def test_dense_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2, 3, 6]:
u, s, v = Linalg.svd(DenseMatrix(x), dim)
np.testing.assert_array_almost_equal(u.mat, u_expected, 2)
np.testing.assert_array_almost_equal(s, s_expected, 2)
np.testing.assert_array_almost_equal(v.mat, v_expected, 2)
u, s, v = Linalg.svd(DenseMatrix(x), 1)
np.testing.assert_array_almost_equal(u.mat, u_expected[:, 0:1], 2)
np.testing.assert_array_almost_equal(s, s_expected[0:1], 2)
np.testing.assert_array_almost_equal(v.mat, v_expected[:, 0:1], 2)
def test_sparse_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2,3,6]:
u, s, v = Linalg.svd(SparseMatrix(x),dim)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()), np.abs(u_expected), 2)
np.testing.assert_array_almost_equal(np.abs(s), np.abs(s_expected), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()), np.abs(v_expected), 2)
u, s, v = Linalg.svd(SparseMatrix(x),1)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()), np.abs(u_expected[:,0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(s), np.abs(s_expected[0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()), np.abs(v_expected[:,0:1]), 2)
def test_dense_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2,3,6]:
u, s, v = Linalg.svd(DenseMatrix(x),dim)
np.testing.assert_array_almost_equal(u.mat, u_expected, 2)
np.testing.assert_array_almost_equal(s, s_expected, 2)
np.testing.assert_array_almost_equal(v.mat, v_expected, 2)
u, s, v = Linalg.svd(DenseMatrix(x),1)
np.testing.assert_array_almost_equal(u.mat, u_expected[:,0:1], 2)
np.testing.assert_array_almost_equal(s, s_expected[0:1], 2)
np.testing.assert_array_almost_equal(v.mat, v_expected[:, 0:1], 2)
def nndsvd_init(self, matrix_):
def matrix_abs(mat_):
mat_p = mat_.get_non_negative()
mat_n_abs = mat_p - mat_
return mat_p + mat_n_abs
def padd_zeros(matrix_, axis, thickness):
matrix_type = type(matrix_)
if axis == 0:
append_mat = matrix_type(
np.zeros((thickness, matrix_.shape[1])))
return matrix_.vstack(append_mat)
elif axis == 1:
append_mat = matrix_type(
np.zeros((matrix_.shape[0], thickness)))
return matrix_.hstack(append_mat)
u, s, v = Linalg.svd(matrix_, self._reduced_dimension)
rank = u.shape[1]
w = [[]] * rank
h = [[]] * rank
vt = v.transpose()
w[0] = sqrt(s[0]) * matrix_abs(u[:, 0])
h[0] = sqrt(s[0]) * matrix_abs(vt[0, :])
for i in range(1, rank):
uu = u[:, i]
vv = vt[i, :]
uup = uu.get_non_negative()
uun = uup - uu
vvp = vv.get_non_negative()
vvn = vvp - vv
n_uup = uup.norm()
n_uun = uun.norm()
n_vvp = vvp.norm()
n_vvn = vvn.norm()
termp = n_uup * n_vvp
termn = n_uun * n_vvn
if (termp >= termn):
w[i] = sqrt(s[i] * termp) * uup / n_uup
h[i] = sqrt(s[i] * termp) * vvp / n_vvp
else:
w[i] = sqrt(s[i] * termn) * uun / n_uun
h[i] = sqrt(s[i] * termn) * vvn / n_vvn
w = matrix_.nary_hstack(w)
h = matrix_.nary_vstack(h)
w.remove_small_values(0.0000000001)
h.remove_small_values(0.0000000001)
if (rank < self._reduced_dimension):
w = padd_zeros(w, 1, self._reduced_dimension - rank)
h = padd_zeros(h, 0, self._reduced_dimension - rank)
return w, h
def nndsvd_init(self,matrix_):
def matrix_abs(mat_):
mat_p = mat_.get_non_negative()
mat_n_abs = mat_p - mat_
return mat_p + mat_n_abs
def padd_zeros(matrix_, axis, thickness):
matrix_type = type(matrix_)
if axis == 0:
append_mat = matrix_type(np.zeros((thickness, matrix_.shape[1])))
return matrix_.vstack(append_mat)
elif axis == 1:
append_mat = matrix_type(np.zeros((matrix_.shape[0], thickness)))
return matrix_.hstack(append_mat)
u, s, v = Linalg.svd(matrix_, self._reduced_dimension);
rank = u.shape[1]
w = [[]]*rank
h = [[]]*rank
vt = v.transpose()
w[0] = sqrt(s[0]) * matrix_abs(u[:,0])
h[0] = sqrt(s[0]) * matrix_abs(vt[0,:])
for i in range(1,rank):
uu = u[:,i]
vv = vt[i,:]
uup = uu.get_non_negative()
uun = uup - uu
vvp = vv.get_non_negative()
vvn = vvp - vv
n_uup = uup.norm()
n_uun = uun.norm()
n_vvp = vvp.norm()
n_vvn = vvn.norm()
termp = n_uup * n_vvp; termn = n_uun * n_vvn
if (termp >= termn):
w[i] = sqrt(s[i] * termp) * uup / n_uup
h[i] = sqrt(s[i] * termp) * vvp / n_vvp
else:
w[i] = sqrt(s[i] * termn) * uun / n_uun
h[i] = sqrt(s[i] * termn) * vvn / n_vvn
w = matrix_.nary_hstack(w)
h = matrix_.nary_vstack(h)
w.remove_small_values(0.0000000001)
h.remove_small_values(0.0000000001)
if (rank < self._reduced_dimension):
w = padd_zeros(w, 1, self._reduced_dimension - rank)
h = padd_zeros(h, 0, self._reduced_dimension - rank)
return w,h
def test_sparse_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2, 3, 6]:
u, s, v = Linalg.svd(SparseMatrix(x), dim)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()),
np.abs(u_expected), 2)
np.testing.assert_array_almost_equal(np.abs(s),
np.abs(s_expected), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()),
np.abs(v_expected), 2)
u, s, v = Linalg.svd(SparseMatrix(x), 1)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()),
np.abs(u_expected[:, 0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(s),
np.abs(s_expected[0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()),
np.abs(v_expected[:, 0:1]), 2)
def apply(self, matrix_):
u, s, v = Linalg.svd(matrix_, self._reduced_dimension)
return u.scale_columns(s), v
def apply(self, matrix_):
u, s, v = Linalg.svd(matrix_, self._reduced_dimension)
return u.scale_columns(s), v
