def test_daulbasis_init(): db = DualBasis() assert isinstance(db, DualBasis) dbe = DualBasisElement(tensor_names=['A'] * 5, tensor_coeffs=[1] * 5, tensor_elements=[(i, i) for i in range(5)]) db = DualBasis(elements=[dbe]) assert db[0] == dbe assert len(db) == 1 for tdbe in db: assert tdbe == dbe db2 = db + dbe assert isinstance(db2, DualBasis) assert len(db2) == 2 tdbe = DualBasisElement(tensor_names=['B'] * 5, tensor_coeffs=[1] * 5, tensor_elements=[(i, i) for i in range(5)]) tdb = DualBasis(elements=[tdbe]) db3 = db + tdb assert isinstance(db3, DualBasis) assert len(db3) == 2 db4 = tdbe + db assert len(db4) == 2 with pytest.raises(TypeError): _ = DualBasis(elements=[tdbe, 4]) with pytest.raises(TypeError): db = DualBasis(elements=[tdbe]) _ = db + 4
def opdm_to_ohdm_mapping(dim: int) -> DualBasis: """ Map the ck to kc D1 + Q1 = I Args: dim: dimension of the spin-orbital basis Returns: DualBasis for the 1-RDM representability constraint """ dbe_list = [] for i in range(dim): for j in range(i, dim): dbe = DualBasisElement() if i != j: dbe.add_element('ck', (i, j), 0.5) dbe.add_element('ck', (j, i), 0.5) dbe.add_element('kc', (j, i), 0.5) dbe.add_element('kc', (i, j), 0.5) dbe.dual_scalar = 0.0 else: dbe.add_element('ck', (i, j), 1.0) dbe.add_element('kc', (i, j), 1.0) dbe.dual_scalar = 1.0 # db += dbe dbe_list.append(dbe) return DualBasis(elements=dbe_list) # db
def tpdm_to_opdm_mapping(dim: int, normalization: Union[float, int]) -> DualBasis: """ Construct the DualBasis for mapping of the tpdm to the opdm Args: dim: dimension of the spin-orbital basis. normalization: Scalar for mapping tpdm to opdm. Generally, this is 1 / (N - 1) where N is the number of electrons. Returns: DualBasis for all dim^2 """ db_basis = DualBasis() for i in range(dim): for j in range(i, dim): dbe = DualBasisElement() # contract over tpdm terms for r in range(dim): # duplicate entries get summed in DualBasisElement dbe.add_element('cckk', (i, r, j, r), 0.5) dbe.add_element('cckk', (j, r, i, r), 0.5) # opdm terms dbe.add_element('ck', (i, j), -0.5 * normalization) dbe.add_element('ck', (j, i), -0.5 * normalization) dbe.simplify() db_basis += dbe return db_basis
def tpdm_antisymmetry_constraint(dim: int) -> DualBasis: """ The dual basis elements representing the antisymmetry constraints :param dim: spinless Fermion basis rank :return: the dual basis of antisymmetry_constraints :rtype: DualBasis """ # dual_basis = DualBasis() dbe_list = [] for p, q, r, s in product(range(dim), repeat=4): if p * dim + q <= r * dim + s: if p < q and r < s: tensor_elements = [ tuple(indices) for indices in _coord_generator(p, q, r, s) ] tensor_names = ['cckk'] * len(tensor_elements) tensor_coeffs = [0.5] * len(tensor_elements) dbe = DualBasisElement() for n, e, c in zip(tensor_names, tensor_elements, tensor_coeffs): dbe.add_element(n, e, c) # dual_basis += dbe dbe_list.append(dbe) return DualBasis(elements=dbe_list)
def __init__(self, tensors, dual_basis=DualBasis()): """ A collection of tensor objects with maps from name to tensor Args: tensors: a dictionary or tuple of tensors and their associated call name. DualBasisElement dual_basis: the set of linear operators restricting the feasible elements of the linear space generated by vectorizing the tensors. """ if not isinstance(tensors, list): raise TypeError("MultiTensor accepts a list") # this preserves the order the user passes with the tensors self.tensors = TMap(tensors) # since all the tensors are indexed from zero...I need to know their # numbering offset when combined with everything. self.off_set_map = self.make_offset_dict(self.tensors) # An iterable object that provides access to the dual basis elements self.dual_basis = dual_basis self.vec_dim = sum([vec.size for vec in self.tensors])
