Python numpy.complex128方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def _eigen_components(self):
        components = [(0, np.diag([1, 1, 1, 0, 1, 0, 0, 1]))]
        nontrivial_part = np.zeros((3, 3), dtype=np.complex128)
        for ij, w in zip([(1, 2), (0, 2), (0, 1)], self.weights):
            nontrivial_part[ij] = w
            nontrivial_part[ij[::-1]] = w.conjugate()
        assert np.allclose(nontrivial_part, nontrivial_part.conj().T)
        eig_vals, eig_vecs = np.linalg.eigh(nontrivial_part)
        for eig_val, eig_vec in zip(eig_vals, eig_vecs.T):
            exp_factor = -eig_val / np.pi
            proj = np.zeros((8, 8), dtype=np.complex128)
            nontrivial_indices = np.array([3, 5, 6], dtype=np.intp)
            proj[nontrivial_indices[:, np.newaxis], nontrivial_indices] = (
                np.outer(eig_vec.conjugate(), eig_vec))
            components.append((exp_factor, proj))
        return components 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def qubit_generator_matrix(self):
        """The (Hermitian) matrix G such that the gate's unitary is
        exp(-i * G).
        """

        generator = np.zeros((1 << 4,) * 2, dtype=np.complex128)

        # w0 |1001><0110| + h.c.
        generator[9, 6] = self.weights[0]
        generator[6, 9] = self.weights[0].conjugate()
        # w1 |1010><0101| + h.c.
        generator[10, 5] = self.weights[1]
        generator[5, 10] = self.weights[1].conjugate()
        # w2 |1100><0011| + h.c.
        generator[12, 3] = self.weights[2]
        generator[3, 12] = self.weights[2].conjugate()
        return generator 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def test_cubic_fermionic_simulation_gate_consistency_docstring(
        weights, exponent):
    generator = np.zeros((8, 8), dtype=np.complex128)
    # w0 |110><101| + h.c.
    generator[6, 5] = weights[0]
    generator[5, 6] = weights[0].conjugate()
    # w1 |110><011| + h.c.
    generator[6, 3] = weights[1]
    generator[3, 6] = weights[1].conjugate()
    # w2 |101><011| + h.c.
    generator[5, 3] = weights[2]
    generator[3, 5] = weights[2].conjugate()
    expected_unitary = la.expm(-1j * exponent * generator)

    gate = ofc.CubicFermionicSimulationGate(weights, exponent=exponent)
    actual_unitary = cirq.unitary(gate)

    assert np.allclose(expected_unitary, actual_unitary) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def test_quartic_fermionic_simulation_unitary(weights, exponent):
    generator = np.zeros((1 << 4,) * 2, dtype=np.complex128)

    # w0 |1001><0110| + h.c.
    generator[9, 6] = weights[0]
    generator[6, 9] = weights[0].conjugate()
    # w1 |1010><0101| + h.c.
    generator[10, 5] = weights[1]
    generator[5, 10] = weights[1].conjugate()
    # w2 |1100><0011| + h.c.
    generator[12, 3] = weights[2]
    generator[3, 12] = weights[2].conjugate()
    expected_unitary = la.expm(-1j * exponent * generator)

    gate = ofc.QuarticFermionicSimulationGate(weights, exponent=exponent)
    actual_unitary = cirq.unitary(gate)

    assert np.allclose(expected_unitary, actual_unitary) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def test_get_matrix_of_eigs():
    """
    Generate the matrix of [exp(i (li - lj)) - 1] / (i(li - lj)
    :return:
    """
    lam_vals = np.random.randn(4) + 1j * np.random.randn(4)
    mat_eigs = np.zeros((lam_vals.shape[0],
                         lam_vals.shape[0]),
                         dtype=np.complex128)
    for i, j in product(range(lam_vals.shape[0]), repeat=2):
        if np.isclose(abs(lam_vals[i] - lam_vals[j]), 0):
            mat_eigs[i, j] = 1
        else:
            mat_eigs[i, j] = (np.exp(1j * (lam_vals[i] - lam_vals[j])) - 1) / (
                        1j * (lam_vals[i] - lam_vals[j]))

    test_mat_eigs = get_matrix_of_eigs(lam_vals)
    assert np.allclose(test_mat_eigs, mat_eigs) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def test_rhf_vcut_sph(self):
        mf = pbchf.RHF(cell, exxdiv='vcut_sph')
        e1 = mf.kernel()
        self.assertAlmostEqual(e1, -4.29190260870812, 8)
        self.assertTrue(mf.mo_coeff.dtype == numpy.double)

        mf = pscf.KRHF(cell, [[0,0,0]], exxdiv='vcut_sph')
        e0 = mf.kernel()
        self.assertTrue(numpy.allclose(e0,e1))

        numpy.random.seed(1)
        k = numpy.random.random(3)
        mf = pbchf.RHF(cell, k, exxdiv='vcut_sph')
        e1 = mf.kernel()
        self.assertAlmostEqual(e1, -4.1379172088570595, 8)
        self.assertTrue(mf.mo_coeff.dtype == numpy.complex128)

        mf = pscf.KRHF(cell, k, exxdiv='vcut_sph')
        e0 = mf.kernel()
        self.assertTrue(numpy.allclose(e0,e1)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def test_rhf_exx_ewald_with_kpt(self):
        numpy.random.seed(1)
        k = numpy.random.random(3)
        mf = pbchf.RHF(cell, k, exxdiv='ewald')
        e1 = mf.kernel()
        self.assertAlmostEqual(e1, -4.2048655827967139, 8)
        self.assertTrue(mf.mo_coeff.dtype == numpy.complex128)

        kmf = pscf.KRHF(cell, k, exxdiv='ewald')
        e0 = kmf.kernel()
        self.assertTrue(numpy.allclose(e0,e1))

