Python numpy.conj方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def test_givens_inverse():
    r"""
    The Givens rotation in OpenFermion is defined as

    .. math::

        \begin{pmatrix}
            \cos(\theta) & -e^{i \varphi} \sin(\theta) \\
            \sin(\theta) &     e^{i \varphi} \cos(\theta)
        \end{pmatrix}.

    confirm numerically its hermitian conjugate is it's inverse
    """
    a = numpy.random.random() + 1j * numpy.random.random()
    b = numpy.random.random() + 1j * numpy.random.random()
    ab_rotation = givens_matrix_elements(a, b, which='right')

    assert numpy.allclose(ab_rotation.dot(numpy.conj(ab_rotation).T),
                          numpy.eye(2))
    assert numpy.allclose(numpy.conj(ab_rotation).T.dot(ab_rotation),
                          numpy.eye(2)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def test_circuit_generation_and_accuracy():
    for dim in range(2, 10):
        qubits = cirq.LineQubit.range(dim)
        u_generator = numpy.random.random(
            (dim, dim)) + 1j * numpy.random.random((dim, dim))
        u_generator = u_generator - numpy.conj(u_generator).T
        assert numpy.allclose(-1 * u_generator, numpy.conj(u_generator).T)

        unitary = scipy.linalg.expm(u_generator)
        circuit = cirq.Circuit()
        circuit.append(optimal_givens_decomposition(qubits, unitary))

        fermion_generator = QubitOperator(()) * 0.0
        for i, j in product(range(dim), repeat=2):
            fermion_generator += jordan_wigner(
                FermionOperator(((i, 1), (j, 0)), u_generator[i, j]))

        true_unitary = scipy.linalg.expm(
            get_sparse_operator(fermion_generator).toarray())
        assert numpy.allclose(true_unitary.conj().T.dot(true_unitary),
                              numpy.eye(2 ** dim, dtype=complex))

        test_unitary = cirq.unitary(circuit)
        assert numpy.isclose(
            abs(numpy.trace(true_unitary.conj().T.dot(test_unitary))), 2 ** dim) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def _gamma1_intermediates(mp, t2=None):
    # Memory optimization should be here
    if t2 is None:
        t2 = mp.t2
    if t2 is None:
        raise NotImplementedError("Run kmp2.kernel with `with_t2=True`")
    nmo = mp.nmo
    nocc = mp.nocc
    nvir = nmo - nocc
    nkpts = mp.nkpts
    dtype = t2.dtype

    dm1occ = np.zeros((nkpts, nocc, nocc), dtype=dtype)
    dm1vir = np.zeros((nkpts, nvir, nvir), dtype=dtype)

    for ki in range(nkpts):
        for kj in range(nkpts):
            for ka in range(nkpts):
                kb = mp.khelper.kconserv[ki, ka, kj]

                dm1vir[kb] += einsum('ijax,ijay->yx', t2[ki][kj][ka].conj(), t2[ki][kj][ka]) * 2 -\
                              einsum('ijax,ijya->yx', t2[ki][kj][ka].conj(), t2[ki][kj][kb])
                dm1occ[kj] += einsum('ixab,iyab->xy', t2[ki][kj][ka].conj(), t2[ki][kj][ka]) * 2 -\
                              einsum('ixab,iyba->xy', t2[ki][kj][ka].conj(), t2[ki][kj][kb])
    return -dm1occ, dm1vir 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def get_j(cell, dm, hermi=1, vhfopt=None, kpt=np.zeros(3), kpts_band=None):
    dm = np.asarray(dm)
    nao = dm.shape[-1]

    coords = gen_grid.gen_uniform_grids(cell)
    if kpts_band is None:
        kpt1 = kpt2 = kpt
        aoR_k1 = aoR_k2 = numint.eval_ao(cell, coords, kpt)
    else:
        kpt1 = kpts_band
        kpt2 = kpt
        aoR_k1 = numint.eval_ao(cell, coords, kpt1)
        aoR_k2 = numint.eval_ao(cell, coords, kpt2)
    ngrids, nao = aoR_k1.shape

    def contract(dm):
        vjR_k2 = get_vjR(cell, dm, aoR_k2)
        vj = (cell.vol/ngrids) * np.dot(aoR_k1.T.conj(), vjR_k2.reshape(-1,1)*aoR_k1)
        return vj

    if dm.ndim == 2:
        vj = contract(dm)
    else:
        vj = lib.asarray([contract(x) for x in dm.reshape(-1,nao,nao)])
    return vj.reshape(dm.shape) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def get_vkR(mf, cell, aoR_k1, aoR_k2, kpt1, kpt2):
    '''Get the real-space 2-index "exchange" potential V_{i,k1; j,k2}(r)
    where {i,k1} = exp^{i k1 r) |i> , {j,k2} = exp^{-i k2 r) <j|
    '''
    coords = gen_grid.gen_uniform_grids(cell)
    ngrids, nao = aoR_k1.shape

