def test_energy_conservation_unequalmasses_python():
# Test that energy is conserved for a simple problem, using Python method
x= numpy.array([-1.1,0.1,1.3])
v= numpy.array([3.,2.,-5.])
m= numpy.array([1.,2.,3.])
g= wendy.nbody_python(x,v,m,0.05)
E= wendy.energy(x,v,m)
cnt= 0
while cnt < 100:
tx,tv= next(g)
assert numpy.fabs(wendy.energy(tx,tv,m)-E) < 10.**-10., "Energy not conserved during simple N-body integration"
cnt+= 1
return None
def test_energy_conservation():
# Test that energy is conserved for a simple problem
x = numpy.array([-1.1, 0.1, 1.3])
v = numpy.array([3., 2., -5.])
m = numpy.array([1., 1., 1.])
g = wendy.nbody(x, v, m, 0.05, approx=True, nleap=100000)
E = wendy.energy(x, v, m)
cnt = 0
while cnt < 100:
tx, tv = next(g)
assert numpy.fabs(
wendy.energy(tx, tv, m) - E
) / E < 10.**-6., "Energy not conserved during approximate N-body integration"
cnt += 1
return None
def test_energy_conservation_unequalmasses():
# Test that energy is conserved for a simple problem
x = numpy.array([-1.1, 0.1, 1.3])
v = numpy.array([3., 2., -5.])
m = numpy.array([1., 2., 3.])
omega = 1.1
g = wendy.nbody(x, v, m, 0.05, omega=omega, approx=True, nleap=100000)
E = wendy.energy(x, v, m, omega=omega)
cnt = 0
while cnt < 100:
tx, tv = next(g)
assert numpy.fabs(
wendy.energy(tx, tv, m, omega=omega) - E
) / E < 10.**-6., "Energy not conserved during approximate N-body integration with external harmonic potential"
cnt += 1
return None
def test_energy_ratio():
# Test that energy ratio gives ratio of kinetic to potential energy
x = numpy.array([-1.1, 0.1, 1.3])
v = numpy.array([3., 2., -5.])
m = numpy.array([1., 1., 1.])
g = wendy.nbody(x, v, m, 0.05)
cnt = 0
while cnt < 10:
tx, tv = next(g)
Erat = wendy.energy(tx, tv, m, energy_type=wendy.EnergyType.RATIO)
Epot = wendy.energy(tx, tv, m, energy_type=wendy.EnergyType.POTENTIAL)
Ekin = wendy.energy(tx, tv, m, energy_type=wendy.EnergyType.KINETIC)
assert Erat == Ekin / Epot, "Energy ratio should be kinetic divided potential energy"
cnt += 1
return None
def test_total_energy():
# Test that total energy is sum of potential and kinetic energy
x = numpy.array([-1.1, 0.1, 1.3])
v = numpy.array([3., 2., -5.])
m = numpy.array([1., 1., 1.])
g = wendy.nbody(x, v, m, 0.05)
cnt = 0
while cnt < 10:
tx, tv = next(g)
Etot = wendy.energy(tx, tv, m, energy_type=wendy.EnergyType.TOTAL)
Epot = wendy.energy(tx, tv, m, energy_type=wendy.EnergyType.POTENTIAL)
Ekin = wendy.energy(tx, tv, m, energy_type=wendy.EnergyType.KINETIC)
assert Etot == Epot + Ekin, "Total energy should be sum of kinetic and potential energies"
cnt += 1
return None
def test_potential_energy():
# Test potential energy for a simple system
x = numpy.array([-2., 0, 3.])
v = numpy.array([1, 2, 3])
m = numpy.array([.3, .3, .3])
assert (wendy.energy(x, v, m, energy_type=wendy.EnergyType.POTENTIAL) -
10.) < 1e-12, "Potential energy not correctly calculated"
def test_kinetic_energy():
# Test that kinetic energy is 0 for 0 velocities
x = numpy.array([-1.1, 0.1, 1.3])
v = numpy.array([0, 0, 0])
m = numpy.array([1., 1., 1.])
assert wendy.energy(
x, v, m, energy_type=wendy.EnergyType.KINETIC
) == 0, "Kinetic energy should be zero when v=0 for all particles."
