def test_lowest_x(self):
# ScalarFunction should remember the lowest func(x) visited.
x0 = np.array([2, 3, 4])
sf = ScalarFunction(rosen, x0, (), rosen_der, rosen_hess,
None, None)
sf.fun([1, 1, 1])
sf.fun(x0)
sf.fun([1.01, 1, 1.0])
sf.grad([1.01, 1, 1.0])
assert_equal(sf._lowest_f, 0.0)
assert_equal(sf._lowest_x, [1.0, 1.0, 1.0])
sf = ScalarFunction(rosen, x0, (), '2-point', rosen_hess,
None, (-np.inf, np.inf))
sf.fun([1, 1, 1])
sf.fun(x0)
sf.fun([1.01, 1, 1.0])
sf.grad([1.01, 1, 1.0])
assert_equal(sf._lowest_f, 0.0)
assert_equal(sf._lowest_x, [1.0, 1.0, 1.0])
def test_finite_difference_grad(self):
ex = ExScalarFunction()
nfev = 0
ngev = 0
x0 = [1.0, 0.0]
analit = ScalarFunction(ex.fun, x0, (), ex.grad,
ex.hess, None, (-np.inf, np.inf))
nfev += 1
ngev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev, nfev)
approx = ScalarFunction(ex.fun, x0, (), '2-point',
ex.hess, None, (-np.inf, np.inf))
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(analit.f, approx.f)
assert_array_almost_equal(analit.g, approx.g)
x = [10, 0.3]
f_analit = analit.fun(x)
g_analit = analit.grad(x)
nfev += 1
ngev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
f_approx = approx.fun(x)
g_approx = approx.grad(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_almost_equal(f_analit, f_approx)
assert_array_almost_equal(g_analit, g_approx)
x = [2.0, 1.0]
g_analit = analit.grad(x)
ngev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
g_approx = approx.grad(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_almost_equal(g_analit, g_approx)
x = [2.5, 0.3]
f_analit = analit.fun(x)
g_analit = analit.grad(x)
nfev += 1
ngev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
f_approx = approx.fun(x)
g_approx = approx.grad(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_almost_equal(f_analit, f_approx)
assert_array_almost_equal(g_analit, g_approx)
x = [2, 0.3]
f_analit = analit.fun(x)
g_analit = analit.grad(x)
nfev += 1
ngev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
f_approx = approx.fun(x)
g_approx = approx.grad(x)
nfev += 3
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_almost_equal(f_analit, f_approx)
assert_array_almost_equal(g_analit, g_approx)
def test_finite_difference_hess_linear_operator(self):
ex = ExScalarFunction()
nfev = 0
ngev = 0
nhev = 0
x0 = [1.0, 0.0]
analit = ScalarFunction(ex.fun, x0, (), ex.grad,
ex.hess, None, (-np.inf, np.inf))
nfev += 1
ngev += 1
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev, nhev)
approx = ScalarFunction(ex.fun, x0, (), ex.grad,
'2-point', None, (-np.inf, np.inf))
assert_(isinstance(approx.H, LinearOperator))
for v 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.g, approx.g)
assert_array_almost_equal(analit.H.dot(v), approx.H.dot(v))
nfev += 1
ngev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [2.0, 1.0]
H_analit = analit.hess(x)
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
H_approx = approx.hess(x)
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))
ngev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [2.1, 1.2]
H_analit = analit.hess(x)
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
H_approx = approx.hess(x)
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))
ngev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [2.5, 0.3]
_ = analit.grad(x)
H_analit = analit.hess(x)
ngev += 1
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
_ = approx.grad(x)
H_approx = approx.hess(x)
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))
ngev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
x = [5.2, 2.3]
_ = analit.grad(x)
H_analit = analit.hess(x)
ngev += 1
nhev += 1
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)
_ = approx.grad(x)
H_approx = approx.hess(x)
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))
ngev += 4
assert_array_equal(ex.nfev, nfev)
assert_array_equal(analit.nfev+approx.nfev, nfev)
assert_array_equal(ex.ngev, ngev)
assert_array_equal(analit.ngev+approx.ngev, ngev)
assert_array_equal(ex.nhev, nhev)
assert_array_equal(analit.nhev+approx.nhev, nhev)