def test_make_augmented_matrix():
np.random.seed(1)
n = 500
x = np.random.uniform(-1, 1, (n, 3))
s = np.dot(x.T, x)
y = np.array(list(range(n)))
w = np.random.uniform(0, 1, n)
nobs, n_columns = x.shape
# matrix_sqrt removes redundant rows,
# if alpha is zero, then no augmentation is needed
alpha = 0
aug_y, aug_x, aug_w = make_augmented_matrix(y, x, alpha * s, w)
expected_aug_x = x
assert_allclose(aug_x, expected_aug_x)
expected_aug_y = y
expected_aug_y[:nobs] = y
assert_allclose(aug_y, expected_aug_y)
expected_aug_w = w
assert_allclose(aug_w, expected_aug_w)
alpha = 1
aug_y, aug_x, aug_w = make_augmented_matrix(y, x, s, w)
rs = matrix_sqrt(alpha * s)
# alternative version to matrix_sqrt using cholesky is not available
# rs = sp.linalg.cholesky(alpha * s)
assert_allclose(np.dot(rs.T, rs), alpha * s)
expected_aug_x = np.vstack([x, rs])
assert_allclose(aug_x, expected_aug_x)
expected_aug_y = np.zeros(shape=(nobs + n_columns, ))
expected_aug_y[:nobs] = y
assert_allclose(aug_y, expected_aug_y)
expected_aug_w = np.concatenate((w, [1] * n_columns), axis=0)
assert_allclose(aug_w, expected_aug_w)
def test_make_augmented_matrix():
np.random.seed(1)
n = 500
x = np.random.uniform(-1, 1, (n, 3))
s = np.dot(x.T, x)
y = np.array(list(range(n)))
w = np.random.uniform(0, 1, n)
nobs, n_columns = x.shape
# matrix_sqrt removes redundant rows,
# if alpha is zero, then no augmentation is needed
alpha = 0
aug_y, aug_x, aug_w = make_augmented_matrix(y, x, alpha * s, w)
expected_aug_x = x
assert_allclose(aug_x, expected_aug_x)
expected_aug_y = y
expected_aug_y[:nobs] = y
assert_allclose(aug_y, expected_aug_y)
expected_aug_w = w
assert_allclose(aug_w, expected_aug_w)
alpha = 1
aug_y, aug_x, aug_w = make_augmented_matrix(y, x, s, w)
rs = matrix_sqrt(alpha * s)
# alternative version to matrix_sqrt using cholesky is not available
# rs = sp.linalg.cholesky(alpha * s)
assert_allclose(np.dot(rs.T, rs), alpha * s)
expected_aug_x = np.vstack([x, rs])
assert_allclose(aug_x, expected_aug_x)
expected_aug_y = np.zeros(shape=(nobs + n_columns,))
expected_aug_y[:nobs] = y
assert_allclose(aug_y, expected_aug_y)
expected_aug_w = np.concatenate((w, [1] * n_columns), axis=0)
assert_allclose(aug_w, expected_aug_w)
def test_get_sqrt():
n = 1000
np.random.seed(1)
x = np.random.normal(0, 1, (n, 3))
x2 = np.dot(x.T, x)
sqrt_x2 = matrix_sqrt(x2)
x2_reconstruction = np.dot(sqrt_x2.T, sqrt_x2)
assert_allclose(x2_reconstruction, x2)
def test_get_sqrt():
n = 1000
np.random.seed(1)
x = np.random.normal(0, 1, (n, 3))
x2 = np.dot(x.T, x)
sqrt_x2 = matrix_sqrt(x2)
x2_reconstruction = np.dot(sqrt_x2.T, sqrt_x2)
assert_allclose(x2_reconstruction, x2)
def _init(cls):
# TODO: CyclicCubicSplines raises when using pandas
cc_h = CyclicCubicSplines(np.asarray(data_mcycle['times']), df=[6])
constraints = np.atleast_2d(cc_h.basis.mean(0))
transf = transf_constraints(constraints)
exog = cc_h.basis.dot(transf)
penalty_matrix = transf.T.dot(cc_h.penalty_matrices[0]).dot(transf)
restriction = matrix_sqrt(penalty_matrix)
return exog, penalty_matrix, restriction
def _init(cls):
# TODO: CyclicCubicSplines raises when using pandas
cc_h = CyclicCubicSplines(np.asarray(data_mcycle['times']), df=[6])
constraints = np.atleast_2d(cc_h.basis.mean(0))
transf = transf_constraints(constraints)
exog = cc_h.basis.dot(transf)
penalty_matrix = transf.T.dot(cc_h.penalty_matrices[0]).dot(transf)
restriction = matrix_sqrt(penalty_matrix)
return exog, penalty_matrix, restriction
def make_augmented_matrix(endog, exog, penalty_matrix, weights):
"""augment endog, exog and weights with stochastic restriction matrix
Parameters
----------
endog : ndarray
response or endogenous variable
exog : ndarray
design matrix, matrix of exogenous or explanatory variables
penalty_matrix : ndarray, 2-Dim square
penality matrix for quadratic penalization
weights : ndarray
weights for WLS
Returns
-------
endog_aug : ndarray
augmented response variable
exog_aug : ndarray
augmented design matrix
weights_aug : ndarray
augmented weights for WLS
"""
y, x, s, = endog, exog, penalty_matrix
nobs = x.shape[0]
# TODO: needs full because of broadcasting with weights
# check what weights should be doing
rs = matrix_sqrt(s)
x1 = np.vstack([x, rs]) # augmented x
n_samp1es_x1 = x1.shape[0]
y1 = np.array([0.] * n_samp1es_x1) # augmented y
y1[:nobs] = y
id1 = np.array([1.] * rs.shape[0])
w1 = np.concatenate([weights, id1])
return y1, x1, w1
def make_augmented_matrix(endog, exog, penalty_matrix, weights):
"""augment endog, exog and weights with stochastic restriction matrix
Parameters
----------
endog : ndarray
response or endogenous variable
exog : ndarray
design matrix, matrix of exogenous or explanatory variables
penalty_matrix : ndarray, 2-Dim square
penality matrix for quadratic penalization
weights : ndarray
weights for WLS
Returns
-------
endog_aug : ndarray
augmented response variable
exog_aug : ndarray
augmented design matrix
weights_aug : ndarray
augmented weights for WLS
"""
y, x, s, = endog, exog, penalty_matrix
nobs = x.shape[0]
# TODO: needs full because of broadcasting with weights
# check what weights should be doing
rs = matrix_sqrt(s)
x1 = np.vstack([x, rs]) # augmented x
n_samp1es_x1 = x1.shape[0]
y1 = np.array([0.] * n_samp1es_x1) # augmented y
y1[:nobs] = y
id1 = np.array([1.] * rs.shape[0])
w1 = np.concatenate([weights, id1])
return y1, x1, w1
