def test_resitance_network_3(self):
''' Test unconnected network of two nodes
'''
# network topology: two unconnected nodes
r_arr = np.array([0, np.inf, 0])
RN = tl.ResistanceNetwork(2, r_arr)
# test resistance is infinite
self.assertTrue(np.isinf(RN.get_two_point_resistance(0, 1)))
def test_resitance_network_4(self):
''' Test two-point resistance of series node network with unconnected node
'''
# network topology: series of 6 nodes with random resistors between
r01, r12, r23, r34, r45 = 3.26096629, 0.90862276, 2.73187024, 3.74048988, np.inf
r_arr = np.array([
0.0, r01, 0.0, np.inf, r12, 0.0, np.inf, np.inf, r23, 0.0, np.inf,
np.inf, np.inf, r34, 0.0, np.inf, np.inf, np.inf, np.inf, r45, 0.0
])
RN = tl.ResistanceNetwork(6, r_arr)
# test two point resistance
er01 = r01
er02 = r01 + r12
er03 = er02 + r23
er04 = er03 + r34
er05 = er04 + r45
er12 = r12
er13 = er12 + r23
er14 = er13 + r34
er15 = er14 + r45
er23 = r23
er24 = er23 + r34
er25 = er24 + r45
er34 = r34
er35 = er34 + r45
er45 = r45
self.assertAlmostEqual(RN.get_two_point_resistance(0, 1), er01)
self.assertAlmostEqual(RN.get_two_point_resistance(0, 2), er02)
self.assertAlmostEqual(RN.get_two_point_resistance(0, 3), er03)
self.assertAlmostEqual(RN.get_two_point_resistance(0, 4), er04)
self.assertAlmostEqual(RN.get_two_point_resistance(1, 2), er12)
self.assertAlmostEqual(RN.get_two_point_resistance(1, 3), er13)
self.assertAlmostEqual(RN.get_two_point_resistance(1, 4), er14)
self.assertAlmostEqual(RN.get_two_point_resistance(2, 3), er23)
self.assertAlmostEqual(RN.get_two_point_resistance(2, 4), er24)
self.assertAlmostEqual(RN.get_two_point_resistance(3, 4), er34)
# singular nodes
self.assertAlmostEqual(RN.get_two_point_resistance(0, 0), 0.0)
self.assertAlmostEqual(RN.get_two_point_resistance(1, 1), 0.0)
self.assertAlmostEqual(RN.get_two_point_resistance(2, 2), 0.0)
self.assertAlmostEqual(RN.get_two_point_resistance(3, 3), 0.0)
self.assertAlmostEqual(RN.get_two_point_resistance(4, 4), 0.0)
self.assertAlmostEqual(RN.get_two_point_resistance(5, 5), 0.0)
# unconnected nodes
self.assertTrue(np.isinf(RN.get_two_point_resistance(0, 5)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(1, 5)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(2, 5)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(3, 5)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(4, 5)))
def test_resitance_network_5(self):
''' Test two-point resistance of 6 node, disconnected network
'''
# network topology: square where opposite nodes 2-4 are directly connect but 1-3 aren't
# See Wu (2004) Section I; Example 1
# two additional nodes are connected to each other but nothing else
r1, r2, r3 = 8.14799202, 7.90884073, 6.726105639263754
r_arr = np.array([
0, r1, 0, np.inf, r1, 0, r1, r2, r1, 0, np.inf, np.inf, np.inf,
np.inf, 0, np.inf, np.inf, np.inf, np.inf, r3, 0
])
RN = tl.ResistanceNetwork(6, r_arr)
c1 = 1.0 / r1
c2 = 1.0 / r2
# test resistance
r02 = (1.0 / (4.0 * c1)) * (0.5 - 0.5)**2 + (1 / (2.0 * c1)) * (
-1.0 / np.sqrt(2.0) -
1.0 / np.sqrt(2))**2 + (1.0 /
(2.0 * c1 + 2.0 * c2)) * (0.0 - 0.0)**2
r01 = (1.0 / (4.0 * c1)) * (0.5 - -0.5)**2 + (1 / (2.0 * c1)) * (
