def test_simple_all_at_once(self):
mr = MultiLstSq((), 2)
A = numpy.hstack((numpy.ones(
(len(self.x_i), 1)), numpy.array(self.x_i)[:, numpy.newaxis]))
b = numpy.array(self.y_i)[:, numpy.newaxis]
mr.add_data(A, b)
mr.switch_to_variance()
mr.add_data(A, b)
mrss = self._construct_mr_step_by_step()
numpy.testing.assert_array_almost_equal(mr._XtX, mrss._XtX)
numpy.testing.assert_array_almost_equal(mr._Xty, mrss._Xty)
numpy.testing.assert_array_almost_equal(mr._rss, mrss._rss)
numpy.testing.assert_array_almost_equal(mr._n_observations,
mrss._n_observations)
# x is a vertical vector contataining the solution
self.assertAlmostEqual(mr.beta[0, 0], -39.062, 3)
self.assertAlmostEqual(mr.beta[1, 0], 61.272, 3)
# variance is the variance-covariance matrix
self.assertAlmostEqual(mr.variance[0, 0], 8.63185, 5)
self.assertAlmostEqual(mr.variance[1, 1], 3.1539, 4)
self.assertAlmostEqual(mr.sigma_2, 0.57619680)
def test_regression_vs_numpy(self):
for dim in range(1, 5):
X = numpy.random.normal(size=(dim * 2, dim))
y = numpy.random.normal(size=(dim * 2, 1))
Xmr = numpy.array([numpy.zeros_like(X), X])
ymr = numpy.array([numpy.zeros_like(y), y])
mr = MultiLstSq((2, ), dim)
mr.add_data(Xmr, ymr)
mr.switch_to_variance()
mr.add_data(Xmr, ymr)
beta_hat = mr.beta[1]
beta_cov = mr.variance
# FIXME: is there a way to compute the covariance with numpy directly?
numpy.testing.assert_almost_equal(
beta_hat,
numpy.linalg.lstsq(X, y, rcond=-1)[0])
def test_multilstsq_masked(self):
mls = MultiLstSq((2, 3), 2)
# 4 observations
X = numpy.ma.masked_all((2, 3, 4, 2))
y = numpy.ma.masked_all((2, 3, 4, 1))
# This is for β₀
X[:, :, :, 0] = 1
# Values of x, as coefficients of β₁
# The first two dims are the problem index
# The third is the observation index
X[0, 0, :, 1] = [1, 2, 3, 4]
X[0, 1, :, 1] = [1, 2, 1, 2]
X[0, 2, :, 1] = [1, 1, 1, 1]
X[1, 0, :, 1] = [-5, -6, 13, 43]
X[1, 1, :3, 1] = [-1, 0, 1] # only 3 observations
X[1, 2, :2, 1] = [4, 8] # only 2 observations
# Observations
y[0, 0, :, 0] = [1, 2, 3, 4]
y[0, 1, :, 0] = [1.1, 2, 0.9, 2.1]
y[0, 2, :, 0] = [3, 4, 5, 6]
y[1, 0, :, 0] = [-5.9, -5.2, 11.9, 42.1]
y[1, 1, :3, 0] = [1, 2, 3] # only 3 observations
y[1, 2, :2, 0] = [4.5, 5] # only 2 observations
mls.add_data(X, y)
mls.switch_to_variance()
mls.add_data(X, y)
self.assertEqual(mls.n_observations[0, 0], 4)
self.assertEqual(mls.n_observations[0, 1], 4)
self.assertEqual(mls.n_observations[0, 2], 4)
self.assertEqual(mls.n_observations[1, 0], 4)
self.assertEqual(mls.n_observations[1, 1], 3)
self.assertEqual(mls.n_observations[1, 2], 2)
def test_2d_one_by_one(self):
mr = MultiLstSq((2, 2), 2)
for i in range(2):
for x, y in zip(self.x_i, self.y_i):
A = numpy.array([[[[1, x]]] * 2] * 2)
b = numpy.array([[[[y]]] * 2] * 2)
mr.add_data(A, b)
mr.switch_to_variance()
mrss = self._construct_mr_step_by_step()
numpy.testing.assert_array_almost_equal(mr._XtX[0, 0], mrss._XtX)
numpy.testing.assert_array_almost_equal(mr._XtX[0, 1], mrss._XtX)
numpy.testing.assert_array_almost_equal(mr._XtX[1, 0], mrss._XtX)
numpy.testing.assert_array_almost_equal(mr._XtX[1, 1], mrss._XtX)
numpy.testing.assert_array_almost_equal(mr._Xty[0, 0], mrss._Xty)
numpy.testing.assert_array_almost_equal(mr._Xty[0, 1], mrss._Xty)
