def test_hermitian(): a = SparseMatrix([[0, I], [-I, 0]]) assert a.is_hermitian a = SparseMatrix([[1, I], [-I, 1]]) assert a.is_hermitian a[0, 0] = 2 * I assert a.is_hermitian is False a[0, 0] = x assert a.is_hermitian is None a[0, 1] = a[1, 0] * I assert a.is_hermitian is False
def test_csrtodok(): h = [[5, 7, 5], [2, 1, 3], [0, 1, 1, 3], [3, 4]] g = [[12, 5, 4], [2, 4, 2], [0, 1, 2, 3], [3, 7]] i = [[1, 3, 12], [0, 2, 4], [0, 2, 3], [2, 5]] j = [[11, 15, 12, 15], [2, 4, 1, 2], [0, 1, 1, 2, 3, 4], [5, 8]] k = [[1, 3], [2, 1], [0, 1, 1, 2], [3, 3]] assert _csrtodok(h) == SparseMatrix(3, 4, {(0, 2): 5, (2, 1): 7, (2, 3): 5}) assert _csrtodok(g) == SparseMatrix(3, 7, {(0, 2): 12, (1, 4): 5, (2, 2): 4}) assert _csrtodok(i) == SparseMatrix([[1, 0, 3, 0, 0], [0, 0, 0, 0, 12]]) assert _csrtodok(j) == SparseMatrix(5, 8, {(0, 2): 11, (2, 4): 15, (3, 1): 12, (4, 2): 15}) assert _csrtodok(k) == SparseMatrix(3, 3, {(0, 2): 1, (2, 1): 3})
def test_MatrixElement_with_values(): M = Matrix([[x, y], [z, w]]) Mij = M[i, j] assert isinstance(Mij, MatrixElement) Ms = SparseMatrix([[2, 3], [4, 5]]) msij = Ms[i, j] assert isinstance(msij, MatrixElement) for oi, oj in [(0, 0), (0, 1), (1, 0), (1, 1)]: assert Mij.subs({i: oi, j: oj}) == M[oi, oj] assert msij.subs({i: oi, j: oj}) == Ms[oi, oj] A = MatrixSymbol('A', 2, 2) assert A[0, 0].subs({A: M}) == x assert A[i, j].subs({A: M}) == M[i, j] assert M[i, j].subs([(M, A)]) == A[i, j] assert isinstance(M[3*i - 2, j], MatrixElement) assert M[3*i - 2, j].subs({i: 1, j: 0}) == M[1, 0] assert isinstance(M[i, 0], MatrixElement) assert M[i, 0].subs({i: 0}) == M[0, 0] assert M[0, i].subs({i: 1}) == M[0, 1] pytest.raises(ValueError, lambda: M[i, 2]) pytest.raises(ValueError, lambda: M[i, -1]) pytest.raises(ValueError, lambda: M[2, i]) pytest.raises(ValueError, lambda: M[-1, i]) pytest.raises(ValueError, lambda: Ms[i, 2]) pytest.raises(ValueError, lambda: Ms[i, -1]) pytest.raises(ValueError, lambda: Ms[2, i]) pytest.raises(ValueError, lambda: Ms[-1, i])
def test_Matrix(): assert mathematica_code(Matrix()) == '{}' m = Matrix([[1, 2], [3, 4444]]) assert mathematica_code(m) == mathematica_code(m.as_immutable()) == '{{1, 2}, {3, 4444}}' m = SparseMatrix(m) assert mathematica_code(m) == mathematica_code(m.as_immutable()) == '{{1, 2}, {3, 4444}}'
def test_sparse(): M = SparseMatrix(5, 6, {}) M[2, 2] = 10 M[1, 2] = 20 M[1, 3] = 22 M[0, 3] = 30 M[3, 0] = x * y assert octave_code(M) == ( 'sparse([4 2 3 1 2], [1 3 3 4 4], [x.*y 20 10 30 22], 5, 6)')
def _csrtodok(csr): """Converts a CSR representation to DOK representation""" smat = {} A, JA, IA, shape = csr for i in range(len(IA) - 1): indices = slice(IA[i], IA[i + 1]) for l, m in zip(A[indices], JA[indices]): smat[i, m] = l return SparseMatrix(*(shape + [smat]))
