def test_bAnnulusn():
"""
Test of numerical annulus outer moments against point gravity.
Tests
-----
bqlmn.annulus : function
"""
mout = gshp.wedge(1, 1, 2, 1, np.pi / 2, 60, 60)
mmout2 = pgm.Qmomentsb(5, glb.translate_point_array(mout, [0, 0, .5]))
Qlmb2 = bqlmn.annulus(5, 2 / (np.pi * (2**2 - 1)), 0, 1, 1, 2, np.pi / 2)
assert (abs(Qlmb2 - mmout2) < .002).all()
mmout3 = pgm.Qmomentsb(5, glb.translate_point_array(mout, [0, 0, -.5]))
Qlmb3 = bqlmn.annulus(5, 2 / (np.pi * (2**2 - 1)), -1, 0, 1, 2, np.pi / 2)
assert (abs(Qlmb3 - mmout3) < .002).all()
mout3 = gshp.wedge(1, 1, 2, 1, np.pi / 3, 60, 60)
mmout3 = pgm.Qmomentsb(5, glb.translate_point_array(mout3, [0, 0, .5]))
Qlmb3 = bqlmn.annulus(5, 3 / (np.pi * (2**2 - 1)), 0, 1, 1, 2, np.pi / 3)
assert (abs(Qlmb3 - mmout3) < .002).all()
mout4 = gshp.wedge(1, 1, 2, 1, np.pi / 4, 60, 60)
mmout4 = pgm.Qmomentsb(5, glb.translate_point_array(mout4, [0, 0, .5]))
Qlmb4 = bqlmn.annulus(5, 4 / (np.pi * (2**2 - 1)), 0, 1, 1, 2, np.pi / 4)
assert (abs(Qlmb4 - mmout4) < .002).all()
mout5 = gshp.wedge(1, 1, 2, 1, np.pi / 5, 60, 60)
mmout5 = pgm.Qmomentsb(5, glb.translate_point_array(mout5, [0, 0, .5]))
Qlmb5 = bqlmn.annulus(5, 5 / (np.pi * (2**2 - 1)), 0, 1, 1, 2, np.pi / 5)
assert (abs(Qlmb5 - mmout5) < .002).all()
def test_bTrapezoidn():
"""
Test of numerical trapezoid outer moments against point gravity.
Tests
-----
bqlmn.trapezoid : function
"""
iR, oR = 1, 2
beta = np.pi / 3
t = 1
vol = (oR - iR) * np.cos(beta) * (oR + iR) * np.sin(beta) * t
mout = gshp.trapezoid(1, iR, oR, t, beta, 60, 60)
mmout2 = pgm.Qmomentsb(5, glb.translate_point_array(mout, [0, 0, .5]))
Qlmb2 = bqlmn.trapezoid(5, 1 / vol, 0, t, iR, oR, beta)
assert (abs(Qlmb2 - mmout2) < .01).all()
mmout3 = pgm.Qmomentsb(5, glb.translate_point_array(mout, [0, 0, -.5]))
Qlmb3 = bqlmn.trapezoid(5, 1 / vol, -t, 0, iR, oR, beta)
assert (abs(Qlmb3 - mmout3) < .01).all()
beta = np.pi / 4
vol = (oR - iR) * np.cos(beta) * (oR + iR) * np.sin(beta) * t
mout4 = gshp.trapezoid(1, iR, oR, t, beta, 60, 60)
mmout4 = pgm.Qmomentsb(5, glb.translate_point_array(mout4, [0, 0, .5]))
Qlmb4 = bqlmn.trapezoid(5, 1 / vol, 0, t, iR, oR, beta)
assert (abs(Qlmb4 - mmout4) < .01).all()
beta = np.pi / 5
vol = (oR - iR) * np.cos(beta) * (oR + iR) * np.sin(beta) * t
mout5 = gshp.trapezoid(1, iR, oR, t, beta, 60, 60)
mmout5 = pgm.Qmomentsb(5, glb.translate_point_array(mout5, [0, 0, .5]))
Qlmb5 = bqlmn.trapezoid(5, 1 / vol, 0, t, iR, oR, beta)
assert (abs(Qlmb5 - mmout5) < .01).all()
def test_bOuter_conen():
"""
Test of numerical outer cone outer moments against point gravity.
Tests
-----
bqlmn.outer_cone : function
"""
iR, oR = 1, 2
beta = np.pi / 3
H = 1
Hp = H * oR / (oR - iR)
vol = beta * (Hp * oR**2 / 3 - H * iR**2 - (Hp - H) * iR**2 / 3)
mout = gshp.outer_cone(1, iR, oR, H, beta, 60, 60)
mmout2 = pgm.Qmomentsb(5, mout)
Qlmb2 = bqlmn.outer_cone(5, 1 / vol, H, iR, oR, beta)
assert (abs(Qlmb2 - mmout2) < .005).all()
beta = np.pi / 4
vol = beta * (Hp * oR**2 / 3 - H * iR**2 - (Hp - H) * iR**2 / 3)
mout4 = gshp.outer_cone(1, iR, oR, H, beta, 60, 60)
mmout4 = pgm.Qmomentsb(5, mout4)
Qlmb4 = bqlmn.outer_cone(5, 1 / vol, H, iR, oR, beta)
assert (abs(Qlmb4 - mmout4) < .01).all()
beta = np.pi / 5
vol = beta * (Hp * oR**2 / 3 - H * iR**2 - (Hp - H) * iR**2 / 3)
mout5 = gshp.outer_cone(1, iR, oR, H, beta, 60, 60)
mmout5 = pgm.Qmomentsb(5, mout5)
Qlmb5 = bqlmn.outer_cone(5, 1 / vol, H, iR, oR, beta)
assert (abs(Qlmb5 - mmout5) < .01).all()
def test_Q2Q():
"""
Check that the outer to outer translate method matches PointGravity.
