Python numpy.kron方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def non_redundant_rotation_generators(
        rhf_objective: RestrictedHartreeFockObjective) -> List[FermionOperator]:  # testpragma: no cover
    # coverage: ignore
    """
    Generate the fermionic representation of all non-redundant rotation
    generators for restricted Hartree-fock

    :param rhf_objective: openfermioncirq.experiments.hfvqe.RestrictedHartreeFock object
    :return: list of fermionic generators.
    """
    rotation_generators = []
    for p in range(rhf_objective.nocc * rhf_objective.nvirt):
        grad_params = np.zeros(rhf_objective.nocc * rhf_objective.nvirt)
        grad_params[p] = 1
        kappa_spatial_orbital = rhf_params_to_matrix(grad_params,
                                                     len(rhf_objective.occ) + len(rhf_objective.virt),
                                                     rhf_objective.occ,
                                                     rhf_objective.virt)
        p0 = np.array([[1, 0], [0, 1]])
        kappa_spin_orbital = np.kron(kappa_spatial_orbital, p0)
        fermion_op = get_one_body_fermion_operator(kappa_spin_orbital)
        rotation_generators.append(fermion_op)
    return rotation_generators 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def energy_from_opdm(opdm, constant, one_body_tensor, two_body_tensor):
    """
    Evaluate the energy of an opdm assuming the 2-RDM is opdm ^ opdm

    :param opdm: single spin-component of the full spin-orbital opdm.
    :param constant: constant shift to the Hamiltonian. Commonly this is the
                     nuclear repulsion energy.
    :param one_body_tensor: spatial one-body integrals
    :param two_body_tensor: spatial two-body integrals
    :return:
    """
    spin_opdm = np.kron(opdm, np.eye(2))
    spin_tpdm = 2 * wedge(spin_opdm, spin_opdm, (1, 1), (1, 1))
    molecular_hamiltonian = generate_hamiltonian(constant=constant,
                                                 one_body_integrals=one_body_tensor,
                                                 two_body_integrals=two_body_tensor)
    rdms = InteractionRDM(spin_opdm, spin_tpdm)
    return rdms.expectation(molecular_hamiltonian).real 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def test_simulate_trotter_simulate_controlled(
        hamiltonian, time, initial_state, exact_state, order, n_steps,
        algorithm, result_fidelity):

    n_qubits = openfermion.count_qubits(hamiltonian)
    qubits = cirq.LineQubit.range(n_qubits)

    control = cirq.LineQubit(-1)
    zero = [1, 0]
    one = [0, 1]
    start_state = (numpy.kron(zero, initial_state)
                   + numpy.kron(one, initial_state)) / numpy.sqrt(2)

    circuit = cirq.Circuit(simulate_trotter(
        qubits, hamiltonian, time, n_steps, order, algorithm, control))

    final_state = circuit.final_wavefunction(start_state)
    correct_state = (numpy.kron(zero, initial_state)
                     + numpy.kron(one, exact_state)) / numpy.sqrt(2)
    assert fidelity(final_state, correct_state) > result_fidelity
    # Make sure the time wasn't too small
    assert fidelity(final_state, start_state) < 0.95 * result_fidelity 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def state_to_stdmx(state_vec):
    """
    Convert a state vector into a density matrix.

    Parameters
    ----------
    state_vec : list or tuple
       State vector in the standard (sigma-z) basis.

    Returns
    -------
    numpy.ndarray
        A density matrix of shape (d,d), corresponding to the pure state
        given by the length-`d` array, `state_vec`.
    """
    st_vec = state_vec.view(); st_vec.shape = (len(st_vec), 1)  # column vector
    dm_mx = _np.kron(_np.conjugate(_np.transpose(st_vec)), st_vec)
    return dm_mx  # density matrix in standard (sigma-z) basis 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def unitary_to_process_mx(U):
    """
    Compute the super-operator which acts on (row)-vectorized
    density matrices from a unitary operator (matrix) U which
    acts on state vectors.  This super-operator is given by
    the tensor product of U and conjugate(U), i.e. kron(U,U.conj).

    Parameters
    ----------
    U : numpy array
        The unitary matrix which acts on state vectors.

