def test_b_bins_at_least_two():
"""Test exception when bins in b are not at least two"""
x_ini = np.histogram(np.zeros(10), bins=3)
b = np.histogram(np.zeros(10), bins=1)
A = np.zeros((1, 3))
cov = np.zeros((1, 1))
with pytest.raises(AssertionError, match=r".*at least 2.*"):
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
def test_exception_for_symmetric_covariance():
"""Test if exception is thrown when the covariance matrix is not symmetric"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=5)
A = np.zeros((5, 5))
cov = np.zeros((5, 5))
cov[0, 1] = 1
with pytest.raises(AssertionError, match=r".*is not symmetric.*"):
svdunfold.SVDunfold(x_ini, b, A, cov)
def test_exception_when_k_out_of_bounds():
"""Test if exception is thrown when critical value k is out of bounds"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.zeros((3, 3))
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
with pytest.raises(AssertionError, match=r".*out of bounds.*"):
unfold.unfold(5)
def test_exception_for_rows_in_response_matrix():
"""Test if exception is thrown when number of bins in b is not the same
as the rows in the response matrix
"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=5)
A = np.zeros((4, 5))
cov = np.zeros((5, 5))
with pytest.raises(AssertionError, match=r".*Wrong dimensions.*"):
svdunfold.SVDunfold(x_ini, b, A, cov)
def test_inverse_covariance_correct_dimensions():
"""Test if the inverse covariance matrix has the correct dimensions"""
x_ini = np.histogram(np.array([1, 2, 3, 4, 5]), bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.eye(3)
A_tilde = np.zeros((3, 5))
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
X_inv = unfold._caclulate_inverse_covariance(A_tilde)
assert X_inv.shape == (5, 5)
def test_expansion_coefficients_dimension():
"""Test if vector of expansion coefficients has correct dimensions"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.array([1, 2, 2, 3, 3, 3]), bins=3)
A = np.zeros((3, 5))
cov = np.eye(3)
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
U = np.ones((3, 5))
b_transformed = np.ones(3)
d = unfold._calculate_expansion_coefficients(U, b_transformed)
assert d.shape == (5, )
def test_transformed_measured_distribution():
"""Test if the transformed measured distribution is correct"""
x_ini = np.histogram(np.zeros(10), bins=3)
b = np.histogram([6, 7, 8, 9, 10], bins=3)
A = np.zeros((3, 3))
cov = cov = np.array([[4, 0, 0], [0, 25, 0], [0, 0, 16]])
Q = np.array([[0., 0., 1.], [1., 0., 0.], [0., 1., 0.]])
r = np.array([5., 4., 2.])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
b_tilde = unfold._transform_b_measured(Q, r)
assert np.array_equal(np.array([2. / 5., 2. / 4., 1. / 2.]), b_tilde)
def test_transformed_response_correct_dimensions():
"""Test if the dimensions of the transposed response matrix are correct"""
x_ini = np.histogram(np.zeros(10), bins=3)
b = np.histogram(np.zeros(10), bins=7)
A = np.zeros((7, 3))
cov = np.eye(7)
Q = np.zeros((7, 7))
r = np.ones(7)
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
A_tilde = unfold._transform_response_matrix(Q, r)
assert A_tilde.shape == (7, 3)
def test_transformed_b_measured_dimension():
"""Test if the dimensions of the transformed measured array are correct"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=4)
A = np.zeros((4, 5))
cov = np.zeros((4, 4))
Q = np.zeros((4, 4))
r = np.ones(4)
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
b_tilde = unfold._transform_b_measured(Q, r)
assert np.size(b_tilde) == 4
def test_expansion_coefficients_correct():
"""Test if vector of expansion coefficients is calculated correctly"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.array([1, 2, 2, 3, 3, 3]), bins=3)
A = np.zeros((3, 5))
cov = np.eye(3)
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
U = np.array([[1, 4, 8, 3, 6], [9, 5, 3, 0, 3], [3, 5, 4, 4, 8]])
b_transformed = np.array([4, 5, 6])
d = unfold._calculate_expansion_coefficients(U, b_transformed)
d_test = np.array([67, 71, 71, 36, 87])
assert np.allclose(d, d_test)
def test_transformed_response_correct_values():
"""Test if the transformed response matrix is correct"""
x_ini = np.histogram(np.zeros(10), bins=3)
b = np.histogram(np.zeros(10), bins=3)
A = np.histogram2d([1, 2, 3, 4, 5], [6, 7, 8, 9, 10], bins=3)[0]
cov = np.array([[4, 0, 0], [0, 25, 0], [0, 0, 16]])
Q = np.array([[0., 0., 1.], [1., 0., 0.], [0., 1., 0.]])
