def test_power_method_opnorm_exceptions():
# Test the exceptions
space = odl.rn(2)
op = odl.IdentityOperator(space)
with pytest.raises(ValueError):
# Too small number of iterates
power_method_opnorm(op, maxiter=0)
with pytest.raises(ValueError):
# Negative number of iterates
power_method_opnorm(op, maxiter=-5)
with pytest.raises(ValueError):
# Input vector is zero
power_method_opnorm(op, maxiter=2, xstart=space.zero())
with pytest.raises(ValueError):
# Input vector in the nullspace
op = odl.MatVecOperator([[0., 1.],
[0., 0.]])
power_method_opnorm(op, maxiter=2, xstart=op.domain.one())
with pytest.raises(ValueError):
# Uneven number of iterates for non square operator
op = odl.MatVecOperator([[1., 2., 3.],
[4., 5., 6.]])
power_method_opnorm(op, maxiter=1, xstart=op.domain.one())
def test_power_method_opnorm_exceptions():
"""Test the exceptions"""
space = odl.rn(2)
op = odl.IdentityOperator(space)
with pytest.raises(ValueError):
# Too small number of iterates
power_method_opnorm(op, maxiter=0)
with pytest.raises(ValueError):
# Negative number of iterates
power_method_opnorm(op, maxiter=-5)
with pytest.raises(ValueError):
# Input vector is zero
power_method_opnorm(op, maxiter=2, xstart=space.zero())
with pytest.raises(ValueError):
# Input vector in the nullspace
op = odl.MatrixOperator([[0., 1.], [0., 0.]])
power_method_opnorm(op, maxiter=2, xstart=op.domain.one())
with pytest.raises(ValueError):
# Uneven number of iterates for non square operator
op = odl.MatrixOperator([[1., 2., 3.], [4., 5., 6.]])
power_method_opnorm(op, maxiter=1, xstart=op.domain.one())
def test_power_method_opnorm_symm():
"""Test the power method on a symmetrix matrix operator"""
# Test matrix with singular values 1.2 and 1.0
mat = np.array([[0.9509044, -0.64566614], [-0.44583952, -0.95923051]])
op = odl.MatrixOperator(mat)
true_opnorm = 1.2
opnorm_est = power_method_opnorm(op, maxiter=100)
assert opnorm_est == pytest.approx(true_opnorm, rel=1e-2)
# Start at a different point
xstart = odl.rn(2).element([0.8, 0.5])
opnorm_est = power_method_opnorm(op, xstart=xstart, maxiter=100)
assert opnorm_est == pytest.approx(true_opnorm, rel=1e-2)
def test_power_method_opnorm_symm():
"""Test the power method on a symmetrix matrix operator"""
# Test matrix with eigenvalues 1 and -2
# Rather nasty case since the eigenvectors are almost parallel
mat = np.array([[10, -18], [6, -11]], dtype=float)
op = odl.MatrixOperator(mat)
true_opnorm = 2
opnorm_est = power_method_opnorm(op)
assert opnorm_est == pytest.approx(true_opnorm, rel=1e-2)
# Start at a different point
xstart = odl.rn(2).element([0.8, 0.5])
opnorm_est = power_method_opnorm(op, xstart=xstart)
assert opnorm_est == pytest.approx(true_opnorm, rel=1e-2)
def test_power_method_opnorm_symm():
# Test the power method on a matrix operator
# Test matrix with eigenvalues 1 and -2
# Rather nasty case since the eigenvectors are almost parallel
mat = np.array([[10, -18], [6, -11]], dtype=float)
op = odl.MatVecOperator(mat)
true_opnorm = 2
opnorm_est = power_method_opnorm(op)
assert almost_equal(opnorm_est, true_opnorm, places=2)
# Start at a different point
xstart = odl.rn(2).element([0.8, 0.5])
opnorm_est = power_method_opnorm(op, xstart=xstart)
assert almost_equal(opnorm_est, true_opnorm, places=2)
def test_power_method_opnorm_symm():
# Test the power method on a matrix operator
# Test matrix with eigenvalues 1 and -2
# Rather nasty case since the eigenvectors are almost parallel
mat = np.array([[10, -18],
[6, -11]], dtype=float)
op = odl.MatVecOperator(mat)
true_opnorm = 2
opnorm_est = power_method_opnorm(op, niter=10)
assert almost_equal(opnorm_est, true_opnorm, places=2)
# Start at a different point
xstart = odl.Rn(2).element([0.8, 0.5])
opnorm_est = power_method_opnorm(op, niter=10, xstart=xstart)
assert almost_equal(opnorm_est, true_opnorm, places=2)
def test_power_method_opnorm_nonsymm():
"""Test the power method on a nonsymmetrix matrix operator"""
# Singular values 5.5 and 6
mat = np.array([[-1.52441557, 5.04276365], [1.90246927, 2.54424763],
[5.32935411, 0.04573162]])
op = odl.MatrixOperator(mat)
true_opnorm = 6
# Start vector (1, 1) is close to the wrong eigenvector
xstart = odl.rn(2).element([1, 1])
opnorm_est = power_method_opnorm(op, xstart=xstart, maxiter=50)
assert opnorm_est == pytest.approx(true_opnorm, rel=1e-2)
# Start close to the correct eigenvector, converges very fast
xstart = odl.rn(2).element([-0.8, 0.5])
opnorm_est = power_method_opnorm(op, xstart=xstart, maxiter=6)
assert opnorm_est == pytest.approx(true_opnorm, rel=1e-2)
def test_power_method_opnorm_nonsymm():
# Test the power method on a matrix operator
# Singular values 5.5 and 6
mat = np.array([[-1.52441557, 5.04276365], [1.90246927, 2.54424763],
[5.32935411, 0.04573162]])
op = odl.MatrixOperator(mat)
true_opnorm = 6
# Start vector (1, 1) is close to the wrong eigenvector
opnorm_est = power_method_opnorm(op, maxiter=50)
assert almost_equal(opnorm_est, true_opnorm, places=2)
# Start close to the correct eigenvector, converges very fast
xstart = odl.rn(2).element([-0.8, 0.5])
opnorm_est = power_method_opnorm(op, maxiter=6, xstart=xstart)
assert almost_equal(opnorm_est, true_opnorm, places=2)
def test_power_method_opnorm_nonsymm():
# Test the power method on a matrix operator
# Singular values 5.5 and 6
mat = np.array([[-1.52441557, 5.04276365],
[1.90246927, 2.54424763],
[5.32935411, 0.04573162]])
op = odl.MatVecOperator(mat)
true_opnorm = 6
# Start vector (1, 1) is close to the wrong eigenvector
opnorm_est = power_method_opnorm(op, niter=50)
assert almost_equal(opnorm_est, true_opnorm, places=2)
# Start close to the correct eigenvector, converges very fast
xstart = odl.Rn(2).element([-0.8, 0.5])
opnorm_est = power_method_opnorm(op, niter=5, xstart=xstart)
assert almost_equal(opnorm_est, true_opnorm, places=2)