def test_copyin(): s = SparseMatrix(3, 3, {}) s[1, 0] = 1 assert s[:, 0] == SparseMatrix(Matrix([0, 1, 0])) assert s[3] == 1 assert s[3:4] == [1] s[1, 1] = 42 assert s[1, 1] == 42 assert s[1, 1:] == SparseMatrix([[42, 0]]) s[1, 1:] = Matrix([[5, 6]]) assert s[1, :] == SparseMatrix([[1, 5, 6]]) s[1, 1:] = [[42, 43]] assert s[1, :] == SparseMatrix([[1, 42, 43]]) s[0, 0] = 17 assert s[:, :1] == SparseMatrix([17, 1, 0]) s[0, 0] = [1, 1, 1] assert s[:, 0] == SparseMatrix([1, 1, 1]) s[0, 0] = Matrix([1, 1, 1]) assert s[:, 0] == SparseMatrix([1, 1, 1]) s[0, 0] = SparseMatrix([1, 1, 1]) assert s[:, 0] == SparseMatrix([1, 1, 1])
def test_sparse_solve(): A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))) assert A.cholesky() == Matrix([[5, 0, 0], [3, 3, 0], [-1, 1, 3]]) assert A.cholesky() * A.cholesky().T == Matrix([[25, 15, -5], [15, 18, 0], [-5, 0, 11]]) A = SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))) L, D = A.LDLdecomposition() assert 15 * L == Matrix([[15, 0, 0], [9, 15, 0], [-3, 5, 15]]) assert D == Matrix([[25, 0, 0], [0, 9, 0], [0, 0, 9]]) assert L * D * L.T == A A = SparseMatrix(((3, 0, 2), (0, 0, 1), (1, 2, 0))) assert A.inv() * A == SparseMatrix(eye(3)) A = SparseMatrix([[2, -1, 0], [-1, 2, -1], [0, 0, 2]]) ans = SparseMatrix([[Rational(2, 3), Rational(1, 3), Rational(1, 6)], [Rational(1, 3), Rational(2, 3), Rational(1, 3)], [0, 0, Rational(1, 2)]]) assert A.inv(method='CH') == ans assert A.inv(method='LDL') == ans assert A * ans == SparseMatrix(eye(3)) s = A.solve(A[:, 0], 'LDL') assert A * s == A[:, 0] s = A.solve(A[:, 0], 'CH') assert A * s == A[:, 0] A = A.col_join(A) s = A.solve_least_squares(A[:, 0], 'CH') assert A * s == A[:, 0] s = A.solve_least_squares(A[:, 0], 'LDL') assert A * s == A[:, 0] pytest.raises(ValueError, lambda: SparseMatrix([[1, 0, 1], [0, 0, 1]]).solve([1, 1])) pytest.raises( ValueError, lambda: SparseMatrix([[1, 0], [0, 0], [2, 1]]).solve([1, 1, 1]))
def test_doktocsr(): a = SparseMatrix([[1, 2, 0, 0], [0, 3, 9, 0], [0, 1, 4, 0]]) b = SparseMatrix(4, 6, [10, 20, 0, 0, 0, 0, 0, 30, 0, 40, 0, 0, 0, 0, 50, 60, 70, 0, 0, 0, 0, 0, 0, 80]) c = SparseMatrix(4, 4, [0, 0, 0, 0, 0, 12, 0, 2, 15, 0, 12, 0, 0, 0, 0, 4]) d = SparseMatrix(10, 10, {(1, 1): 12, (3, 5): 7, (7, 8): 12}) e = SparseMatrix([[0, 0, 0], [1, 0, 2], [3, 0, 0]]) f = SparseMatrix(7, 8, {(2, 3): 5, (4, 5): 12}) assert _doktocsr(a) == [[1, 2, 3, 9, 1, 4], [0, 1, 1, 2, 1, 2], [0, 2, 4, 6], [3, 4]] assert _doktocsr(b) == [[10, 20, 30, 40, 50, 60, 70, 80], [0, 1, 1, 3, 2, 3, 4, 5], [0, 2, 4, 7, 8], [4, 6]] assert _doktocsr(c) == [[12, 2, 15, 12, 4], [1, 3, 0, 2, 3], [0, 0, 2, 4, 5], [4, 4]] assert _doktocsr(d) == [[12, 7, 12], [1, 5, 8], [0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3], [10, 10]] assert _doktocsr(e) == [[1, 2, 3], [0, 2, 0], [0, 0, 2, 3], [3, 3]] assert _doktocsr(f) == [[5, 12], [3, 5], [0, 0, 0, 1, 1, 2, 2, 2], [7, 8]]