        # test bands
        numpy.random.seed(1)
        kpt_band = numpy.random.random(3)
        e1, c1 = mf.get_bands(kpt_band)
        e0, c0 = kmf.get_bands(kpt_band)
        self.assertAlmostEqual(abs(e0-e1).max(), 0, 7)
        self.assertAlmostEqual(lib.finger(e1), -6.8312867098806249, 7) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def cc_Fov(cc, t1, t2, eris):
    t1a, t1b = t1
    t2aa, t2ab, t2bb = t2
    nkpts, nocc_a, nvir_a = t1a.shape
    nocc_b, nvir_b = t1b.shape[1:]

    fov = eris.fock[0][:,:nocc_a,nocc_a:]
    fOV = eris.fock[1][:,:nocc_b,nocc_b:]

    fa = np.zeros((nkpts,nocc_a,nvir_a), dtype=np.complex128)
    fb = np.zeros((nkpts,nocc_b,nvir_b), dtype=np.complex128)

    for km in range(nkpts):
        fa[km]+=fov[km]
        fb[km]+=fOV[km]
        for kn in range(nkpts):
            fa[km]+=einsum('nf,menf->me',t1a[kn],eris.ovov[km,km,kn])
            fa[km]+=einsum('nf,menf->me',t1b[kn],eris.ovOV[km,km,kn])
            fa[km]-=einsum('nf,mfne->me',t1a[kn],eris.ovov[km,kn,kn])
            fb[km]+=einsum('nf,menf->me',t1b[kn],eris.OVOV[km,km,kn])
            fb[km]+=einsum('nf,nfme->me',t1a[kn],eris.ovOV[kn,kn,km])
            fb[km]-=einsum('nf,mfne->me',t1b[kn],eris.OVOV[km,kn,kn])

    return fa,fb 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def get_M_mat(self):
        '''
        Construct the ovelap matrix: M_{m,n}^{(\mathbf{k,b})}
        Equation (25) in MV, Phys. Rev. B 56, 12847
        '''

        M_matrix_loc = np.empty([self.num_kpts_loc, self.nntot_loc, self.num_bands_loc, self.num_bands_loc], dtype = np.complex128)

        for k_id in range(self.num_kpts_loc):
            for nn in range(self.nntot_loc):
                    k1 = self.cell.get_abs_kpts(self.kpt_latt_loc[k_id])
                    k_id2 = self.nn_list[nn, k_id, 0] - 1
                    k2_ = self.kpt_latt_loc[k_id2]
                    k2_scaled = k2_ + self.nn_list[nn, k_id, 1:4]
                    k2 = self.cell.get_abs_kpts(k2_scaled)
                    s_AO = df.ft_ao.ft_aopair(self.cell, -k2+k1, kpti_kptj=[k2,k1], q = np.zeros(3))[0]
                    Cm = self.mo_coeff_kpts[k_id][:,self.band_included_list]
                    Cn = self.mo_coeff_kpts[k_id2][:,self.band_included_list]
                    M_matrix_loc[k_id, nn,:,:] = np.einsum('nu,vm,uv->nm', Cn.T.conj(), Cm, s_AO, optimize = True).conj()

        return M_matrix_loc 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def export_unk(self, grid = [50,50,50]):
        '''
        Export the periodic part of BF in a real space grid for plotting with wannier90
        '''

        from scipy.io import FortranFile
        grids_coor, weights = periodic_grid(self.cell, grid, order = 'F')

        for k_id in range(self.num_kpts_loc):
            spin = '.1'
            if self.spin_up != None and self.spin_up == False : spin = '.2'
            kpt = self.cell.get_abs_kpts(self.kpt_latt_loc[k_id])
            ao = numint.eval_ao(self.cell, grids_coor, kpt = kpt)
            u_ao = np.einsum('x,xi->xi', np.exp(-1j*np.dot(grids_coor, kpt)), ao, optimize = True)
            unk_file = FortranFile('UNK' + "%05d" % (k_id + 1) + spin, 'w')
            unk_file.write_record(np.asarray([grid[0], grid[1], grid[2], k_id + 1, self.num_bands_loc], dtype = np.int32))
            mo_included = self.mo_coeff_kpts[k_id][:,self.band_included_list]
            u_mo = np.einsum('xi,in->xn', u_ao, mo_included, optimize = True)
            for band in range(len(self.band_included_list)):
                unk_file.write_record(np.asarray(u_mo[:,band], dtype = np.complex128))
            unk_file.close() 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def test_get_eri_gamma(self):
        odf = df.DF(cell)
        odf.linear_dep_threshold = 1e-7
        odf.auxbasis = 'weigend'
        odf.mesh = (6,)*3
        eri0000 = odf.get_eri()
        self.assertTrue(eri0000.dtype == numpy.double)
        self.assertAlmostEqual(eri0000.real.sum(), 41.61280626625331, 9)
        self.assertAlmostEqual(finger(eri0000), 1.9981472468639465, 9)

