Python numpy.real_if_close方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def updateinternals(self, e, epos, mask=None):
        """Update any internals given that electron e moved to epos. mask is a Boolean array 
        which allows us to update only certain walkers"""
        # MAY want to vectorize later if it really hangs here, shouldn't!

        s = int(e >= self._nelec[0])
        if mask is None:
            mask = [True] * epos.configs.shape[0]
        eeff = e - s * self._nelec[0]
        ao = np.real_if_close(
            self._mol.eval_gto(self.pbc_str + "GTOval_sph", epos.configs), tol=1e4
        )
        self._aovals[:, e, :] = ao
        mo = ao.dot(self.parameters[self._coefflookup[s]])

        mo_vals = mo[:, self._det_occup[s]]
        det_ratio, self._inverse[s][mask, :, :, :] = sherman_morrison_ms(
            eeff, self._inverse[s][mask, :, :, :], mo_vals[mask, :]
        )

        self._updateval(det_ratio, s, mask) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def laplacian(self, e, epos):
        """ Compute the laplacian Psi/ Psi. """
        s = int(e >= self._nelec[0])
        ao = np.real_if_close(
            self._mol.eval_gto(self.pbc_str + "GTOval_sph_deriv2", epos.configs)[
                [0, 4, 7, 9]
            ],
            tol=1e4,
        )
        molap = np.dot(
            [ao[0], ao[1:].sum(axis=0)], self.parameters[self._coefflookup[s]]
        )
        molap_vals = self._testrow(e, molap[1][:, self._det_occup[s]])
        testvalue = self._testrow(e, molap[0][:, self._det_occup[s]])

        return molap_vals / testvalue 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def stdmx_to_vec(m, basis):
    """
    Convert a matrix in the standard basis to
     a vector in the Pauli basis.

    Parameters
    ----------
    m : numpy array
        The matrix, shape 2x2 (1Q) or 4x4 (2Q)

    Returns
    -------
    numpy array
        The vector, length 4 or 16 respectively.
    """

    assert(len(m.shape) == 2 and m.shape[0] == m.shape[1])
    basis = Basis.cast(basis, m.shape[0]**2)
    v = _np.empty((basis.size, 1))
    for i, mx in enumerate(basis.elements):
        if basis.real:
            v[i, 0] = _np.real(_mt.trace(_np.dot(mx, m)))
        else:
            v[i, 0] = _np.real_if_close(_mt.trace(_np.dot(mx, m)))
    return v 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def invpowerspd(self, n):
        '''autocovariance from spectral density

        scaling is correct, but n needs to be large for numerical accuracy
        maybe padding with zero in fft would be faster
        without slicing it returns 2-sided autocovariance with fftshift

        >>> ArmaFft([1, -0.5], [1., 0.4], 40).invpowerspd(2**8)[:10]
        array([ 2.08    ,  1.44    ,  0.72    ,  0.36    ,  0.18    ,  0.09    ,
                0.045   ,  0.0225  ,  0.01125 ,  0.005625])
        >>> ArmaFft([1, -0.5], [1., 0.4], 40).acovf(10)
        array([ 2.08    ,  1.44    ,  0.72    ,  0.36    ,  0.18    ,  0.09    ,
                0.045   ,  0.0225  ,  0.01125 ,  0.005625])
        '''
        hw = self.fftarma(n)
        return np.real_if_close(fft.ifft(hw*hw.conj()), tol=200)[:n] 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def __init__(self, cum, name='Edgeworth expanded normal', **kwds):
        if len(cum) < 2:
            raise ValueError("At least two cumulants are needed.")
        self._coef, self._mu, self._sigma = self._compute_coefs_pdf(cum)
        self._herm_pdf = HermiteE(self._coef)
        if self._coef.size > 2:
            self._herm_cdf = HermiteE(-self._coef[1:])
        else:
            self._herm_cdf = lambda x: 0.

