class SVD2DTest(unittest.TestCase):
def setUp(self):
self.tensor = DictTensor(2)
# Note: this command actually puts 20 values in tensor!
self.tensor.update(nested_list_to_dict(svd_2d_test_matrix))
self.svd = self.tensor.svd(k=3, offset_for_row=offset_for_row, offset_for_col=offset_for_col)
self.u, self.svals, self.v = self.svd.u, self.svd.svals, self.svd.v
def test_decomposition(self):
self.assertEqual(self.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.svals), self.u.shape[1])
self.assertEqual(len(self.svals), self.v.shape[1])
self.assertEqual(self.v.shape[0], self.tensor.shape[1])
assertTensorEqual(self.u,
[[0, 0, 1],
[0, -1, 0],
[0, 0, 0],
[-1, 0, 0]], abs=True)
assertTensorEqual(self.v,
[[0, 0, sqrt(.2)],
[-1, 0, 0],
[0, -1, 0],
[0, 0, 0],
[0, 0, sqrt(.8)]], abs=True)
assertTensorEqual(self.svals,
[4, 3, sqrt(5)])
def test_reconstructed(self):
assertTensorEqual(self.svd.reconstructed,
[[1, 0, 0, 0, 2],
[0, 0, 3, 0, 0],
[0, 0, 0, 0, 0],
[0, 4, 0, 0, 0]])
assertTensorEqual(self.svd.reconstructed[1,:],
[0, 0, 3, 0, 0])
assertTensorEqual(self.svd.reconstructed[:,2],
[0, 3, 0, 0])
def test_orthonormality(self):
identity = [[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]
assertTensorEqual(self.u.T * self.u,
identity)
assertTensorEqual(self.v.T * self.v,
identity)
class NormalizedSVD2DTest(unittest.TestCase):
def setUp(self):
self.tensor = DictTensor(2)
self.tensor.update(
nested_list_to_dict(numpy.random.random_sample((10, 12))))
self.normalized_tensor = self.tensor.normalized()
self.svd = self.normalized_tensor.svd(k=3)
self.u, self.svals, self.v = self.svd.u, self.svd.svals, self.svd.v
def test_decomposition(self):
self.assertEqual(self.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.svals), self.u.shape[1])
self.assertEqual(len(self.svals), self.v.shape[1])
self.assertEqual(self.v.shape[0], self.tensor.shape[1])
# Assert that the singular values are decreasing
for i in range(1, len(self.svals)):
self.assert_(self.svals[i] < self.svals[i - 1])
def test_reconstructed(self):
pass # TODO
def test_orthonormality(self):
assertTensorEqual(self.u.T * self.u, numpy.eye(self.u.shape[1]))
assertTensorEqual(self.v.T * self.v, numpy.eye(self.u.shape[1]))
def test_variance(self):
return # TODO
# Assert that the SVD explained some of the variance.
diff_k3 = self.tensor - self.svd.reconstructed
tensor_mag = self.tensor.magnitude()
diff_k3_mag = diff_k3.magnitude()
self.assert_(tensor_mag > diff_k3_mag)
# Check that a smaller SVD explains less of the variance, but still some.
svd_k1 = self.tensor.svd(k=1)
diff_k1 = self.tensor - svd_k1.reconstructed
diff_k1_mag = diff_k1.magnitude()
self.assert_(tensor_mag > diff_k1_mag > diff_k3_mag)
class NormalizedSVD2DTest(unittest.TestCase):
def setUp(self):
self.tensor = DictTensor(2)
self.tensor.update(nested_list_to_dict(
numpy.random.random_sample((10, 12))))
self.normalized_tensor = self.tensor.normalized()
self.svd = self.normalized_tensor.svd(k=3)
self.u, self.svals, self.v = self.svd.u, self.svd.svals, self.svd.v
def test_decomposition(self):
self.assertEqual(self.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.svals), self.u.shape[1])
self.assertEqual(len(self.svals), self.v.shape[1])
self.assertEqual(self.v.shape[0], self.tensor.shape[1])
# Assert that the singular values are decreasing
for i in range(1,len(self.svals)):
self.assert_(self.svals[i] < self.svals[i-1])
def test_reconstructed(self):
pass # TODO
def test_orthonormality(self):
assertTensorEqual(self.u.T * self.u, numpy.eye(self.u.shape[1]))
assertTensorEqual(self.v.T * self.v, numpy.eye(self.u.shape[1]))
def test_variance(self):
