ai-content-maker/.venv/Lib/site-packages/sympy/polys/matrices/tests/test_sdm.py

445 lines
14 KiB
Python

"""
Tests for the basic functionality of the SDM class.
"""
from itertools import product
from sympy.core.singleton import S
from sympy.external.gmpy import HAS_GMPY
from sympy.testing.pytest import raises
from sympy.polys.domains import QQ, ZZ, EXRAW
from sympy.polys.matrices.sdm import SDM
from sympy.polys.matrices.ddm import DDM
from sympy.polys.matrices.exceptions import (DMBadInputError, DMDomainError,
DMShapeError)
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(DMBadInputError, lambda: SDM({5:{1:ZZ(0)}}, (2, 2), ZZ))
raises(DMBadInputError, lambda: SDM({0:{5:ZZ(0)}}, (2, 2), 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_new():
A = SDM({0:{0:ZZ(1)}}, (2, 2), ZZ)
B = A.new({}, (2, 2), ZZ)
assert B == SDM({}, (2, 2), ZZ)
def test_SDM_copy():
A = SDM({0:{0:ZZ(1)}}, (2, 2), ZZ)
B = A.copy()
assert A == B
A[0][0] = ZZ(2)
assert A != B
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(DMBadInputError, lambda: SDM.from_list([[ZZ(0)], [ZZ(0), ZZ(1)]], (2, 2), ZZ))
raises(DMBadInputError, lambda: SDM.from_list([[ZZ(0), ZZ(1)]], (2, 2), ZZ))
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_to_list_flat():
A = SDM({0:{1: ZZ(1)}}, (2, 2), ZZ)
assert A.to_list_flat() == [ZZ(0), ZZ(1), ZZ(0), ZZ(0)]
def test_SDM_to_dok():
A = SDM({0:{1: ZZ(1)}}, (2, 2), ZZ)
assert A.to_dok() == {(0, 1): ZZ(1)}
def test_SDM_from_ddm():
A = DDM([[ZZ(1), ZZ(0)], [ZZ(1), ZZ(0)]], (2, 2), ZZ)
B = SDM.from_ddm(A)
assert B.domain == ZZ
assert B.shape == (2, 2)
assert dict(B) == {0:{0:ZZ(1)}, 1:{0:ZZ(1)}}
def test_SDM_to_ddm():
A = SDM({0:{1: ZZ(1)}}, (2, 2), ZZ)
B = DDM([[ZZ(0), ZZ(1)], [ZZ(0), ZZ(0)]], (2, 2), ZZ)
assert A.to_ddm() == B
def test_SDM_to_sdm():
A = SDM({0:{1: ZZ(1)}}, (2, 2), ZZ)
assert A.to_sdm() == A
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_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)))
def test_SDM_extract_slice():
A = SDM({0:{0:ZZ(1), 1:ZZ(2)}, 1:{0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
B = A.extract_slice(slice(1, 2), slice(1, 2))
assert B == SDM({0:{0:ZZ(4)}}, (1, 1), ZZ)
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_SDM_zeros():
A = SDM.zeros((2, 2), ZZ)
assert A.domain == ZZ
assert A.shape == (2, 2)
assert dict(A) == {}
def test_SDM_ones():
A = SDM.ones((1, 2), QQ)
assert A.domain == QQ
assert A.shape == (1, 2)
assert dict(A) == {0:{0:QQ(1), 1:QQ(1)}}
def test_SDM_eye():
A = SDM.eye((2, 2), ZZ)
assert A.domain == ZZ
assert A.shape == (2, 2)
assert dict(A) == {0:{0:ZZ(1)}, 1:{1:ZZ(1)}}
def test_SDM_diag():
A = SDM.diag([ZZ(1), ZZ(2)], ZZ, (2, 3))
assert A == SDM({0:{0:ZZ(1)}, 1:{1:ZZ(2)}}, (2, 3), ZZ)
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_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_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(DMDomainError, lambda: Aq.mul_elementwise(B))
raises(DMShapeError, lambda: A1.mul_elementwise(B))
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) == A*A == B