def test_dual_basis_element(): de = DualBasisElement() de_2 = DualBasisElement() db_0 = de + de_2 assert isinstance(db_0, DualBasis) db_1 = db_0 + db_0 assert isinstance(db_1, DualBasis) dim = 2 opdm = np.random.random((dim, dim)) opdm = (opdm.T + opdm) / 2 opdm = Tensor(tensor=opdm, name='opdm') rdm = MultiTensor([opdm]) def generate_dual_basis_element(i, j): element = DualBasisElement(tensor_names=["opdm"], tensor_elements=[(i, j)], tensor_coeffs=[-1.0], bias=1 if i == j else 0, scalar=0) return element opdm_to_oqdm_map = DualBasis() for _, idx in opdm.all_iterator(): i, j = idx opdm_to_oqdm_map += generate_dual_basis_element(i, j) rdm.dual_basis = opdm_to_oqdm_map A, b, _ = rdm.synthesize_dual_basis() Adense = A.todense() opdm_flat = opdm.data.reshape((-1, 1)) oqdm = Adense.dot(opdm_flat) test_oqdm = oqdm + b.todense() assert np.allclose(test_oqdm.reshape((dim, dim)), np.eye(dim) - opdm.data)
def spin_orbital_linear_constraints( dim: int, num_alpha: Union[int, float], num_beta: Union[int, float], constraint_list: List[str], sz: Optional[Union[None, float, int]] = None) -> DualBasis: """ Construct dual basis constraints for 2-positivity in a spin-orbital basis Args: dim: Dimension of the spin-orbital basis num_alpha: number of spin-up electrons. num_beta: number of spin-down electrons. constraint_list: list of which matrices to include in the 2-pos set. sz: target magnetic quantum number. Returns: DualBasis element. """ N = num_alpha + num_beta dual_basis = DualBasis() if 'cckk' in constraint_list: # Natural constraints on particle-conserving 2-RDMs # trace constraint on D2 dual_basis += tpdm_trace_constraint(dim, N * (N - 1)) # antisymmetry constraint dual_basis += tpdm_antisymmetry_constraint(dim) if 'ck' in constraint_list: dual_basis += tpdm_to_opdm_mapping(dim, N - 1) if sz is not None: dual_basis += sz_constraint(dim, sz) dual_basis += na_constraint(dim, num_alpha) dual_basis += nb_constraint(dim, num_beta) if 'kc' in constraint_list: dual_basis += opdm_to_ohdm_mapping(dim) # d2 -> q2 if 'kkcc' in constraint_list: print('tqdm constraints') dual_basis += tpdm_to_thdm_mapping(dim) # d2 -> g2 if "ckck" in constraint_list: print('phdm constraints') dual_basis += tpdm_to_phdm_mapping(dim) return dual_basis
def tpdm_to_thdm_mapping(dim: int) -> DualBasis: """ Generate the dual basis elements for a mapping of the 2-RDM to the two-hole-RDM Args: dim: Dimension of the spin-orbital basis Returns: DualBasis representing the equality constraint. """ dbe_list = [] def d2q2element(p: int, q: int, r: int, s: int, factor: Union[float, int])\ -> DualBasisElement: """ Build the dual basis element for symmetric form of 2-marginal :param p: tensor index :param q: tensor index :param r: tensor index :param s: tensor index :param factor: scaling coeff for a symmetric constraint :return: the dual basis of the mapping """ dbe = DualBasisElement() dbe.add_element('cckk', (p, q, r, s), -1.0 * factor) dbe.add_element('kkcc', (r, s, p, q), +1.0 * factor) if q == s: dbe.add_element('ck', (p, r), factor) if p == r: dbe.add_element('ck', (q, s), factor) if