return # TODO
# Assert that the SVD explained some of the variance.
diff_k3 = self.tensor - self.svd.reconstructed
tensor_mag = self.tensor.magnitude()
diff_k3_mag = diff_k3.magnitude()
self.assert_(tensor_mag > diff_k3_mag)
# Check that a smaller SVD explains less of the variance, but still some.
svd_k1 = self.tensor.svd(k=1)
diff_k1 = self.tensor - svd_k1.reconstructed
diff_k1_mag = diff_k1.magnitude()
self.assert_(tensor_mag > diff_k1_mag > diff_k3_mag)
class SVD2DTest(unittest.TestCase):
def setUp(self):
self.tensor = DictTensor(2)
# Note: this command actually puts 20 values in tensor!
self.tensor.update(nested_list_to_dict(svd_2d_test_matrix))
self.svd = self.tensor.svd(k=3,
offset_for_row=offset_for_row,
offset_for_col=offset_for_col)
self.u, self.svals, self.v = self.svd.u, self.svd.svals, self.svd.v
def test_decomposition(self):
self.assertEqual(self.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.svals), self.u.shape[1])
self.assertEqual(len(self.svals), self.v.shape[1])
self.assertEqual(self.v.shape[0], self.tensor.shape[1])
assertTensorEqual(self.u,
[[0, 0, 1], [0, -1, 0], [0, 0, 0], [-1, 0, 0]],
abs=True)
assertTensorEqual(self.v, [[0, 0, sqrt(.2)], [-1, 0, 0], [0, -1, 0],
[0, 0, 0], [0, 0, sqrt(.8)]],
abs=True)
assertTensorEqual(self.svals, [4, 3, sqrt(5)])
def test_reconstructed(self):
assertTensorEqual(self.svd.reconstructed,
[[1, 0, 0, 0, 2], [0, 0, 3, 0, 0], [0, 0, 0, 0, 0],
[0, 4, 0, 0, 0]])
assertTensorEqual(self.svd.reconstructed[1, :], [0, 0, 3, 0, 0])
assertTensorEqual(self.svd.reconstructed[:, 2], [0, 3, 0, 0])
def test_orthonormality(self):
identity = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
assertTensorEqual(self.u.T * self.u, identity)
assertTensorEqual(self.v.T * self.v, identity)
class SVD2DTest(unittest.TestCase):
def setUp(self):
self.tensor = DictTensor(2)
# Note: this command actually puts 20 values in tensor!
self.tensor.update(nested_list_to_dict(svd_2d_test_matrix))
self.svd = self.tensor.svd(k=3)
self.incremental = self.tensor.incremental_svd(k=3, niter=200)
self.u, self.svals, self.v = self.svd.u, self.svd.svals, self.svd.v
def test_incremental(self):
self.assertEqual(self.incremental.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.incremental.svals), self.incremental.u.shape[1])
self.assertEqual(len(self.incremental.svals), self.incremental.v.shape[1])
self.assertEqual(self.incremental.v.shape[0], self.tensor.shape[1])
assertTensorEqual(self.incremental.u,
[[0, 0, 1],
[0, 1, 0],
[0, 0, 0],
[1, 0, 0]])
assertTensorEqual(self.incremental.v,
[[0, 0, sqrt(.2)],
[1, 0, 0],
[0, 1, 0],
[0, 0, 0],
[0, 0, sqrt(.8)]])
assertTensorEqual(self.incremental.svals,
[4, 3, sqrt(5)])
def test_decomposition(self):
self.assertEqual(self.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.svals), self.u.shape[1])
self.assertEqual(len(self.svals), self.v.shape[1])
self.assertEqual(self.v.shape[0], self.tensor.shape[1])
assertTensorEqual(self.u,
[[0, 0, 1],
[0, -1, 0],
[0, 0, 0],
[-1, 0, 0]], abs=True)
assertTensorEqual(self.v,
[[0, 0, sqrt(.2)],
[-1, 0, 0],
[0, -1, 0],
[0, 0, 0],
[0, 0, sqrt(.8)]], abs=True)
assertTensorEqual(self.svals,
[4, 3, sqrt(5)])
def test_reconstructed(self):
assertTensorEqual(self.svd.reconstructed,
[[1, 0, 0, 0, 2],
[0, 0, 3, 0, 0],
[0, 0, 0, 0, 0],
[0, 4, 0, 0, 0]])
assertTensorEqual(self.svd.reconstructed[1,:],
[0, 0, 3, 0, 0])
assertTensorEqual(self.svd.reconstructed[:,2],
[0, 3, 0, 0])
def test_orthonormality(self):
identity = [[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]
assertTensorEqual(self.u.T * self.u,
identity)
assertTensorEqual(self.v.T * self.v,
identity)
def test_variance(self):