def tomatrix(self): """ Converts MutableDenseNDimArray to Matrix. Can convert only 2-dim array, else will raise error. Examples ======== >>> from diofant.tensor.array import MutableSparseNDimArray >>> a = MutableSparseNDimArray([1 for i in range(9)], (3, 3)) >>> b = a.tomatrix() >>> b Matrix([ [1, 1, 1], [1, 1, 1], [1, 1, 1]]) """ if self.rank() != 2: raise ValueError('Dimensions must be of size of 2') mat_sparse = {} for key, value in self._sparse_array.items(): mat_sparse[self._get_tuple_index(key)] = value return SparseMatrix(self.shape[0], self.shape[1], mat_sparse)
def test_trace(): assert SparseMatrix(((1, 2), (3, 4))).trace() == 5 assert SparseMatrix(((0, 0), (0, 4))).trace() == 4
def test_SparseMatrix(): M = SparseMatrix([[x**+1, 1], [y, x + y]]) assert str(M) == "Matrix([\n[x, 1],\n[y, x + y]])" assert sstr(M) == "Matrix([\n[x, 1],\n[y, x + y]])"
def test_fill(): a = SparseMatrix([[0, I], [-I, 0]]) a.fill(0) assert a == Matrix([[0, 0], [0, 0]])
def test_len(): assert not SparseMatrix() assert SparseMatrix() == SparseMatrix([]) assert SparseMatrix() == SparseMatrix([[]])
def test_errors(): pytest.raises(ValueError, lambda: SparseMatrix(1.4, 2, lambda i, j: 0)) pytest.raises(ValueError, lambda: SparseMatrix(2, 2, 1)) pytest.raises(TypeError, lambda: SparseMatrix([1, 2, 3], [1, 2])) pytest.raises(ValueError, lambda: SparseMatrix([[1, 2], [3, 4]])[(1, 2, 3)]) pytest.raises(IndexError, lambda: SparseMatrix([[1, 2], [3, 4]])[5]) pytest.raises(ValueError, lambda: SparseMatrix([[1, 2], [3, 4]])[1, 2, 3]) pytest.raises( TypeError, lambda: SparseMatrix([[1, 2], [3, 4]]).copyin_list([0, 1], set())) pytest.raises(IndexError, lambda: SparseMatrix([[1, 2], [3, 4]])[1, 2]) pytest.raises(TypeError, lambda: SparseMatrix([1, 2, 3]).cross(1)) pytest.raises(IndexError, lambda: SparseMatrix(1, 2, [1, 2])[3]) pytest.raises( ShapeError, lambda: SparseMatrix(1, 2, [1, 2]) + SparseMatrix(2, 1, [2, 1])) pytest.raises(IndexError, lambda: SparseMatrix([1, 2, 3])[3, 0]) pytest.raises(TypeError, lambda: SparseMatrix([1, 2, 3]).applyfunc(1)) pytest.raises(ValueError, lambda: SparseMatrix([1, 2, 3]).reshape(2, 2)) pytest.raises(ValueError, lambda: SparseMatrix([[2, 3], [4, 1]]).cholesky()) pytest.raises(ValueError, lambda: SparseMatrix([[2, 3], [4, 1]]).LDLdecomposition()) pytest.raises(ValueError, lambda: SparseMatrix([[2, 3], [4, 1]]).add(1)) pytest.raises( ShapeError, lambda: SparseMatrix([[1, 2], [3, 4]]).row_join(Matrix([[1, 2]]))) pytest.raises( ShapeError, lambda: SparseMatrix([[1, 2], [3, 4]]).col_join(Matrix([1, 2]))) pytest.raises( ShapeError, lambda: SparseMatrix([[1, 2], [3, 4]]).copyin_matrix([1, 0], Matrix([1, 2])))
def test_add(): assert SparseMatrix(((1, 0), (0, 1))) + SparseMatrix(((0, 1), (1, 0))) == \ SparseMatrix(((1, 1), (1, 1))) a = SparseMatrix(100, 100, lambda i, j: int(j != 0 and i % j == 0)) b = SparseMatrix(100, 100, lambda i, j: int(i != 0 and j % i == 0)) assert (len(a._smat) + len(b._smat) - len((a + b)._smat) > 0)
