def test_multiple_vector_valued(self):
"""
For a function that returns a vector rather than a scalar, make
sure Dofs.f(), Dofs.jac(), and Dofs.fd_jac() behave correctly.
"""
for nparams1 in range(1, 5):
for nvals1 in range(1, 5):
nparams2 = np.random.randint(1, 6)
nparams3 = np.random.randint(1, 6)
nvals2 = np.random.randint(1, 6)
nvals3 = np.random.randint(1, 6)
o1 = Affine(nparams=nparams1, nvals=nvals1)
o2 = Affine(nparams=nparams2, nvals=nvals2)
o3 = Affine(nparams=nparams3, nvals=nvals3)
dofs = Dofs([o1, o2, o3], diff_method="centered")
dofs.set(
(np.random.rand(nparams1 + nparams2 + nparams3) - 0.5) * 4)
f1 = np.matmul(o1.A, o1.x) + o1.B
f2 = np.matmul(o2.A, o2.x) + o2.B
f3 = np.matmul(o3.A, o3.x) + o3.B
np.testing.assert_allclose(dofs.f(), np.concatenate((f1, f2, f3)), \
rtol=1e-13, atol=1e-13)
true_jac = np.zeros(
(nvals1 + nvals2 + nvals3, nparams1 + nparams2 + nparams3))
true_jac[0:nvals1, 0:nparams1] = o1.A
true_jac[nvals1:nvals1 + nvals2,
nparams1:nparams1 + nparams2] = o2.A
true_jac[nvals1 + nvals2:nvals1 + nvals2 + nvals3, \
nparams1 + nparams2:nparams1 + nparams2 + nparams3] = o3.A
np.testing.assert_allclose(dofs.jac(),
true_jac,
rtol=1e-13,
atol=1e-13)
np.testing.assert_allclose(dofs.fd_jac(), \
true_jac, rtol=1e-7, atol=1e-7)
def test_mixed_vector_valued(self):
"""
For a mixture of functions that return a scalar vs return a
vector, make sure Dofs.f(), Dofs.jac(), and Dofs.fd_jac()
behave correctly.
"""
for nparams1 in range(1, 5):
for nvals1 in range(1, 5):
nparams2 = np.random.randint(1, 6)
nparams3 = np.random.randint(1, 6)
nvals2 = np.random.randint(1, 6)
nvals3 = np.random.randint(1, 6)
o1 = Affine(nparams=nparams1, nvals=nvals1)
o2 = Affine(nparams=nparams2, nvals=nvals2)
o3 = Affine(nparams=nparams3, nvals=nvals3)
a1 = Adder(n=2)
a2 = Adder(n=3)
dofs = Dofs([o1, o2, a1, o3, a2], diff_method="centered")
dofs.set(
(np.random.rand(nparams1 + nparams2 + nparams3 + 5) - 0.5)
* 4)
f1 = np.matmul(o1.A, o1.x) + o1.B
f2 = np.matmul(o2.A, o2.x) + o2.B
f3 = np.array([a1.f])
f4 = np.matmul(o3.A, o3.x) + o3.B
f5 = np.array([a2.f])
np.testing.assert_allclose(dofs.f(), np.concatenate((f1, f2, f3, f4, f5)), \
rtol=1e-13, atol=1e-13)
true_jac = np.zeros((nvals1 + nvals2 + nvals3 + 2,
nparams1 + nparams2 + nparams3 + 5))
true_jac[0:nvals1, 0:nparams1] = o1.A
true_jac[nvals1:nvals1 + nvals2,
nparams1:nparams1 + nparams2] = o2.A
true_jac[nvals1 + nvals2:nvals1 + nvals2 + 1, \
nparams1 + nparams2:nparams1 + nparams2 + 2] = np.ones(2)
true_jac[nvals1 + nvals2 + 1:nvals1 + nvals2 + 1 + nvals3, \
nparams1 + nparams2 + 2:nparams1 + nparams2 + 2 + nparams3] = o3.A
true_jac[nvals1 + nvals2 + 1 + nvals3:nvals1 + nvals2 + nvals3 + 2, \
nparams1 + nparams2 + nparams3 + 2:nparams1 + nparams2 + nparams3 + 5] = np.ones(3)
np.testing.assert_allclose(dofs.jac(),
true_jac,
rtol=1e-13,
atol=1e-13)
np.testing.assert_allclose(dofs.fd_jac(), \
true_jac, rtol=1e-7, atol=1e-7)
def test_vector_valued(self):
"""
For a function that returns a vector rather than a scalar, make
sure Dofs.f(), Dofs.jac(), and Dofs.fd_jac() behave correctly.
