def test_P():
"""Test permutation matrix _P(m)"""
Pm0 = _P(m)
X = np.random.normal(0.0, 1.0, (N, m, 1))
Y = np.random.normal(0.0, 1.0, (N, m, 1))
assert (Pm0.shape == (m**2, m**2))
assert (np.allclose(Pm0, Pm0.T)) # symmetric
assert (np.allclose(np.dot(Pm0, Pm0), np.eye(m**2))) # is its own inverse
Pm = broadcast_to(Pm0, (N, m**2, m**2))
for n in range(0, N):
assert (np.allclose(np.dot(Pm0, np.kron(X[n, :, 0], Y[n, :, 0])),
np.kron(Y[n, :, 0], X[n, :, 0])))
# next line is equivalent to the previous 3 lines:
assert (np.allclose(_dot(Pm, _kp(X, Y)), _kp(Y, X)))
def test_P():
"""Test permutation matrix _P(m)"""
Pm0 = _P(m)
X = np.random.normal(0.0, 1.0, (N, m, 1))
Y = np.random.normal(0.0, 1.0, (N, m, 1))
assert(Pm0.shape == (m**2, m**2))
assert(np.allclose(Pm0, Pm0.T)) # symmetric
assert(np.allclose(np.dot(Pm0, Pm0), np.eye(m**2))) # is its own inverse
Pm = broadcast_to(Pm0, (N, m**2, m**2))
for n in range(0, N):
assert(np.allclose(np.dot(Pm0, np.kron(X[n,:,0], Y[n,:,0])),
np.kron(Y[n,:,0], X[n,:,0])))
# next line is equivalent to the previous 3 lines:
assert(np.allclose(_dot(Pm, _kp(X, Y)), _kp(Y, X)))
def test_kp():
"""Test our special case Kronecker tensor product function _kp() by
comparing it against the built-in numpy function np.kron()
"""
X = np.random.normal(0.0, 1.0, (N, m, 1))
Y = np.random.normal(0.0, 1.0, (N, m, 1))
XkY = _kp(X, Y)
for n in range(0, N):
assert (np.allclose(np.kron(X[n, :, 0], Y[n, :, 0]), XkY[n, :, 0]))
def test_kp():
"""Test our special case Kronecker tensor product function _kp() by
comparing it against the built-in numpy function np.kron()
"""
X = np.random.normal(0.0, 1.0, (N, m, 1))
Y = np.random.normal(0.0, 1.0, (N, m, 1))
XkY = _kp(X, Y)
for n in range(0, N):
assert(np.allclose(np.kron(X[n,:,0], Y[n,:,0]), XkY[n,:,0]))
