def test_x_storage_overlap(self):
# Scalar_Function 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.
def f(x):
return np.sum(np.asarray(x)**2)
x = np.array([1., 2., 3.])
sf = ScalarFunction(f, x, (), '3-point', lambda x: x, None,
(-np.inf, np.inf))
assert x is not sf.x
assert_equal(sf.fun(x), 14.0)
assert x is not sf.x
x[0] = 0.
f1 = sf.fun(x)
assert_equal(f1, 13.0)
x[0] = 1
f2 = sf.fun(x)
assert_equal(f2, 14.0)
assert x is not sf.x
# now test with a HessianUpdate strategy specified
hess = BFGS()
x = np.array([1., 2., 3.])
sf = ScalarFunction(f, x, (), '3-point', hess, None, (-np.inf, np.inf))
assert x is not sf.x
assert_equal(sf.fun(x), 14.0)
assert x is not sf.x
x[0] = 0.
f1 = sf.fun(x)
assert_equal(f1, 13.0)
x[0] = 1
f2 = sf.fun(x)
assert_equal(f2, 14.0)
assert x is not sf.x
# gh13740 x is changed in user function
def ff(x):
x *= x # overwrite x
return np.sum(x)
x = np.array([1., 2., 3.])
sf = ScalarFunction(ff, x, (), '3-point', lambda x: x, None,
(-np.inf, np.inf))
assert x is not sf.x
assert_equal(sf.fun(x), 14.0)
assert_equal(sf.x, np.array([1., 2., 3.]))
assert x is not sf.x
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_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])