    Returns
    -------
    numpy array
       The super-operator process matrix.
    """
    # U -> kron(U,Uc) since U rho U_dag -> kron(U,Uc)
    #  since AXB --row-vectorize--> kron(A,B.T)*vec(X)
    return _np.kron(U, _np.conjugate(U)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def dictionary_from_transform(transform, n, K, normalized=True, inverse=True):
    """
    Builds a Dictionary matrix from a given transform

    Args:
        transform: A valid transform (e.g. Haar, DCT-II)
        n: number of rows transform dictionary
        K: number of columns transform dictionary
        normalized: If True, the columns will be l2-normalized
        inverse: Uses the inverse transform (as usually needed in applications)

    Returns:
        Dictionary build from the Kronecker-Delta of the transform applied to the identity.
    """
    H = np.zeros((K, n))
    for i in range(n):
        v = np.zeros(n)
        v[i] = 1.0
        H[:, i] = transform(v, sampling_factor=K)
    if inverse:
        H = H.T
    return np.kron(H.T, H.T) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def random_dictionary(n, K, normalized=True, seed=None):
    """
    Build a random dictionary matrix with K = n
    Args:
        n: square of signal dimension
        K: square of desired dictionary atoms
        normalized: If true, columns will be l2-normalized
        seed: Random seed

    Returns:
        Random dictionary
    """
    if seed:
        np.random.seed(seed)
    H = np.random.rand(n, K) * 255
    if normalized:
        for k in range(K):
            H[:, k] *= 1 / np.linalg.norm(H[:, k])
    return np.kron(H, H) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def middle_bond_hamiltonian(Jx, Jz, hx, hz, L):
    """" Returns the spin operators sigma_x and sigma_z for L sites."""
    sx = np.array([[0., 1.], [1., 0.]])
    sz = np.array([[1., 0.], [0., -1.]])

    H_bond = Jx * np.kron(sx, sx) + Jz * np.kron(sz, sz)
    H_bond = H_bond + hx / 2 * np.kron(sx, np.eye(2)) + hx / 2 * np.kron(np.eye(2), sx)
    H_bond = H_bond + hz / 2 * np.kron(sz, np.eye(2)) + hz / 2 * np.kron(np.eye(2), sz)
    H_bond = H_bond.reshape(2, 2, 2, 2).transpose(0, 2, 1, 3).reshape(4, 4)  #i1 i2 i1' i2' -->
    U, s, V = np.linalg.svd(H_bond)

    M1 = np.dot(U, np.diag(s)).reshape(2, 2, 1, 4).transpose(2, 3, 0, 1)
    M2 = V.reshape(4, 1, 2, 2)
    M0 = np.tensordot(np.tensordot([1], [1], axes=0), np.eye(2), axes=0)
    W = []

    for i in range(L):
        if i == L / 2 - 1:
            W.append(M1)
        elif i == L / 2:
            W.append(M2)
        else:
            W.append(M0)
    return W 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def init_H_bonds(self):
        """Initialize `H_bonds` hamiltonian.

        Called by __init__().
        """
        sx, sz, id = self.sigmax, self.sigmaz, self.id
        d = self.d
        nbonds = self.L - 1 if self.bc == 'finite' else self.L
        H_list = []
        for i in range(nbonds):
            gL = gR = 0.5 * self.g
            if self.bc == 'finite':
                if i == 0:
                    gL = self.g
                if i + 1 == self.L - 1:
                    gR = self.g
            H_bond = -self.J * np.kron(sx, sx) - gL * np.kron(sz, id) - gR * np.kron(id, sz)
            # H_bond has legs ``i, j, i*, j*``
            H_list.append(np.reshape(H_bond, [d, d, d, d]))
        self.H_bonds = H_list

    # (note: not required for TEBD) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def test_Kroneker(par):
    """Dot-test, inversion and comparison with np.kron for Kronecker operator
    """
    np.random.seed(10)
    G1 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype(par['dtype'])
    G2 = np.random.normal(0, 10, (par['ny'], par['nx'])).astype(par['dtype'])
    x = np.ones(par['nx']**2) + par['imag']*np.ones(par['nx']**2)

    Kop = Kronecker(MatrixMult(G1, dtype=par['dtype']),
                    MatrixMult(G2, dtype=par['dtype']),
                    dtype=par['dtype'])
    assert dottest(Kop, par['ny']**2, par['nx']**2,
                   complexflag=0 if par['imag'] == 0 else 3)

    xlsqr = lsqr(Kop, Kop * x, damp=1e-20, iter_lim=300, show=0)[0]
    assert_array_almost_equal(x, xlsqr, decimal=2)

