def test_DDM_copy(): ddm1 = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) ddm2 = ddm1.copy() assert (ddm1 == ddm2) is True ddm1[0][0] = QQ(-1) assert (ddm1 == ddm2) is False ddm2[0][0] = QQ(-1) assert (ddm1 == ddm2) is True
def test_DDM_init(): items = [[ZZ(0), ZZ(1), ZZ(2)], [ZZ(3), ZZ(4), ZZ(5)]] shape = (2, 3) ddm = DDM(items, shape, ZZ) assert ddm.shape == shape assert ddm.rows == 2 assert ddm.cols == 3 assert ddm.domain == ZZ raises(DDMBadInputError, lambda: DDM([[ZZ(2), ZZ(3)]], (2, 2), ZZ)) raises(DDMBadInputError, lambda: DDM([[ZZ(1)], [ZZ(2), ZZ(3)]], (2, 2), ZZ))
def test_DDM_charpoly(): A = DDM([], (0, 0), ZZ) assert A.charpoly() == [ZZ(1)] A = DDM([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(4), ZZ(5), ZZ(6)], [ZZ(7), ZZ(8), ZZ(9)]], (3, 3), ZZ) Avec = [ZZ(1), ZZ(-15), ZZ(-18), ZZ(0)] assert A.charpoly() == Avec A = DDM([[ZZ(1), ZZ(2)]], (1, 2), ZZ) raises(DDMShapeError, lambda: A.charpoly())
def test_DDM_str(): ddm = DDM([[ZZ(0), ZZ(1)], [ZZ(2), ZZ(3)]], (2, 2), ZZ) if HAS_GMPY: assert str( ddm) == 'DDM([[mpz(0), mpz(1)], [mpz(2), mpz(3)]], (2, 2), ZZ)' else: assert str(ddm) == 'DDM([[0, 1], [2, 3]], (2, 2), ZZ)'
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.shape == (2, 2) assert A.domain == ZZ raises(DDMBadInputError, lambda: DomainMatrix([[ZZ(1), ZZ(2)]], (2, 2), ZZ))
def test_DomainMatrix_from_Matrix(): ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A = DomainMatrix.from_Matrix(Matrix([[1, 2], [3, 4]])) assert A.rep == ddm assert A.shape == (2, 2) assert A.domain == ZZ K = QQ.algebraic_field(sqrt(2)) ddm = DDM([[ K.convert(1 + sqrt(2)), K.convert(2 + sqrt(2)) ], [K.convert(3 + sqrt(2)), 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 == ddm assert A.shape == (2, 2) assert A.domain == K
def test_DDM_lu(): A = DDM([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) L, U, swaps = A.lu() assert L == DDM([[QQ(1), QQ(0)], [QQ(3), QQ(1)]], (2, 2), QQ) assert U == DDM([[QQ(1), QQ(2)], [QQ(0), QQ(-2)]], (2, 2), QQ) assert swaps == [] A = [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [0, 0, 1, 2]] Lexp = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 1, 1]] Uexp = [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [0, 0, 0, 1]] to_dom = lambda rows, dom: [[dom(e) for e in row] for row in rows] A = DDM(to_dom(A, QQ), (4, 4), QQ) Lexp = DDM(to_dom(Lexp, QQ), (4, 4), QQ) Uexp = DDM(to_dom(Uexp, QQ), (4, 4), QQ) L, U, swaps = A.lu() assert L == Lexp assert U == Uexp assert swaps == []
