def test_SDM_rref():
eye2 = SDM({0:{0:QQ(1)}, 1:{1:QQ(1)}}, (2, 2), QQ)
A = SDM({0:{0:QQ(1), 1:QQ(2)}, 1:{0:QQ(3), 1:QQ(4)}}, (2, 2), QQ)
assert A.rref() == (eye2, [0, 1])
A = SDM({0:{0:QQ(1)}, 1:{0:QQ(3), 1:QQ(4)}}, (2, 2), QQ)
assert A.rref() == (eye2, [0, 1])
A = SDM({0:{1:QQ(2)}, 1:{0:QQ(3), 1:QQ(4)}}, (2, 2), QQ)
assert A.rref() == (eye2, [0, 1])
A = SDM({0:{0:QQ(1), 1:QQ(2), 2:QQ(3)},
1:{0:QQ(4), 1:QQ(5), 2:QQ(6)},
2:{0:QQ(7), 1:QQ(8), 2:QQ(9)} }, (3, 3), QQ)
Arref = SDM({0:{0:QQ(1), 2:QQ(-1)}, 1:{1:QQ(1), 2:QQ(2)}}, (3, 3), QQ)
assert A.rref() == (Arref, [0, 1])
A = SDM({0:{0:QQ(1), 1:QQ(2), 3:QQ(1)},
1:{0:QQ(1), 1:QQ(1), 2:QQ(9)}}, (2, 4), QQ)
Arref = SDM({0:{0:QQ(1), 2:QQ(18), 3:QQ(-1)},
1:{1:QQ(1), 2:QQ(-9), 3:QQ(1)}}, (2, 4), QQ)
assert A.rref() == (Arref, [0, 1])
A = SDM({0:{0:QQ(1), 1:QQ(1), 2:QQ(1)},
1:{0:QQ(1), 1:QQ(2), 2:QQ(2)}}, (2, 3), QQ)
Arref = SDM(
{0: {0: QQ(1,1)}, 1: {1: QQ(1,1), 2: QQ(1,1)}},
(2, 3), QQ)
assert A.rref() == (Arref, [0, 1])
def test_DomainMatrix_from_Matrix():
sdm = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
A = DomainMatrix.from_Matrix(Matrix([[1, 2], [3, 4]]))
assert A.rep == sdm
assert A.shape == (2, 2)
assert A.domain == ZZ
K = QQ.algebraic_field(sqrt(2))
sdm = SDM(
{
0: {
0: K.convert(1 + sqrt(2)),
1: K.convert(2 + sqrt(2))
},
1: {
0: K.convert(3 + sqrt(2)),
1: K.convert(4 + sqrt(2))
}
}, (2, 2), K)
A = DomainMatrix.from_Matrix(Matrix([[1 + sqrt(2), 2 + sqrt(2)],
[3 + sqrt(2), 4 + sqrt(2)]]),
extension=True)
assert A.rep == sdm
assert A.shape == (2, 2)
assert A.domain == K
A = DomainMatrix.from_Matrix(Matrix([[QQ(1, 2), QQ(3, 4)],
[QQ(0, 1), QQ(0, 1)]]),
fmt='dense')
ddm = DDM([[QQ(1, 2), QQ(3, 4)], [QQ(0, 1), QQ(0, 1)]], (2, 2), QQ)
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == QQ
def test_SDM_sub():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(-1), 1: ZZ(1)}, 1: {0: ZZ(4)}}, (2, 2), ZZ)
assert A.sub(B) == A - B == C
raises(TypeError, lambda: A - [])
def test_SDM():
A = SDM({0: {0: ZZ(1)}}, (2, 2), ZZ)
assert A.domain == ZZ
assert A.shape == (2, 2)
assert dict(A) == {0: {0: ZZ(1)}}
raises(DDMBadInputError, lambda: SDM({5: {1: ZZ(0)}}, (2, 2), ZZ))
raises(DDMBadInputError, lambda: SDM({0: {5: ZZ(0)}}, (2, 2), ZZ))
def test_SDM_lu():
A = SDM({0: {0: QQ(1), 1: QQ(2)}, 1: {0: QQ(3), 1: QQ(4)}}, (2, 2), QQ)
L = SDM({0: {0: QQ(1)}, 1: {0: QQ(3), 1: QQ(1)}}, (2, 2), QQ)
#U = SDM({0:{0:QQ(1), 1:QQ(2)}, 1:{0:QQ(3), 1:QQ(-2)}}, (2, 2), QQ)
#swaps = []