C = SDM({0:{0:ZZ(2)}}, (2, 2), QQ)
raises(DMDomainError, 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) == A*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(DMShapeError, lambda: A23 @ A22)
raises(DMShapeError, lambda: A23.matmul(A22))
A = SDM({0: {0: ZZ(-1), 1: ZZ(1)}}, (1, 2), ZZ)
B = SDM({0: {0: ZZ(-1)}, 1: {0: ZZ(-1)}}, (2, 1), ZZ)
assert A.matmul(B) == A*B == SDM({}, (1, 1), ZZ)
def test_matmul_exraw():
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)
values = [S.NegativeInfinity, S.NegativeOne, S.Zero, S.One, S.Infinity]
for a, b, c, d in product(*[values]*4):
Ad = dm({0: {0:a, 1:b}, 1: {0:c, 1:d}})
Ad2 = dm({0: {0:a*a + b*c, 1:a*b + b*d}, 1:{0:c*a + d*c, 1: c*b + d*d}})
assert Ad * Ad == Ad2
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_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_neg():
A = SDM({0:{1:ZZ(1)}, 1:{0:ZZ(2), 1:ZZ(3)}}, (2, 2), ZZ)
B = SDM({0:{1:ZZ(-1)}, 1:{0:ZZ(-2), 1:ZZ(-3)}}, (2, 2), ZZ)
assert A.neg() == -A == B
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_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_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_applyfunc():
A = SDM({0:{1:ZZ(1)}}, (2, 2), ZZ)
B = SDM({0:{1:ZZ(2)}}, (2, 2), ZZ)
assert A.applyfunc(lambda x: 2*x, ZZ) == 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 test_SDM_det():
A = SDM({0:{0:QQ(1), 1:QQ(2)}, 1:{0:QQ(3), 1:QQ(4)}}, (2, 2), QQ)
assert A.det() == QQ(-2)
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_lu_solve():
A = SDM({0:{0:QQ(1), 1:QQ(2)}, 1:{0:QQ(3), 1:QQ(4)}}, (2, 2), QQ)
b = SDM({0:{0:QQ(1)}, 1:{0:QQ(2)}}, (2, 1), QQ)
x = SDM({1:{0:QQ(1, 2)}}, (2, 1), QQ)
assert A.matmul(x) == b
assert A.lu_solve(b) == x
def test_SDM_charpoly():
A = SDM({0:{0:ZZ(1), 1:ZZ(2)}, 1:{0:ZZ(3), 1:ZZ(4)}}, (2, 2), ZZ)
assert A.charpoly() == [ZZ(1), ZZ(-5), ZZ(-2)]
def test_SDM_nullspace():
A = SDM({0:{0:QQ(1), 1:QQ(1)}}, (2, 2), QQ)
assert A.nullspace()[0] == SDM({0:{0:QQ(-1), 1:QQ(1)}}, (1, 2), QQ)
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_SDM_particular():
A = SDM({0:{0:QQ(1)}}, (2, 2), QQ)
Apart = SDM.zeros((1, 2), QQ)
assert A.particular() == Apart
def test_SDM_is_zero_matrix():
A = SDM({0: {0: QQ(1)}}, (2, 2), QQ)
Azero = SDM.zeros((1, 2), QQ)
assert A.is_zero_matrix() is False
assert Azero.is_zero_matrix() is True
def test_SDM_is_upper():
A = SDM({0: {0: QQ(1), 1: QQ(2), 2: QQ(3), 3: QQ(4)},
1: {1: QQ(5), 2: QQ(6), 3: QQ(7)},
2: {2: QQ(8), 3: QQ(9)}}, (3, 4), QQ)
B = SDM({0: {0: QQ(1), 1: QQ(2), 2: QQ(3), 3: QQ(4)},
1: {1: QQ(5), 2: QQ(6), 3: QQ(7)},
2: {1: QQ(7), 2: QQ(8), 3: QQ(9)}}, (3, 4), QQ)
assert A.is_upper() is True
assert B.is_upper() is False
def test_SDM_is_lower():
A = SDM({0: {0: QQ(1), 1: QQ(2), 2: QQ(3), 3: QQ(4)},
1: {1: QQ(5), 2: QQ(6), 3: QQ(7)},
2: {2: QQ(8), 3: QQ(9)}}, (3, 4), QQ
).transpose()
B = SDM({0: {0: QQ(1), 1: QQ(2), 2: QQ(3), 3: QQ(4)},
1: {1: QQ(5), 2: QQ(6), 3: QQ(7)},
2: {1: QQ(7), 2: QQ(8), 3: QQ(9)}}, (3, 4), QQ
).transpose()
assert A.is_lower() is True
assert B.is_lower() is False