def test_ddm_charpoly(): A = [] assert ddm_berk(A, ZZ) == [[ZZ(1)]] A = [[ZZ(1), ZZ(2), ZZ(3)], [ZZ(4), ZZ(5), ZZ(6)], [ZZ(7), ZZ(8), ZZ(9)]] Avec = [[ZZ(1)], [ZZ(-15)], [ZZ(-18)], [ZZ(0)]] assert ddm_berk(A, ZZ) == Avec A = DDM([[ZZ(1), ZZ(2)]], (1, 2), ZZ) raises(DDMShapeError, lambda: ddm_berk(A, ZZ))
def test_DDM_getsetitem(): ddm = DDM([[ZZ(2), ZZ(3)], [ZZ(4), ZZ(5)]], (2, 2), ZZ) assert ddm[0][0] == ZZ(2) assert ddm[0][1] == ZZ(3) assert ddm[1][0] == ZZ(4) assert ddm[1][1] == ZZ(5) raises(IndexError, lambda: ddm[2][0]) raises(IndexError, lambda: ddm[0][2]) ddm[0][0] = ZZ(-1) assert ddm[0][0] == ZZ(-1)
def test_DDM_add(): A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) B = DDM([[ZZ(3)], [ZZ(4)]], (2, 1), ZZ) C = DDM([[ZZ(4)], [ZZ(6)]], (2, 1), ZZ) AQ = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) assert A + B == A.add(B) == C raises(DDMShapeError, lambda: A + DDM([[ZZ(5)]], (1, 1), ZZ)) raises(TypeError, lambda: A + ZZ(1)) raises(TypeError, lambda: ZZ(1) + A) raises(DDMDomainError, lambda: A + AQ) raises(DDMDomainError, lambda: AQ + A)
def test_DDM_eq(): items = [[ZZ(0), ZZ(1)], [ZZ(2), ZZ(3)]] ddm1 = DDM(items, (2, 2), ZZ) ddm2 = DDM(items, (2, 2), ZZ) assert (ddm1 == ddm1) is True assert (ddm1 == items) is False assert (items == ddm1) is False assert (ddm1 == ddm2) is True assert (ddm2 == ddm1) is True assert (ddm1 != ddm1) is False assert (ddm1 != items) is True assert (items != ddm1) is True assert (ddm1 != ddm2) is False assert (ddm2 != ddm1) is False ddm3 = DDM([[ZZ(0), ZZ(1)], [ZZ(3), ZZ(3)]], (2, 2), ZZ) ddm3 = DDM(items, (2, 2), QQ) assert (ddm1 == ddm3) is False assert (ddm3 == ddm1) is False assert (ddm1 != ddm3) is True assert (ddm3 != ddm1) is True
def test_DomainMatrix_from_list_sympy(): ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A = DomainMatrix.from_list_sympy(2, 2, [[1, 2], [3, 4]]) assert A.rep == ddm assert A.shape == (2, 2) assert A.domain == ZZ
def test_DomainMatrix_from_ddm(): ddm = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) A = DomainMatrix.from_ddm(ddm) assert A.rep == ddm assert A.shape == (2, 2) assert A.domain == ZZ
def test_ddm_ilu_solve(): # Basic example # A = [[QQ(1), QQ(2)], [QQ(3), QQ(4)]] U = [[QQ(1), QQ(2)], [QQ(0), QQ(-2)]] L = [[QQ(1), QQ(0)], [QQ(3), QQ(1)]] swaps = [] b = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) x = DDM([[QQ(0)], [QQ(0)]], (2, 1), QQ) xexp = DDM([[QQ(0)], [QQ(1, 2)]], (2, 1), QQ) ddm_ilu_solve(x, L, U, swaps, b) assert x == xexp # Example with swaps # A = [[QQ(0), QQ(2)], [QQ(3), QQ(4)]] U = [[QQ(3), QQ(4)], [QQ(0), QQ(2)]] L = [[QQ(1), QQ(0)], [QQ(0), QQ(1)]] swaps = [(0, 1)] b = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) x = DDM([[QQ(0)], [QQ(0)]], (2, 1), QQ) xexp = DDM([[QQ(0)], [QQ(1, 2)]], (2, 1), QQ) ddm_ilu_solve(x, L, U, swaps, b) assert x == xexp # Overdetermined, consistent # A = DDM([[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]], (3, 2), QQ) U = [[QQ(1), QQ(2)], [QQ(0), QQ(-2)], [QQ(0), QQ(0)]] L = [[QQ(1), QQ(0), QQ(0)], [QQ(3), QQ(1), QQ(0)], [QQ(5), QQ(2), QQ(1)]] swaps = [] b = DDM([[QQ(1)], [QQ(2)], [QQ(3)]], (3, 1), QQ) x = DDM([[QQ(0)], [QQ(0)]], (2, 1), QQ) xexp = DDM([[QQ(0)], [QQ(1, 2)]], (2, 1), QQ) ddm_ilu_solve(x, L, U, swaps, b) assert x == xexp # Overdetermined, inconsistent b = DDM([[QQ(1)], [QQ(2)], [QQ(4)]], (3, 1), QQ) raises(NonInvertibleMatrixError, lambda: ddm_ilu_solve(x, L, U, swaps, b)) # Square, noninvertible # A = DDM([[QQ(1), QQ(2)], [QQ(1), QQ(2)]], (2, 2), QQ) U = [[QQ(1), QQ(2)], [QQ(0), QQ(0)]] L = [[QQ(1), QQ(0)], [QQ(1), QQ(1)]] swaps = [] b = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) raises(NonInvertibleMatrixError, lambda: ddm_ilu_solve(x, L, U, swaps, b)) # Underdetermined # A = DDM([[QQ(1), QQ(2)]], (1, 2), QQ) U = [[QQ(1), QQ(2)]] L = [[QQ(1)]] swaps = [] b = DDM([[QQ(3)]], (1, 1), QQ) raises(NotImplementedError, lambda: ddm_ilu_solve(x, L, U, swaps, b)) # Shape mismatch b3 = DDM([[QQ(1)], [QQ(2)], [QQ(3)]], (3, 1), QQ) raises(DDMShapeError, lambda: ddm_ilu_solve(x, L, U, swaps, b3)) # Empty shape mismatch U = [[QQ(1)]] L = [[QQ(1)]] swaps = [] x = [[QQ(1)]] b = [] raises(DDMShapeError, lambda: ddm_ilu_solve(x, L, U, swaps, b)) # Empty system U = [] L = [] swaps = [] b = [] x = [] ddm_ilu_solve(x, L, U, swaps, b) assert x == []
def test_DDM_sub(): A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) B = DDM([[ZZ(3)], [ZZ(4)]], (2, 1), ZZ) C = DDM([[ZZ(-2)], [ZZ(-2)]], (2, 1), ZZ) AQ = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) D = DDM([[ZZ(5)]], (1, 1), ZZ) assert A - B == A.sub(B) == C raises(TypeError, lambda: A - ZZ(1)) raises(TypeError, lambda: ZZ(1) - A) raises(DDMShapeError, lambda: A - D) raises(DDMShapeError, lambda: D - A) raises(DDMShapeError, lambda: A.sub(D)) raises(DDMShapeError, lambda: D.sub(A)) raises(DDMDomainError, lambda: A - AQ) raises(DDMDomainError, lambda: AQ - A) raises(DDMDomainError, lambda: A.sub(AQ)) raises(DDMDomainError, lambda: AQ.sub(A))
def test_DDM_neg(): A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) An = DDM([[ZZ(-1)], [ZZ(-2)]], (2, 1), ZZ) assert -A == A.neg() == An assert -An == An.neg() == A