# This doesn't quite work. U has some nonzero elements in the lower part.
#assert A.lu() == (L, U, swaps)
assert A.lu()[0] == L
def test_SDM_vstack():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = SDM({1: {1: ZZ(1)}}, (2, 2), ZZ)
AA = SDM({0: {1: ZZ(1)}, 2: {1: ZZ(1)}}, (4, 2), ZZ)
AB = SDM({0: {1: ZZ(1)}, 3: {1: ZZ(1)}}, (4, 2), ZZ)
assert SDM.vstack(A) == A
assert SDM.vstack(A, A) == AA
assert SDM.vstack(A, B) == AB
def test_SDM_hstack():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = SDM({1: {1: ZZ(1)}}, (2, 2), ZZ)
AA = SDM({0: {1: ZZ(1), 3: ZZ(1)}}, (2, 4), ZZ)
AB = SDM({0: {1: ZZ(1)}, 1: {3: ZZ(1)}}, (2, 4), ZZ)
assert SDM.hstack(A) == A
assert SDM.hstack(A, A) == AA
assert SDM.hstack(A, B) == AB
def test_SDM_mul():
A = SDM({0: {0: ZZ(2)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(4)}}, (2, 2), ZZ)
assert A * ZZ(2) == B
assert ZZ(2) * A == B
raises(TypeError, lambda: A * QQ(1, 2))
raises(TypeError, lambda: QQ(1, 2) * A)
def test_SDM_to_list():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
assert A.to_list() == [[ZZ(0), ZZ(1)], [ZZ(0), ZZ(0)]]
A = SDM({}, (0, 2), ZZ)
assert A.to_list() == []
A = SDM({}, (2, 0), ZZ)
assert A.to_list() == [[], []]
def test_SDM_convert_to():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {1: QQ(1)}, 1: {0: QQ(2), 1: QQ(3)}}, (2, 2), QQ)
C = A.convert_to(QQ)
assert C == B
assert C.domain == QQ
D = A.convert_to(ZZ)
assert D == A
assert D.domain == ZZ
def test_SDM_matmul():
A = SDM({0: {0: ZZ(2)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(4)}}, (2, 2), ZZ)
assert A.matmul(A) == B
C = SDM({0: {0: ZZ(2)}}, (2, 2), QQ)
raises(DDMDomainError, lambda: A.matmul(C))
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(7), 1: ZZ(10)}, 1: {0: ZZ(15), 1: ZZ(22)}}, (2, 2), ZZ)
assert A.matmul(A) == B
def test_SDM_mul_elementwise():
A = SDM({0: {0: ZZ(2), 1: ZZ(2)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(4)}, 1: {0: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(8)}}, (2, 2), ZZ)
assert A.mul_elementwise(B) == C
assert B.mul_elementwise(A) == C
Aq = A.convert_to(QQ)
A1 = SDM({0: {0: ZZ(1)}}, (1, 1), ZZ)
raises(DDMDomainError, lambda: Aq.mul_elementwise(B))
raises(DDMShapeError, lambda: A1.mul_elementwise(B))
def test_SDM_inv():
A = SDM({0: {0: QQ(1), 1: QQ(2)}, 1: {0: QQ(3), 1: QQ(4)}}, (2, 2), QQ)
B = SDM({
0: {
0: QQ(-2),
1: QQ(1)
},
1: {
0: QQ(3, 2),
1: QQ(-1, 2)
}
}, (2, 2), QQ)
assert A.inv() == B
def dm(d):
result = {}
for i, row in d.items():
row = {j: val for j, val in row.items() if val}
if row:
result[i] = row
return SDM(result, (2, 2), EXRAW)
def test_DomainMatrix_init():
lol = [[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]]