    expmikr = np.exp(-1j*np.dot(kpt1-kpt2,coords.T))
    coulG = tools.get_coulG(cell, kpt1-kpt2, exx=True, mf=mf)
    def prod(ij):
        i, j = divmod(ij, nao)
        rhoR = aoR_k1[:,i] * aoR_k2[:,j].conj()
        rhoG = tools.fftk(rhoR, cell.mesh, expmikr)
        vG = coulG*rhoG
        vR = tools.ifftk(vG, cell.mesh, expmikr.conj())
        return vR

    if aoR_k1.dtype == np.double and aoR_k2.dtype == np.double:
        vR = numpy.asarray([prod(ij).real for ij in range(nao**2)])
    else:
        vR = numpy.asarray([prod(ij) for ij in range(nao**2)])
    return vR.reshape(nao,nao,-1).transpose(2,0,1) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def __init__(self, j):
    self._j = j
    self._c2r = np.zeros( (2*j+1, 2*j+1), dtype=np.complex128)
    self._c2r[j,j]=1.0
    for m in range(1,j+1):
      self._c2r[m+j, m+j] = sgn[m] * np.sqrt(0.5) 
      self._c2r[m+j,-m+j] = np.sqrt(0.5) 
      self._c2r[-m+j,-m+j]= 1j*np.sqrt(0.5)
      self._c2r[-m+j, m+j]= -sgn[m] * 1j * np.sqrt(0.5)
    
    self._hc_c2r = np.conj(self._c2r).transpose()
    self._conj_c2r = np.conjugate(self._c2r) # what is the difference ? conj and conjugate
    self._tr_c2r = np.transpose(self._c2r)
    
    #print(abs(self._hc_c2r.conj().transpose()-self._c2r).sum())

  #
  #
  # 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def get_k(self,dm):
        """
        Update Exact Exchange Matrix

        Args:
            dm: float or complex
                AO density matrix.
        Returns:
            kmat: float or complex
                Exact Exchange in AO basis
        """
        naux = self.auxmol.nao_nr()
        nao = self.ks.mol.nao_nr()
        kpj = np.einsum("ijp,jk->ikp", self.eri3c, dm)
        pik = np.linalg.solve(self.eri2c, kpj.reshape(-1,naux).T.conj())
        kmat = np.einsum("pik,kjp->ij", pik.reshape(naux,nao,nao), self.eri3c)
        return kmat 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [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 conj [as 別名]
def svd_dotH(self,s1,q1):
        """
        Performs diagonal matrix multiplication conjugate
        
        Implements :math:`q_0 = \\mathrm{diag}(s_1)^* q_1`.
        
        :param s1: diagonal parameters
        :param q1: input to the diagonal multiplication
        :returns: :code:`q0` diagonal multiplication output
        """
        srep = repeat_axes(np.conj(s1),self.sshape,self.srep_axes,rep=False)
        q0 = srep*q1
        return q0
        
    #def __str__(self):
    #    string = str(self.name) + '\n'\
    #              + 'Input: ' + str(self.shape0) + ',' + str(self.dtype0)
    #    return string 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def azimuthal_symmetry(X, Y, n, m):
    p1 = 2
    p2 = 1
    p = np.sqrt(p1**2 + p2**2)

    detX = np.real(X.hvhv*(X.hhhh*X.vvvv - X.hhvv*np.conj(X.hhvv)))
    detY = np.real(Y.hvhv*(Y.hhhh*Y.vvvv - Y.hhvv*np.conj(Y.hhvv)))
    detXY = np.real((X.hvhv+Y.hvhv) * ((X.hhhh+Y.hhhh)*(X.vvvv+Y.vvvv) - (X.hhvv+Y.hhvv)*(np.conj(X.hhvv)+np.conj(Y.hhvv))))

    lnq = (p*(n+m)*np.log(n+m) - p*n*np.log(n) - p*m*np.log(m)
            + n*np.log(detX) + m*np.log(detY) - (n+m)*np.log(detXY))

    rho1 = 1 - (2*p1**2 - 1)/(6*p1) * (1/n + 1/m - 1/(n+m))
    rho2 = 1 - (2*p2**2 - 1)/(6*p2) * (1/n + 1/m - 1/(n+m))
    rho = 1/p**2 * (p1**2 * rho1 + p2**2 * rho2)

    w2 = - p**2/4 * (1-1/rho)**2 + (p1**2*(p1**2-1) + p2**2*(p2**2-1))/24 * (1/n**2 + 1/m**2 - 1/(n+m)**2) * 1/rho**2

    return lnq, rho, w2 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def fexpand(x, ns=1, axis=None):
    """
    Reconstructs full spectrum from positive frequencies
    Works on the last dimension (contiguous in c-stored array)