def test_DDM_mul(): A = DDM([[ZZ(1)]], (1, 1), ZZ) raises(TypeError, lambda: [[1]] * A) raises(TypeError, lambda: A * [[1]])
def test_DDM_lu_solve(): # Basic example A = DDM([[QQ(1), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) b = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) x = DDM([[QQ(0)], [QQ(1, 2)]], (2, 1), QQ) assert A.lu_solve(b) == x # Example with swaps A = DDM([[QQ(0), QQ(2)], [QQ(3), QQ(4)]], (2, 2), QQ) assert A.lu_solve(b) == x # Overdetermined, consistent A = DDM([[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]], (3, 2), QQ) b = DDM([[QQ(1)], [QQ(2)], [QQ(3)]], (3, 1), QQ) assert A.lu_solve(b) == x # Overdetermined, inconsistent b = DDM([[QQ(1)], [QQ(2)], [QQ(4)]], (3, 1), QQ) raises(NonInvertibleMatrixError, lambda: A.lu_solve(b)) # Square, noninvertible A = DDM([[QQ(1), QQ(2)], [QQ(1), QQ(2)]], (2, 2), QQ) b = DDM([[QQ(1)], [QQ(2)]], (2, 1), QQ) raises(NonInvertibleMatrixError, lambda: A.lu_solve(b)) # Underdetermined A = DDM([[QQ(1), QQ(2)]], (1, 2), QQ) b = DDM([[QQ(3)]], (1, 1), QQ) raises(NotImplementedError, lambda: A.lu_solve(b)) # Domain mismatch bz = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) raises(DDMDomainError, lambda: A.lu_solve(bz)) # Shape mismatch b3 = DDM([[QQ(1)], [QQ(2)], [QQ(3)]], (3, 1), QQ) raises(DDMShapeError, lambda: A.lu_solve(b3))
def test_DDM_zeros(): ddmz = DDM.zeros((3, 4), QQ) assert list(ddmz) == [[QQ(0)] * 4] * 3 assert ddmz.shape == (3, 4) assert ddmz.domain == QQ
def test_DDM_inv(): A = DDM([[QQ(1, 1), QQ(2, 1)], [QQ(3, 1), QQ(4, 1)]], (2, 2), QQ) Ainv = DDM([[QQ(-2, 1), QQ(1, 1)], [QQ(3, 2), QQ(-1, 2)]], (2, 2), QQ) assert A.inv() == Ainv A = DDM([[QQ(1), QQ(2)]], (1, 2), QQ) raises(DDMShapeError, lambda: A.inv()) A = DDM([[ZZ(2)]], (1, 1), ZZ) raises(ValueError, lambda: A.inv()) A = DDM([], (0, 0), QQ) assert A.inv() == A A = DDM([[QQ(1), QQ(2)], [QQ(2), QQ(4)]], (2, 2), QQ) raises(NonInvertibleMatrixError, lambda: A.inv())
def test_DDM_det(): # 0x0 case A = DDM([], (0, 0), ZZ) assert A.det() == ZZ(1) # 1x1 case A = DDM([[ZZ(2)]], (1, 1), ZZ) assert A.det() == ZZ(2) # 2x2 case A = DDM([[ZZ(1), ZZ(2)], [ZZ(3), ZZ(4)]], (2, 2), ZZ) assert A.det() == ZZ(-2) # 3x3 with swap A = DDM([[ZZ(1), ZZ(2), ZZ(3)], [ZZ(1), ZZ(2), ZZ(4)], [ZZ(1), ZZ(2), ZZ(5)]], (3, 3), ZZ) assert A.det() == ZZ(0) # 2x2 QQ case A = DDM([[QQ(1, 2), QQ(1, 2)], [QQ(1, 3), QQ(1, 4)]], (2, 2), QQ) assert A.det() == QQ(-1, 24) # Nonsquare error A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) raises(DDMShapeError, lambda: A.det()) # Nonsquare error with empty matrix A = DDM([], (0, 1), ZZ) raises(DDMShapeError, lambda: A.det())
