def test_num_jac():
def fun(t, y):
return np.vstack([
-0.04 * y[0] + 1e4 * y[1] * y[2],
0.04 * y[0] - 1e4 * y[1] * y[2] - 3e7 * y[1] ** 2,
3e7 * y[1] ** 2
])
def jac(t, y):
return np.array([
[-0.04, 1e4 * y[2], 1e4 * y[1]],
[0.04, -1e4 * y[2] - 6e7 * y[1], -1e4 * y[1]],
[0, 6e7 * y[1], 0]
])
t = 1
y = np.array([1, 0, 0])
J_true = jac(t, y)
threshold = 1e-5
f = fun(t, y).ravel()
J_num, factor = num_jac(fun, t, y, f, threshold, None)
assert_allclose(J_num, J_true, rtol=1e-5, atol=1e-5)
J_num, factor = num_jac(fun, t, y, f, threshold, factor)
assert_allclose(J_num, J_true, rtol=1e-5, atol=1e-5)
def test_num_jac():
def fun(t, y):
return np.vstack([
-0.04 * y[0] + 1e4 * y[1] * y[2],
0.04 * y[0] - 1e4 * y[1] * y[2] - 3e7 * y[1] ** 2,
3e7 * y[1] ** 2
])
def jac(t, y):
return np.array([
[-0.04, 1e4 * y[2], 1e4 * y[1]],
[0.04, -1e4 * y[2] - 6e7 * y[1], -1e4 * y[1]],
[0, 6e7 * y[1], 0]
])
t = 1
y = np.array([1, 0, 0])
J_true = jac(t, y)
threshold = 1e-5
f = fun(t, y).ravel()
J_num, factor = num_jac(fun, t, y, f, threshold, None)
assert_allclose(J_num, J_true, rtol=1e-5, atol=1e-5)
J_num, factor = num_jac(fun, t, y, f, threshold, factor)
assert_allclose(J_num, J_true, rtol=1e-5, atol=1e-5)
def test_num_jac_sparse():
def fun(t, y):
e = y[1:]**3 - y[:-1]**2
z = np.zeros(y.shape[1])
return np.vstack((z, 3 * e)) + np.vstack((2 * e, z))
def structure(n):
A = np.zeros((n, n), dtype=int)
A[0, 0] = 1
A[0, 1] = 1
for i in range(1, n - 1):
A[i, i - 1:i + 2] = 1
A[-1, -1] = 1
A[-1, -2] = 1
return A
np.random.seed(0)
n = 20
y = np.random.randn(n)
A = structure(n)
groups = group_columns(A)
f = fun(0, y[:, None]).ravel()
# Compare dense and sparse results, assuming that dense implementation
# is correct (as it is straightforward).
J_num_sparse, factor_sparse = num_jac(fun,
0,
y.ravel(),
f,
1e-8,
None,
sparsity=(A, groups))
J_num_dense, factor_dense = num_jac(fun, 0, y.ravel(), f, 1e-8, None)
assert_allclose(J_num_dense,
J_num_sparse.toarray(),
rtol=1e-12,
atol=1e-14)
assert_allclose(factor_dense, factor_sparse, rtol=1e-12, atol=1e-14)
# Take small factors to trigger their recomputing inside.
factor = np.random.uniform(0, 1e-12, size=n)
J_num_sparse, factor_sparse = num_jac(fun,
0,
y.ravel(),
f,
1e-8,
factor,
sparsity=(A, groups))
J_num_dense, factor_dense = num_jac(fun, 0, y.ravel(), f, 1e-8, factor)
assert_allclose(J_num_dense,
J_num_sparse.toarray(),
rtol=1e-12,
atol=1e-14)
assert_allclose(factor_dense, factor_sparse, rtol=1e-12, atol=1e-14)
def test_num_jac_sparse():
def fun(t, y):
e = y[1:]**3 - y[:-1]**2
z = np.zeros(y.shape[1])
return np.vstack((z, 3 * e)) + np.vstack((2 * e, z))
def structure(n):
A = np.zeros((n, n), dtype=int)
A[0, 0] = 1
A[0, 1] = 1
for i in range(1, n - 1):
A[i, i - 1: i + 2] = 1
A[-1, -1] = 1
A[-1, -2] = 1
return A
np.random.seed(0)
n = 20
y = np.random.randn(n)
A = structure(n)
groups = group_columns(A)
f = fun(0, y[:, None]).ravel()
# Compare dense and sparse results, assuming that dense implementation
# is correct (as it is straightforward).
J_num_sparse, factor_sparse = num_jac(fun, 0, y.ravel(), f, 1e-8, None,
sparsity=(A, groups))
J_num_dense, factor_dense = num_jac(fun, 0, y.ravel(), f, 1e-8, None)
assert_allclose(J_num_dense, J_num_sparse.toarray(),
rtol=1e-12, atol=1e-14)
assert_allclose(factor_dense, factor_sparse, rtol=1e-12, atol=1e-14)
# Take small factors to trigger their recomputing inside.
factor = np.random.uniform(0, 1e-12, size=n)
J_num_sparse, factor_sparse = num_jac(fun, 0, y.ravel(), f, 1e-8, factor,
sparsity=(A, groups))
J_num_dense, factor_dense = num_jac(fun, 0, y.ravel(), f, 1e-8, factor)
assert_allclose(J_num_dense, J_num_sparse.toarray(),
rtol=1e-12, atol=1e-14)
assert_allclose(factor_dense, factor_sparse, rtol=1e-12, atol=1e-14)
def jac_wrapped(y):
f = fun_vectorized(y)
t = None # Scipy's numjac method assumes time is a separate variable
global jac_factor # TODO: object oriented implementation of the Newton solver ?
J, jac_factor = num_jac(fun=lambda t, y: fun_vectorized(y),
t=t,
y=y,
f=f,
threshold=atol,
factor=jac_factor,
sparsity=sparsity)
return J
def jac_wrapped(t, y, f):
self.njev += 1
J, self.jac_factor = num_jac(self.fun_vectorized, t, y, f,
self.atol, self.jac_factor,
sparsity)
return J