        # warn if pdf(x) < 0 for some values of x within 4 sigma 
        r = np.real_if_close(self._herm_pdf.roots())
        r = (r - self._mu) / self._sigma
        if r[(np.imag(r) == 0) & (np.abs(r) < 4)].any():
            mesg = 'PDF has zeros at %s ' % r
            warnings.warn(mesg, RuntimeWarning)

        kwds.update({'name': name,
                     'momtype': 0})   # use pdf, not ppf in self.moment()
        super(ExpandedNormal, self).__init__(**kwds) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def test_graph_embed(self, setup_eng, tol):
        """Test that embedding a traceless adjacency matrix A
        results in the property Amat/A = c J, where c is a real constant,
        and J is the all ones matrix"""
        N = 3
        eng, prog = setup_eng(3)

        with prog.context as q:
            ops.GraphEmbed(A) | q

        state = eng.run(prog).state
        Amat = eng.backend.circuit.Amat()

        # check that the matrix Amat is constructed to be of the form
        # Amat = [[B^\dagger, 0], [0, B]]
        assert np.allclose(Amat[:N, :N], Amat[N:, N:].conj().T, atol=tol)
        assert np.allclose(Amat[:N, N:], np.zeros([N, N]), atol=tol)
        assert np.allclose(Amat[N:, :N], np.zeros([N, N]), atol=tol)

        ratio = np.real_if_close(Amat[N:, N:] / A)
        ratio /= ratio[0, 0]
        assert np.allclose(ratio, np.ones([N, N]), atol=tol) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def _recast_dressed_eigendata(self, dressed_eigendata):
        """
        Parameters
        ----------
        dressed_eigendata: list of tuple(evals, qutip evecs)

        Returns
        -------
        SpectrumData
        """
        evals_count = self.evals_count
        energy_table = np.empty(shape=(self.param_count, evals_count), dtype=np.float_)
        state_table = []  # for dressed states, entries are Qobj
        for j in range(self.param_count):
            energy_table[j] = np.real_if_close(dressed_eigendata[j][0])
            state_table.append(dressed_eigendata[j][1])
        specdata = storage.SpectrumData(energy_table, system_params={}, param_name=self.param_name,
                                        param_vals=self.param_vals, state_table=state_table)
        return specdata 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def spectral_radius(self):
        """Compute the spectral radius of the matrix of l1 norm of Hawkes
        kernels.

        Notes
        -----
        If the spectral radius is greater that 1, the hawkes process is not
        stable
        """

        get_norm = np.vectorize(lambda kernel: kernel.get_norm())
        norms = get_norm(self.kernels)

        # It might happens that eig returns a complex number but with a
        # negligible complex part, in this case we keep only the real part
        spectral_radius = max(eig(norms)[0])
        spectral_radius = np.real_if_close(spectral_radius)
        return spectral_radius 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def test_displaced_single_mode_state_hafnian(self, sample_func):
        """Test the sampling routines by comparing the photon number frequencies and the exact
        probability distribution of a single mode coherent state
        """
        n_samples = 1000
        n_cut = 6
        sigma = np.identity(2)
        mean = 10 * np.array([0.1, 0.25])

        samples = sample_func(sigma, samples=n_samples, mean=mean, cutoff=n_cut)

        probs = np.real_if_close(
            np.array([density_matrix_element(mean, sigma, [i], [i]) for i in range(n_cut)])
        )
        freq, _ = np.histogram(samples[:, 0], bins=np.arange(0, n_cut + 1))
        rel_freq = freq / n_samples
        assert np.allclose(
            rel_freq, probs, rtol=rel_tol / np.sqrt(n_samples), atol=rel_tol / np.sqrt(n_samples)
        ) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def test_displaced_two_mode_state_hafnian(self, sample_func):
        """Test the sampling routines by comparing the photon number frequencies and the exact
        probability distribution of a two mode coherent state
        """
        n_samples = 1000
        n_cut = 6
        sigma = np.identity(4)
        mean = 5 * np.array([0.1, 0.25, 0.1, 0.25])
        samples = sample_func(sigma, samples=n_samples, mean=mean, cutoff=n_cut)
        # samples = hafnian_sample_classical_state(sigma, mean = mean, samples = n_samples)
        probs = np.real_if_close(
            np.array(
                [
                    [density_matrix_element(mean, sigma, [i, j], [i, j]) for i in range(n_cut)]
                    for j in range(n_cut)
                ]
            )
        )
        freq, _, _ = np.histogram2d(samples[:, 1], samples[:, 0], bins=np.arange(0, n_cut + 1))
        rel_freq = freq / n_samples

        assert np.allclose(
            rel_freq, probs, rtol=rel_tol / np.sqrt(n_samples), atol=rel_tol / np.sqrt(n_samples)
        ) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def rectify_evecs(eigs):
    """
    eigs: output of linalg.eig
    normalizes evecs by L1 norm, truncates small complex components,
    ensures things are positive
    """
    evecs = eigs[1].T
    l1_norm = np.abs(evecs).sum(axis=1)
    norm_evecs = evecs / l1_norm[:, np.newaxis]
    real_evals = [np.around(np.real_if_close(l), decimals=5) for l in eigs[0]]
    real_evecs = []

    for v in norm_evecs:
        real_v = np.real_if_close(v)
        if (real_v < 0).all():
            real_v *= -1
        real_evecs.append(real_v)

    # skip sorting for now: argsort is pain because numpy will typecase to complex arr
    #    desc_idx = np.argsort(real_evals)[::-1]
    #   return real_evals[desc_idx], real_evecs[desc_idx]
    return real_evals, real_evecs 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def purity(rho: np.ndarray, dim_renorm=False, tol: float = 1000) -> float:
    """
    Calculates the purity :math:`P = tr[ρ^2]` of a quantum state ρ.