def test_DDM_rref(): A = DDM([], (0, 4), QQ) assert A.rref() == (A, []) A = DDM([[QQ(0), QQ(1)], [QQ(1), QQ(1)]], (2, 2), QQ) Ar = DDM([[QQ(1), QQ(0)], [QQ(0), QQ(1)]], (2, 2), QQ) pivots = [0, 1] assert A.rref() == (Ar, pivots) A = DDM([[QQ(1), QQ(2), QQ(1)], [QQ(3), QQ(4), QQ(1)]], (2, 3), QQ) Ar = DDM([[QQ(1), QQ(0), QQ(-1)], [QQ(0), QQ(1), QQ(1)]], (2, 3), QQ) pivots = [0, 1] assert A.rref() == (Ar, pivots) A = DDM([[QQ(3), QQ(4), QQ(1)], [QQ(1), QQ(2), QQ(1)]], (2, 3), QQ) Ar = DDM([[QQ(1), QQ(0), QQ(-1)], [QQ(0), QQ(1), QQ(1)]], (2, 3), QQ) pivots = [0, 1] assert A.rref() == (Ar, pivots) A = DDM([[QQ(1), QQ(0)], [QQ(1), QQ(3)], [QQ(0), QQ(1)]], (3, 2), QQ) Ar = DDM([[QQ(1), QQ(0)], [QQ(0), QQ(1)], [QQ(0), QQ(0)]], (3, 2), QQ) pivots = [0, 1] assert A.rref() == (Ar, pivots) A = DDM([[QQ(1), QQ(0), QQ(1)], [QQ(3), QQ(0), QQ(1)]], (2, 3), QQ) Ar = DDM([[QQ(1), QQ(0), QQ(0)], [QQ(0), QQ(0), QQ(1)]], (2, 3), QQ) pivots = [0, 2] assert A.rref() == (Ar, pivots)
def test_DDM_matmul(): A = DDM([[ZZ(1)], [ZZ(2)]], (2, 1), ZZ) B = DDM([[ZZ(3), ZZ(4)]], (1, 2), ZZ) AB = DDM([[ZZ(3), ZZ(4)], [ZZ(6), ZZ(8)]], (2, 2), ZZ) BA = DDM([[ZZ(11)]], (1, 1), ZZ) assert A @ B == A.matmul(B) == AB assert B @ A == B.matmul(A) == BA raises(TypeError, lambda: A @ 1) raises(TypeError, lambda: A @ [[3, 4]]) Bq = DDM([[QQ(3), QQ(4)]], (1, 2), QQ) raises(DDMDomainError, lambda: A @ Bq) raises(DDMDomainError, lambda: Bq @ A) C = DDM([[ZZ(1)]], (1, 1), ZZ) assert A @ C == A.matmul(C) == A raises(DDMShapeError, lambda: C @ A) raises(DDMShapeError, lambda: C.matmul(A)) Z04 = DDM([], (0, 4), ZZ) Z40 = DDM([[]] * 4, (4, 0), ZZ) Z50 = DDM([[]] * 5, (5, 0), ZZ) Z05 = DDM([], (0, 5), ZZ) Z45 = DDM([[0] * 5] * 4, (4, 5), ZZ) Z54 = DDM([[0] * 4] * 5, (5, 4), ZZ) Z00 = DDM([], (0, 0), ZZ) assert Z04 @ Z45 == Z04.matmul(Z45) == Z05 assert Z45 @ Z50 == Z45.matmul(Z50) == Z40 assert Z00 @ Z04 == Z00.matmul(Z04) == Z04 assert Z50 @ Z00 == Z50.matmul(Z00) == Z50 assert Z00 @ Z00 == Z00.matmul(Z00) == Z00 assert Z50 @ Z04 == Z50.matmul(Z04) == Z54 raises(DDMShapeError, lambda: Z05 @ Z40) raises(DDMShapeError, lambda: Z05.matmul(Z40))
def test_DDM_eye(): ddmz = DDM.eye(3, QQ) f = lambda i, j: QQ(1) if i == j else QQ(0) assert list(ddmz) == [[f(i, j) for i in range(3)] for j in range(3)] assert ddmz.shape == (3, 3) assert ddmz.domain == QQ
def test_DomainMatrix_eye(): A = DomainMatrix.eye(3, QQ) assert A.rep == DDM.eye(3, QQ) assert A.shape == (3, 3) assert A.domain == QQ