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_vector_mul_NotEqualFields_ExpectedAssertionError(self):
with self.assertRaises(AssertionError):
N1 = Mat(
({1, 3, 5, 7}, {'a'}), {
(1, 'a'): -1,
(1, 'b'): 2,
(3, 'a'): 1,
(3, 'b'): 4,
(7, 'a'): 3,
(5, 'b'): -1
})
u1 = Vec({'a', 'b'}, {'a': 1, 'b': 2})
N1 * u1
with self.assertRaises(AssertionError):
N1 = Mat(
({1, 3, 5, 7}, {'a', 'b'}), {
(1, 'a'): -1,
(1, 'b'): 2,
(3, 'a'): 1,
(3, 'b'): 4,
(7, 'a'): 3,
(5, 'b'): -1
})
u1 = Vec({'a'}, {'a': 1, 'b': 2})
N1 * u1
def test_setitem_NotExist_ExpectedAssertionError(self):
with self.assertRaises(AssertionError):
M = Mat(({1, 3, 5}, {'a'}), {(1, 'a'): 4, (5, 'a'): 2})
M[1, 'e'] = 0
with self.assertRaises(AssertionError):
M = Mat(({1, 3, 5}, {'a'}), {(1, 'a'): 4, (5, 'a'): 2})
M[2, 'a'] = 0
def test_add_NotEqualFields_ExpectedAssertionError(self):
with self.assertRaises(AssertionError):
Mat(({3, 6}, {'x', 'y'}), {(3, 'x'): -2}) + Mat(
({3, 6}, {'x'}), {(3, 'x'): -2})
with self.assertRaises(AssertionError):
Mat(({3, 6}, {'x'}), {(3, 'x'): -2}) + Mat(
({3, 6}, {'x', 'y'}), {(3, 'x'): -2})
def test_equal_NotEqualFields_ExpectedAssertionError(self):
with self.assertRaises(AssertionError):
Mat(({'a', 'b'}, {'A', 'B'}), {
('a', 'B'): 2,
('b', 'A'): 1
}) == Mat(({'a'}, {'A', 'B'}), {
('a', 'B'): 2,
('b', 'A'): 1
})
def test_scalar_mul(self):
M = Mat(({1, 3, 5}, {2, 4}), {(1, 2): 4, (5, 4): 2, (3, 4): 3})
self.assertEqual(0 * M, Mat(({1, 3, 5}, {2, 4}), {}))
self.assertEqual(1 * M, M)
self.assertEqual(
0.25 * M,
Mat(({1, 3, 5}, {2, 4}), {
(1, 2): 1.0,
(5, 4): 0.5,
(3, 4): 0.75
}))
def coldict2mat(coldict):
"""
Given a dictionary or list whose values are Vecs, returns the Mat having these
Vecs as its columns. This is the inverse of mat2coldict.
Assumes all the Vecs have the same label-set.
Assumes coldict is nonempty.
If coldict is a dictionary then its keys will be the column-labels of the Mat.
If coldict is a list then {0...len(coldict)-1} will be the column-labels of the Mat.