-1.0 / np.sqrt(2.0) -
0.0)**2 + (1.0 /
(2.0 * c1 + 2.0 * c2)) * (0.0 - -1.0 / np.sqrt(2.0))**2
r45 = r3
self.assertAlmostEqual(RN.get_two_point_resistance(0, 2), r02)
self.assertAlmostEqual(RN.get_two_point_resistance(0, 1), r01)
self.assertAlmostEqual(RN.get_two_point_resistance(4, 5), r45)
self.assertTrue(np.isinf(RN.get_two_point_resistance(0, 4)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(1, 4)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(2, 4)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(3, 4)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(0, 5)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(1, 5)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(2, 5)))
self.assertTrue(np.isinf(RN.get_two_point_resistance(3, 5)))
def test_resitance_network_1(self):
''' Test laplacian matrix and two-point resistance of 4 node network
'''
# network topology: square where opposit nodes 2-4 are directly connect but 1-3 aren't
# See Wu (2004) Section I; Example 1
r1, r2 = 8.14799202, 7.90884073
r_arr = np.array([0, r1, 0, np.inf, r1, 0, r1, r2, r1, 0])
RN = tl.ResistanceNetwork(4, r_arr)
c1 = 1.0 / r1
c2 = 1.0 / r2
# test laplacian
L = RN.laplacian_matrix
self.assertAlmostEqual(L[0][0], 2 * c1)
self.assertAlmostEqual(L[0][1], -c1)
self.assertAlmostEqual(L[0][2], 0.0)
self.assertAlmostEqual(L[0][3], -c1)
self.assertAlmostEqual(L[1][0], -c1)
self.assertAlmostEqual(L[1][1], 2 * c1 + c2)
self.assertAlmostEqual(L[1][2], -c1)
self.assertAlmostEqual(L[1][3], -c2)
self.assertAlmostEqual(L[2][0], 0.0)
self.assertAlmostEqual(L[2][1], -c1)
self.assertAlmostEqual(L[2][2], 2 * c1)
self.assertAlmostEqual(L[2][3], -c1)
self.assertAlmostEqual(L[3][0], -c1)
self.assertAlmostEqual(L[3][1], -c2)
self.assertAlmostEqual(L[3][2], -c1)
self.assertAlmostEqual(L[3][3], 2 * c1 + c2)
# test eigen pairs
expected_eigenpairs = []
expected_eigenpairs.append([4 * c1, [0.5, -0.5, 0.5, -0.5]])
expected_eigenpairs.append(
[2 * c1, [-1.0 / np.sqrt(2), 0.0, 1.0 / np.sqrt(2), 0.0]])
expected_eigenpairs.append(
[2 * c1 + 2 * c2, [0.0, -1.0 / np.sqrt(2), 0.0, 1.0 / np.sqrt(2)]])
eigenpairs = RN.get_nonzero_eigenpairs()
for i, p in enumerate(eigenpairs):
self.assertTrue(
any(np.isclose(p[0], [ep[0] for ep in expected_eigenpairs])))
# j = np.where(np.isclose(p[0], [ep[0] for ep in expected_eigenpairs]))[0][0]
# self.assertAlmostEqual(p[1][0], list(reversed(expected_eigenpairs[j][1]))[0])
# self.assertAlmostEqual(p[1][1], list(reversed(expected_eigenpairs[j][1]))[1])
# self.assertAlmostEqual(p[1][2], list(reversed(expected_eigenpairs[j][1]))[2])
# self.assertAlmostEqual(p[1][3], list(reversed(expected_eigenpairs[j][1]))[3])
# test resistance
r02 = (1.0 / (4.0 * c1)) * (0.5 - 0.5)**2 + (1 / (2.0 * c1)) * (
-1.0 / np.sqrt(2.0) -
1.0 / np.sqrt(2))**2 + (1.0 /
(2.0 * c1 + 2.0 * c2)) * (0.0 - 0.0)**2
r01 = (1.0 / (4.0 * c1)) * (0.5 - -0.5)**2 + (1 / (2.0 * c1)) * (
-1.0 / np.sqrt(2.0) -
0.0)**2 + (1.0 /
(2.0 * c1 + 2.0 * c2)) * (0.0 - -1.0 / np.sqrt(2.0))**2
self.assertAlmostEqual(RN.get_two_point_resistance(0, 2), r02)
self.assertAlmostEqual(RN.get_two_point_resistance(0, 1), r01)