def test_matrices(): for c in (Matrix, Matrix([1, 2, 3]), SparseMatrix, SparseMatrix([[1, 2], [3, 4]])): check(c)
def test_immutability(): with pytest.raises(TypeError): IM[2, 2] = 5 ISM = SparseMatrix(IM).as_immutable() with pytest.raises(TypeError): ISM[2, 2] = 5
def test_transpose(): assert SparseMatrix(((1, 2), (3, 4))).transpose() == \ SparseMatrix(((1, 3), (2, 4)))
def test_eq(): A = SparseMatrix(((1, 2), (3, 4))) assert A != 1 assert A != zeros(2, 1)
def test_sparse_matrix(): def sparse_eye(n): return SparseMatrix.eye(n) def sparse_zeros(n): return SparseMatrix.zeros(n) # creation args pytest.raises(TypeError, lambda: SparseMatrix(1, 2)) pytest.raises(ValueError, lambda: SparseMatrix(2, 2, (1, 3, 4, 5, 6))) a = SparseMatrix(((1, 0), (0, 1))) assert SparseMatrix(a) == a a = MutableSparseMatrix([]) b = MutableDenseMatrix([1, 2]) assert a.row_join(b) == b assert a.col_join(b) == b assert type(a.row_join(b)) == type(a) assert type(a.col_join(b)) == type(a) # test element assignment a = SparseMatrix(((1, 0), (0, 1))) a[3] = 4 assert a[1, 1] == 4 a[3] = 1 a[0, 0] = 2 assert a == SparseMatrix(((2, 0), (0, 1))) a[1, 0] = 5 assert a == SparseMatrix(((2, 0), (5, 1))) a[1, 1] = 0 assert a == SparseMatrix(((2, 0), (5, 0))) assert a._smat == {(0, 0): 2, (1, 0): 5} # test_multiplication a = SparseMatrix(( (1, 2), (3, 1), (0, 6), )) b = SparseMatrix(( (1, 2), (3, 0), )) c = a * b assert c[0, 0] == 7 assert c[0, 1] == 2 assert c[1, 0] == 6 assert c[1, 1] == 6 assert c[2, 0] == 18 assert c[2, 1] == 0 c = b * x assert isinstance(c, SparseMatrix) assert c[0, 0] == x assert c[0, 1] == 2 * x assert c[1, 0] == 3 * x assert c[1, 1] == 0 c = 5 * b assert isinstance(c, SparseMatrix) assert c[0, 0] == 5 assert c[0, 1] == 2 * 5 assert c[1, 0] == 3 * 5 assert c[1, 1] == 0 # test_power A = SparseMatrix([[2, 3], [4, 5]]) assert (A**5)[:] == [6140, 8097, 10796, 14237] A = SparseMatrix([[2, 1, 3], [4, 2, 4], [6, 12, 1]]) assert (A**3)[:] == [290, 262, 251, 448, 440, 368, 702, 954, 433] # test_creation a = SparseMatrix([[x, 0], [0, 0]]) m = a assert m.cols == m.rows assert m.cols == 2 assert m[:] == [x, 0, 0, 0] b = SparseMatrix(2, 2, [x, 0, 0, 0]) m = b assert m.cols == m.rows assert m.cols == 2 assert m[:] == [x, 0, 0, 0] assert a == b S = sparse_eye(3) del S[1, :] assert S == SparseMatrix([[1, 0, 0], [0, 0, 1]]) S = sparse_eye(3) del S[:, 1] assert S == SparseMatrix([[1, 0], [0, 0], [0, 1]]) S = SparseMatrix.eye(3) S[2, 1] = 2 S.col_swap(1, 0) assert S == SparseMatrix([[0, 1, 0], [1, 0, 0], [2, 0, 1]]) S.row_swap(0, 1) assert S == SparseMatrix([[1, 0, 0], [0, 1, 0], [2, 0, 1]]) S.col_swap(0, 1) assert S == SparseMatrix([[0, 1, 0], [1, 0, 0], [0, 2, 1]]) S.row_swap(0, 2) assert S == SparseMatrix([[0, 2, 1], [1, 0, 0], [0, 1, 0]]) S.col_swap(0, 2) assert S == SparseMatrix([[1, 2, 0], [0, 0, 1], [0, 1, 0]]) a = SparseMatrix(1, 2, [1, 2]) b = a.copy() c = a.copy() assert a[0] == 1 del a[0, :] assert a == SparseMatrix(0, 