e.g.:
>>> A = {0:Vec({0,1},{0:1,1:2}),1:Vec({0,1},{0:3,1:4})}
>>> B = [Vec({0,1},{0:1,1:2}),Vec({0,1},{0:3,1:4})]
>>> mat2coldict(coldict2mat(A)) == A
True
>>> coldict2mat(A)
Mat(({0, 1}, {0, 1}), {(0, 1): 3, (1, 0): 2, (0, 0): 1, (1, 1): 4})
>>> coldict2mat(A) == coldict2mat(B)
True
"""
row_labels = value(
coldict
).D # value(coldict) if A, Vec({0,1},{0:1,1:2}) about 0 / coldict's D is row_label
return Mat((row_labels, set(keys(coldict))), {(r, c): coldict[c][r]
for c in keys(coldict)
for r in row_labels})
def efficient_rowdict2mat(rowdict):
col_labels = value(rowdict).D
M = Mat((set(keys(rowdict)), col_labels), {})
for r in rowdict:
for c in rowdict[r].f:
M[r, c] = rowdict[r][c]
return M
def identity(D, one):
"""Given a set D and the field's one, returns the DxD identity matrix
e.g.:
>>> identity({0,1,2}, 1)
Mat(({0, 1, 2}, {0, 1, 2}), {(0, 0): 1, (1, 1): 1, (2, 2): 1})
"""
return Mat((D, D), {(d, d): one for d in D})
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_matrix_matrix_mul_NotEqualFields_ExpectedAssertionError(self):
with self.assertRaises(AssertionError):
A = Mat(({0, 1, 2}, {0, 1}), {
(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
})
A * B
def test_vector_matrix_mul_NotEqualFields_ExpectedAssertionError(self):
with self.assertRaises(AssertionError):
v1 = Vec({1, 2}, {1: 1, 2: 8})
M1 = Mat(({1, 2, 3}, {'a', 'b', 'c'}), {
(1, 'b'): 2,
(2, 'a'): -1,
(3, 'a'): 1,
(3, 'c'): 7
})
v1 * M1
with self.assertRaises(AssertionError):
v1 = Vec({1, 2, 3}, {1: 1, 2: 8})
M1 = Mat(({1, 2}, {'a', 'b', 'c'}), {
(1, 'b'): 2,
(2, 'a'): -1,
(3, 'a'): 1,
(3, 'c'): 7
})
v1 * M1
def test_setitem(self):
M = Mat(({'a', 'b', 'c'}, {5}), {('a', 5): 3, ('b', 5): 7})
M['b', 5] = 9
M['c', 5] = 13
self.assertEqual(
M,
Mat(({'a', 'b', 'c'}, {5}), {
('a', 5): 3,
('b', 5): 9,
('c', 5): 13
}))
N = Mat(({((), ), 7}, {True, False}), {})
N[(7, False)] = 1
N[(((), ), True)] = 2
self.assertEqual(
N,
Mat(({((), ), 7}, {True, False}), {
(7, False): 1,
(((), ), True): 2
}))
def test_matrix_vector_mul(self):
N1 = Mat(
({1, 3, 5, 7}, {'a', 'b'}), {
(1, 'a'): -1,
(1, 'b'): 2,
(3, 'a'): 1,
(3, 'b'): 4,
(7, 'a'): 3,
(5, 'b'): -1
})
u1 = Vec({'a', 'b'}, {'a': 1, 'b': 2})
self.assertEqual(N1 * u1, Vec({1, 3, 5, 7}, {1: 3, 3: 9, 5: -2, 7: 3}))
self.assertEqual(
N1,
Mat(
({1, 3, 5, 7}, {'a', 'b'}), {
(1, 'a'): -1,
(1, 'b'): 2,
(3, 'a'): 1,
(3, 'b'): 4,
(7, 'a'): 3,
(5, 'b'): -1
}))
self.assertEqual(u1, Vec({'a', 'b'}, {'a': 1, 'b': 2}))
N2 = Mat(({('a', 'b'), ('c', 'd')}, {1, 2, 3, 5, 8}), {})