dod = {0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}
ddm = DDM(lol, (2, 2), ZZ)
sdm = SDM(dod, (2, 2), ZZ)
A = DomainMatrix(lol, (2, 2), ZZ)
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == ZZ
A = DomainMatrix(dod, (2, 2), ZZ)
assert A.rep == sdm
assert A.shape == (2, 2)
assert A.domain == ZZ
raises(TypeError, lambda: DomainMatrix(ddm, (2, 2), ZZ))
raises(TypeError, lambda: DomainMatrix(sdm, (2, 2), ZZ))
raises(TypeError, lambda: DomainMatrix(Matrix([[1]]), (1, 1), ZZ))
for fmt, rep in [('sparse', sdm), ('dense', ddm)]:
A = DomainMatrix(lol, (2, 2), ZZ, fmt=fmt)
assert A.rep == rep
A = DomainMatrix(dod, (2, 2), ZZ, fmt=fmt)
assert A.rep == rep
raises(ValueError, lambda: DomainMatrix(lol, (2, 2), ZZ, fmt='invalid'))
raises(DMBadInputError, lambda: DomainMatrix([[ZZ(1), ZZ(2)]], (2, 2), ZZ))
def test_DomainMatrix_from_rep():
# ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
ddm = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
A = DomainMatrix.from_rep(ddm)
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == ZZ
def test_DDM_str():
sdm = SDM({0: {0: ZZ(1)}, 1: {1: ZZ(1)}}, (2, 2), ZZ)
assert str(sdm) == '{0: {0: 1}, 1: {1: 1}}'
if HAS_GMPY: # pragma: no cover
assert repr(sdm) == 'SDM({0: {0: mpz(1)}, 1: {1: mpz(1)}}, (2, 2), ZZ)'
else: # pragma: no cover
assert repr(sdm) == 'SDM({0: {0: 1}, 1: {1: 1}}, (2, 2), ZZ)'
def test_SDM_from_list():
A = SDM.from_list([[ZZ(0), ZZ(1)], [ZZ(1), ZZ(0)]], (2, 2), ZZ)
assert A == SDM({0: {1: ZZ(1)}, 1: {0: ZZ(1)}}, (2, 2), ZZ)
raises(DDMBadInputError,
lambda: SDM.from_list([[ZZ(0)], [ZZ(0), ZZ(1)]], (2, 2), ZZ))
raises(DDMBadInputError, lambda: SDM.from_list([[ZZ(0), ZZ(1)]],
(2, 2), ZZ))
def test_SDM_getitem():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
assert A.getitem(0, 0) == ZZ.zero
assert A.getitem(0, 1) == ZZ.one
assert A.getitem(1, 0) == ZZ.zero
assert A.getitem(-2, -2) == ZZ.zero
assert A.getitem(-2, -1) == ZZ.one
assert A.getitem(-1, -2) == ZZ.zero
raises(IndexError, lambda: A.getitem(2, 0))
raises(IndexError, lambda: A.getitem(0, 2))
def test_DomainMatrix_from_dict_sympy():
sdm = SDM({0: {0: QQ(1, 2)}, 1: {1: QQ(2, 3)}}, (2, 2), QQ)
sympy_dict = {0: {0: Rational(1, 2)}, 1: {1: Rational(2, 3)}}
A = DomainMatrix.from_dict_sympy(2, 2, sympy_dict)
assert A.rep == sdm
assert A.shape == (2, 2)
assert A.domain == QQ
fds = DomainMatrix.from_dict_sympy
raises(DMBadInputError, lambda: fds(2, 2, {3: {0: Rational(1, 2)}}))
raises(DMBadInputError, lambda: fds(2, 2, {0: {3: Rational(1, 2)}}))
def test_DomainMatrix_from_dict_sympy():
sdm = SDM({0: {0: QQ(1, 2)}, 1: {1: QQ(2, 3)}}, (2, 2), QQ)
A = DomainMatrix.from_dict_sympy(2, 2, {
0: {
0: QQ(1, 2)
},
1: {
1: QQ(2, 3)
}
})
