def test_dot_invalid(self):
# setup
test_list = self._generate_random_list(row=3, col=4)
test_mat = Matrix(test_list)
# exercise and verify
with self.assertRaises(ValueError):
test_mat.dot(test_mat)
def test_eigen_jacob(self):
# setup
test_list = [
[[1, 2, 3],
[2, 4, 5],
[3, 5, 1]],
[[1, 2, 3, 4],
[2, 5, 4, 0],
[3, 4, 1, 1],
[4, 0, 1, 2]]]
# Numpyの結果とベクトルの並びが違うので，参考ソースとの結果を比較する
# Rigen values and vectors have no restricted alignment.
# So I compare my result with reference code's one.
expected_list = [
{
'val': np.array([9.15554844, 0.03424156, -3.18979]),
'vec': np.array([[0.3890768121223604, 0.8484624273927595 , -0.3587906681778219],
[0.7146655786221864, -0.523764686501912 , -0.4635986021400077],
[0.5812678771455694, 0.07603987425252731, 0.8101515861382627]])
},
{
'val': np.array([9.584292205173988, 4.243778959253601, -1.5548070077212375, -3.2732641567063494]),
'vec': np.array(
[[0.47493891922778086, 0.41787359408281666, 0.18749368737154454, 0.7514391522717447],
[0.6475162083223736, -0.5703677880234859, -0.5042468744699627, 0.03374071623848818],
[0.5046314170201278, -0.101105766474563, 0.7325633929135483, -0.44550604070521777],
[0.31702194863892624, 0.699885611896042, -0.41705165405029304, -0.48551532642749406]])
}]
# exercise and verify
for mat, expected in zip(test_list, expected_list):
test_mat = Matrix(mat)
# exercise
test_val, test_vec = test_mat.eigen(method='jacob')
# verify
self.assertEqual(len(expected['val']), len(test_val))
for v, e in zip(test_val, expected['val']):
self.assertAlmostEqual(v, e)
self.assertEqual(expected['vec'].shape[0], test_vec.row)
self.assertEqual(expected['vec'].shape[1], test_vec.col)
for r in range(test_vec.row):
for c in range(test_vec.col):
self.assertAlmostEqual(expected['vec'][r, c], test_vec[r, c])
# VVinv = I
V = test_vec
I = matrices.eye(V.row)
for r in range(V.row):
for c in range(V.col):
self.assertAlmostEqual(I[r, c], (V @ V.inv())[r, c])
# VSVinv = A
S = matrices.diag(test_val)
for r in range(test_mat.row):
for c in range(test_mat.col):
self.assertAlmostEqual(test_mat[r, c], (V @ S @ V.inv())[r, c])
def test_tolist(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
# exercise
test_tolist = test_mat.tolist()
# verify
self.assertEqual(test_list, test_tolist)
def test_trance(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
trace_test = test_mat.trace()
trace_np = np_mat.trace()
self.assertAlmostEqual(trace_test, trace_np)
def test_diag_mat(self):
# setup
test_list = self._generate_random_list(row=4, col=3)
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_diag = test_mat.diag()
np_diag = np.diag(np_mat)
# verify
self._compare_all_elements(test_diag, np.matrix(np_diag))
def test_det_valid(self):
# setup
test_list = self._generate_random_list(row=5, col=5)
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_det = test_mat.det()
np_det = LA.det(np_mat)
# verify
self.assertAlmostEqual(test_det, np_det, places=3)
def test_transpose(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
transposed_test_mat = test_mat.transpose()
transposed_np_mat = np_mat.transpose()
# verify
self._compare_all_elements(transposed_test_mat, transposed_np_mat)
def test_dot_valid(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_dot = test_mat.dot(test_mat.transpose())
np_dot = np_mat.dot(np_mat.transpose())
# verify
self._compare_all_elements(test_dot, np_dot)
self.assertEqual(test_dot.row, test_dot.col)
def test_mean(self):
# setup
test_data = [[1, 2, 3, 4], [2, 3, 4, 5], [3, 4, 5, 6]]
test_mat = Matrix(test_data)
np_mat = np.matrix(test_data)
# exercise
test_mean_axis_none = test_mat.mean()
test_mean_axis_1 = test_mat.mean(1)
np_mean_axis_none = np_mat.mean()
np_mean_axis_1 = np_mat.mean(1)
# verify
self.assertAlmostEqual(np_mean_axis_none, test_mean_axis_none)
self._compare_all_elements(test_mean_axis_1, np_mean_axis_1)
def test_inv_invalid_value(self):
# setup
test_list = \
[
[
j + 5 * i
for j in range(5)
]
for i in range(5)
]
test_mat = Matrix(test_list)
# exercise and verify
with self.assertRaises(ValueError):
test_mat.inv()
def test_reshape(self):
# setup
row_list = [1, 8, 4,]
col_list = [16, 2, 4]
test_list = self._generate_random_list(row=2, col=8)
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise and verify
for to_row, to_col in zip(row_list, col_list):
test_reshape = test_mat.reshape(to_row, to_col)
np_reshape = np_mat.reshape(to_row, to_col)
self._compare_all_elements(test_reshape, np_reshape)
self.assertEqual(test_reshape.row, np_reshape.shape[0])
self.assertEqual(test_reshape.col, np_reshape.shape[1])
def test_svd(self):
# setup
test_mat = Matrix([
[1, 1, 1],
[1, 0, 0],
[1, 0, 0],
[0, 1, 1],
[0, 1, 0],
[0, 0, 1]])
# exercise
U, Z, V = test_mat.svd()
# verify
for r in range(test_mat.row):
for c in range(test_mat.col):
self.assertAlmostEqual(test_mat[r, c], (U @ Z @ V.transpose())[r, c])
def test_init_valid(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise and verify
self._compare_all_elements(test_mat, np_mat)
def test_inv_invalid_value(self):
# setup
test_list = \
[
[1., 2., 3., 4.],
[8., 7., 6., 8.],
[9., 12., 11., 12.],
[16., 15., 14., 13.],
]
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_inv = test_mat.inv()
np_inv = LA.inv(np_mat)
# verify
self._compare_all_elements(test_inv, np_inv)
def test_argmax(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_arg = matrices.argmax(test_mat)
np_arg = np.argmax(np_mat.reshape(1, np_mat.shape[0] * np_mat.shape[1]))
# verify
self.assertEqual(test_arg, np_arg)
def test_outer(self):
# setup
test_list = self._generate_random_list(row=4, col=3)
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_outer = matrices.outer(test_mat, test_mat)
np_outer = np.outer(np_mat, np_mat)
# verify
self._compare_all_elements(test_outer, np_outer)
def test_max(self):
# setup
test_list = self._generate_random_list(row=4, col=3)
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_max = matrices.max(test_mat)
np_max = np.max(np_mat)
# verify
self.assertEqual(np_max, test_max)
def test_shape(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
t_row = test_mat.row
t_col = test_mat.col
# verify
self.assertEqual(t_row, np_mat.shape[0])
self.assertEqual(t_col, np_mat.shape[1])
def test_abs(self):
# setup
test_list = self._generate_random_list()
test_mat = Matrix(test_list)
np_mat = np.array(test_list)
# exercise
test_abs = matrices.abs(test_mat)
np_abs = np.abs(np_mat)
# verify
self._compare_all_elements(test_abs, np_abs)
self.assertEqual(test_mat.row, np_mat.shape[0])
self.assertEqual(test_mat.col, np_mat.shape[1])