u2 = Vec({1, 2, 3, 5, 8}, {})
self.assertEqual(N2 * u2, Vec({('a', 'b'), ('c', 'd')}, {}))
M3 = Mat(({0, 1}, {'a', 'b'}), {
(0, 'a'): 1,
(0, 'b'): 1,
(1, 'a'): 1,
(1, 'b'): 1
})
v3 = Vec({'a', 'b'}, {'a': 1, 'b': 1})
self.assertEqual(M3 * v3, Vec({0, 1}, {0: 2, 1: 2}))
def test_vector_matrix_mul(self):
v1 = Vec({1, 2, 3}, {1: 1, 2: 8})
M1 = Mat(({1, 2, 3}, {'a', 'b', 'c'}), {
(1, 'b'): 2,
(2, 'a'): -1,
(3, 'a'): 1,
(3, 'c'): 7
})
self.assertEqual(v1 * M1,
Vec({'a', 'b', 'c'}, {
'a': -8,
'b': 2,
'c': 0
}))
self.assertEqual(v1, Vec({1, 2, 3}, {1: 1, 2: 8}))
self.assertEqual(
M1,
Mat(({1, 2, 3}, {'a', 'b', 'c'}), {
(1, 'b'): 2,
(2, 'a'): -1,
(3, 'a'): 1,
(3, 'c'): 7
}))
v2 = Vec({'a', 'b'}, {})
M2 = Mat(({'a', 'b'}, {0, 2, 4, 6, 7}), {})
self.assertEqual(v2 * M2, Vec({0, 2, 4, 6, 7}, {}))
v3 = Vec({'a', 'b'}, {'a': 1, 'b': 1})
M3 = Mat(({'a', 'b'}, {0, 1}), {
('a', 1): 1,
('b', 1): 1,
('a', 0): 1,
('b', 0): 1
})
self.assertEqual(v3 * M3, Vec({0, 1}, {0: 2, 1: 2}))
def listlist2mat(L):
"""Given a list of lists of field elements, return a matrix whose ith row consists
of the elements of the ith list. The row-labels are {0...len(L)}, and the
column-labels are {0...len(L[0])}
>>> A=listlist2mat([[10,20,30,40],[50,60,70,80]])
>>> print(A)
<BLANKLINE>
0 1 2 3
-------------
0 | 10 20 30 40
1 | 50 60 70 80
<BLANKLINE>
"""
m, n = len(L), len(L[0])
return Mat((set(range(m)), set(range(n))), {(r, c): L[r][c]
for r in range(m)
for c in range(n)})
def test_add(self):
A1 = Mat(({3, 6}, {'x', 'y'}), {(3, 'x'): -2, (6, 'y'): 3})
A2 = Mat(({3, 6}, {'x', 'y'}), {(3, 'y'): 4})
B = Mat(({3, 6}, {'x', 'y'}), {(3, 'x'): -2, (3, 'y'): 4, (6, 'y'): 3})
self.assertEqual(A1 + A2, B)
self.assertEqual(A2 + A1, B)
self.assertEqual(
A1, Mat(({3, 6}, {'x', 'y'}), {
(3, 'x'): -2,
(6, 'y'): 3
}))
zero = Mat(({3, 6}, {'x', 'y'}), {})
self.assertEqual(B + zero, B)
C1 = Mat(({1, 3}, {2, 4}), {(1, 2): 2, (3, 4): 3})
C2 = Mat(({1, 3}, {2, 4}), {(1, 4): 1, (1, 2): 4})
D = Mat(({1, 3}, {2, 4}), {(1, 2): 6, (1, 4): 1, (3, 4): 3})
self.assertEqual(C1 + C2, D)
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 rowdict2mat(rowdict):
"""
Given a dictionary or list whose values are Vecs, returns the Mat having these
Vecs as its rows. This is the inverse of mat2rowdict.
Assumes all the Vecs have the same label-set.
Assumes row_dict is nonempty.
If rowdict is a dictionary then its keys will be the row-labels of the Mat.
If rowdict is a list then {0...len(rowdict)-1} will be the row-labels of the Mat.
