def test_transpose(self):
M = Mat(({0, 1}, {0, 1}), {(0, 1): 3, (1, 0): 2, (1, 1): 4})
self.assertEqual(M.transpose(), Mat(({0, 1}, {0, 1}), {(0, 1): 2, (1, 0): 3, (1, 1): 4}))
M = Mat(({'x', 'y', 'z'}, {2, 4}), {('x', 4): 3, ('x', 2): 2, ('y', 4): 4, ('z', 4): 5})
Mt = Mat(({2, 4}, {'x', 'y', 'z'}), {(4, 'x'): 3, (2, 'x'): 2, (4, 'y'): 4, (4, 'z'): 5})
self.assertEqual(M.transpose(), Mt)
def test_matrix_matrix_mul(self):
A = Mat(({0, 1, 2}, {0, 1, 2}), {(1, 1): 4, (0, 0): 0, (1, 2): 1, (1, 0): 5, (0, 1): 3, (0, 2): 2})
B = Mat(({0, 1, 2}, {0, 1, 2}), {(1, 0): 5, (2, 1): 3, (1, 1): 2, (2, 0): 0, (0, 0): 1, (0, 1): 4})
self.assertEqual(A * B, Mat(({0, 1, 2}, {0, 1, 2}), {(0, 0): 15, (0, 1): 12, (1, 0): 25, (1, 1): 31}))
C = Mat(({0, 1, 2}, {'a', 'b'}), {(0, 'a'): 4, (0, 'b'): -3, (1, 'a'): 1, (2, 'a'): 1, (2, 'b'): -2})
D = Mat(({'a', 'b'}, {'x', 'y'}), {('a', 'x'): 3, ('a', 'y'): -2, ('b', 'x'): 4, ('b', 'y'): -1})
self.assertEqual(C * D, Mat(({0, 1, 2}, {'x', 'y'}), {(0, 'y'): -5, (1, 'x'): 3, (1, 'y'): -2, (2, 'x'): -5}))
M = Mat(({0, 1}, {'a', 'c', 'b'}), {})
N = Mat(({'a', 'c', 'b'}, {(1, 1), (2, 2)}), {})
self.assertEqual(M * N, Mat(({0, 1}, {(1, 1), (2, 2)}), {}))
E = Mat(({'a', 'b'}, {'A', 'B'}), {('a', 'A'): 1, ('a', 'B'): 2, ('b', 'A'): 3, ('b', 'B'): 4})
F = Mat(({'A', 'B'}, {'c', 'd'}), {('A', 'd'): 5})
self.assertEqual(E * F, Mat(({'a', 'b'}, {'d', 'c'}), {('b', 'd'): 15, ('a', 'd'): 5}))
self.assertEqual(F.transpose() * E.transpose(), Mat(({'d', 'c'}, {'a', 'b'}), {('d', 'b'): 15, ('d', 'a'): 5}))
def test_transpose(self):
M = Mat(({0, 1}, {0, 1}), {(0, 1): 3, (1, 0): 2, (1, 1): 4})
self.assertEqual(
M.transpose(),
Mat(({0, 1}, {0, 1}), {
(0, 1): 2,
(1, 0): 3,
(1, 1): 4
}))
M = Mat(({'x', 'y', 'z'}, {2, 4}), {
('x', 4): 3,
('x', 2): 2,
('y', 4): 4,
('z', 4): 5
})
Mt = Mat(({2, 4}, {'x', 'y', 'z'}), {
(4, 'x'): 3,
(2, 'x'): 2,
(4, 'y'): 4,
(4, 'z'): 5
})
self.assertEqual(M.transpose(), Mt)
R = {'gnome', 'hoop', 'slinky', 'putty', 'shooter'}
u = Vec(R, {'putty': 133, 'gnome': 240, 'slinky': 150, 'hoop': 55, 'shooter': 90})
print(u * M)
# Example 5.5.12
B = coldict2mat(button_vectors(5))
print(B)
s = Vec(B.D[0], {(2, 2): one})
# Example 5.5.15
b = Vec(D, {'water': 373.1, 'concrete': 312.0, 'plastic': 215.4, 'metal': 51.0, 'electricity': 356.0})
# help(solve)
print(isinstance(M, Mat))
print(isinstance(b, Vec))
print(b.D == M.transpose().D[0])
solution = solve(M.transpose(), b)
print(solution)
residual = b - solution * M
print(residual * residual)
# Example 5.5.16
# sol = solve(B, s)
# print(sol)
# print(B * sol == s)
# print([(i, j) for (i, j) in sol.D if sol[i, j] == one])
# Example 5.6.4
# D_high = {(i, j) for i in range(3000) for j in range(2000)}
print(B)
s = Vec(B.D[0], {(2, 2): one})
# Example 5.5.15
b = Vec(
D, {
'water': 373.1,
'concrete': 312.0,
'plastic': 215.4,
'metal': 51.0,
'electricity': 356.0
})
# help(solve)
print(isinstance(M, Mat))
print(isinstance(b, Vec))
print(b.D == M.transpose().D[0])
solution = solve(M.transpose(), b)
print(solution)
residual = b - solution * M
print(residual * residual)
# Example 5.5.16
# sol = solve(B, s)
# print(sol)
# print(B * sol == s)
# print([(i, j) for (i, j) in sol.D if sol[i, j] == one])
# Example 5.6.4
# D_high = {(i, j) for i in range(3000) for j in range(2000)}
def test_matrix_matrix_mul(self):
A = Mat(({0, 1, 2}, {0, 1, 2}), {
(1, 1): 4,
(0, 0): 0,
(1, 2): 1,
(1, 0): 5,
(0, 1): 3,
(0, 2): 2
})
B = Mat(({0, 1, 2}, {0, 1, 2}), {
(1, 0): 5,
(2, 1): 3,
(1, 1): 2,
(2, 0): 0,
(0, 0): 1,
(0, 1): 4
})
self.assertEqual(
A * B,
Mat(({0, 1, 2}, {0, 1, 2}), {
(0, 0): 15,
(0, 1): 12,
(1, 0): 25,
(1, 1): 31
}))
C = Mat(({0, 1, 2}, {'a', 'b'}), {
(0, 'a'): 4,
(0, 'b'): -3,
(1, 'a'): 1,
(2, 'a'): 1,
(2, 'b'): -2
})
D = Mat(({'a', 'b'}, {'x', 'y'}), {
('a', 'x'): 3,
('a', 'y'): -2,
('b', 'x'): 4,
('b', 'y'): -1
})
self.assertEqual(
C * D,
Mat(({0, 1, 2}, {'x', 'y'}), {
(0, 'y'): -5,
(1, 'x'): 3,
(1, 'y'): -2,
(2, 'x'): -5
}))
M = Mat(({0, 1}, {'a', 'c', 'b'}), {})
N = Mat(({'a', 'c', 'b'}, {(1, 1), (2, 2)}), {})
self.assertEqual(M * N, Mat(({0, 1}, {(1, 1), (2, 2)}), {}))
E = Mat(({'a', 'b'}, {'A', 'B'}), {
('a', 'A'): 1,
('a', 'B'): 2,
('b', 'A'): 3,
('b', 'B'): 4
})
F = Mat(({'A', 'B'}, {'c', 'd'}), {('A', 'd'): 5})
self.assertEqual(
E * F,
Mat(({'a', 'b'}, {'d', 'c'}), {
('b', 'd'): 15,
('a', 'd'): 5
}))
self.assertEqual(
F.transpose() * E.transpose(),
Mat(({'d', 'c'}, {'a', 'b'}), {
('d', 'b'): 15,
('d', 'a'): 5
}))