r = np.array([5., 4., 2.])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
A_tilde = unfold._transform_response_matrix(Q, r)
assert np.array_equal(
np.array([[0, 0, 2. / 5.], [2. / 4., 0, 0], [0, 1. / 2., 0]]), A_tilde)
def test_expansion_coefficients():
"""Test if expansion coefficients are returned correctly with 3-bin b and 5-bin x_ini and
second inverse derivative xi=0.01 """
x_ini = np.histogram([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], bins=5)
b = np.histogram([1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3], bins=3)
A = np.array([[1, 2, 0, 0, 0], [0, 0, 3, 2, 0], [0, 0, 0, 2, 5]])
cov = np.array([[1.5, 0., 0.], [0., 1.5, 0.], [0., 0., 1.5]])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
unfold.transform_system()
d_test = np.abs(np.array([-7.0796561, 1.42501533, -1.78357341]))
d = unfold.get_abs_d()
assert np.allclose(d_test, d)
def test_singular_values():
"""Test if singular values are returned correctly with 3-bin b and 5-bin x_ini and
second inverse derivative xi=0.01 """
x_ini = np.histogram([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], bins=5)
b = np.histogram([1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3], bins=3)
A = np.array([[1, 2, 0, 0, 0], [0, 0, 3, 2, 0], [0, 0, 0, 2, 5]])
cov = np.array([[1.5, 0., 0.], [0., 1.5, 0.], [0., 0., 1.5]])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
unfold.transform_system()
s_test = np.array([332.72483635, 6.42101093, 1.62637087])
s = unfold.get_singular_values()
assert np.allclose(s_test, s)
def test_regularized_expansion_coefficients():
"""Test if regularized expansion coefficients are calculated correctly"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.ones((3, 5))
cov = np.eye(3)
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
unfold._d = np.array([5, 4, 1, 0.1, 1])
unfold._S = np.array([10, 3, 2, 1, 0.01])
d_reg = np.array([4.80769231, 2.76923077, 0.5, 0.02, 2.49993750e-05])
tau = 4
d_reg_test = unfold._calculate_regularized_d(tau)
assert np.allclose(d_reg, d_reg_test)
def test_inverse_covariance_correct_values_3x3():
"""Test if the inverse covariance matrix is correct for A_tilde(3x3)"""
x_ini = np.histogram(np.array([1, 2, 2, 3, 3, 3]), bins=3)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 3))
cov = np.eye(3)
A_tilde = np.array([[1, 0, 1], [0, 2, 2], [3, 1, 0]])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
X_inv = unfold._caclulate_inverse_covariance(A_tilde)
assert np.array_equal(
X_inv,
np.array([[10., 3. / 2, 1. / 3.], [3. / 2., 5. / 4., 2. / 3.],
[1. / 3., 2. / 3., 5. / 9.]]))
def test_unfolded_distribution():
"""Test calculation of unfolded distribution x"""
x_ini = np.histogram(np.array(
[1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]),
bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.zeros((3, 3))
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
w_solution = np.array([2, 1, 5, 6, 3])
x = unfold._calculate_unfolded_distribution(w_solution)
x_test = np.array([2, 2, 15, 24, 15])
assert np.allclose(x, x_test)
def test_svd_on_covariance_matrix():
"""Test svd on covariance matrix"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.array([[4, 0, 0], [0, 25, 0], [0, 0, 16]])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
Q_test = np.array([[0., 0., 1.], [1., 0., 0.], [0., 1., 0.]])
r_test = np.array([5., 4., 2.])
QT_test = np.array([[0., 1., 0.], [0., 0., 1.], [1., 0., 0.]])
Q, r, QT = unfold._perform_svd_on_covariance()
assert np.array_equal(Q, Q_test)
assert np.array_equal(r, r_test)
assert np.array_equal(QT, QT_test)
def test_unfolded_covariance():
"""Test calculation of unfolded covariance X_cov_unfolded"""
x_ini = np.histogram(np.array(
[1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]),
bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.zeros((3, 3))
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
W_covar = np.array([[6, 5, 4, 4, 3], [5, 5, 4, 4, 4], [9, 3, 6, 2, 5],
[5, 2, 2, 4, 5], [6, 2, 5, 5, 6]])
X_cov = unfold._calculate_unfolded_distribution_covariance(W_covar)
X_cov_test = np.array([[6, 10, 12, 16, 15], [10, 20, 24, 32, 40],
[27, 18, 54, 24, 75], [20, 16, 24, 64, 100],
[30, 20, 75, 100, 150]])
assert np.allclose(X_cov, X_cov_test)
def test_transform_system_3x5():
"""Test X_inv from transform system proceedure with 3-bin b and 5-bin x_ini and
second inverse derivative xi=0.01
"""
x_ini = np.histogram([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], bins=5)
b = np.histogram([1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3], bins=3)
A = np.array([[1, 2, 0, 0, 0], [0, 0, 3, 2, 0], [0, 0, 0, 2, 5]])
cov = np.array([[1.5, 0., 0.], [0., 1.5, 0.], [0., 0., 1.5]])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
unfold.transform_system()
X_inv = np.array([[0.66666667, 0.66666667, 0., 0., 0.],
[0.66666667, 0.66666667, 0., 0., 0.],
[0., 0., 0.66666667, 0.33333333, 0.],
[0., 0., 0.33333333, 0.33333333, 0.33333333],
[0., 0., 0., 0.33333333, 0.66666667]])
assert np.allclose(unfold._X_inv, X_inv)
def test_inverse_covariance_correct_values_3x5():
"""Test if the inverse covariance matrix is correct for A_tilde(3x3)"""
x_ini = np.histogram(np.array(
[1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]),
bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.eye(3)
A_tilde = np.array([[1, 0, 1, 4, 9], [0, 2, 2, 0, 5], [3, 1, 0, 1, 1]])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
X_inv = unfold._caclulate_inverse_covariance(A_tilde)
X_inv_test = np.array(
[[10., 3. / 2., 1. / 3., 7. / 4., 12. / 5.],
[3. / 2., 5. / 4., 2. / 3., 1. / 8., 11. / 10.],
[1. / 3., 2. / 3., 5. / 9., 1. / 3., 19. / 15.],
[7. / 4., 1. / 8., 1. / 3., 17. / 16., 37. / 20.],
[12. / 5., 11. / 10., 19. / 15., 37. / 20, 107. / 25.]])