"""
for nparams in range(1, 5):
for nvals in range(1, 5):
o = Affine(nparams=nparams, nvals=nvals)
o.set_dofs((np.random.rand(nparams) - 0.5) * 4)
dofs = Dofs([o], diff_method="centered")
np.testing.assert_allclose(dofs.f(), np.matmul(o.A, o.x) + o.B, \
rtol=1e-13, atol=1e-13)
np.testing.assert_allclose(dofs.jac(),
o.A,
rtol=1e-13,
atol=1e-13)
np.testing.assert_allclose(dofs.fd_jac(), \
o.A, rtol=1e-7, atol=1e-7)
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)
def test_Jacobian(self):
for n in range(1, 20):
v1 = np.random.rand() * 4 - 2
v2 = np.random.rand() * 4 - 2
o = TestObject2(v1, v2)
o.adder.set_dofs(np.random.rand(2) * 4 - 2)
o.t.set_dofs([np.random.rand() * 4 - 2])
o.t.adder1.set_dofs(np.random.rand(3) * 4 - 2)
o.t.adder2.set_dofs(np.random.rand(2) * 4 - 2)
r = Rosenbrock(b=3.0)
r.set_dofs(np.random.rand(2) * 3 - 1.5)
a = Affine(nparams=3, nvals=3)
# Randomly fix some of the degrees of freedom
o.fixed = np.random.rand(2) > 0.5
o.adder.fixed = np.random.rand(2) > 0.5
o.t.adder1.fixed = np.random.rand(3) > 0.5
o.t.adder2.fixed = np.random.rand(2) > 0.5
r.fixed = np.random.rand(2) > 0.5
a.fixed = np.random.rand(3) > 0.5
rtol = 1e-6
atol = 1e-6
for j in range(4):
# Try different sets of the objects:
if j == 0:
dofs = Dofs([o.J, r.terms, o.t.J])
nvals = 4
nvals_per_func = [1, 2, 1]
elif j == 1:
dofs = Dofs([r.term2, r.terms])
nvals = 3
nvals_per_func = [1, 2]
elif j == 2:
dofs = Dofs(
[r.term2,
Target(o.t, 'f'), r.term1,
Target(o, 'f')])
nvals = 4
nvals_per_func = [1, 1, 1, 1]
elif j == 3:
dofs = Dofs([a, o])
nvals = 4
nvals_per_func = [3, 1]
jac = dofs.jac()
dofs.diff_method = "forward"
fd_jac = dofs.fd_jac()
dofs.diff_method = "centered"
fd_jac_centered = dofs.fd_jac()
#print('j=', j, ' Diff in Jacobians:', jac - fd_jac)
#print('jac: ', jac)
#print('fd_jac: ', fd_jac)
#print('fd_jac_centered: ', fd_jac_centered)
#print('shapes: jac=', jac.shape, ' fd_jac=', fd_jac.shape, ' fd_jac_centered=', fd_jac_centered.shape)
np.testing.assert_allclose(jac, fd_jac, rtol=rtol, atol=atol)
np.testing.assert_allclose(fd_jac,
fd_jac_centered,
rtol=rtol,
atol=atol)
self.assertEqual(dofs.nvals, nvals)
self.assertEqual(list(dofs.nvals_per_func), nvals_per_func)