e.g.:
>>> A = {0:Vec({0,1},{0:1,1:2}),1:Vec({0,1},{0:3,1:4})}
>>> B = [Vec({0,1},{0:1,1:2}),Vec({0,1},{0:3,1:4})]
>>> mat2rowdict(rowdict2mat(A)) == A
True
>>> rowdict2mat(A)
Mat(({0, 1}, {0, 1}), {(0, 1): 2, (1, 0): 3, (0, 0): 1, (1, 1): 4})
>>> rowdict2mat(A) == rowdict2mat(B)
True
"""
col_labels = value(rowdict).D
return Mat((set(keys(rowdict)), col_labels), {(r, c): rowdict[r][c]
for r in keys(rowdict)
for c in col_labels})
def test_equal(self):
self.assertEqual(Mat(({'a', 'b'}, {'A', 'B'}), {('a', 'B'): 0}),
Mat(({'a', 'b'}, {'A', 'B'}), {('b', 'B'): 0}))
A = Mat(({'a', 'b'}, {'A', 'B'}), {('a', 'B'): 2, ('b', 'A'): 1})
B = Mat(({'a', 'b'}, {'A', 'B'}), {
('a', 'B'): 2,
('b', 'A'): 1,
('b', 'B'): 0
})
C = Mat(({'a', 'b'}, {'A', 'B'}), {
('a', 1): 2,
('b', 'A'): 1,
('b', 'B'): 5
})
self.assertEqual(A, B)
self.assertEqual(B, A)
self.assertFalse(C == A)
self.assertEqual(
A, Mat(({'a', 'b'}, {'A', 'B'}), {
('a', 'B'): 2,
('b', 'A'): 1
}))
def test_getitem(self):
M = Mat(({1, 3, 5}, {'a'}), {(1, 'a'): 4, (5, 'a'): 2})
self.assertEqual(M[1, 'a'], 4)
self.assertEqual(M[3, 'a'], 0)
def submatrix(M, rows, cols):
return Mat((M.D[0] & rows, M.D[1] & cols),
{(r, c): val
for (r, c), val in M.f.items() if r in rows and c in cols})
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
}))
}),
'#': Vec({'a', 'b'}, {
'a': 2,
'b': 20
}),
'?': Vec({'a', 'b'}, {
'a': 3,
'b': 30
})
})
# Quiz 5.1.7
print(
Mat(({'a', 'b', 'c'}, {'a', 'b', 'c'}), {
('a', 'a'): 1,
('b', 'b'): 1,
('c', 'c'): 1
}))
# Quiz 5.1.8
print(identity({'a', 'b', 'c'}))
M = Mat(
({'a', 'b'}, {'@', '#', '?'}), {
('a', '@'): 1,
('a', '#'): 2,
('a', '?'): 3,
('b', '@'): 10,
('b', '#'): 20,
('b', '?'): 30
})
def identity(D):
return Mat((D, D), {(d, d): 1 for d in D})
# Quiz 5.1.4
print(Vec({'a', 'b'}, {'a': 3, 'b': 30}))
# Quiz 5.1.5
print({'@': Vec({'a', 'b'}, {'a': 1, 'b': 10}),
'#': Vec({'a', 'b'}, {'a': 2, 'b': 20}),
'?': Vec({'a', 'b'}, {'a': 3, 'b': 30})})
# Quiz 5.1.7
print(Mat(({'a', 'b', 'c'}, {'a', 'b', 'c'}), {('a', 'a'): 1, ('b', 'b'): 1, ('c', 'c'): 1}))
# Quiz 5.1.8
print(identity({'a', 'b', 'c'}))
M = Mat(({'a', 'b'}, {'@', '#', '?'}),
{('a', '@'): 1, ('a', '#'): 2, ('a', '?'): 3, ('b', '@'): 10, ('b', '#'): 20, ('b', '?'): 30})
# Quiz 5.1.9
print(mat2rowdict(M))
# Quiz 5.1.10
print(mat2coldict(M))
# Quiz 5.3.1
print(mat2vec(M))
# Quiz 5.4.2
print(transpose(M))
# Example 5.5.10
D = {'metal', 'concrete', 'plastic', 'water', 'electricity'}
def transpose(M):
return Mat((M.D[1], M.D[0]), {(c, r): M.f[r, c]
for r in M.D[0] for c in M.D[1]})
def diag(D, entries):
return Mat((D, D), {(d, d): entries[d] for d in D})