def test_x_storage_overlap(self):
# VectorFunction should not store references to arrays, it should
# store copies - this checks that updating an array in-place causes
# Scalar_Function.x to be updated.
ex = ExVectorialFunction()
x0 = np.array([1.0, 0.0])
vf = VectorFunction(ex.fun, x0, '3-point', ex.hess, None, None,
(-np.inf, np.inf), None)
assert x0 is not vf.x
assert_equal(vf.fun(x0), ex.fun(x0))
assert x0 is not vf.x
x0[0] = 2.
assert_equal(vf.fun(x0), ex.fun(x0))
assert x0 is not vf.x
x0[0] = 1.
assert_equal(vf.fun(x0), ex.fun(x0))
assert x0 is not vf.x
# now test with a HessianUpdate strategy specified
hess = BFGS()
x0 = np.array([1.0, 0.0])
vf = VectorFunction(ex.fun, x0, '3-point', hess, None, None,
(-np.inf, np.inf), None)
with pytest.warns(UserWarning):
# filter UserWarning because ExVectorialFunction is linear and
# a quasi-Newton approximation is used for the Hessian.
assert x0 is not vf.x
assert_equal(vf.fun(x0), ex.fun(x0))
assert x0 is not vf.x
x0[0] = 2.
assert_equal(vf.fun(x0), ex.fun(x0))
assert x0 is not vf.x
x0[0] = 1.
assert_equal(vf.fun(x0), ex.fun(x0))
assert x0 is not vf.x
def test_finite_difference_hess_linear_operator(self):
ex = ExVectorialFunction()
nfev = 0
njev = 0
nhev = 0
x0 = [1.0, 0.0]
v0 = [1.0, 2.0]
analit = VectorFunction(ex.fun, x0, ex.jac, ex.hess, None, None,
(-np.inf, np.inf), None)
nfev += 1
njev += 1
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev, nhev)
approx = VectorFunction(ex.fun, x0, ex.jac, '2-point', None, None,
(-np.inf, np.inf), None)
assert_(isinstance(approx.H, LinearOperator))
for p in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
assert_array_equal(analit.f, approx.f)
assert_array_almost_equal(analit.J, approx.J)
assert_array_almost_equal(analit.H.dot(p), approx.H.dot(p))
nfev += 1
njev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [2.0, 1.0]
H_analit = analit.hess(x, v0)
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
H_approx = approx.hess(x, v0)
assert_(isinstance(H_approx, LinearOperator))
for p in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
assert_array_almost_equal(H_analit.dot(p), H_approx.dot(p),
decimal=5)
njev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [2.1, 1.2]
v = [1.0, 1.0]
H_analit = analit.hess(x, v)
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
H_approx = approx.hess(x, v)
assert_(isinstance(H_approx, LinearOperator))
for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v))
njev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [2.5, 0.3]
_ = analit.jac(x)
H_analit = analit.hess(x, v0)
njev += 1
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
_ = approx.jac(x)
H_approx = approx.hess(x, v0)
assert_(isinstance(H_approx, LinearOperator))
for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v), decimal=4)
njev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [5.2, 2.3]
v = [2.3, 5.2]
_ = analit.jac(x)
H_analit = analit.hess(x, v)
njev += 1
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
_ = approx.jac(x)
H_approx = approx.hess(x, v)
assert_(isinstance(H_approx, LinearOperator))
for v in ([1.0, 2.0], [3.0, 4.0], [5.0, 2.0]):
assert_array_almost_equal(H_analit.dot(v), H_approx.dot(v), decimal=4)
njev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
def test_finite_difference_jac(self):
ex = ExVectorialFunction()
nfev = 0
njev = 0
x0 = [1.0, 0.0]
v0 = [0.0, 1.0]
analit = VectorFunction(ex.fun, x0, ex.jac, ex.hess, None, None,
(-np.inf, np.inf), None)
nfev += 1
njev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev, njev)
approx = VectorFunction(ex.fun, x0, '2-point', ex.hess, None, None,
(-np.inf, np.inf), None)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_equal(analit.f, approx.f)
assert_array_almost_equal(analit.J, approx.J)
x = [10, 0.3]
f_analit = analit.fun(x)
J_analit = analit.jac(x)
nfev += 1
njev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
f_approx = approx.fun(x)
J_approx = approx.jac(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_almost_equal(f_analit, f_approx)
assert_array_almost_equal(J_analit, J_approx, decimal=4)
x = [2.0, 1.0]
J_analit = analit.jac(x)
njev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
J_approx = approx.jac(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_almost_equal(J_analit, J_approx)
x = [2.5, 0.3]
f_analit = analit.fun(x)
J_analit = analit.jac(x)
nfev += 1
njev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
f_approx = approx.fun(x)
J_approx = approx.jac(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_almost_equal(f_analit, f_approx)
assert_array_almost_equal(J_analit, J_approx)
x = [2, 0.3]
f_analit = analit.fun(x)
J_analit = analit.jac(x)
nfev += 1
njev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
f_approx = approx.fun(x)
J_approx = approx.jac(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.njev, njev)
assert_array_equal(analit.njev+approx.njev, njev)
assert_array_almost_equal(f_analit, f_approx)
assert_array_almost_equal(J_analit, J_approx)