    # Comparison with numpy
    assert_array_almost_equal(np.kron(G1, G2), Kop * np.eye(par['nx']**2),
                              decimal=3) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def graymap(x):

    x = x[..., np.newaxis]
    return np.concatenate([x, x, x], axis=-1)*0.5+0.5

# --------------------------------------
# Visualizing data
# --------------------------------------

# def visualize(x,colormap,name):
#
#     N = len(x)
#     assert(N <= 16)
#
#     x = colormap(x/np.abs(x).max())
#
#     # Create a mosaic and upsample
#     x = x.reshape([1, N, 29, 29, 3])
#     x = np.pad(x, ((0, 0), (0, 0), (2, 2), (2, 2), (0, 0)), 'constant', constant_values=1)
#     x = x.transpose([0, 2, 1, 3, 4]).reshape([1*33, N*33, 3])
#     x = np.kron(x, np.ones([2, 2, 1]))
#
#     PIL.Image.fromarray((x*255).astype('byte'), 'RGB').save(name) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def plt_vector(x, colormap, num_headers):
    N = len(x)
    assert (N <= 16)
    len_x = 54
    len_y = num_headers
    # size = int(np.ceil(np.sqrt(len(x[0]))))
    length = len_y*len_x
    data = np.zeros((N, length), dtype=np.float64)
    data[:, :x.shape[1]] = x
    data = colormap(data / np.abs(data).max())
    # data = data.reshape([1, N, size, size, 3])
    data = data.reshape([1, N, len_y, len_x, 3])
    # data = np.pad(data, ((0, 0), (0, 0), (2, 2), (2, 2), (0, 0)), 'constant', constant_values=1)
    data = data.transpose([0, 2, 1, 3, 4]).reshape([1 * (len_y), N * (len_x), 3])
    return data
    # data = np.kron(data, np.ones([2, 2, 1])) # scales 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def test_perform(self):
        if not imported_scipy:
            raise SkipTest('kron tests need the scipy package to be installed')

        for shp0 in [(2,), (2, 3), (2, 3, 4), (2, 3, 4, 5)]:
            x = tensor.tensor(dtype='floatX',
                              broadcastable=(False,) * len(shp0))
            a = numpy.asarray(self.rng.rand(*shp0)).astype(config.floatX)
            for shp1 in [(6,), (6, 7), (6, 7, 8), (6, 7, 8, 9)]:
                if len(shp0) + len(shp1) == 2:
                    continue
                y = tensor.tensor(dtype='floatX',
                                  broadcastable=(False,) * len(shp1))
                f = function([x, y], kron(x, y))
                b = self.rng.rand(*shp1).astype(config.floatX)
                out = f(a, b)
                # Newer versions of scipy want 4 dimensions at least,
                # so we have to add a dimension to a and flatten the result.
                if len(shp0) + len(shp1) == 3:
                    scipy_val = scipy.linalg.kron(
                        a[numpy.newaxis, :], b).flatten()
                else:
                    scipy_val = scipy.linalg.kron(a, b)
                utt.assert_allclose(out, scipy_val) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def cov_params_default(self):  # p.296 (7.2.21)
        # Sigma_co described on p. 287
        beta = self.beta
        if self.det_coef_coint.size > 0:
            beta = vstack((beta, self.det_coef_coint))
        dt = self.deterministic
        num_det = ("co" in dt) + ("lo" in dt)
        num_det += (self.seasons-1) if self.seasons else 0
        if self.exog is not None:
            num_det += self.exog.shape[1]
        b_id = scipy.linalg.block_diag(beta,
                                       np.identity(self.neqs * (self.k_ar-1) +
                                                   num_det))

        y_lag1 = self._y_lag1
        b_y = beta.T.dot(y_lag1)
        omega11 = b_y.dot(b_y.T)
        omega12 = b_y.dot(self._delta_x.T)
        omega21 = omega12.T
        omega22 = self._delta_x.dot(self._delta_x.T)
        omega = np.bmat([[omega11, omega12],
                         [omega21, omega22]]).A

        mat1 = b_id.dot(inv(omega)).dot(b_id.T)
        return np.kron(mat1, self.sigma_u) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import kron [as 別名]
def _orth_cov(self):
        # Lutkepohl 3.7.8

        Ik = np.eye(self.neqs)
        PIk = np.kron(self.P.T, Ik)
        H = self.H

        covs = self._empty_covm(self.periods + 1)
        for i in range(self.periods + 1):
            if i == 0:
                apiece = 0
            else:
                Ci = np.dot(PIk, self.G[i-1])
                apiece = chain_dot(Ci, self.cov_a, Ci.T)

            Cibar = np.dot(np.kron(Ik, self.irfs[i]), H)
            bpiece = chain_dot(Cibar, self.cov_sig, Cibar.T) / self.T

            # Lutkepohl typo, cov_sig correct
            covs[i] = apiece + bpiece

        return covs