        eri1111 = kmdf.get_eri((kpts[0],kpts[0],kpts[0],kpts[0]))
        self.assertTrue(eri1111.dtype == numpy.double)
        self.assertAlmostEqual(eri1111.real.sum(), 41.61280626625331, 9)
        self.assertAlmostEqual(eri1111.imag.sum(), 0, 9)
        self.assertAlmostEqual(finger(eri1111), 1.9981472468639465, 9)
        self.assertAlmostEqual(abs(eri1111-eri0000).max(), 0, 9)

        eri4444 = kmdf.get_eri((kpts[4],kpts[4],kpts[4],kpts[4]))
        self.assertTrue(eri4444.dtype == numpy.complex128)
        self.assertAlmostEqual(eri4444.real.sum(), 62.55120674032798, 9)
        self.assertAlmostEqual(abs(eri4444.imag).sum(), 0.0016507912195378644, 7)
        self.assertAlmostEqual(finger(eri4444), 0.6206014899350296-7.413680313987067e-05j, 8)
        eri0000 = ao2mo.restore(1, eri0000, cell.nao_nr()).reshape(eri4444.shape)
        self.assertAlmostEqual(abs(eri0000-eri4444).max(), 0, 4) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def _contract_rho(bra, ket):
    #:rho  = numpy.einsum('pi,pi->p', bra.real, ket.real)
    #:rho += numpy.einsum('pi,pi->p', bra.imag, ket.imag)
    bra = bra.T
    ket = ket.T
    nao, ngrids = bra.shape
    rho = numpy.empty(ngrids)

    if not (bra.flags.c_contiguous and ket.flags.c_contiguous):
        rho  = numpy.einsum('ip,ip->p', bra.real, ket.real)
        rho += numpy.einsum('ip,ip->p', bra.imag, ket.imag)
    elif bra.dtype == numpy.double and ket.dtype == numpy.double:
        libdft.VXC_dcontract_rho(rho.ctypes.data_as(ctypes.c_void_p),
                                 bra.ctypes.data_as(ctypes.c_void_p),
                                 ket.ctypes.data_as(ctypes.c_void_p),
                                 ctypes.c_int(nao), ctypes.c_int(ngrids))
    elif bra.dtype == numpy.complex128 and ket.dtype == numpy.complex128:
        libdft.VXC_zcontract_rho(rho.ctypes.data_as(ctypes.c_void_p),
                                 bra.ctypes.data_as(ctypes.c_void_p),
                                 ket.ctypes.data_as(ctypes.c_void_p),
                                 ctypes.c_int(nao), ctypes.c_int(ngrids))
    else:
        rho  = numpy.einsum('ip,ip->p', bra.real, ket.real)
        rho += numpy.einsum('ip,ip->p', bra.imag, ket.imag)
    return rho 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [as 別名]
def so_by_shell(mol, shls):
    '''Spin-orbit coupling ECP in spinor basis
    i/2 <Pauli_matrix dot l U(r)>
    '''
    li = mol.bas_angular(shls[0])
    lj = mol.bas_angular(shls[1])
    di = (li*4+2) * mol.bas_nctr(shls[0])
    dj = (lj*4+2) * mol.bas_nctr(shls[1])
    bas = numpy.vstack((mol._bas, mol._ecpbas))
    mol._env[AS_ECPBAS_OFFSET] = len(mol._bas)
    mol._env[AS_NECPBAS] = len(mol._ecpbas)
    buf = numpy.empty((di,dj), order='F', dtype=numpy.complex128)
    cache = numpy.empty(buf.size*48)
    fn = libecp.ECPso_spinor
    fn(buf.ctypes.data_as(ctypes.c_void_p),
       (ctypes.c_int*2)(di, dj),
       (ctypes.c_int*2)(*shls),
       mol._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.natm),
       bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.nbas),
       mol._env.ctypes.data_as(ctypes.c_void_p), lib.c_null_ptr(),
       cache.ctypes.data_as(ctypes.c_void_p))
    return buf 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import complex128 [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 complex128 [as 別名]
def test_three_qubit_rotation_gates_on_simulator(gate: cirq.Gate,
                                                 initial_state: np.ndarray,
                                                 correct_state: np.ndarray):
    op = gate(*cirq.LineQubit.range(3))
    result = cirq.Circuit(op).final_wavefunction(
        initial_state, dtype=np.complex128)
    cirq.testing.assert_allclose_up_to_global_phase(result,
                                                    correct_state,
                                                    atol=1e-8)