def test_rotateA2():
d = 1
m = 1
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
qm1 = pgm.qmoments(10, m1)
alpha = -np.pi/4
qm1b = pgm.qmoments(10, glb.rotate_point_array(m1, alpha, [0, 0, 1]))
qm1c = rot.rotate_qlm(qm1, alpha, 0, 0)
assert (abs(qm1c-qm1b) < 20*np.finfo(float).eps).all()
def test_rotateB():
d = 1
m = 1
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
qm1 = pgm.qmoments(10, m1)
beta = np.pi/4
qm1b = pgm.qmoments(10, glb.rotate_point_array(m1, beta, [0, 1, 0]))
qm1c = rot.rotate_qlm(qm1, 0, beta, 0)
assert (abs(qm1c-qm1b) < 10*np.finfo(float).eps).all()
def test_rotateAB():
d = 1
m = 1
m1 = np.array([[m, d, 0, 0]])
qm1 = pgm.qmoments(10, m1)
alpha = -np.pi/4
beta = np.pi/4
# Rotate around z first by alpha
m2 = glb.rotate_point_array(m1, alpha, [0, 0, 1])
# Rotate around y second by beta and get new moments
qm1b = pgm.qmoments(10, glb.rotate_point_array(m2, beta, [0, 1, 0]))
qm1c = rot.rotate_qlm(qm1, 0, beta, alpha)
assert (abs(qm1c-qm1b) < 20*np.finfo(float).eps).all()
def test_q2q():
"""
Check that the inner to inner translate method matches PointGravity.
"""
d = 1
m = 1
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
# Find inner moments around origin
qm1 = pgm.qmoments(10, m1)
# Find inner moments if translated by [.1, 0, 0]
qm1p = pgm.qmoments(10, glb.translate_point_array(m1, [.1, 0, 0]))
# Find moments translated by [.1, 0, 0]
qlmp = trs.translate_qlm(qm1, [0.1, 0, 0])
assert (abs(qlmp-qm1p) < 11*np.finfo(float).eps).all()
def test_q2q_RR():
"""
Check that the inner to inner translate method matches EGA translation.
"""
d = 1
m = 1
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
# Find inner moments around origin
qm1 = pgm.qmoments(10, m1)
# Find inner moments if translated by [.1, 0, 0]
qm1p = pgm.qmoments(10, glb.translate_point_array(m1, [0, 0, 0.1]))
# Find moments translated by [.1, 0, 0]
rrms = trr.transl_newt_z_RR(10, .1)
qlmp = trr.apply_trans_mat(qm1, rrms)
assert (abs(qlmp-qm1p) < 11*np.finfo(float).eps).all()
def test_quadrupole_torque():
"""
Compare the point matrix calculation to an analytic formulation of a
quadrupole torque.
Tests
-----
glb.point_matrix_gravity : function
"""
d = 1
R = rand.rand() * 100 + 1.1
m, M = 1, 1
N = 60
L = 10
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
m2 = np.array([[M, R, 0, 0], [M, -R, 0, 0]])
qlm = pgm.qmoments(L, m1)
tau = np.zeros(N)
ts = np.zeros([60, 3])
d2R2 = d**2 + R**2
tc = np.zeros([N, L + 1], dtype='complex')
ts = np.zeros([N, L + 1], dtype='complex')
for k in range(N):
a = 2 * np.pi * k / N
ca = np.cos(a)
Q = glb.rotate_point_array(m2, a, [0, 0, 1])
Qlmb = pgm.Qmomentsb(L, Q)
tau[k] = 2 * mplb.BIG_G * M * m * d * R * np.sin(a)
tau[k] *= 1 / (d2R2 - 2 * d * R * ca)**(3 / 2) - 1 / (
d2R2 + 2 * d * R * ca)**(3 / 2)
tlm, tc[k], ts[k] = mplb.torque_lm(L, qlm, Qlmb)
# XXX should be np.sum(tc, 1)-tau, but existing sign error!
assert (abs(np.sum(tc, 1) + tau) < 10 * np.finfo(float).eps).all()
def test_q2Q():
"""
Check that the inner to outer translate method matches PointGravity. This
translation method is worse for smaller translations. For R=10, the error
approaches 1e7*epsilon.