    As stated above lower value of the purity depends on the dimension of ρ's Hilbert space. For
    some applications this can be undesirable. For this reason we introduce an optional dimensional
    renormalization flag with the following behavior

    If the dimensional renormalization flag is FALSE (default) then  1/dim ≤ P ≤ 1.
    If the dimensional renormalization flag is TRUE then 0 ≤ P ≤ 1.

    where dim is the dimension of ρ's Hilbert space.

    :param rho: Is a dim by dim positive matrix with unit trace.
    :param dim_renorm: Boolean, default False.
    :param tol: Tolerance in machine epsilons for np.real_if_close.
    :return: P the purity of the state.
    """
    p = np.trace(rho @ rho)
    if dim_renorm:
        dim = rho.shape[0]
        p = (dim / (dim - 1.0)) * (p - 1.0 / dim)
    return np.ndarray.item(np.real_if_close(p, tol)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def impurity(rho: np.ndarray, dim_renorm=False, tol: float = 1000) -> float:
    """
    Calculates the impurity (or linear entropy) :math:`L = 1 - tr[ρ^2]` of a quantum state ρ.

    As stated above the lower value of the impurity depends on the dimension of ρ's Hilbert space.
    For some applications this can be undesirable. For this reason we introduce an optional
    dimensional renormalization flag with the following behavior

    If the dimensional renormalization flag is FALSE (default) then  0 ≤ L ≤ 1/dim.
    If the dimensional renormalization flag is TRUE then 0 ≤ L ≤ 1.

    where dim is the dimension of ρ's Hilbert space.

    :param rho: Is a dim by dim positive matrix with unit trace.
    :param dim_renorm: Boolean, default False.
    :param tol: Tolerance in machine epsilons for np.real_if_close.
    :return: L the impurity of the state.
    """
    imp = 1 - np.trace(rho @ rho)
    if dim_renorm:
        dim = rho.shape[0]
        imp = (dim / (dim - 1.0)) * imp
    return np.ndarray.item(np.real_if_close(imp, tol)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def fidelity(rho: np.ndarray, sigma: np.ndarray, tol: float = 1000) -> float:
    r"""
    Computes the fidelity :math:`F(\rho, \sigma)` between two quantum states rho and sigma.

    If the states are pure the expression reduces to

    .. math::

        F(|psi>,|phi>) = |<psi|phi>|^2

    The fidelity obeys :math:`0 ≤ F(\rho, \sigma) ≤ 1`, where
    :math:`F(\rho, \sigma)=1 iff \rho = \sigma`.

    :param rho: Is a dim by dim positive matrix with unit trace.
    :param sigma: Is a dim by dim positive matrix with unit trace.
    :param tol: Tolerance in machine epsilons for np.real_if_close.
    :return: Fidelity which is a scalar.
    """
    sqrt_rho = sqrtm_psd(rho)
    fid = (np.trace(sqrtm_psd(sqrt_rho @ sigma @ sqrt_rho))) ** 2
    return np.ndarray.item(np.real_if_close(fid, tol)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import real_if_close [as 別名]
def hilbert_schmidt_ip(A: np.ndarray, B: np.ndarray, tol: float = 1000) -> float:
    r"""
    Computes the Hilbert-Schmidt (HS) inner product between two operators A and B.

    This inner product is defined as

    .. math::

        HS = (A|B) = Tr[A^\dagger B]

    where :math:`|B) = vec(B)` and :math:`(A|` is the dual vector to :math:`|A)`.

    :param A: Is a dim by dim positive matrix with unit trace.
    :param B: Is a dim by dim positive matrix with unit trace.
    :param tol: Tolerance in machine epsilons for np.real_if_close.
    :return: HS inner product which is a scalar.
    """
    hs_ip = np.trace(np.matmul(np.transpose(np.conj(A)), B))
    return np.ndarray.item(np.real_if_close(hs_ip, tol))