y,
wavelength),
batoid.zernikeGQ(rotTel, theta_x, theta_y,
wavelength),
atol=1e-7)
for item in telescope.itemDict:
rotTel = telescope.withLocallyRotatedOptic(item, rot)
rotTel = rotTel.withLocallyRotatedOptic(item, rotInv)
rotTel2 = telescope.withLocallyRotatedOptic(item, np.eye(3))
theta_x = rng.uniform(-0.005, 0.005)
theta_y = rng.uniform(-0.005, 0.005)
np.testing.assert_allclose(batoid.zernikeGQ(telescope, theta_x,
theta_y, wavelength),
batoid.zernikeGQ(rotTel, theta_x, theta_y,
wavelength),
atol=1e-7)
np.testing.assert_allclose(batoid.zernikeGQ(telescope, theta_x,
theta_y, wavelength),
batoid.zernikeGQ(rotTel2, theta_x, theta_y,
wavelength),
atol=1e-7)
# Test with non-fully-qualified name
rotTel = telescope.withLocallyRotatedOptic('G1', rot)
rotTel = rotTel.withLocallyRotatedOptic('G1', rotInv)
rotTel2 = rotTel.withLocallyRotatedOptic('G1', np.eye(3))
np.testing.assert_allclose(batoid.zernikeGQ(telescope, theta_x, theta_y,
wavelength),
batoid.zernikeGQ(rotTel, theta_x, theta_y,
wavelength),
atol=1e-7)
np.testing.assert_allclose(batoid.zernikeGQ(telescope, theta_x, theta_y,
wavelength),
batoid.zernikeGQ(rotTel2, theta_x, theta_y,
wavelength),
atol=1e-7)
def test_params():
rng = np.random.default_rng(5)
for _ in range(30):
origin = rng.uniform(size=3)
rot = (batoid.RotX(rng.uniform()) @ batoid.RotY(rng.uniform())
@ batoid.RotZ(rng.uniform()))
coordSys = batoid.CoordSys(origin, rot)
np.testing.assert_equal(coordSys.origin, origin)
np.testing.assert_equal(coordSys.rot, rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
coordSys = batoid.CoordSys(origin=origin)
np.testing.assert_equal(coordSys.origin, origin)
np.testing.assert_equal(coordSys.rot, np.eye(3))
np.testing.assert_equal(coordSys.xhat, [1, 0, 0])
np.testing.assert_equal(coordSys.yhat, [0, 1, 0])
np.testing.assert_equal(coordSys.zhat, [0, 0, 1])
coordSys = batoid.CoordSys(rot=rot)
np.testing.assert_equal(coordSys.origin, np.zeros(3))
np.testing.assert_equal(coordSys.rot, rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
coordSys = batoid.CoordSys()
np.testing.assert_equal(coordSys.origin, np.zeros(3))
np.testing.assert_equal(coordSys.rot, np.eye(3))
np.testing.assert_equal(coordSys.xhat, [1, 0, 0])
np.testing.assert_equal(coordSys.yhat, [0, 1, 0])
np.testing.assert_equal(coordSys.zhat, [0, 0, 1])
coordSys = batoid.CoordSys()
coordSys = coordSys.rotateGlobal(rot).shiftGlobal(origin)
np.testing.assert_equal(coordSys.origin, origin)
np.testing.assert_equal(coordSys.rot, rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
coordSys = batoid.CoordSys()
coordSys = coordSys.rotateLocal(rot).shiftGlobal(origin)
np.testing.assert_equal(coordSys.origin, origin)
np.testing.assert_equal(coordSys.rot, rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
coordSys = batoid.CoordSys()
coordSys = coordSys.shiftLocal(origin).rotateLocal(rot)
np.testing.assert_equal(coordSys.origin, origin)
np.testing.assert_equal(coordSys.rot, rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
coordSys = batoid.CoordSys()
coordSys = coordSys.shiftGlobal(origin).rotateLocal(rot)
np.testing.assert_equal(coordSys.origin, origin)
np.testing.assert_equal(coordSys.rot, rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
# Can't simply do a global rotation after a shift, since that will
# change the origin too. Works if we manually specify the rotation
# center though
coordSys = batoid.CoordSys()
coordSys1 = coordSys.shiftGlobal(origin)
coordSys = coordSys1.rotateGlobal(rot, origin, coordSys)
np.testing.assert_equal(coordSys.origin, origin)
np.testing.assert_equal(coordSys.rot, rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
def test_rotate():
rng = np.random.default_rng(57)
for _ in range(10):
r1 = batoid.RotX(rng.uniform())
r2 = batoid.RotY(rng.uniform())
r3 = batoid.RotZ(rng.uniform())
r4 = batoid.RotX(rng.uniform())
r5 = batoid.RotY(rng.uniform())
r6 = batoid.RotZ(rng.uniform())
rot = r6 @ r5 @ r4 @ r3 @ r2 @ r1
coordSys = batoid.CoordSys().rotateGlobal(rot)
np.testing.assert_equal(coordSys.xhat, rot[:, 0])
np.testing.assert_equal(coordSys.yhat, rot[:, 1])
np.testing.assert_equal(coordSys.zhat, rot[:, 2])
np.testing.assert_equal(coordSys.origin, 0)
rot1 = r3 @ r2 @ r1
rot2 = r6 @ r5 @ r4
coordSys = batoid.CoordSys().rotateGlobal(rot1).rotateGlobal(rot2)
np.testing.assert_allclose(coordSys.xhat, rot[:, 0])
np.testing.assert_allclose(coordSys.yhat, rot[:, 1])
np.testing.assert_allclose(coordSys.zhat, rot[:, 2])
np.testing.assert_equal(coordSys.origin, 0)
coordSys = batoid.CoordSys(rot=rot1)
coordSys2 = coordSys.rotateLocal(batoid.RotX(np.pi / 2))
# Since second rotation was about the local X, both should have same
# xhat
np.testing.assert_allclose(coordSys.xhat, coordSys2.xhat)
# 90 degree positive rotation then means y -> -z, z -> y
np.testing.assert_allclose(coordSys.yhat, -coordSys2.zhat)
np.testing.assert_allclose(coordSys.zhat, coordSys2.yhat)
# Try a loop
coordSys = batoid.CoordSys(rot=rot)
coordSys = coordSys.rotateGlobal(batoid.RotX(0.1))
coordSys = coordSys.rotateGlobal(batoid.RotZ(np.pi))
coordSys = coordSys.rotateGlobal(batoid.RotX(0.1))
coordSys = coordSys.rotateGlobal(batoid.RotZ(np.pi))
# Should be back where we started...
np.testing.assert_allclose(coordSys.rot, rot)
# Miscentered origins
origin = rng.uniform(size=3)
coordSys = batoid.CoordSys(origin=origin, rot=rot)
np.testing.assert_equal(origin, coordSys.origin)
coordSys2 = coordSys.rotateGlobal(rot)
np.testing.assert_equal(rot @ origin, coordSys2.origin)
coordSys3 = coordSys.rotateLocal(rot)
np.testing.assert_equal(origin, coordSys3.origin)
# Miscentered rotation axes
# Global with center specified is same as local
coordSys = batoid.CoordSys(origin=origin, rot=rot)
coordSys2 = coordSys.rotateLocal(rot)
coordSys3 = coordSys.rotateGlobal(rot, origin, batoid.CoordSys())
np.testing.assert_allclose(coordSys2.origin, origin)
np.testing.assert_allclose(coordSys2.origin, coordSys3.origin)
np.testing.assert_allclose(coordSys2.rot, coordSys3.rot)