# Test that kinetic energy is given by 1/2 mv^2
x = numpy.array([-1, 0, 1])
v = numpy.array([1.2, 2.3, -4.2])
m = numpy.array([.3, .3, .3])
ke = numpy.sum(0.5 * m * v**2)
assert ((wendy.energy(x, v, m, energy_type=wendy.EnergyType.KINETIC) - ke)
< 1e-12), "Kinetic energy should be 1/2 mv^2."
def test_samex():
# Test that the code works if two particles are at the exact same position
# middle ones setup such that they end up in the same place for the first
# force evaluation
x = numpy.array(
[-1.1, -2. * 0.05 / 2. / 10000, 0.3 * 0.05 / 2. / 10000, 1.3])
v = numpy.array([3., 2., -.3, -5.])
m = numpy.array([1., 1., 1., 1.])
g = wendy.nbody(x, v, m, 0.05, approx=True, nleap=10000)
E = wendy.energy(x, v, m)
cnt = 0
while cnt < 1:
tx, tv = next(g)
assert numpy.fabs(
wendy.energy(tx, tv, m) - E
) / E < 10.**-6., "Energy not conserved during approximate N-body integration"
cnt += 1
return None
def test_energy_conservation_sech2disk_manyparticles():
# Test that energy is conserved for a self-gravitating disk
N= 101
totmass= 1.
sigma= 1.
zh= 2.*sigma**2./totmass
x= numpy.arctanh(2.*numpy.random.uniform(size=N)-1)*zh
v= numpy.random.normal(size=N)*sigma
v-= numpy.mean(v) # stabilize
m= numpy.ones_like(x)/N*(1.+0.1*(2.*numpy.random.uniform(size=N)-1))
g= wendy.nbody(x,v,m,0.05)
E= wendy.energy(x,v,m)
cnt= 0
while cnt < 100:
tx,tv= next(g)
assert numpy.fabs(wendy.energy(tx,tv,m)-E) < 10.**-10., "Energy not conserved during simple N-body integration"
cnt+= 1
return None
def test_energy_conservation_sech2disk_manyparticles():
# Test that energy is conserved for a self-gravitating disk
N = 101
totmass = 1.
sigma = 1.
zh = 2. * sigma**2. / totmass
x = numpy.arctanh(2. * numpy.random.uniform(size=N) - 1) * zh
v = numpy.random.normal(size=N) * sigma
v -= numpy.mean(v) # stabilize
m = numpy.ones_like(x) / N * (1. + 0.1 *
(2. * numpy.random.uniform(size=N) - 1))
omega = 1.1
g = wendy.nbody(x, v, m, 0.05, omega=omega, approx=True, nleap=1000)
E = wendy.energy(x, v, m, omega=omega)
cnt = 0
while cnt < 100:
tx, tv = next(g)
assert numpy.fabs(
wendy.energy(tx, tv, m, omega=omega) - E
) / E < 10.**-6., "Energy not conserved during approximate N-body integration with external harmonic potential"
cnt += 1
return None
def test_energy_individual():
# Simple test that the individual energies are calculated correctly
x= numpy.array([-1.1,0.1,1.3])
v= numpy.array([3.,2.,-5.])
m= numpy.array([1.,2.,3.])
E= wendy.energy(x,v,m,individual=True)
assert numpy.fabs(E[0]-m[0]*v[0]**2./2.-m[0]*(m[1]*numpy.fabs(x[0]-x[1])
+m[2]*numpy.fabs(x[0]-x[2]))) < 10.**-10
assert numpy.fabs(E[1]-m[1]*v[1]**2./2.-m[1]*(m[0]*numpy.fabs(x[0]-x[1])
+m[2]*numpy.fabs(x[2]-x[1]))) < 10.**-10
assert numpy.fabs(E[2]-m[2]*v[2]**2./2.-m[2]*(m[0]*numpy.fabs(x[0]-x[2])
+m[1]*numpy.fabs(x[2]-x[1]))) < 10.**-10
return None
def test_notracermasses():
# approx should work with tracer sheets
# Test that energy is conserved for a self-gravitating disk
N = 101
totmass = 1.
sigma = 1.
zh = 2. * sigma**2. / totmass
x = numpy.arctanh(2. * numpy.random.uniform(size=N) - 1) * zh
v = numpy.random.normal(size=N) * sigma
v -= numpy.mean(v) # stabilize
m = numpy.ones_like(x) / N * (1. + 0.1 *
(2. * numpy.random.uniform(size=N) - 1))
m[N // 2:] = 0.
m *= 2.
g = wendy.nbody(x, v, m, 0.05, approx=True, nleap=1000)
E = wendy.energy(x, v, m)
cnt = 0
while cnt < 100:
tx, tv = next(g)
assert numpy.fabs(
wendy.energy(tx, tv, m) - E
) / E < 10.**-6., "Energy not conserved during approximate N-body integration with some tracer particles"
cnt += 1
return None