def test_updateMultipliers(self):
nP = 10
m = np.random.rand(nP)
W1 = sdiag(np.random.rand(nP))
W2 = sdiag(np.random.rand(nP))
phi1 = objectivefunction.L2ObjectiveFunction(W=W1)
phi2 = objectivefunction.L2ObjectiveFunction(W=W2)
phi = phi1 + phi2
self.assertTrue(phi(m) == phi1(m) + phi2(m))
phi.multipliers[0] = Zero()
self.assertTrue(phi(m) == phi2(m))
phi.multipliers[0] = 1.
phi.multipliers[1] = Zero()
self.assertTrue(len(phi.objfcts) == 2)
self.assertTrue(len(phi.multipliers) == 2)
self.assertTrue(len(phi) == 2)
self.assertTrue(phi(m) == phi1(m))
def test_2sum(self):
nP = 80
alpha1 = 100
alpha2 = 200
phi1 = (
objectivefunction.L2ObjectiveFunction(
W=sdiag(np.random.rand(nP))
) +
alpha1 * objectivefunction.L2ObjectiveFunction()
)
phi2 = objectivefunction.L2ObjectiveFunction() + alpha2 * phi1
self.assertTrue(phi2.test(eps=EPS))
self.assertTrue(len(phi1.multipliers) == 2)
self.assertTrue(len(phi2.multipliers) == 2)
self.assertTrue(len(phi1.objfcts) == 2)
self.assertTrue(len(phi2.objfcts) == 2)
self.assertTrue(len(phi2) == 2)
self.assertTrue(len(phi1) == 2)
self.assertTrue(len(phi2) == 2)
self.assertTrue(np.all(phi1.multipliers == np.r_[1., alpha1]))
self.assertTrue(np.all(phi2.multipliers == np.r_[1., alpha2]))
def test_early_exits(self):
nP = 10
m = np.random.rand(nP)
v = np.random.rand(nP)
W1 = sdiag(np.random.rand(nP))
phi1 = objectivefunction.L2ObjectiveFunction(W=W1)
phi2 = Error_if_Hit_ObjFct()
with self.assertRaises(Exception):
phi2(m)
with self.assertRaises(Exception):
phi2.deriv(m)
with self.assertRaises(Exception):
phi2.deriv2(m)
objfct = phi1 + 0 * phi2
self.assertTrue(len(objfct) == 2)
self.assertTrue(np.all(objfct.multipliers == np.r_[1, 0]))
self.assertTrue(objfct(m) == phi1(m))
self.assertTrue(np.all(objfct.deriv(m) == phi1.deriv(m)))
self.assertTrue(np.all(objfct.deriv2(m, v) == phi1.deriv2(m, v)))
objfct.multipliers[1] = Zero()
self.assertTrue(len(objfct) == 2)
self.assertTrue(np.all(objfct.multipliers == np.r_[1, 0]))
self.assertTrue(objfct(m) == phi1(m))
self.assertTrue(np.all(objfct.deriv(m) == phi1.deriv(m)))
self.assertTrue(np.all(objfct.deriv2(m, v) == phi1.deriv2(m, v)))
def test_zero(self):
z = Zero()
assert z == 0
assert not (z < 0)
assert z <= 0
assert not (z > 0)
assert z >= 0
assert +z == z
assert -z == z
assert z + 1 == 1
assert z + 3 + z == 3
assert z - 3 == -3
assert z - 3 - z == -3
assert 3 * z == 0
assert z * 3 == 0
assert z / 3 == 0
a = 1
a += z
assert a == 1
a = 1
a += z
assert a == 1
self.assertRaises(ZeroDivisionError, lambda: 3 / z)
assert mkvc(z) == 0
assert sdiag(z) * a == 0
assert z.T == 0
assert z.transpose() == 0
def test_sum_fail(self):
nP1 = 10
nP2 = 30
phi1 = objectivefunction.L2ObjectiveFunction(
W=sdiag(np.random.rand(nP1))
)
phi2 = objectivefunction.L2ObjectiveFunction(
W=sdiag(np.random.rand(nP2))
)
with self.assertRaises(Exception):
phi1 + phi2
with self.assertRaises(Exception):
phi1 + 100 * phi2
def test_mat_shape(self):
o = Identity()
S = sdiag(np.r_[2, 3])[:1, :]
self.assertRaises(ValueError, lambda: S + o)
def check(exp, ans):
assert np.all((exp).todense() == ans)
check(S * o, [[2, 0]])
check(S * -o, [[-2, 0]])
def test_scalarmul(self):
scalar = 10.
nP = 100
objfct_a = objectivefunction.L2ObjectiveFunction(
W=sdiag(np.random.randn(nP))
)
objfct_b = scalar * objfct_a
m = np.random.rand(nP)
objfct_c = objfct_a + objfct_b
self.assertTrue(scalar * objfct_a(m) == objfct_b(m))
self.assertTrue(objfct_b.test())
self.assertTrue(objfct_c(m) == objfct_a(m) + objfct_b(m))
self.assertTrue(len(objfct_c.objfcts) == 2)
self.assertTrue(len(objfct_c.multipliers) == 2)
self.assertTrue(len(objfct_c) == 2)
def test_mat_one(self):
o = Identity()
S = sdiag(np.r_[2, 3])
def check(exp, ans):
assert np.all((exp).todense() == ans)
check(S * o, [[2, 0], [0, 3]])
check(o * S, [[2, 0], [0, 3]])
check(S * -o, [[-2, 0], [0, -3]])
check(-o * S, [[-2, 0], [0, -3]])
check(S / o, [[2, 0], [0, 3]])
check(S / -o, [[-2, 0], [0, -3]])
self.assertRaises(NotImplementedError, lambda: o / S)
check(S + o, [[3, 0], [0, 4]])
check(o + S, [[3, 0], [0, 4]])
check(S - o, [[1, 0], [0, 2]])
check(S + -o, [[1, 0], [0, 2]])
check(-o + S, [[1, 0], [0, 2]])
def test_invXXXBlockDiagonal(self):
a = [np.random.rand(5, 1) for i in range(4)]
B = inv2X2BlockDiagonal(*a)
A = sp.vstack((sp.hstack(
(sdiag(a[0]), sdiag(a[1]))), sp.hstack(
(sdiag(a[2]), sdiag(a[3])))))
Z2 = B * A - sp.identity(10)
self.assertTrue(np.linalg.norm(Z2.todense().ravel(), 2) < TOL)
a = [np.random.rand(5, 1) for i in range(9)]
B = inv3X3BlockDiagonal(*a)
A = sp.vstack((sp.hstack((sdiag(a[0]), sdiag(a[1]), sdiag(a[2]))),
sp.hstack((sdiag(a[3]), sdiag(a[4]), sdiag(a[5]))),
sp.hstack((sdiag(a[6]), sdiag(a[7]), sdiag(a[8])))))
Z3 = B * A - sp.identity(15)
self.assertTrue(np.linalg.norm(Z3.todense().ravel(), 2) < TOL)
def test_mat_zero(self):
z = Zero()
S = sdiag(np.r_[2, 3])
assert S * z == 0