def test_Kroneker_Derivative(par):
"""Use Kronecker operator to apply the Derivative operator over one axis
and compare with FirstDerivative(... dir=axis)
"""
Dop = FirstDerivative(par["ny"], sampling=1, edge=True, dtype="float32")
D2op = FirstDerivative(
par["ny"] * par["nx"],
dims=(par["ny"], par["nx"]),
dir=0,
sampling=1,
edge=True,
dtype="float32",
)
Kop = Kronecker(Dop,
Identity(par["nx"], dtype=par["dtype"]),
dtype=par["dtype"])
x = np.zeros((par["ny"], par["nx"])) + par["imag"] * np.zeros(
(par["ny"], par["nx"]))
x[par["ny"] // 2, par["nx"] // 2] = 1
y = D2op * x.ravel()
yk = Kop * x.ravel()
assert_array_equal(y, yk)
def test_Kroneker(par):
"""Dot-test and inversion for Kronecker operator
"""
np.random.seed(10)
G1 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype(par['dtype'])
G2 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype(par['dtype'])
x = np.ones(par['nx']**2) + par['imag'] * np.ones(par['nx']**2)
Kop = Kronecker(MatrixMult(G1, dtype=par['dtype']),
MatrixMult(G2, dtype=par['dtype']),
dtype=par['dtype'])
assert dottest(Kop,
par['ny']**2,
par['nx']**2,
complexflag=0 if par['imag'] == 0 else 3)
xlsqr = lsqr(Kop, Kop * x, damp=1e-20, iter_lim=300, show=0)[0]
assert_array_almost_equal(x, xlsqr, decimal=2)
def test_Kroneker_Derivative(par):
"""Use Kronecker operator to apply the Derivative operator over one axis
and compare with FirstDerivative(... dir=axis)
"""
Dop = FirstDerivative(par['ny'], sampling=1, edge=True, dtype='float32')
D2op = FirstDerivative(par['ny'] * par['nx'],
dims=(par['ny'], par['nx']),
dir=0,
sampling=1,
edge=True,
dtype='float32')
Kop = Kronecker(Dop,
Identity(par['nx'], dtype=par['dtype']),
dtype=par['dtype'])
x = np.zeros((par['ny'], par['nx'])) + \
par['imag']*np.zeros((par['ny'], par['nx']))
x[par['ny'] // 2, par['nx'] // 2] = 1
y = D2op * x.flatten()
yk = Kop * x.flatten()
assert_array_equal(y, yk)
def test_Kroneker(par):
"""Dot-test, inversion and comparison with np.kron for Kronecker operator"""
np.random.seed(10)
G1 = np.random.normal(0, 10, (par["ny"], par["nx"])).astype(par["dtype"])
G2 = np.random.normal(0, 10, (par["ny"], par["nx"])).astype(par["dtype"])
x = np.ones(par["nx"]**2) + par["imag"] * np.ones(par["nx"]**2)
Kop = Kronecker(
MatrixMult(G1, dtype=par["dtype"]),
MatrixMult(G2, dtype=par["dtype"]),
dtype=par["dtype"],
)
assert dottest(Kop,
par["ny"]**2,
par["nx"]**2,
complexflag=0 if par["imag"] == 0 else 3)
xlsqr = lsqr(Kop, Kop * x, damp=1e-20, iter_lim=300, show=0)[0]
assert_array_almost_equal(x, xlsqr, decimal=2)
# Comparison with numpy
assert_array_almost_equal(np.kron(G1, G2),
Kop * np.eye(par["nx"]**2),
decimal=3)