2, []) del b[:, 1] assert b == SparseMatrix(1, 1, [1]) # test_determinant assert SparseMatrix(1, 1, [0]).det() == 0 assert SparseMatrix([[1]]).det() == 1 assert SparseMatrix(((-3, 2), (8, -5))).det() == -1 assert SparseMatrix(((x, 1), (y, 2 * y))).det() == 2 * x * y - y assert SparseMatrix(((1, 1, 1), (1, 2, 3), (1, 3, 6))).det() == 1 assert SparseMatrix(((3, -2, 0, 5), (-2, 1, -2, 2), (0, -2, 5, 0), (5, 0, 3, 4))).det() == -289 assert SparseMatrix(((1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16))).det() == 0 assert SparseMatrix(((3, 2, 0, 0, 0), (0, 3, 2, 0, 0), (0, 0, 3, 2, 0), (0, 0, 0, 3, 2), (2, 0, 0, 0, 3))).det() == 275 assert SparseMatrix(((1, 0, 1, 2, 12), (2, 0, 1, 1, 4), (2, 1, 1, -1, 3), (3, 2, -1, 1, 8), (1, 1, 1, 0, 6))).det() == -55 assert SparseMatrix(((-5, 2, 3, 4, 5), (1, -4, 3, 4, 5), (1, 2, -3, 4, 5), (1, 2, 3, -2, 5), (1, 2, 3, 4, -1))).det() == 11664 assert SparseMatrix(((2, 7, -1, 3, 2), (0, 0, 1, 0, 1), (-2, 0, 7, 0, 2), (-3, -2, 4, 5, 3), (1, 0, 0, 0, 1))).det() == 123 # test_slicing m0 = sparse_eye(4) assert m0[:3, :3] == sparse_eye(3) assert m0[2:4, 0:2] == sparse_zeros(2) m1 = SparseMatrix(3, 3, lambda i, j: i + j) assert m1[0, :] == SparseMatrix(1, 3, (0, 1, 2)) assert m1[1:3, 1] == SparseMatrix(2, 1, (2, 3)) m2 = SparseMatrix([[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]]) assert m2[:, -1] == SparseMatrix(4, 1, [3, 7, 11, 15]) assert m2[-2:, :] == SparseMatrix([[8, 9, 10, 11], [12, 13, 14, 15]]) assert SparseMatrix([[1, 2], [3, 4]])[[1], [1]] == Matrix([[4]]) # test_submatrix_assignment m = sparse_zeros(4) m[2:4, 2:4] = sparse_eye(2) assert m == SparseMatrix([(0, 0, 0, 0), (0, 0, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)]) assert len(m._smat) == 2 m[:2, :2] = sparse_eye(2) assert m == sparse_eye(4) m[:, 0] = SparseMatrix(4, 1, (1, 2, 3, 4)) assert m == SparseMatrix([(1, 0, 0, 0), (2, 1, 0, 0), (3, 0, 1, 0), (4, 0, 0, 1)]) m[:, :] = sparse_zeros(4) assert m == sparse_zeros(4) m[:, :] = ((1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16)) assert m == SparseMatrix( ((1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16))) m[:2, 0] = [0, 0] assert m == SparseMatrix( ((0, 2, 3, 4), (0, 6, 7, 8), (9, 10, 11, 12), (13, 14, 15, 16))) # test_reshape m0 = sparse_eye(3) assert m0.reshape(1, 9) == SparseMatrix(1, 9, (1, 0, 0, 0, 1, 0, 0, 0, 1)) m1 = SparseMatrix(3, 4, lambda i, j: i + j) assert m1.reshape(4, 3) == \ SparseMatrix([(0, 1, 2), (3, 1, 2), (3, 4, 2), (3, 4, 5)]) assert m1.reshape(2, 6) == \ SparseMatrix([(0, 1, 2, 3, 1, 2), (3, 4, 2, 3, 4, 5)]) # test_applyfunc m0 = sparse_eye(3) assert m0.applyfunc(lambda x: 2 * x) == sparse_eye(3) * 2 assert m0.applyfunc(lambda x: 0) == sparse_zeros(3) # test_LUdecomp testmat = SparseMatrix([[0, 2, 5, 3], [3, 3, 7, 4], [8, 4, 0, 2], [-2, 6, 3, 4]]) L, U, p = testmat.LUdecomposition() assert L.is_lower assert U.is_upper assert (L * U).permuteBkwd(p) - testmat == sparse_zeros(4) testmat = SparseMatrix([[6, -2, 7, 4], [0, 3, 6, 7], [1, -2, 7, 4], [-9, 2, 6, 3]]) L, U, p = testmat.LUdecomposition() assert L.is_lower assert U.is_upper assert (L * U).permuteBkwd(p) - testmat == sparse_zeros(4) M = Matrix(((1, x, 1), (2, y, 0), (y, 0, z))) L, U, p = M.LUdecomposition() assert L.is_lower assert U.is_upper assert (L * U).permuteBkwd(p) - M == sparse_zeros(3) # test_LUsolve A = SparseMatrix([[2, 3, 5], [3, 6, 2], [8, 3, 6]]) B = SparseMatrix(3, 1, [3, 7, 5]) b = A * B soln = A.LUsolve(b) assert soln == B A = SparseMatrix([[0, -1, 2], [5, 10, 7], [8, 3, 4]]) B = SparseMatrix(3, 1, [-1, 2, 5]) b = A * B soln = A.LUsolve(b) assert soln == B # test_inverse A = sparse_eye(4) assert A.inv() == sparse_eye(4) assert A.inv(method='CH') == sparse_eye(4) assert A.inv(method='LDL') == sparse_eye(4) A = SparseMatrix([[2, 3, 5], [3, 6, 2], [7, 2, 6]]) Ainv = SparseMatrix(Matrix(A).inv()) assert A * Ainv == sparse_eye(3) assert A.inv(method='CH') == Ainv assert A.inv(method='LDL') == Ainv A = SparseMatrix([[2, 3, 5], [3, 6, 2], [5, 2, 6]]) Ainv = SparseMatrix(Matrix(A).inv()) assert A * Ainv == sparse_eye(3) assert A.inv(method='CH') == Ainv assert A.inv(method='LDL') == Ainv # test_cross v1 = Matrix(1, 3, [1, 2, 3]) v2 = Matrix(1, 3, [3, 4, 5]) assert v1.cross(v2) == Matrix(1, 3, [-2, 4, -2]) assert v1.norm(2)**2 == 14 # conjugate a = SparseMatrix(((1, 2 + I), (3, 4))) assert a.C == SparseMatrix([[1, 2 - I], [3, 4]]) # mul assert a * Matrix(2, 2, [1, 0, 0, 1]) == a assert a + Matrix(2, 2, [1, 1, 1, 1]) == SparseMatrix([[2, 3 + I], [4, 5]]) assert a * 0 == Matrix([[0, 0], [0, 0]]) # col join assert a.col_join(sparse_eye(2)) == SparseMatrix([[1, 2 + I], [3, 4], [1, 0], [0, 1]]) A = SparseMatrix(ones(3)) B = eye(3) assert A.col_join(B) == Matrix([[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 0, 0], [0, 1, 0], [0, 0, 1]]) # row join A = SparseMatrix(((1, 0, 1), (0, 1, 0), (1, 1, 0))) B = Matrix(((1, 0, 0), (0, 1, 0), (0, 0, 1))) assert A.row_join(B) == Matrix([[1, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [1, 1, 0, 0, 0, 1]]) # symmetric assert not a.is_symmetric(simplify=False) assert sparse_eye(3).is_symmetric(simplify=False) # test_cofactor assert sparse_eye(3) == sparse_eye(3).cofactorMatrix() test = SparseMatrix([[1, 3, 2], [2, 6, 3], [2, 3, 6]]) assert test.cofactorMatrix() == \ SparseMatrix([[27, -6, -6], [-12, 2, 3], [-3, 1, 0]]) test = SparseMatrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) assert test.cofactorMatrix() == \ SparseMatrix([[-3, 6, -3], [6, -12, 6], [-3, 6, -3]]) # test_jacobian L = SparseMatrix(1, 2, [x**2 * y, 2 * y**2 + x * y]) syms = [x, y] assert L.jacobian(syms) == Matrix([[2 * x * y, x**2], [y, 4 * y + x]]) L = SparseMatrix(1, 2, [x, x**2 * y**3]) assert L.jacobian(syms) == SparseMatrix([[1, 0], [2 * x * y**3, x**2 * 3 * y**2]]) # test_QR