def test_jac(mesh, ref1, ref2, refi):
X, cells = mesh()
jac = cpt.jac_uniform(X, cells)
nc = jac.flatten()
norm1 = numpy.linalg.norm(nc, ord=1)
norm2 = numpy.linalg.norm(nc, ord=2)
normi = numpy.linalg.norm(nc, ord=numpy.inf)
tol = 1.0e-12
assert abs(norm1 - ref1) < tol * ref1
assert abs(norm2 - ref2) < tol * ref2
assert abs(normi - refi) < tol * refi
return
def test_simple1_jac():
X, cells = simple1()
# First assert that the Jacobian at interior points coincides with the finite
# difference computed for the energy component from that point. Note that the
# contribution from all other points is disregarded here, just like in the
# definition of the Jacobian of Chen-Holst; it's only an approximation after all.
jac = cpt.jac_uniform(X, cells)
for j in [0, 1]:
eps = 1.0e-7
x0 = X.copy()
x1 = X.copy()
x0[4, j] -= eps
x1[4, j] += eps
f1 = cpt._energy_uniform_per_node(x1, cells)
f0 = cpt._energy_uniform_per_node(x0, cells)
dE = (f1 - f0) / (2 * eps)
assert abs(dE[4] - jac[4, j]) < 1.0e-10
return