# Assert that the SVD explained some of the variance.
diff_k3 = self.tensor - self.svd.reconstructed
tensor_mag = self.tensor.magnitude()
diff_k3_mag = diff_k3.magnitude()
self.assert_(tensor_mag > diff_k3_mag)
# Check that a smaller SVD explains less of the variance, but still some.
svd_k1 = self.tensor.svd(k=1)
diff_k1 = self.tensor - svd_k1.reconstructed
diff_k1_mag = diff_k1.magnitude()
self.assert_(tensor_mag > diff_k1_mag > diff_k3_mag)
class SVD2DTest(unittest.TestCase):
def setUp(self):
self.tensor = DictTensor(2)
# Note: this command actually puts 20 values in tensor!
self.tensor.update(nested_list_to_dict(svd_2d_test_matrix))
self.svd = self.tensor.svd(k=3)
self.incremental = self.tensor.incremental_svd(k=3, niter=200)
self.u, self.svals, self.v = self.svd.u, self.svd.svals, self.svd.v
def test_incremental(self):
self.assertEqual(self.incremental.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.incremental.svals),
self.incremental.u.shape[1])
self.assertEqual(len(self.incremental.svals),
self.incremental.v.shape[1])
self.assertEqual(self.incremental.v.shape[0], self.tensor.shape[1])
assertTensorEqual(self.incremental.u,
[[0, 0, 1], [0, 1, 0], [0, 0, 0], [1, 0, 0]])
assertTensorEqual(self.incremental.v,
[[0, 0, sqrt(.2)], [1, 0, 0], [0, 1, 0], [0, 0, 0],
[0, 0, sqrt(.8)]])
assertTensorEqual(self.incremental.svals, [4, 3, sqrt(5)])
def test_decomposition(self):
self.assertEqual(self.u.shape[0], self.tensor.shape[0])
self.assertEqual(len(self.svals), self.u.shape[1])
self.assertEqual(len(self.svals), self.v.shape[1])
self.assertEqual(self.v.shape[0], self.tensor.shape[1])
assertTensorEqual(self.u,
[[0, 0, 1], [0, -1, 0], [0, 0, 0], [-1, 0, 0]],
abs=True)
assertTensorEqual(self.v, [[0, 0, sqrt(.2)], [-1, 0, 0], [0, -1, 0],
[0, 0, 0], [0, 0, sqrt(.8)]],
abs=True)
assertTensorEqual(self.svals, [4, 3, sqrt(5)])
def test_reconstructed(self):
assertTensorEqual(self.svd.reconstructed,
[[1, 0, 0, 0, 2], [0, 0, 3, 0, 0], [0, 0, 0, 0, 0],
[0, 4, 0, 0, 0]])
assertTensorEqual(self.svd.reconstructed[1, :], [0, 0, 3, 0, 0])
assertTensorEqual(self.svd.reconstructed[:, 2], [0, 3, 0, 0])
def test_orthonormality(self):
identity = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
assertTensorEqual(self.u.T * self.u, identity)
assertTensorEqual(self.v.T * self.v, identity)
def test_variance(self):
# Assert that the SVD explained some of the variance.
diff_k3 = self.tensor - self.svd.reconstructed
tensor_mag = self.tensor.magnitude()
diff_k3_mag = diff_k3.magnitude()
self.assert_(tensor_mag > diff_k3_mag)
# Check that a smaller SVD explains less of the variance, but still some.
svd_k1 = self.tensor.svd(k=1)
diff_k1 = self.tensor - svd_k1.reconstructed
diff_k1_mag = diff_k1.magnitude()
self.assert_(tensor_mag > diff_k1_mag > diff_k3_mag)