"""
R = 100
M = 1
m2 = np.array([[M, R, 0, 0], [M, -R, 0, 0]])
# Get outer moments of points at +/-R
Qm2 = pgm.Qmomentsb(10, m2)
# Get outer moments of translated points
Qm2b = pgm.Qmomentsb(10, glb.translate_point_array(m2, [0.1, 0, 0]))
# Find outer moments from inner qm0 and qm0b translated to +/-R
Qlmp2 = trs.translate_Qlmb(Qm2, [0.1, 0, 0])
assert (abs(Qlmp2-Qm2b) < 10*np.finfo(float).eps).all()
def test_Q2Q_SS():
"""
Check that the outer to outer translate method matches CS translation.
"""
R = 100
M = 1
m2 = np.array([[M, R, 0, 0], [M, -R, 0, 0]])
# Get outer moments of points at +/-R
Qm2 = pgm.Qmomentsb(10, m2)
# Get outer moments of translated points
Qm2b = pgm.Qmomentsb(10, glb.translate_point_array(m2, [0, 0, 0.1]))
# Find outer moments from inner qm0 and qm0b translated to +/-R
ssms = trr.transl_newt_z_SS(10, .1)
Qlmp2 = trr.apply_trans_mat(Qm2, ssms)
assert (abs(Qlmp2-Qm2b) < 10*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_bAnnulus():
"""
Test of explicit annulus outer moments against point gravity.
Tests
-----
bqlm.annulus : function
"""
mout = gshp.wedge(1, 1, 2, 1, np.pi / 2, 60, 60)
mmout2 = pgm.Qmomentsb(5, glb.translate_point_array(mout, [0, 0, .5]))
Qlmb2 = bqlm.annulus(5, 2 / (np.pi * (2**2 - 1)), 1, 1, 2, 0, np.pi / 2)
assert (abs(Qlmb2 - mmout2) < .002).all()
mmout3 = pgm.Qmomentsb(5, glb.translate_point_array(mout, [0, 0, -.5]))
Qlmb3 = bqlm.annulus(5, 2 / (np.pi * (2**2 - 1)), -1, 1, 2, 0, np.pi / 2)
assert (abs(Qlmb3 - mmout3) < .002).all()
mout3 = gshp.wedge(1, 1, 2, 1, np.pi / 3, 60, 60)
mmout3 = pgm.Qmomentsb(5, glb.translate_point_array(mout3, [0, 0, .5]))
Qlmb3 = bqlm.annulus(5, 3 / (np.pi * (2**2 - 1)), 1, 1, 2, 0, np.pi / 3)
assert (abs(Qlmb3 - mmout3) < .002).all()
mout4 = gshp.wedge(1, 1, 2, 1, np.pi / 4, 60, 60)
mmout4 = pgm.Qmomentsb(5, glb.translate_point_array(mout4, [0, 0, .5]))
Qlmb4 = bqlm.annulus(5, 4 / (np.pi * (2**2 - 1)), 1, 1, 2, 0, np.pi / 4)
assert (abs(Qlmb4 - mmout4) < .002).all()
mout5 = gshp.wedge(1, 1, 2, 1, np.pi / 5, 60, 60)
mmout5 = pgm.Qmomentsb(5, glb.translate_point_array(mout5, [0, 0, .5]))
Qlmb5 = bqlm.annulus(5, 5 / (np.pi * (2**2 - 1)), 1, 1, 2, 0, np.pi / 5)
assert (abs(Qlmb5 - mmout5) < .002).all()
# Test that a L<5 works (we'll do 3)
Qlmb3 = bqlm.annulus(3, 3 / (np.pi * (2**2 - 1)), 1, 1, 2, 0, np.pi / 3)
mmout3 = pgm.Qmomentsb(3, glb.translate_point_array(mout3, [0, 0, .5]))
assert (np.shape(Qlmb3) == (4, 7))
assert (abs(Qlmb3 - mmout3) < .002).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_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)
def test_Q2Q_durso():
"""
Check that the outer to outer translate method matches analytic.
"""
ar = 50
rp = 1
m = 1
m1 = np.array([[m, ar, 0, 0], [-m, -ar, 0, 0]])
# Find outer moments around origin
Qm1 = pgm.Qmomentsb(10, m1)
# Find outer moments translated by [1, 0, 0]
Qlmp = trs.translate_Qlmb(Qm1, [rp, 0, 0])
# Analytic Q22 moment
Q22 = (1/4)*np.sqrt(15/2/np.pi)*((ar+rp)**(-3) - (ar-rp)**(-3))
assert abs(Qlmp[2, 12] - Q22) < 10*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_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()