assert np.array_equal(X_inv, X_inv_test)
def test_transformed_system_solution():
"""Test the calculation of the stransformed system solution"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.zeros((3, 3))
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
V = np.array(
[[-0.44869132, 0.61939546, 0.42855687, -0.35523906, -0.32429862],
[-0.44844725, 0.33245276, -0.61537921, -0.09660769, 0.54803796],
[-0.44678007, 0.00384851, 0.31004087, 0.82961209, 0.12645634],
[-0.44606964, -0.33232921, -0.47011051, 0.04126636, -0.68401197],
[-0.44607244, -0.62878209, 0.34715732, -0.41774758, 0.33259768]])
d = np.array([5, 4, 1, 0.1, 1])
unfold._S = np.array([10, 3, 2, 1, 0.01])
tau = 4
w = unfold._calculate_transformed_system_solution(tau, d, V)
w_test = np.array(
[-23.13863676, -22.45199401, -21.60395838, -20.65671022, -20.14252922])
assert np.allclose(w, w_test)
def test_svd_on_transformed_system():
"""Test svd on transformed system"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.eye(3)
A_tilde = np.array([[1, 0, 6, 3, 8], [9, 3, 6, 4, 0], [1, 5, 3, 7, 5]])
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
U_test = np.array([[-0.50933966, 0.58444234, -0.63166467],
[-0.62247852, -0.75704201, -0.1985142],
[-0.5942168, 0.29208653, 0.74939432]])
S_test = np.array([1580.51138731, 21.14648575, 1.60524919])
VT_test = np.array(
[[-0.44869132, -0.44844725, -0.44678007, -0.44606964, -0.44607244],
[0.61939546, 0.33245276, 0.00384851, -0.33232921, -0.62878209],
[0.42855687, -0.61537921, 0.31004087, -0.47011051, 0.34715732],
[-0.35523906, -0.09660769, 0.82961209, 0.04126636, -0.41774758],
[-0.32429862, 0.54803796, 0.12645634, -0.68401197, 0.33259768]])
U, S, VT = unfold._perform_svd_on_transformed_system(A_tilde)
assert np.allclose(U, U_test)
assert np.allclose(S, S_test)
assert np.allclose(VT, VT_test)
def test_transformed_system_covariance():
"""Test the calculation of the transformed system covariance"""
x_ini = np.histogram(np.zeros(10), bins=5)
b = np.histogram(np.zeros(10), bins=3)
A = np.zeros((3, 5))
cov = np.zeros((3, 3))
unfold = svdunfold.SVDunfold(x_ini, b, A, cov)
V = np.array(
[[-0.44869132, 0.61939546, 0.42855687, -0.35523906, -0.32429862],
[-0.44844725, 0.33245276, -0.61537921, -0.09660769, 0.54803796],
[-0.44678007, 0.00384851, 0.31004087, 0.82961209, 0.12645634],
[-0.44606964, -0.33232921, -0.47011051, 0.04126636, -0.68401197],
[-0.44607244, -0.62878209, 0.34715732, -0.41774758, 0.33259768]])
unfold._S = np.array([10, 3, 2, 1, 0.01])
tau = 4
W_cov = unfold._calculate_transformed_system_covariance(tau, V)
W_cov_t = np.array([[18.65430, 18.58575, 18.49273, 18.40675, 18.35836],
[18.58575, 18.55553, 18.49723, 18.44252, 18.40052],
[18.49273, 18.49723, 18.50056, 18.48892, 18.47695],
[18.40675, 18.44252, 18.48892, 18.53564, 18.56115],
[18.35836, 18.40052, 18.47695, 18.56115, 18.62346]])
assert np.allclose(W_cov, W_cov_t)
