def test_get_dofs(self):
"""
Test that we can convert the degrees of freedom into a 1D vector
"""
# First try an axisymmetric surface for simplicity:
s = SurfaceRZFourier()
s.rc[0, 0] = 1.3
s.rc[1, 0] = 0.4
s.zs[0, 0] = 0.3
s.zs[1, 0] = 0.2
dofs = s.get_dofs()
self.assertEqual(dofs.shape, (3, ))
self.assertAlmostEqual(dofs[0], 1.3)
self.assertAlmostEqual(dofs[1], 0.4)
self.assertAlmostEqual(dofs[2], 0.2)
# Now try a nonaxisymmetric shape:
s = SurfaceRZFourier(mpol=3, ntor=1)
s.rc[:, :] = [[100, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
s.zs[:, :] = [[101, 102, 13], [14, 15, 16], [17, 18, 19], [20, 21, 22]]
dofs = s.get_dofs()
self.assertEqual(dofs.shape, (21, ))
for j in range(21):
self.assertAlmostEqual(dofs[j], j + 2)
def get_surface(surfacetype, stellsym, phis=None, thetas=None):
np.random.seed(2)
mpol = 4
ntor = 3
nfp = 2
phis = phis if phis is not None else np.linspace(0, 1, 31, endpoint=False)
thetas = thetas if thetas is not None else np.linspace(
0, 1, 31, endpoint=False)
if surfacetype == "SurfaceRZFourier":
from simsopt.geo.surfacerzfourier import SurfaceRZFourier
s = SurfaceRZFourier(nfp=nfp,
stellsym=stellsym,
mpol=mpol,
ntor=ntor,
quadpoints_phi=phis,
quadpoints_theta=thetas)
s.set_dofs(s.get_dofs() * 0.)
s.rc[0, ntor + 0] = 1
s.rc[1, ntor + 0] = 0.3
s.zs[1, ntor + 0] = 0.3
elif surfacetype == "SurfaceXYZFourier":
from simsopt.geo.surfacexyzfourier import SurfaceXYZFourier
s = SurfaceXYZFourier(nfp=nfp,
stellsym=stellsym,
mpol=mpol,
ntor=ntor,
quadpoints_phi=phis,
quadpoints_theta=thetas)
s.set_dofs(s.get_dofs() * 0.)
s.xc[0, ntor + 1] = 1.
s.xc[1, ntor + 1] = 0.1
s.ys[0, ntor + 1] = 1.
s.ys[1, ntor + 1] = 0.1
s.zs[1, ntor] = 0.1
elif surfacetype == "SurfaceXYZTensorFourier":
from simsopt.geo.surfacexyztensorfourier import SurfaceXYZTensorFourier
s = SurfaceXYZTensorFourier(nfp=nfp,
stellsym=stellsym,
mpol=mpol,
ntor=ntor,
quadpoints_phi=phis,
quadpoints_theta=thetas)
s.set_dofs(s.get_dofs() * 0.)
s.x[0, 0] = 1.0
s.x[1, 0] = 0.1
s.z[mpol + 1, 0] = 0.1
else:
assert False
dofs = np.asarray(s.get_dofs())
np.random.seed(2)
rand_scale = 0.01
s.set_dofs(dofs +
rand_scale * np.random.rand(len(dofs)).reshape(dofs.shape))
return s
def test_surface_sampling(self):
np.random.seed(1)
nquadpoints = int(4e2)
surface = SurfaceRZFourier(nfp=1, stellsym=True, mpol=1, ntor=0, quadpoints_phi=nquadpoints, quadpoints_theta=nquadpoints)
dofs = surface.get_dofs()
dofs[0] = 1
dofs[1] = 0.8
surface.set_dofs(dofs)
n = np.linalg.norm(surface.normal(), axis=2)
print(np.min(n), np.max(n))
start = int(0.2*nquadpoints)
stop = int(0.5*nquadpoints)
from scipy.integrate import simpson
quadpoints_phi = surface.quadpoints_phi
quadpoints_theta = surface.quadpoints_theta
lineintegrals = [simpson(y=n[i, start:stop], x=quadpoints_theta[start:stop]) for i in range(start, stop)]
area_of_subset = simpson(y=lineintegrals, x=quadpoints_phi[start:stop])
total_area = surface.area()
print("area_of_subset/total_area", area_of_subset/total_area)
nsamples = int(1e6)
xyz, idxs = draw_uniform_on_surface(surface, nsamples, safetyfactor=10)
samples_in_range = np.sum((idxs[0] >= start) * (idxs[0] < stop)*(idxs[1] >= start) * (idxs[1] < stop))
print("samples_in_range/nsamples", samples_in_range/nsamples)
print("fraction of samples if uniform", (stop-start)**2/(nquadpoints**2))
assert abs(samples_in_range/nsamples - area_of_subset/total_area) < 1e-2
def test_change_resolution(self):
"""
Check that we can change mpol and ntor.
"""
for mpol in [1, 2]:
for ntor in [0, 1]:
s = SurfaceRZFourier(mpol=mpol, ntor=ntor)
n = len(s.get_dofs())
s.set_dofs((np.random.rand(n) - 0.5) * 0.01)
s.set_rc(0, 0, 1.0)
s.set_rc(1, 0, 0.1)
s.set_zs(1, 0, 0.13)
v1 = s.volume()
a1 = s.area()
s.change_resolution(mpol + 1, ntor)
s.recalculate = True
v2 = s.volume()
a2 = s.area()
self.assertAlmostEqual(v1, v2)
self.assertAlmostEqual(a1, a2)
s.change_resolution(mpol, ntor + 1)
s.recalculate = True
v2 = s.volume()
a2 = s.area()
self.assertAlmostEqual(v1, v2)
self.assertAlmostEqual(a1, a2)
s.change_resolution(mpol + 1, ntor + 1)
s.recalculate = True
v2 = s.volume()
a2 = s.area()
self.assertAlmostEqual(v1, v2)
self.assertAlmostEqual(a1, a2)
def test_convert_back(self):
"""
If we start with a SurfaceRZFourier, convert to Garabedian, and
convert back to SurfaceFourier, we should get back what we
started with.
"""
for mpol in range(1, 4):
for ntor in range(5):
for nfp in range(1, 4):
sf1 = SurfaceRZFourier(nfp=nfp, mpol=mpol, ntor=ntor)
# Set all dofs to random numbers in [-2, 2]:
sf1.set_dofs(
(np.random.rand(len(sf1.get_dofs())) - 0.5) * 4)
sg = sf1.to_Garabedian()
sf2 = sg.to_RZFourier()
np.testing.assert_allclose(sf1.rc, sf2.rc)
np.testing.assert_allclose(sf1.zs, sf2.zs)
def test_derivatives(self):
"""
Check the automatic differentiation for area and volume.
"""
for mpol in range(1, 3):
for ntor in range(2):
for nfp in range(1, 4):
s = SurfaceRZFourier(nfp=nfp, mpol=mpol, ntor=ntor)
x0 = s.get_dofs()
x = np.random.rand(len(x0)) - 0.5
x[0] = np.random.rand() + 2
# This surface will probably self-intersect, but I
# don't think this actually matters here.
s.set_dofs(x)
dofs = Dofs([s.area, s.volume])
jac = dofs.jac()
fd_jac = dofs.fd_jac()
print('difference for surface test_derivatives:',
jac - fd_jac)
np.testing.assert_allclose(jac,
fd_jac,
rtol=1e-4,
atol=1e-4)