numpy.testing.assert_array_almost_equal(mr._Xty[1, 0], mrss._Xty)
numpy.testing.assert_array_almost_equal(mr._Xty[1, 1], mrss._Xty)
numpy.testing.assert_array_almost_equal(mr._rss[0, 0], mrss._rss)
numpy.testing.assert_array_almost_equal(mr._rss[0, 1], mrss._rss)
numpy.testing.assert_array_almost_equal(mr._rss[1, 0], mrss._rss)
numpy.testing.assert_array_almost_equal(mr._rss[1, 1], mrss._rss)
numpy.testing.assert_array_almost_equal(mr._n_observations,
mrss._n_observations)
numpy.testing.assert_array_almost_equal(mr.beta[0, 0], mr.beta[0, 1])
numpy.testing.assert_array_almost_equal(mr.beta[0, 0], mr.beta[1, 0])
numpy.testing.assert_array_almost_equal(mr.beta[0, 0], mr.beta[1, 1])
numpy.testing.assert_array_almost_equal(mr.variance[0, 0],
mr.variance[0, 1])
numpy.testing.assert_array_almost_equal(mr.variance[0, 0],
mr.variance[1, 0])
numpy.testing.assert_array_almost_equal(mr.variance[0, 0],
mr.variance[1, 1])
# x is a vertical vector contataining the solution
self.assertAlmostEqual(mr.beta[0, 0][0, 0], -39.062, 3)
self.assertAlmostEqual(mr.beta[0, 0][1, 0], 61.272, 3)
# variance is the variance-covariance matrix
self.assertAlmostEqual(mr.variance[0, 0][0, 0], 8.63185, 5)
self.assertAlmostEqual(mr.variance[0, 0][1, 1], 3.1539, 4)
def test_weights(self):
mr = MultiLstSq((), 1)
mr.add_data(numpy.array([[1], [1]]),
numpy.array([[0], [3]]),
w=numpy.array([[1], [2]]))
self.assertAlmostEqual(mr.beta[0], 2, 5)
def test_type_validation(self):
with self.assertRaises(TypeError):
mr = MultiLstSq([], 1)
with self.assertRaises(TypeError):
mr = MultiLstSq((0, 1), 1)
with self.assertRaises(TypeError):
mr = MultiLstSq((-1, 1), 1)
with self.assertRaises(TypeError):
mr = MultiLstSq((), -1)
mr = MultiLstSq((), 2)
with self.assertRaises(ValueError):
mr.add_data(numpy.array([]), numpy.array([]))
with self.assertRaises(ValueError):
mr.add_data(numpy.array([[1, 1]]), numpy.array([]))
with self.assertRaises(ValueError):
mr.add_data(numpy.array([[1, 1]]), numpy.array([[1]]),
numpy.array([]))
def test_variance(self):
mr1 = MultiLstSq((), 2)
for i in range(2):
for x, y in zip([1, 2, 3], [2.1, 3.9, 6]):
A = numpy.array([[1, x]])
b = numpy.array([[y]])
mr1.add_data(A, b)
mr1.switch_to_variance()
mr2 = MultiLstSq((), 2)
for i in range(2):
mr2.add_data(numpy.array([[0, 0]]), numpy.array([[0]]))
mr2.add_data(numpy.array([[0, 0], [0, 0]]), numpy.array([[0],
[0]]))
for x, y in zip([1, 2, 3], [2.1, 3.9, 6]):
A = numpy.array([[1, x]])
b = numpy.array([[y]])
mr2.add_data(A, b)
mr2.add_data(numpy.array([[0, 0]]), numpy.array([[0]]))
mr2.add_data(numpy.array([[0, 0]]), numpy.array([[0]]))
mr2.add_data(numpy.array([[0, 0]]), numpy.array([[0]]))
mr2.switch_to_variance()
# print(mr1.x.T)
# print(mr2.x.T)
numpy.testing.assert_almost_equal(mr1.beta, mr2.beta)
numpy.testing.assert_almost_equal(mr1.variance, mr2.variance)
return mr1
def _construct_mr_step_by_step(self):
mr = MultiLstSq((), 2)
for i in range(2):
for x, y in zip(self.x_i, self.y_i):
A = numpy.array([[1, x]])
b = numpy.array([[y]])
mr.add_data(A, b)
mr.switch_to_variance()
mr.switch_to_read_only()
with self.assertRaises(RuntimeError):
mr.add_data(A, b)
with self.assertRaises(RuntimeError):
mr.switch_to_variance()
return mr
def test_empty(self):
mr = MultiLstSq((), 1)
print(mr.beta)