q == r: dbe.add_element('ck', (p, s), -1. * factor) if p == s: dbe.add_element('ck', (q, r), -1. * factor) dbe.dual_scalar = ( kronecker_delta(q, s) * kronecker_delta(p, r) - kronecker_delta(q, r) * kronecker_delta(p, s)) * factor return dbe for i, j, k, l in product(range(dim), repeat=4): if i * dim + j <= k * dim + l: db_element = d2q2element(i, j, k, l, 0.5) db_element_2 = d2q2element(k, l, i, j, 0.5) dbe_list.append(db_element.join_elements(db_element_2)) return DualBasis(elements=dbe_list)
def nb_constraint(dim, nb): """ Constraint the trace of the alpha block of the opdm to equal the number of spin-down electrons Args: dim: Dimension of the spin-orbital basis. na: Number of spin down electrons Returns: DualBasis representing the cosntraint that is length 1 """ dbe = DualBasisElement() for i in range(dim // 2): dbe.add_element('ck', (2 * i + 1, 2 * i + 1), 1.0) dbe.dual_scalar = nb return DualBasis(elements=[dbe])
def sz_constraint(dim: int, sz: Union[float, int]) -> DualBasis: """ Constraint on the 1-RDM Args: dim: dimension of the spin-orbital basis. sz: expectation value of the magnetic quantum number. Returns: DualBasis """ dbe = DualBasisElement() for i in range(dim // 2): dbe.add_element('ck', (2 * i, 2 * i), 0.5) dbe.add_element('ck', (2 * i + 1, 2 * i + 1), -0.5) dbe.dual_scalar = sz return DualBasis(elements=[dbe])
def na_constraint(dim: int, na: Union[float, int]) -> DualBasis: """ Constraint the trace of the alpha block of the opdm to equal the number of spin-up electrons Args: dim: Dimension of the spin-orbital basis. na: Number of spin up electrons Returns: DualBasis representing the cosntraint that is length 1 """ dbe = DualBasisElement() for i in range(dim // 2): dbe.add_element('ck', (2 * i, 2 * i), 1.0) dbe.dual_scalar = na return DualBasis(elements=[dbe])
def test_synthesis_dualbasis(): a = np.random.random((5, 5)) b = np.random.random((4, 4)) c = np.random.random((3, 3)) at = Tensor(tensor=a, name='a') bt = Tensor(tensor=b, name='b') ct = Tensor(tensor=c, name='c') dbe = DualBasisElement() dbe.add_element('a', (0, 1), 4) dbe.add_element('a', (1, 0), 4) mt = MultiTensor([at, bt, ct], DualBasis(elements=[dbe])) A, c, b = mt.synthesize_dual_basis() assert isinstance(A, sp.sparse.csr_matrix) assert isinstance(c, sp.sparse.csr_matrix) assert isinstance(b, sp.sparse.csr_matrix) assert A.shape == (1, 50) assert b.shape == (1, 1) assert c.shape == (1, 1)
def tpdm_to_phdm_mapping(dim: int) -> DualBasis: """ Args: dim: Dimension of the spin-orbital basis Returns: DualBasis representing the equality constraint """ dbe_list = [] def g2d2map(p: int, q: int, r: int, s: int, factor: Optional[Union[float, int]] = 1) -> DualBasisElement: """ Build the dual basis element for a symmetric 2-marginal :param p: tensor index :param q: tensor index :param r: tensor index :param s: tensor index :param factor: weighting of the element :return: the dual basis element """ dbe = DualBasisElement() if q == s: dbe.add_element('ck', (p, r), -1. * factor) dbe.add_element('ckck', (p, s, r, q), 1.0 * factor) dbe.add_element('cckk', (p, q, r, s), 1.0 * factor) dbe.dual_scalar = 0 return dbe for i, j, k, l in product(range(dim), repeat=4): if i * dim + j <= k * dim + l: db_element = g2d2map(i, j, k, l, factor=0.5) db_element_2 = g2d2map(k, l, i, j, factor=0.5) dbe_list.append(db_element.join_elements(db_element_2)) return DualBasis(elements=dbe_list)