def test_frodiff(self):
fro = util.frodiff(xp.array([1, 1j, 0, 0]), xp.array([1, 0, 1j, 0]))
self.assertAlmostEqual(fro,
2.0,
msg="The Frobenius norm calculation is wrong")
fro = util.frodiff(util.randn_c(int(1e6)), util.randn_c(int(1e6)))
self.assertAlmostEqual(fro / 2e6, 1.0, places=2)
def test_getRandomHermitianMatrix(self):
xp.set_printoptions(linewidth=xp.inf)
H = util.getRandomHermitianMatrix(4)
np.testing.assert_almost_equal(H, H.conj().T)
H = util.getRandomHermitianMatrix(8)
np.testing.assert_almost_equal(H, H.conj().T)
H = util.getRandomHermitianMatrix(16)
np.testing.assert_almost_equal(H, H.conj().T)
def test_getErrorBitsTable(self):
t = util.getErrorBitsTable(4)
np.testing.assert_almost_equal(
t,
xp.array([[0, 1, 1, 2], [1, 0, 2, 1], [1, 2, 0, 1], [2, 1, 1, 0]]))
t = util.getErrorBitsTable(8)
np.testing.assert_almost_equal(
t,
xp.array([[0, 1, 1, 2, 1, 2, 2, 3], [1, 0, 2, 1, 2, 1, 3, 2],
[1, 2, 0, 1, 2, 3, 1, 2], [2, 1, 1, 0, 3, 2, 2, 1],
[1, 2, 2, 3, 0, 1, 1, 2], [2, 1, 3, 2, 1, 0, 2, 1],
[2, 3, 1, 2, 1, 2, 0, 1], [3, 2, 2, 1, 2, 1, 1, 0]]))
def test_getDFTMatrix(self):
W = util.getDFTMatrix(4)
np.testing.assert_almost_equal(W.dot(W.conj().T),
xp.eye(4, dtype=xp.complex),
decimal=3)
W = util.getDFTMatrix(8)
np.testing.assert_almost_equal(W.dot(W.conj().T),
xp.eye(8, dtype=xp.complex),
decimal=3)
W = util.getDFTMatrix(16)
np.testing.assert_almost_equal(W.dot(W.conj().T),
xp.eye(16, dtype=xp.complex),
decimal=3)
def test_randn(self):
ret = util.randn(int(1e6))
meanPower = xp.mean(xp.power(xp.abs(ret), 2))
self.assertAlmostEqual(meanPower,
1.0,
places=2,
msg="The mean power of randn differs from 1.0")
def test_getMinimumEuclideanDistance(self):
codes = Modulator("PSK", 4).symbols.reshape(4, 1, 1)
med = util.getMinimumEuclideanDistance(xp.array(codes))
self.assertAlmostEqual(med, 2.0)
codes = Modulator("SQAM", 16).symbols.reshape(16, 1, 1)
med = util.getMinimumEuclideanDistance(xp.array(codes))
self.assertAlmostEqual(med, 0.2343145750507619)
codes = IMCode("opt", 4, 2, 4, "PSK", 4, 1).codes
med = util.getMinimumEuclideanDistance(xp.array(codes))
self.assertAlmostEqual(med, 1.0)
codes = IMCode("opt", 8, 4, 64, "PSK", 2, 1).codes
med = util.getMinimumEuclideanDistance(xp.array(codes))
self.assertAlmostEqual(med, 0.5)
def test_getEuclideanDistances(self):
codes = Modulator("PSK", 4).symbols.reshape(4, 1, 1)
ret = util.asnumpy(util.getEuclideanDistances(xp.array(codes)))
np.testing.assert_almost_equal(ret, [2., 2., 4., 4., 2., 2.])
#
codes = IMCode("opt", 2, 1, 2, "PSK", 1, 1).codes
ret = util.asnumpy(util.getEuclideanDistances(xp.array(codes)))
np.testing.assert_almost_equal(ret, [2.])
#
codes = IMCode("opt", 4, 2, 4, "PSK", 1, 1).codes
ret = util.asnumpy(util.getEuclideanDistances(xp.array(codes)))
np.testing.assert_almost_equal(ret, [1., 1., 2., 2., 1., 1.])
#
codes = DiagonalUnitaryCode(2, 2).codes
ret = util.asnumpy(util.getEuclideanDistances(xp.array(codes)))
np.testing.assert_almost_equal(ret, [16.])
def test_countErrorBits(self):
self.assertEqual(util.countErrorBits(1, 2), 2)
self.assertEqual(util.countErrorBits(1, 5), 1)
def test_inv_dB(self):
self.assertAlmostEqual(
util.inv_dB(0.0),
1.0,
msg="The implementation of inv_dB may be wrong.")
def test_kurtosis(self):
self.assertAlmostEqual(util.kurtosis(util.randn(10000000)),
0.0,
places=2)
def test_getGrayIndixes(self):
self.assertEqual(util.getGrayIndixes(2), [0, 1, 3, 2])
self.assertEqual(
util.getGrayIndixes(4),
[0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8])
def test_CayleyTransform(self):
U = util.CayleyTransform(util.asnumpy(
util.getRandomHermitianMatrix(4)))
np.testing.assert_almost_equal(util.asnumpy(U.dot(U.conj().T)),
np.eye(4, dtype=np.complex))
U = util.CayleyTransform(util.asnumpy(
util.getRandomHermitianMatrix(8)))
np.testing.assert_almost_equal(util.asnumpy(U.dot(U.conj().T)),
np.eye(8, dtype=np.complex))
U = util.CayleyTransform(
util.asnumpy(util.getRandomHermitianMatrix(16)))
np.testing.assert_almost_equal(util.asnumpy(U.dot(U.conj().T)),
np.eye(16, dtype=np.complex))
def test_getXCorrespondingToY(self):
a = util.getXCorrespondingToY(xp.array([0, 1]), xp.array([0, 1]), 0.5)
np.testing.assert_almost_equal(a, xp.array(0.5))
def test_getXORtoErrorBitsArray(self):
a = util.getXORtoErrorBitsArray(4)
np.testing.assert_almost_equal(a, xp.array([0, 1, 1, 2, 1]))
a = util.getXORtoErrorBitsArray(16)
np.testing.assert_almost_equal(
a, xp.array([0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1]))