"""
d = 1
R = 100
m, M = 1, 1
dr = 99
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
m2 = np.array([[M, R, 0, 0], [M, -R, 0, 0]])
# Create inner moments of each points at +/-r
qm0 = pgm.qmoments(10, np.array([m1[0]]))
qm0b = pgm.qmoments(10, np.array([m1[1]]))
# Get outer moments of points at +/-R
Qm2 = pgm.Qmomentsb(10, m2)
# Find outer moments from inner qm0 and qm0b translated to +/-R
Qlm = trs.translate_q2Q(qm0, [dr, 0, 0])
Qlmb = trs.translate_q2Q(qm0b, [-dr, 0, 0])
assert (abs(Qlm+Qlmb-Qm2) < 11*np.finfo(float).eps).all()
def test_force2():
"""
Test gravitational force from point mass at two meters on point mass away
from the origin.
Tests
-----
mplb.multipole_force : function
"""
m1b = np.array([[1, 0, 0, 1]])
m2 = np.array([[1, 0, 0, 2]])
q1b = pgm.qmoments(20, m1b)
q2 = pgm.Qmomentsb(20, m2)
# Check force for where m1 is placed
force = mplb.multipole_force(20, q1b, q2, 0, 0, 0)
assert (abs(force[2] - mplb.BIG_G) < 10 * np.finfo(float).eps)
# Check force at if displace inner moments to origin
force = mplb.multipole_force(20, q1b, q2, 0, 0, -1)
assert (abs(force[2] - mplb.BIG_G / 4) < 10 * np.finfo(float).eps)
m1b = np.array([[1, 1, 0, 0]])
m2 = np.array([[1, 2, 0, 0]])
q1b = pgm.qmoments(20, m1b)
q2 = pgm.Qmomentsb(20, m2)
# Check force for where m1 is placed
force = mplb.multipole_force(20, q1b, q2, 0, 0, 0)
assert (abs(force[0] - mplb.BIG_G) < 10 * np.finfo(float).eps)
# Check force at if displace inner moments to origin
force = mplb.multipole_force(20, q1b, q2, -1, 0, 0)
assert (abs(force[0] - mplb.BIG_G / 4) < 10 * np.finfo(float).eps)
m1b = np.array([[1, 0, 1, 0]])
m2 = np.array([[1, 0, 2, 0]])
q1b = pgm.qmoments(20, m1b)
q2 = pgm.Qmomentsb(20, m2)
# Check force for where m1 is placed
force = mplb.multipole_force(20, q1b, q2, 0, 0, 0)
assert (abs(force[1] - mplb.BIG_G) < 10 * np.finfo(float).eps)
# Check force at if displace inner moments to origin
force = mplb.multipole_force(20, q1b, q2, 0, -1, 0)
assert (abs(force[1] - mplb.BIG_G / 4) < 10 * np.finfo(float).eps)
def test_q2q_durso():
"""
Check that the inner to inner translate method matches analytic expression.
"""
ar = 1
rp = .1
m = 1
m1 = np.array([[m, ar, 0, 0], [-m, -ar, 0, 0]])
# Find inner moments around origin
qm1 = pgm.qmoments(4, m1)
# Find moments translated by [.1, 0, 0]
qlmp = trs.translate_qlm(qm1, [rp, 0, 0])
# Analytic q44 moment
q44 = 3*np.sqrt(35/8/np.pi)*(rp*ar**3 + ar*rp**3)
assert abs(qlmp[4, 8] - q44) < 11*np.finfo(float).eps
def test_hexapole_torque():
"""
Compare the point matrix calculation to an analytic formulation of a
hexapole torque.