    :param x: numpy.ndarray
    :param axis: axis along which to perform reduction (last axis by default)
    :return: numpy.ndarray
    """
    if axis is None:
        axis = x.ndim - 1
    # dec = int(ns % 2) * 2 - 1
    # xcomp = np.conj(np.flip(x[..., 1:x.shape[-1] + dec], axis=axis))
    ilast = int((ns + (ns % 2)) / 2)
    xcomp = np.conj(np.flip(np.take(x, np.arange(1, ilast), axis=axis), axis=axis))
    return np.concatenate((x, xcomp), axis=axis) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def _power_spectrum(daft, dim, N, density):

    ps = (daft * np.conj(daft)).real

    if density:
        ps /= (np.asarray(N).prod()) ** 2
        for i in dim:
            ps /= daft['freq_' + i + '_spacing']

    return ps 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def _cross_spectrum(daft1, daft2, dim, N, density):
    cs = (daft1 * np.conj(daft2)).real

    if density:
        cs /= (np.asarray(N).prod())**2
        for i in dim:
            cs /= daft1['freq_' + i + '_spacing']

    return cs 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def test_power_spectrum(self, dask):
        """Test the power spectrum function"""
        N = 16
        da = xr.DataArray(np.random.rand(2,N,N), dims=['time','y','x'],
                         coords={'time':np.array(['2019-04-18', '2019-04-19'],
                                                dtype='datetime64'),
                                'y':range(N),'x':range(N)}
                         )
        if dask:
            da = da.chunk({'time': 1})
        ps = xrft.power_spectrum(da, dim=['y','x'], window=True, density=False,
                                detrend='constant')
        daft = xrft.dft(da, dim=['y','x'], detrend='constant', window=True)
        npt.assert_almost_equal(ps.values, np.real(daft*np.conj(daft)))
        npt.assert_almost_equal(np.ma.masked_invalid(ps).mask.sum(), 0.)

        ps = xrft.power_spectrum(da, dim=['y'], real='x', window=True,
                                density=False, detrend='constant')
        daft = xrft.dft(da, dim=['y'], real='x', detrend='constant', window=True)
        npt.assert_almost_equal(ps.values, np.real(daft*np.conj(daft)))

        ### Normalized
        ps = xrft.power_spectrum(da, dim=['y','x'], window=True, detrend='constant')
        daft = xrft.dft(da, dim=['y','x'], window=True, detrend='constant')
        test = np.real(daft*np.conj(daft))/N**4
        dk = np.diff(np.fft.fftfreq(N, 1.))[0]
        test /= dk**2
        npt.assert_almost_equal(ps.values, test)
        npt.assert_almost_equal(np.ma.masked_invalid(ps).mask.sum(), 0.)

        ### Remove least-square fit
        ps = xrft.power_spectrum(da, dim=['y','x'],
                                window=True, density=False, detrend='linear'
                                )
        daft = xrft.dft(da, dim=['y','x'], window=True, detrend='linear')
        npt.assert_almost_equal(ps.values, np.real(daft*np.conj(daft)))
        npt.assert_almost_equal(np.ma.masked_invalid(ps).mask.sum(), 0.) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import conj [as 別名]
def test_cross_spectrum(self, dask):
        """Test the cross spectrum function"""
        N = 16
        dim = ['x','y']
        da = xr.DataArray(np.random.rand(2,N,N), dims=['time','x','y'],
                          coords={'time':np.array(['2019-04-18', '2019-04-19'],
                                                 dtype='datetime64'),
                                 'x':range(N), 'y':range(N)})
        da2 = xr.DataArray(np.random.rand(2,N,N), dims=['time','x','y'],
                          coords={'time':np.array(['2019-04-18', '2019-04-19'],
                                                 dtype='datetime64'),
                                  'x':range(N), 'y':range(N)})
        if dask:
            da = da.chunk({'time': 1})
            da2 = da2.chunk({'time': 1})

        daft = xrft.dft(da, dim=dim, shift=True, detrend='constant',
                        window=True)
        daft2 = xrft.dft(da2, dim=dim, shift=True, detrend='constant',
                        window=True)
        cs = xrft.cross_spectrum(da, da2, dim=dim, window=True, density=False,
                                detrend='constant')
        npt.assert_almost_equal(cs.values, np.real(daft*np.conj(daft2)))
        npt.assert_almost_equal(np.ma.masked_invalid(cs).mask.sum(), 0.)

        cs = xrft.cross_spectrum(da, da2, dim=dim, shift=True, window=True,
                                detrend='constant')
        test = (daft * np.conj(daft2)).real.values/N**4

        dk = np.diff(np.fft.fftfreq(N, 1.))[0]
        test /= dk**2
        npt.assert_almost_equal(cs.values, test)
        npt.assert_almost_equal(np.ma.masked_invalid(cs).mask.sum(), 0.)