assert A.rep == sdm
assert A.shape == (2, 2)
assert A.domain == QQ
def test_DomainMatrix_unify():
Az = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
Aq = DomainMatrix([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ)
assert Az.unify(Az) == (Az, Az)
assert Az.unify(Aq) == (Aq, Aq)
assert Aq.unify(Az) == (Aq, Aq)
assert Aq.unify(Aq) == (Aq, Aq)
As = DomainMatrix({0: {1: ZZ(1)}, 1: {0: ZZ(2)}}, (2, 2), ZZ)
Ad = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert As.unify(As) == (As, As)
assert Ad.unify(Ad) == (Ad, Ad)
Bs, Bd = As.unify(Ad, fmt='dense')
assert Bs.rep == DDM([[0, 1], [2, 0]], (2, 2), ZZ)
assert Bd.rep == DDM([[1, 2], [3, 4]], (2, 2), ZZ)
Bs, Bd = As.unify(Ad, fmt='sparse')
assert Bs.rep == SDM({0: {1: 1}, 1: {0: 2}}, (2, 2), ZZ)
assert Bd.rep == SDM({0: {0: 1, 1: 2}, 1: {0: 3, 1: 4}}, (2, 2), ZZ)
raises(ValueError, lambda: As.unify(Ad, fmt='invalid'))
def test_SDM_matmul():
A = SDM({0:{0:ZZ(2)}}, (2, 2), ZZ)
B = SDM({0:{0:ZZ(4)}}, (2, 2), ZZ)
assert A.matmul(A) == B
C = SDM({0:{0:ZZ(2)}}, (2, 2), QQ)
raises(DDMDomainError, lambda: A.matmul(C))
A = SDM({0:{0:ZZ(1), 1:ZZ(2)}, 1:{0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
B = SDM({0:{0:ZZ(7), 1:ZZ(10)}, 1:{0:ZZ(15), 1:ZZ(22)}}, (2, 2), ZZ)
assert A.matmul(A) == B
A22 = SDM({0:{0:ZZ(4)}}, (2, 2), ZZ)
A32 = SDM({0:{0:ZZ(2)}}, (3, 2), ZZ)
A23 = SDM({0:{0:ZZ(4)}}, (2, 3), ZZ)
A33 = SDM({0:{0:ZZ(8)}}, (3, 3), ZZ)
A22 = SDM({0:{0:ZZ(8)}}, (2, 2), ZZ)
assert A32.matmul(A23) == A33
assert A23.matmul(A32) == A22
# XXX: @ not supported by SDM...
#assert A32.matmul(A23) == A32 @ A23 == A33
#assert A23.matmul(A32) == A23 @ A32 == A22
#raises(DDMShapeError, lambda: A23 @ A22)
raises(DDMShapeError, lambda: A23.matmul(A22))
def test_DomainMatrix_from_rep():
ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
A = DomainMatrix.from_rep(ddm)
assert A.rep == ddm
assert A.shape == (2, 2)
assert A.domain == ZZ
sdm = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
A = DomainMatrix.from_rep(sdm)
assert A.rep == sdm
assert A.shape == (2, 2)
assert A.domain == ZZ
A = DomainMatrix([[ZZ(1)]], (1, 1), ZZ)
raises(TypeError, lambda: DomainMatrix.from_rep(A))
def test_SDM_add():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(1), 1: ZZ(1)}, 1: {1: ZZ(6)}}, (2, 2), ZZ)
assert A.add(B) == C
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(1), 1: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
assert A.add(B) == C
assert B.add(A) == C
def test_SDM_add():
A = SDM({0: {1: ZZ(1)}, 1: {0: ZZ(2), 1: ZZ(3)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(1), 1: ZZ(1)}, 1: {1: ZZ(6)}}, (2, 2), ZZ)
assert A.add(B) == B.add(A) == A + B == B + A == C
