def test_derivs(self):
ns = range(1, 6)
for ee, d in (self.e, 1e-6), (self.p, 1e-6):
xd = self.x + [[0, 0, 0], [d, 0, 0], [0, d, 0], [0, 0, d]]
for n in ns:
p = utils.expand_tensor(ee.potential(self.x, n))[0]
pd = utils.expand_tensor(ee.potential(xd, n-1))
pd = (pd[1:] - pd[0])/d
nptest.assert_allclose(p, pd, rtol=d, atol=1e-14,
err_msg="ee=%s, n=%i" % (ee, n))
def test_derivs(self):
ns = range(1, 6)
d = 1e-7
xd = self.x + [[0, 0, 0], [d, 0, 0], [0, d, 0], [0, 0, d]]
for n in ns:
p = utils.expand_tensor(self.e.potential(self.x, n))[0]
pd = utils.expand_tensor(self.e.potential(xd, n-1))
pd = (pd[1:] - pd[0])/d
for k, (i, j) in enumerate(zip(p.ravel(), pd.ravel())):
nptest.assert_allclose(i, j, rtol=d, atol=d/100,
err_msg="n=%i, k=%i" % (n,k))
def test_expand_tensor(self):
a = np.array([1, 2, 3.])[None, :]
nptest.assert_equal(utils.expand_tensor(a), a)
b = np.array([1, 2, 3, 4, 5])[None, :]
b1 = np.array([1, 2, 3, 2, 4, 5, 3, 5, -5] # triu
).reshape((1, 3, 3))
nptest.assert_equal(utils.expand_tensor(b), b1)
c = np.random.random(5)
ti, tj = np.triu_indices(3)
ce = utils.expand_tensor(c[None, :])[0, ti, tj]
nptest.assert_equal(ce[:5], c)
nptest.assert_equal(ce[5], -c[0]-c[3])
def test_expand_tensor_trace(self):
d = np.random.random(5)[None, :]
de = utils.expand_tensor(d)
nptest.assert_almost_equal(de[0].trace(), 0)
d = np.random.random(7)[None, :]
de = utils.expand_tensor(d)
nptest.assert_almost_equal(de[0].trace(), np.zeros((3)))
d = np.random.random(9)[None, :]
de = utils.expand_tensor(d)
nptest.assert_almost_equal(de[0].trace(), np.zeros((3,3)))
d = np.random.random(11)[None, :]
de = utils.expand_tensor(d)
nptest.assert_almost_equal(de[0].trace(), np.zeros((3,3,3)))
def test_derivs(self):
ns = range(1, 6)
for ee, d in (self.e, 1e-6), (self.p, 1e-6):
xd = self.x + [[0, 0, 0], [d, 0, 0], [0, d, 0], [0, 0, d]]
for n in ns:
p = utils.expand_tensor(ee.potential(self.x, n))[0]
pd = utils.expand_tensor(ee.potential(xd, n - 1))
pd = (pd[1:] - pd[0]) / d
nptest.assert_allclose(p,
pd,
rtol=d,
atol=1e-14,
err_msg="ee=%s, n=%i" % (ee, n))
def test_derivs(self):
ns = range(1, 6)
d = 1e-7
xd = self.x + [[0, 0, 0], [d, 0, 0], [0, d, 0], [0, 0, d]]
for n in ns:
p = utils.expand_tensor(self.e.potential(self.x, n))[0]
pd = utils.expand_tensor(self.e.potential(xd, n - 1))
pd = (pd[1:] - pd[0]) / d
for k, (i, j) in enumerate(zip(p.ravel(), pd.ravel())):
nptest.assert_allclose(i,
j,
rtol=d,
atol=d / 100,
err_msg="n=%i, k=%i" % (n, k))
def test_expand_select_tensor(self):
for n in 3, 5, 7, 9, 11:
d = np.random.random(n)[None, :]
de = utils.expand_tensor(d)
ds = utils.select_tensor(de)
nptest.assert_equal(d, ds)