A = Matrix([[1, 2], [2, 3]]) Q, S = A.QRdecomposition() R = Rational assert Q == Matrix([[5**R(-1, 2), (R(2) / 5) * (R(1) / 5)**R(-1, 2)], [2 * 5**R(-1, 2), (-R(1) / 5) * (R(1) / 5)**R(-1, 2)]]) assert S == Matrix([[5**R(1, 2), 8 * 5**R(-1, 2)], [0, (R(1) / 5)**R(1, 2)]]) assert Q * S == A assert Q.T * Q == sparse_eye(2) R = Rational # test nullspace # first test reduced row-ech form M = SparseMatrix([[5, 7, 2, 1], [1, 6, 2, -1]]) out, tmp = M.rref() assert out == Matrix([[1, 0, -R(2) / 23, R(13) / 23], [0, 1, R(8) / 23, R(-6) / 23]]) M = SparseMatrix([[1, 3, 0, 2, 6, 3, 1], [-2, -6, 0, -2, -8, 3, 1], [3, 9, 0, 0, 6, 6, 2], [-1, -3, 0, 1, 0, 9, 3]]) out, tmp = M.rref() assert out == Matrix([[1, 3, 0, 0, 2, 0, 0], [0, 0, 0, 1, 2, 0, 0], [0, 0, 0, 0, 0, 1, R(1) / 3], [0, 0, 0, 0, 0, 0, 0]]) # now check the vectors basis = M.nullspace() assert basis[0] == Matrix([-3, 1, 0, 0, 0, 0, 0]) assert basis[1] == Matrix([0, 0, 1, 0, 0, 0, 0]) assert basis[2] == Matrix([-2, 0, 0, -2, 1, 0, 0]) assert basis[3] == Matrix([0, 0, 0, 0, 0, R(-1) / 3, 1]) # test eigen sparse_eye3 = sparse_eye(3) assert sparse_eye3.charpoly(x) == PurePoly(((x - 1)**3)) assert sparse_eye3.charpoly(y) == PurePoly(((y - 1)**3)) # test values M = Matrix([(0, 1, -1), (1, 1, 0), (-1, 0, 1)]) vals = M.eigenvals() assert sorted(vals) == [-1, 1, 2] R = Rational M = Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) assert M.eigenvects() == [ (1, 3, [Matrix([1, 0, 0]), Matrix([0, 1, 0]), Matrix([0, 0, 1])]) ] M = Matrix([[5, 0, 2], [3, 2, 0], [0, 0, 1]]) assert M.eigenvects() == [(1, 1, [Matrix([R(-1) / 2, R(3) / 2, 1])]), (2, 1, [Matrix([0, 1, 0])]), (5, 1, [Matrix([1, 1, 0])])] assert M.zeros(3, 5) == SparseMatrix(3, 5, {}) A = SparseMatrix( 10, 10, { (0, 0): 18, (0, 9): 12, (1, 4): 18, (2, 7): 16, (3, 9): 12, (4, 2): 19, (5, 7): 16, (6, 2): 12, (9, 7): 18 }) assert A.row_list() == [(0, 0, 18), (0, 9, 12), (1, 4, 18), (2, 7, 16), (3, 9, 12), (4, 2, 19), (5, 7, 16), (6, 2, 12), (9, 7, 18)] assert A.col_list() == [(0, 0, 18), (4, 2, 19), (6, 2, 12), (1, 4, 18), (2, 7, 16), (5, 7, 16), (9, 7, 18), (0, 9, 12), (3, 9, 12)] assert SparseMatrix.eye(2).nnz() == 2 M = SparseMatrix.eye(3) * 2 M[1, 0] = -1 M.col_op(1, lambda v, i: v + 2 * M[i, 0]) assert M == Matrix([[2, 4, 0], [-1, 0, 0], [0, 0, 2]]) M = SparseMatrix.zeros(3) M.fill(1) assert M == ones(3) assert SparseMatrix(ones(0, 3)).tolist() == []
def test_as_immutable(): X = Matrix([[1, 2], [3, 4]]) assert sympify(X) == X.as_immutable() == ImmutableMatrix([[1, 2], [3, 4]]) X = SparseMatrix(5, 5, {}) assert sympify(X) == X.as_immutable() == ImmutableSparseMatrix( [[0 for i in range(5)] for i in range(5)])
def test_CL_RL(): assert SparseMatrix(((1, 2), (3, 4))).row_list() == \ [(0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 4)] assert SparseMatrix(((1, 2), (3, 4))).col_list() == \ [(0, 0, 1), (1, 0, 3), (0, 1, 2), (1, 1, 4)]