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
C = SDM({0: {0: ZZ(1), 1: ZZ(1)}, 1: {0: ZZ(-2), 1: ZZ(3)}}, (2, 2), ZZ)
assert A.add(B) == B.add(A) == A + B == B + A == C
raises(TypeError, lambda: A + [])
def test_SDM_transpose():
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
B = SDM({0: {0: ZZ(1), 1: ZZ(3)}, 1: {0: ZZ(2), 1: ZZ(4)}}, (2, 2), ZZ)
assert A.transpose() == B
A = SDM({0: {1: ZZ(2)}}, (2, 2), ZZ)
B = SDM({1: {0: ZZ(2)}}, (2, 2), ZZ)
assert A.transpose() == B
A = SDM({0: {1: ZZ(2)}}, (1, 2), ZZ)
B = SDM({1: {0: ZZ(2)}}, (2, 1), ZZ)
assert A.transpose() == B
def test_SDM_extract():
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
B = A.extract([1], [1])
assert B == SDM({0: {0: ZZ(4)}}, (1, 1), ZZ)
B = A.extract([1, 0], [1, 0])
assert B == SDM({
0: {
0: ZZ(4),
1: ZZ(3)
},
1: {
0: ZZ(2),
1: ZZ(1)
}
}, (2, 2), ZZ)
B = A.extract([1, 1], [1, 1])
assert B == SDM({
0: {
0: ZZ(4),
1: ZZ(4)
},
1: {
0: ZZ(4),
1: ZZ(4)
}
}, (2, 2), ZZ)
B = A.extract([-1], [-1])
assert B == SDM({0: {0: ZZ(4)}}, (1, 1), ZZ)
A = SDM({}, (2, 2), ZZ)
B = A.extract([0, 1, 0], [0, 0])
assert B == SDM({}, (3, 2), ZZ)
A = SDM({0: {0: ZZ(1), 1: ZZ(2)}, 1: {0: ZZ(3), 1: ZZ(4)}}, (2, 2), ZZ)
assert A.extract([], []) == SDM.zeros((0, 0), ZZ)
assert A.extract([1], []) == SDM.zeros((1, 0), ZZ)
assert A.extract([], [1]) == SDM.zeros((0, 1), ZZ)
raises(IndexError, lambda: A.extract([2], [0]))
raises(IndexError, lambda: A.extract([0], [2]))
raises(IndexError, lambda: A.extract([-3], [0]))
raises(IndexError, lambda: A.extract([0], [-3]))
def test_DomainMatrix_init():
A = DomainMatrix([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
# assert A.rep == DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ)
assert A.rep == SDM({
0: {
0: ZZ(1),
1: ZZ(2)
},
1: {
0: ZZ(3),
1: ZZ(4)
}
}, (2, 2), ZZ)
assert A.shape == (2, 2)
assert A.domain == ZZ
raises(DDMBadInputError, lambda: DomainMatrix([[ZZ(1), ZZ(2)]],
(2, 2), ZZ))
def test_SDM_setitem():
A = SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
A.setitem(0, 0, ZZ(1))
assert A == SDM({0: {0: ZZ(1), 1: ZZ(1)}}, (2, 2), ZZ)
A.setitem(1, 0, ZZ(1))
assert A == SDM({0: {0: ZZ(1), 1: ZZ(1)}, 1: {0: ZZ(1)}}, (2, 2), ZZ)
A.setitem(1, 0, ZZ(0))
assert A == SDM({0: {0: ZZ(1), 1: ZZ(1)}}, (2, 2), ZZ)
# Repeat the above test so that this time the row is empty
A.setitem(1, 0, ZZ(0))
assert A == SDM({0: {0: ZZ(1), 1: ZZ(1)}}, (2, 2), ZZ)
A.setitem(0, 0, ZZ(0))
assert A == SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
# This time the row is there but column is empty
A.setitem(0, 0, ZZ(0))
assert A == SDM({0: {1: ZZ(1)}}, (2, 2), ZZ)
raises(IndexError, lambda: A.setitem(2, 0, ZZ(1)))
raises(IndexError, lambda: A.setitem(0, 2, ZZ(1)))