Tests
-----
glb.point_matrix_gravity : function
"""
d = 1
z = rand.randn() * 10
R = rand.rand() * 100 + 1.1
m, M = 1, 1
N = 60
m0 = np.array([m, d, 0, 0])
m1 = np.copy(m0)
m2 = np.array([M, R, 0, z])
m3 = np.copy(m2)
zhat = [0, 0, 1]
for k in range(1, 3):
m1 = np.vstack(
[m1, glb.rotate_point_array(m0, 2 * k * np.pi / 3, zhat)])
m3 = np.vstack(
[m3, glb.rotate_point_array(m2, 2 * k * np.pi / 3, zhat)])
L = 10
qlm = pgm.qmoments(L, m1)
tau = np.zeros(N)
tc = np.zeros([N, L + 1], dtype='complex')
ts = np.zeros([N, L + 1], dtype='complex')
d2R2 = d**2 + R**2 + z**2
for k in range(N):
a = 2 * np.pi * k / N
Q = glb.rotate_point_array(m3, a, zhat)
Qlmb = pgm.Qmomentsb(L, Q)
fac = 3 * glb.BIG_G * M * m * d * R
tau[k] = np.sin(a) / (d2R2 - 2 * d * R * np.cos(a))**(3 / 2)
tau[k] += np.sin(a + 2 * np.pi / 3) / (
d2R2 - 2 * d * R * np.cos(a + 2 * np.pi / 3))**(3 / 2)
tau[k] += np.sin(a + 4 * np.pi / 3) / (
d2R2 - 2 * d * R * np.cos(a + 4 * np.pi / 3))**(3 / 2)
tau[k] *= fac
tlm, tc[k], ts[k] = mplb.torque_lm(L, qlm, Qlmb)
# XXX should be np.sum(tc, 1)-tau, but existing sign error!
assert (abs(np.sum(tc, 1) + tau) < 10 * np.finfo(float).eps).all()
def test_q2Q_SR():
"""
Check that the inner to outer translate method matches PointGravity. This
translation method is worse for smaller translations. For R=10, the error
approaches 1e7*epsilon.
"""
d = 1
R = 100
m = 1
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
m2 = glb.translate_point_array(m1, [0, 0, R])
# Create inner moments of each points at +/-r
qm0 = pgm.qmoments(10, np.array(m1))
# Get outer moments of points at +/-R
Qm2 = pgm.Qmomentsb(10, m2)
# Find outer moments from inner qm0 and qm0b translated to +/-R
srms = trr.transl_newt_z_SR(10, R)
Qlm = trr.apply_trans_mat(qm0, srms)
assert (abs(Qlm-Qm2) < 11*np.finfo(float).eps).all()
def test_force1():
"""
Test gravitational force from point mass at a meter on a point mass at the
origin.
Tests
-----
mplb.multipole_force : function
"""
m1 = np.array([[1, 0, 0, 0]])
m2 = np.array([[1, 1, 0, 0]])
q1 = pgm.qmoments(10, m1)
q2 = pgm.Qmomentsb(10, m2)
force = mplb.multipole_force(10, q1, q2, 0, 0, 0)
assert (abs(force[0] - mplb.BIG_G) < 10 * np.finfo(float).eps)
m2 = np.array([[1, 0, 1, 0]])
q2 = pgm.Qmomentsb(10, m2)
force = mplb.multipole_force(10, q1, q2, 0, 0, 0)
assert (abs(force[1] - mplb.BIG_G) < 10 * np.finfo(float).eps)
m2 = np.array([[1, 0, 0, 1]])
q2 = pgm.Qmomentsb(10, m2)
force = mplb.multipole_force(10, q1, q2, 0, 0, 0)
assert (abs(force[2] - mplb.BIG_G) < 10 * np.finfo(float).eps)
import newt.translations as trs
import newt.rotations as rot
import newt.translationRecurs as trr
"""
Script for comparison of translation methods. Fast rotation + z-translation
vs regular translation.
"""
lmax = 20
# Create 2 points with mass1, at x=+/-1
d = 1
m = 1
m1 = np.array([[m, d, 0, 0], [m, -d, 0, 0]])
# Find inner moments around origin
qm1 = pgm.qmoments(lmax, m1)
# Find inner moments if translated by [.1, 0, 0]
rvec = [0.1, 0, 0]
qm1p = pgm.qmoments(lmax, glb.translate_point_array(m1, rvec))
# Find moments translated by [.1, 0, 0] using d'Urso, Adelberger
tic1 = time.perf_counter()
qm1p2 = trs.translate_qlm(qm1, rvec)
toc1 = time.perf_counter()
# Time the recursive method combined with recursive translation
tic2 = time.perf_counter()
r = np.sqrt(rvec[0]**2 + rvec[1]**2 + rvec[2]**2)
if r == 0 or r == rvec[2]:
phi, theta = 0, 0
else: