Esempio n. 1
0
    def get_projections(self, locfun, spin=0):
        """Project wave functions onto localized functions

        Determine the projections of the Kohn-Sham eigenstates
        onto specified localized functions of the format::

          locfun = [[spos_c, l, sigma], [...]]

        spos_c can be an atom index, or a scaled position vector. l is
        the angular momentum, and sigma is the (half-) width of the
        radial gaussian.

        Return format is::

          f_kni = <psi_kn | f_i>

        where psi_kn are the wave functions, and f_i are the specified
        localized functions.

        As a special case, locfun can be the string 'projectors', in which
        case the bound state projectors are used as localized functions.
        """

        wfs = self.wfs

        if locfun == 'projectors':
            f_kin = []
            for kpt in wfs.kpt_u:
                if kpt.s == spin:
                    f_in = []
                    for a, P_ni in kpt.P_ani.items():
                        i = 0
                        setup = wfs.setups[a]
                        for l, n in zip(setup.l_j, setup.n_j):
                            if n >= 0:
                                for j in range(i, i + 2 * l + 1):
                                    f_in.append(P_ni[:, j])
                            i += 2 * l + 1
                    f_kin.append(f_in)
            f_kni = np.array(f_kin).transpose(0, 2, 1)
            return f_kni.conj()

        from gpaw.lfc import LocalizedFunctionsCollection as LFC
        from gpaw.spline import Spline
        from gpaw.utilities import _fact

        nkpts = len(wfs.ibzk_kc)
        nbf = np.sum([2 * l + 1 for pos, l, a in locfun])
        f_kni = np.zeros((nkpts, wfs.nbands, nbf), wfs.dtype)

        spos_ac = self.atoms.get_scaled_positions() % 1.0
        spos_xc = []
        splines_x = []
        for spos_c, l, sigma in locfun:
            if isinstance(spos_c, int):
                spos_c = spos_ac[spos_c]
            spos_xc.append(spos_c)
            alpha = .5 * Bohr**2 / sigma**2
            r = np.linspace(0, 6. * sigma, 500)
            f_g = (_fact[l] * (4 * alpha)**(l + 3 / 2.) *
                   np.exp(-alpha * r**2) /
                   (np.sqrt(4 * np.pi) * _fact[2 * l + 1]))
            splines_x.append([Spline(l, rmax=r[-1], f_g=f_g, points=61)])

        lf = LFC(wfs.gd, splines_x, wfs.kpt_comm, dtype=wfs.dtype)
        if not wfs.gamma:
            lf.set_k_points(wfs.ibzk_qc)
        lf.set_positions(spos_xc)

        k = 0
        f_ani = lf.dict(wfs.nbands)
        for kpt in wfs.kpt_u:
            if kpt.s != spin:
                continue
            lf.integrate(kpt.psit_nG[:], f_ani, kpt.q)
            i1 = 0
            for x, f_ni in f_ani.items():
                i2 = i1 + f_ni.shape[1]
                f_kni[k, :, i1:i2] = f_ni
                i1 = i2
            k += 1

        return f_kni.conj()
Esempio n. 2
0
class FDWaveFunctions(FDPWWaveFunctions):
    def __init__(self, stencil, diagksl, orthoksl, initksl,
                 gd, nvalence, setups, bd,
                 dtype, world, kd, timer=None):
        FDPWWaveFunctions.__init__(self, diagksl, orthoksl, initksl,
                                   gd, nvalence, setups, bd,
                                   dtype, world, kd, timer)

        # Kinetic energy operator:
        self.kin = Laplace(self.gd, -0.5, stencil, self.dtype)

        self.matrixoperator = MatrixOperator(self.orthoksl)

        self.taugrad_v = None  # initialized by MGGA functional

    def empty(self, n=(), global_array=False, realspace=False, q=-1):
        return self.gd.empty(n, self.dtype, global_array)

    def integrate(self, a_xg, b_yg=None, global_integral=True):
        return self.gd.integrate(a_xg, b_yg, global_integral)

    def bytes_per_wave_function(self):
        return self.gd.bytecount(self.dtype)

    def set_setups(self, setups):
        self.pt = LFC(self.gd, [setup.pt_j for setup in setups],
                      self.kd, dtype=self.dtype, forces=True)
        FDPWWaveFunctions.set_setups(self, setups)

    def set_positions(self, spos_ac):
        FDPWWaveFunctions.set_positions(self, spos_ac)

    def summary(self, fd):
        fd.write('Wave functions: Uniform real-space grid\n')
        fd.write('Kinetic energy operator: %s\n' % self.kin.description)
        
    def make_preconditioner(self, block=1):
        return Preconditioner(self.gd, self.kin, self.dtype, block)
    
    def apply_pseudo_hamiltonian(self, kpt, hamiltonian, psit_xG, Htpsit_xG):
        self.timer.start('Apply hamiltonian')
        self.kin.apply(psit_xG, Htpsit_xG, kpt.phase_cd)
        hamiltonian.apply_local_potential(psit_xG, Htpsit_xG, kpt.s)
        self.timer.stop('Apply hamiltonian')

    def add_orbital_density(self, nt_G, kpt, n):
        if self.dtype == float:
            axpy(1.0, kpt.psit_nG[n]**2, nt_G)
        else:
            axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
            axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)

    def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
        # Used in calculation of response part of GLLB-potential
        nt_G = nt_sG[kpt.s]
        if self.dtype == float:
            for f, psit_G in zip(f_n, kpt.psit_nG):
                axpy(f, psit_G**2, nt_G)
        else:
            for f, psit_G in zip(f_n, kpt.psit_nG):
                axpy(f, psit_G.real**2, nt_G)
                axpy(f, psit_G.imag**2, nt_G)

        # Hack used in delta-scf calculations:
        if hasattr(kpt, 'c_on'):
            assert self.bd.comm.size == 1
            d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
                            dtype=complex)
            for ne, c_n in zip(kpt.ne_o, kpt.c_on):
                d_nn += ne * np.outer(c_n.conj(), c_n)
            for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
                for d, psi_G in zip(d_n, kpt.psit_nG):
                    if abs(d) > 1.e-12:
                        nt_G += (psi0_G.conj() * d * psi_G).real

    def calculate_kinetic_energy_density(self):
        if self.taugrad_v is None:
            self.taugrad_v = [
                Gradient(self.gd, v, n=3, dtype=self.dtype).apply
                for v in range(3)]
            
        assert not hasattr(self.kpt_u[0], 'c_on')
        if self.kpt_u[0].psit_nG is None:
            raise RuntimeError('No wavefunctions yet')
        if isinstance(self.kpt_u[0].psit_nG, FileReference):
            # XXX initialize
            raise RuntimeError('Wavefunctions have not been initialized.')

        taut_sG = self.gd.zeros(self.nspins)
        dpsit_G = self.gd.empty(dtype=self.dtype)
        for kpt in self.kpt_u:
            for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
                for v in range(3):
                    self.taugrad_v[v](psit_G, dpsit_G, kpt.phase_cd)
                    axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])

        self.kpt_comm.sum(taut_sG)
        self.band_comm.sum(taut_sG)
        return taut_sG
        
    def apply_mgga_orbital_dependent_hamiltonian(self, kpt, psit_xG,
                                                 Htpsit_xG, dH_asp,
                                                 dedtaut_G):
        a_G = self.gd.empty(dtype=psit_xG.dtype)
        for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
            for v in range(3):
                self.taugrad_v[v](psit_G, a_G, kpt.phase_cd)
                self.taugrad_v[v](dedtaut_G * a_G, a_G, kpt.phase_cd)
                axpy(-0.5, a_G, Htpsit_G)

    def ibz2bz(self, atoms):
        """Transform wave functions in IBZ to the full BZ."""

        assert self.kd.comm.size == 1

        # New k-point descriptor for full BZ:
        kd = KPointDescriptor(self.kd.bzk_kc, nspins=self.nspins)
        kd.set_symmetry(atoms, self.setups, usesymm=None)
        kd.set_communicator(serial_comm)

        self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
                      kd, dtype=self.dtype)
        self.pt.set_positions(atoms.get_scaled_positions())

        self.initialize_wave_functions_from_restart_file()

        weight = 2.0 / kd.nspins / kd.nbzkpts
        
        # Build new list of k-points:
        kpt_u = []
        for s in range(self.nspins):
            for k in range(kd.nbzkpts):
                # Index of symmetry related point in the IBZ
                ik = self.kd.bz2ibz_k[k]
                r, u = self.kd.get_rank_and_index(s, ik)
                assert r == 0
                kpt = self.kpt_u[u]
            
                phase_cd = np.exp(2j * np.pi * self.gd.sdisp_cd *
                                  kd.bzk_kc[k, :, np.newaxis])

                # New k-point:
                kpt2 = KPoint(weight, s, k, k, phase_cd)
                kpt2.f_n = kpt.f_n / kpt.weight / kd.nbzkpts * 2 / self.nspins
                kpt2.eps_n = kpt.eps_n.copy()
                
                # Transform wave functions using symmetry operation:
                Psit_nG = self.gd.collect(kpt.psit_nG)
                if Psit_nG is not None:
                    Psit_nG = Psit_nG.copy()
                    for Psit_G in Psit_nG:
                        Psit_G[:] = self.kd.transform_wave_function(Psit_G, k)
                kpt2.psit_nG = self.gd.empty(self.bd.nbands, dtype=self.dtype)
                self.gd.distribute(Psit_nG, kpt2.psit_nG)

                # Calculate PAW projections:
                kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
                self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)
                
                kpt_u.append(kpt2)

        self.kd = kd
        self.kpt_u = kpt_u

    def write(self, writer, write_wave_functions=False):
        writer['Mode'] = 'fd'

        if not write_wave_functions:
            return

        writer.add('PseudoWaveFunctions',
                   ('nspins', 'nibzkpts', 'nbands',
                    'ngptsx', 'ngptsy', 'ngptsz'),
                   dtype=self.dtype)

        if hasattr(writer, 'hdf5'):
            parallel = (self.world.size > 1)
            for kpt in self.kpt_u:
                indices = [kpt.s, kpt.k]
                indices.append(self.bd.get_slice())
                indices += self.gd.get_slice()
                writer.fill(kpt.psit_nG, parallel=parallel, *indices)
        else:
            for s in range(self.nspins):
                for k in range(self.nibzkpts):
                    for n in range(self.bd.nbands):
                        psit_G = self.get_wave_function_array(n, k, s)
                        writer.fill(psit_G, s, k, n)

    def read(self, reader, hdf5):
        if ((not hdf5 and self.bd.comm.size == 1) or
            (hdf5 and self.world.size == 1)):
            # We may not be able to keep all the wave
            # functions in memory - so psit_nG will be a special type of
            # array that is really just a reference to a file:
            for kpt in self.kpt_u:
                kpt.psit_nG = reader.get_reference('PseudoWaveFunctions',
                                                   (kpt.s, kpt.k))
        else:
            for kpt in self.kpt_u:
                kpt.psit_nG = self.empty(self.bd.mynbands)
                if hdf5:
                    indices = [kpt.s, kpt.k]
                    indices.append(self.bd.get_slice())
                    indices += self.gd.get_slice()
                    reader.get('PseudoWaveFunctions', out=kpt.psit_nG,
                               parallel=(self.world.size > 1), *indices)
                else:
                    # Read band by band to save memory
                    for myn, psit_G in enumerate(kpt.psit_nG):
                        n = self.bd.global_index(myn)
                        if self.gd.comm.rank == 0:
                            big_psit_G = np.array(
                                reader.get('PseudoWaveFunctions',
                                           kpt.s, kpt.k, n),
                                self.dtype)
                        else:
                            big_psit_G = None
                        self.gd.distribute(big_psit_G, psit_G)
        
    def initialize_from_lcao_coefficients(self, basis_functions, mynbands):
        for kpt in self.kpt_u:
            kpt.psit_nG = self.gd.zeros(self.bd.mynbands, self.dtype)
            basis_functions.lcao_to_grid(kpt.C_nM,
                                         kpt.psit_nG[:mynbands], kpt.q)
            kpt.C_nM = None

    def random_wave_functions(self, nao):
        """Generate random wave functions."""

        gpts = self.gd.N_c[0] * self.gd.N_c[1] * self.gd.N_c[2]
        
        if self.bd.nbands < gpts / 64:
            gd1 = self.gd.coarsen()
            gd2 = gd1.coarsen()

            psit_G1 = gd1.empty(dtype=self.dtype)
            psit_G2 = gd2.empty(dtype=self.dtype)

            interpolate2 = Transformer(gd2, gd1, 1, self.dtype).apply
            interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply

            shape = tuple(gd2.n_c)
            scale = np.sqrt(12 / abs(np.linalg.det(gd2.cell_cv)))

            old_state = np.random.get_state()

            np.random.seed(4 + self.world.rank)

            for kpt in self.kpt_u:
                for psit_G in kpt.psit_nG[nao:]:
                    if self.dtype == float:
                        psit_G2[:] = (np.random.random(shape) - 0.5) * scale
                    else:
                        psit_G2.real = (np.random.random(shape) - 0.5) * scale
                        psit_G2.imag = (np.random.random(shape) - 0.5) * scale

                    interpolate2(psit_G2, psit_G1, kpt.phase_cd)
                    interpolate1(psit_G1, psit_G, kpt.phase_cd)
            np.random.set_state(old_state)
        
        elif gpts / 64 <= self.bd.nbands < gpts / 8:
            gd1 = self.gd.coarsen()

            psit_G1 = gd1.empty(dtype=self.dtype)

            interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply

            shape = tuple(gd1.n_c)
            scale = np.sqrt(12 / abs(np.linalg.det(gd1.cell_cv)))

            old_state = np.random.get_state()

            np.random.seed(4 + self.world.rank)

            for kpt in self.kpt_u:
                for psit_G in kpt.psit_nG[nao:]:
                    if self.dtype == float:
                        psit_G1[:] = (np.random.random(shape) - 0.5) * scale
                    else:
                        psit_G1.real = (np.random.random(shape) - 0.5) * scale
                        psit_G1.imag = (np.random.random(shape) - 0.5) * scale

                    interpolate1(psit_G1, psit_G, kpt.phase_cd)
            np.random.set_state(old_state)
               
        else:
            shape = tuple(self.gd.n_c)
            scale = np.sqrt(12 / abs(np.linalg.det(self.gd.cell_cv)))

            old_state = np.random.get_state()

            np.random.seed(4 + self.world.rank)

            for kpt in self.kpt_u:
                for psit_G in kpt.psit_nG[nao:]:
                    if self.dtype == float:
                        psit_G[:] = (np.random.random(shape) - 0.5) * scale
                    else:
                        psit_G.real = (np.random.random(shape) - 0.5) * scale
                        psit_G.imag = (np.random.random(shape) - 0.5) * scale

            np.random.set_state(old_state)

    def estimate_memory(self, mem):
        FDPWWaveFunctions.estimate_memory(self, mem)
Esempio n. 3
0
class WaveFunctions:
    """Class for wave-function related stuff (e.g. projectors)."""
    
    def __init__(self, nbands, kpt_u, setups, kd, gd, dtype=float):
        """Store and initialize required attributes.

        Parameters
        ----------
        nbands: int
            Number of occupied bands.
        kpt_u: list of KPoints
            List of KPoint instances from a ground-state calculation (i.e. the
            attribute ``calc.wfs.kpt_u``).
        setups: Setups
            LocalizedFunctionsCollection setups.
        kd: KPointDescriptor
            K-point and symmetry related stuff.
        gd: GridDescriptor
            Descriptor for the coarse grid.            
        dtype: dtype
            This is the ``dtype`` for the wave-function derivatives (same as
            the ``dtype`` for the ground-state wave-functions).

        """

        self.dtype = dtype
        # K-point related attributes
        self.kd = kd
        # Number of occupied bands
        self.nbands = nbands
        # Projectors
        self.pt = LFC(gd, [setup.pt_j for setup in setups], dtype=self.dtype)
        # Store grid
        self.gd = gd

        # Unfold the irreducible BZ to the full BZ
        # List of KPointContainers for the k-points in the full BZ
        self.kpt_u = []

        # No symmetries or only time-reversal symmetry used
        if kd.symmetry is None:
            # For now, time-reversal symmetry not allowed
            assert len(kpt_u) == kd.nbzkpts            

            for k in range(kd.nbzkpts):
                kpt_ = kpt_u[k]

                psit_nG = gd.empty(nbands, dtype=self.dtype)

                for n, psit_G in enumerate(psit_nG):
                    psit_G[:] = kpt_.psit_nG[n]
                    # psit_0 = psit_G[0, 0, 0]
                    # psit_G *= psit_0.conj() / (abs(psit_0))
                    
                # Strip off KPoint attributes and store in the KPointContainer
                # Note, only the occupied GS wave-functions are retained here !
                kpt = KPointContainer(weight=kpt_.weight,
                                      k=kpt_.k,
                                      s=kpt_.s,
                                      phase_cd=kpt_.phase_cd,
                                      eps_n=kpt_.eps_n[:nbands],
                                      psit_nG=psit_nG,
                                      psit1_nG=None,
                                      P_ani=None,
                                      dP_aniv=None)
                                       # q=kpt.q,
                                       # f_n=kpt.f_n[:nbands])
            
                self.kpt_u.append(kpt)

        else:
            assert len(kpt_u) == kd.nibzkpts

            for k, k_c in enumerate(kd.bzk_kc):

                # Index of symmetry related point in the irreducible BZ
                ik = kd.kibz_k[k]
                # Index of point group operation
                s = kd.sym_k[k]
                # Time-reversal symmetry used
                time_reversal = kd.time_reversal_k[k]

                # Coordinates of symmetry related point in the irreducible BZ
                ik_c = kd.ibzk_kc[ik]
                # Point group operation
                op_cc = kd.symmetry.op_scc[s]
                    
                # KPoint from ground-state calculation
                kpt_ = kpt_u[ik]
                weight = 1. / kd.nbzkpts * (2 - kpt_.s)
                phase_cd = np.exp(2j * pi * gd.sdisp_cd * k_c[:, np.newaxis])

                psit_nG = gd.empty(nbands, dtype=self.dtype)

                for n, psit_G in enumerate(psit_nG):
                    #XXX Seems to corrupt my memory somehow ???
                    psit_G[:] = kd.symmetry.symmetrize_wavefunction(
                        kpt_.psit_nG[n], ik_c, k_c, op_cc, time_reversal)
                    # Choose gauge
                    # psit_0 = psit_G[0, 0, 0]
                    # psit_G *= psit_0.conj() / (abs(psit_0))

                kpt = KPointContainer(weight=weight,
                                      k=k,
                                      s=kpt_.s,
                                      phase_cd=phase_cd,
                                      eps_n=kpt_.eps_n[:nbands],
                                      psit_nG=psit_nG,
                                      psit1_nG=None,
                                      P_ani=None,
                                      dP_aniv=None)
                
                self.kpt_u.append(kpt)
                
    def initialize(self, spos_ac):
        """Initialize projectors according to the ``gamma`` attribute."""

        # Set positions on LFC's
        self.pt.set_positions(spos_ac)
        
        if not self.kd.gamma:
            # Set k-vectors and update
            self.pt.set_k_points(self.kd.ibzk_kc)
            self.pt._update(spos_ac)

        # Calculate projector coefficients for the GS wave-functions
        self.calculate_projector_coef()

    def reset(self):
        """Make fresh arrays for wave-function derivatives."""

        for kpt in self.kpt_u:
            kpt.psit1_nG = self.gd.zeros(n=self.nbands, dtype=self.dtype)
        
    def calculate_projector_coef(self):
        """Coefficients for the derivative of the non-local part of the PP.

        Parameters
        ----------
        k: int
            Index of the k-point of the Bloch state on which the non-local
            potential operates on.

        The calculated coefficients are the following (except for an overall
        sign of -1; see ``derivative`` member function of class ``LFC``):

        1. Coefficients from the projector functions::

                        /      a          
               P_ani =  | dG  p (G) Psi (G)  ,
                        /      i       n
                          
        2. Coefficients from the derivative of the projector functions::

                          /      a           
               dP_aniv =  | dG dp  (G) Psi (G)  ,
                          /      iv       n   

        where::
                       
                 a        d       a
               dp  (G) =  ---  Phi (G) .
                 iv         a     i
                          dR

        """

        n = self.nbands

        for kpt in self.kpt_u:

            # K-point index and wave-functions
            k = kpt.k
            psit_nG = kpt.psit_nG
            
            # Integration dicts
            P_ani   = self.pt.dict(shape=n)
            dP_aniv = self.pt.dict(shape=n, derivative=True)
    
            # 1) Integrate with projectors
            self.pt.integrate(psit_nG, P_ani, q=k)
            kpt.P_ani = P_ani
            
            # 2) Integrate with derivative of projectors
            self.pt.derivative(psit_nG, dP_aniv, q=k)
            kpt.dP_aniv = dP_aniv
Esempio n. 4
0
a = 4.0
gd = GridDescriptor(N_c=[16, 20, 20], cell_cv=[a, a + 1, a + 2],
                    pbc_c=(0, 1, 1))
spos_ac = np.array([[0.25, 0.15, 0.35], [0.5, 0.5, 0.5]])
kpts_kc = None
s = Spline(l=0, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
p = Spline(l=1, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
spline_aj = [[s], [s, p]]
c = LFC(gd, spline_aj, cut=True, forces=True)
c.set_positions(spos_ac)
C_ani = c.dict(3, zero=True)
if 1 in C_ani:
    C_ani[1][:, 1:] = np.eye(3)
psi = gd.zeros(3)
c.add(psi, C_ani)
c.integrate(psi, C_ani)
if 1 in C_ani:
    d = C_ani[1][:, 1:].diagonal()
    assert d.ptp() < 4e-6
    C_ani[1][:, 1:] -= np.diag(d)
    assert abs(C_ani[1]).max() < 5e-17
d_aniv = c.dict(3, derivative=True)
c.derivative(psi, d_aniv)
if 1 in d_aniv:
    for v in range(3):
        assert abs(d_aniv[1][v - 1, 0, v] + 0.2144) < 5e-5
        d_aniv[1][v - 1, 0, v] = 0
    assert abs(d_aniv[1]).max() < 3e-16
eps = 0.0001
pos_av = np.dot(spos_ac, gd.cell_cv)
for v in range(3):
class WaveFunctions:
    """Class for wave-function related stuff (e.g. projectors)."""
    
    def __init__(self, nbands, kpt_u, setups, kd, gd, dtype=float):
        """Store and initialize required attributes.

        Parameters
        ----------
        nbands: int
            Number of occupied bands.
        kpt_u: list of KPoints
            List of KPoint instances from a ground-state calculation (i.e. the
            attribute ``calc.wfs.kpt_u``).
        setups: Setups
            LocalizedFunctionsCollection setups.
        kd: KPointDescriptor
            K-point and symmetry related stuff.
        gd: GridDescriptor
            Descriptor for the coarse grid.            
        dtype: dtype
            This is the ``dtype`` for the wave-function derivatives (same as
            the ``dtype`` for the ground-state wave-functions).

        """

        self.dtype = dtype
        # K-point related attributes
        self.kd = kd
        # Number of occupied bands
        self.nbands = nbands
        # Projectors
        self.pt = LFC(gd, [setup.pt_j for setup in setups], kd,
                      dtype=self.dtype)
        # Store grid
        self.gd = gd

        # Unfold the irreducible BZ to the full BZ
        # List of KPointContainers for the k-points in the full BZ
        self.kpt_u = []

        # No symmetries or only time-reversal symmetry used
        assert kd.symmetry.point_group == False
        if kd.symmetry.time_reversal == False:
            # For now, time-reversal symmetry not allowed
            assert len(kpt_u) == kd.nbzkpts

            for k in range(kd.nbzkpts):
                kpt_ = kpt_u[k]

                psit_nG = gd.empty(nbands, dtype=self.dtype)

                for n, psit_G in enumerate(psit_nG):
                    psit_G[:] = kpt_.psit_nG[n]
                    # psit_0 = psit_G[0, 0, 0]
                    # psit_G *= psit_0.conj() / (abs(psit_0))

                # Strip off KPoint attributes and store in the KPointContainer
                # Note, only the occupied GS wave-functions are retained here !
                kpt = KPointContainer(weight=kpt_.weight,
                                      k=kpt_.k,
                                      s=kpt_.s,
                                      phase_cd=kpt_.phase_cd,
                                      eps_n=kpt_.eps_n[:nbands],
                                      psit_nG=psit_nG,
                                      psit1_nG=None,
                                      P_ani=None,
                                      dP_aniv=None)
                                       # q=kpt.q,
                                       # f_n=kpt.f_n[:nbands])
            
                self.kpt_u.append(kpt)

        else:
            assert len(kpt_u) == kd.nibzkpts

            for k, k_c in enumerate(kd.bzk_kc):

                # Index of symmetry related point in the irreducible BZ
                ik = kd.bz2ibz_k[k]
                # Index of point group operation
                s = kd.sym_k[k]
                # Time-reversal symmetry used
                time_reversal = kd.time_reversal_k[k]

                # Coordinates of symmetry related point in the irreducible BZ
                ik_c = kd.ibzk_kc[ik]
                # Point group operation
                op_cc = kd.symmetry.op_scc[s]
                    
                # KPoint from ground-state calculation
                kpt_ = kpt_u[ik]
                weight = 1. / kd.nbzkpts * (2 - kpt_.s)
                phase_cd = np.exp(2j * pi * gd.sdisp_cd * k_c[:, np.newaxis])

                psit_nG = gd.empty(nbands, dtype=self.dtype)

                for n, psit_G in enumerate(psit_nG):
                    #XXX Seems to corrupt my memory somehow ???
                    psit_G[:] = kd.symmetry.symmetrize_wavefunction(
                        kpt_.psit_nG[n], ik_c, k_c, op_cc, time_reversal)
                    # Choose gauge
                    # psit_0 = psit_G[0, 0, 0]
                    # psit_G *= psit_0.conj() / (abs(psit_0))

                kpt = KPointContainer(weight=weight,
                                      k=k,
                                      s=kpt_.s,
                                      phase_cd=phase_cd,
                                      eps_n=kpt_.eps_n[:nbands],
                                      psit_nG=psit_nG,
                                      psit1_nG=None,
                                      P_ani=None,
                                      dP_aniv=None)
                
                self.kpt_u.append(kpt)
                
    def initialize(self, spos_ac):
        """Initialize projectors according to the ``gamma`` attribute."""

        # Set positions on LFC's
        self.pt.set_positions(spos_ac)
        
        # Calculate projector coefficients for the GS wave-functions
        self.calculate_projector_coef()

    def reset(self):
        """Make fresh arrays for wave-function derivatives."""

        for kpt in self.kpt_u:
            kpt.psit1_nG = self.gd.zeros(n=self.nbands, dtype=self.dtype)
        
    def calculate_projector_coef(self):
        """Coefficients for the derivative of the non-local part of the PP.

        Parameters
        ----------
        k: int
            Index of the k-point of the Bloch state on which the non-local
            potential operates on.

        The calculated coefficients are the following (except for an overall
        sign of -1; see ``derivative`` member function of class ``LFC``):

        1. Coefficients from the projector functions::

                        /      a          
               P_ani =  | dG  p (G) Psi (G)  ,
                        /      i       n
                          
        2. Coefficients from the derivative of the projector functions::

                          /      a           
               dP_aniv =  | dG dp  (G) Psi (G)  ,
                          /      iv       n   

        where::
                       
                 a        d       a
               dp  (G) =  ---  Phi (G) .
                 iv         a     i
                          dR

        """

        n = self.nbands

        for kpt in self.kpt_u:

            # K-point index and wave-functions
            k = kpt.k
            psit_nG = kpt.psit_nG
            
            # Integration dicts
            P_ani   = self.pt.dict(shape=n)
            dP_aniv = self.pt.dict(shape=n, derivative=True)
    
            # 1) Integrate with projectors
            self.pt.integrate(psit_nG, P_ani, q=k)
            kpt.P_ani = P_ani
            
            # 2) Integrate with derivative of projectors
            self.pt.derivative(psit_nG, dP_aniv, q=k)
            kpt.dP_aniv = dP_aniv
Esempio n. 6
0
class FDWaveFunctions(FDPWWaveFunctions):
    mode = 'fd'

    def __init__(self,
                 stencil,
                 diagksl,
                 orthoksl,
                 initksl,
                 gd,
                 nvalence,
                 setups,
                 bd,
                 dtype,
                 world,
                 kd,
                 kptband_comm,
                 timer=None):
        FDPWWaveFunctions.__init__(self, diagksl, orthoksl, initksl, gd,
                                   nvalence, setups, bd, dtype, world, kd,
                                   kptband_comm, timer)

        # Kinetic energy operator:
        self.kin = Laplace(self.gd, -0.5, stencil, self.dtype)

        self.matrixoperator = MatrixOperator(self.orthoksl)

        self.taugrad_v = None  # initialized by MGGA functional

    def empty(self, n=(), global_array=False, realspace=False, q=-1):
        return self.gd.empty(n, self.dtype, global_array)

    def integrate(self, a_xg, b_yg=None, global_integral=True):
        return self.gd.integrate(a_xg, b_yg, global_integral)

    def bytes_per_wave_function(self):
        return self.gd.bytecount(self.dtype)

    def set_setups(self, setups):
        self.pt = LFC(self.gd, [setup.pt_j for setup in setups],
                      self.kd,
                      dtype=self.dtype,
                      forces=True)
        FDPWWaveFunctions.set_setups(self, setups)

    def set_positions(self, spos_ac):
        FDPWWaveFunctions.set_positions(self, spos_ac)

    def summary(self, fd):
        fd.write('Wave functions: Uniform real-space grid\n')
        fd.write('Kinetic energy operator: %s\n' % self.kin.description)

    def make_preconditioner(self, block=1):
        return Preconditioner(self.gd, self.kin, self.dtype, block)

    def apply_pseudo_hamiltonian(self, kpt, hamiltonian, psit_xG, Htpsit_xG):
        self.timer.start('Apply hamiltonian')
        self.kin.apply(psit_xG, Htpsit_xG, kpt.phase_cd)
        hamiltonian.apply_local_potential(psit_xG, Htpsit_xG, kpt.s)
        self.timer.stop('Apply hamiltonian')

    def add_orbital_density(self, nt_G, kpt, n):
        if self.dtype == float:
            axpy(1.0, kpt.psit_nG[n]**2, nt_G)
        else:
            axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
            axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)

    def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
        # Used in calculation of response part of GLLB-potential
        nt_G = nt_sG[kpt.s]
        if self.dtype == float:
            for f, psit_G in zip(f_n, kpt.psit_nG):
                axpy(f, psit_G**2, nt_G)
        else:
            for f, psit_G in zip(f_n, kpt.psit_nG):
                axpy(f, psit_G.real**2, nt_G)
                axpy(f, psit_G.imag**2, nt_G)

        # Hack used in delta-scf calculations:
        if hasattr(kpt, 'c_on'):
            assert self.bd.comm.size == 1
            d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
                            dtype=complex)
            for ne, c_n in zip(kpt.ne_o, kpt.c_on):
                d_nn += ne * np.outer(c_n.conj(), c_n)
            for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
                for d, psi_G in zip(d_n, kpt.psit_nG):
                    if abs(d) > 1.e-12:
                        nt_G += (psi0_G.conj() * d * psi_G).real

    def calculate_kinetic_energy_density(self):
        if self.taugrad_v is None:
            self.taugrad_v = [
                Gradient(self.gd, v, n=3, dtype=self.dtype).apply
                for v in range(3)
            ]

        assert not hasattr(self.kpt_u[0], 'c_on')
        if self.kpt_u[0].psit_nG is None:
            raise RuntimeError('No wavefunctions yet')
        if isinstance(self.kpt_u[0].psit_nG, FileReference):
            # XXX initialize
            raise RuntimeError('Wavefunctions have not been initialized.')

        taut_sG = self.gd.zeros(self.nspins)
        dpsit_G = self.gd.empty(dtype=self.dtype)
        for kpt in self.kpt_u:
            for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
                for v in range(3):
                    self.taugrad_v[v](psit_G, dpsit_G, kpt.phase_cd)
                    axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])

        self.kd.comm.sum(taut_sG)
        self.band_comm.sum(taut_sG)
        return taut_sG

    def apply_mgga_orbital_dependent_hamiltonian(self, kpt, psit_xG, Htpsit_xG,
                                                 dH_asp, dedtaut_G):
        a_G = self.gd.empty(dtype=psit_xG.dtype)
        for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
            for v in range(3):
                self.taugrad_v[v](psit_G, a_G, kpt.phase_cd)
                self.taugrad_v[v](dedtaut_G * a_G, a_G, kpt.phase_cd)
                axpy(-0.5, a_G, Htpsit_G)

    def ibz2bz(self, atoms):
        """Transform wave functions in IBZ to the full BZ."""

        assert self.kd.comm.size == 1

        # New k-point descriptor for full BZ:
        kd = KPointDescriptor(self.kd.bzk_kc, nspins=self.nspins)
        #kd.set_symmetry(atoms, self.setups, enabled=False)
        kd.set_communicator(serial_comm)

        self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
                      kd,
                      dtype=self.dtype)
        self.pt.set_positions(atoms.get_scaled_positions())

        self.initialize_wave_functions_from_restart_file()

        weight = 2.0 / kd.nspins / kd.nbzkpts

        # Build new list of k-points:
        kpt_u = []
        for s in range(self.nspins):
            for k in range(kd.nbzkpts):
                # Index of symmetry related point in the IBZ
                ik = self.kd.bz2ibz_k[k]
                r, u = self.kd.get_rank_and_index(s, ik)
                assert r == 0
                kpt = self.kpt_u[u]

                phase_cd = np.exp(2j * np.pi * self.gd.sdisp_cd *
                                  kd.bzk_kc[k, :, np.newaxis])

                # New k-point:
                kpt2 = KPoint(weight, s, k, k, phase_cd)
                kpt2.f_n = kpt.f_n / kpt.weight / kd.nbzkpts * 2 / self.nspins
                kpt2.eps_n = kpt.eps_n.copy()

                # Transform wave functions using symmetry operation:
                Psit_nG = self.gd.collect(kpt.psit_nG)
                if Psit_nG is not None:
                    Psit_nG = Psit_nG.copy()
                    for Psit_G in Psit_nG:
                        Psit_G[:] = self.kd.transform_wave_function(Psit_G, k)
                kpt2.psit_nG = self.gd.empty(self.bd.nbands, dtype=self.dtype)
                self.gd.distribute(Psit_nG, kpt2.psit_nG)

                # Calculate PAW projections:
                kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
                self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)

                kpt_u.append(kpt2)

        self.kd = kd
        self.kpt_u = kpt_u

    def write(self, writer, write_wave_functions=False):
        writer['Mode'] = 'fd'

        if not write_wave_functions:
            return

        writer.add(
            'PseudoWaveFunctions',
            ('nspins', 'nibzkpts', 'nbands', 'ngptsx', 'ngptsy', 'ngptsz'),
            dtype=self.dtype)

        if hasattr(writer, 'hdf5'):
            parallel = (self.world.size > 1)
            for kpt in self.kpt_u:
                indices = [kpt.s, kpt.k]
                indices.append(self.bd.get_slice())
                indices += self.gd.get_slice()
                writer.fill(kpt.psit_nG, parallel=parallel, *indices)
        else:
            for s in range(self.nspins):
                for k in range(self.kd.nibzkpts):
                    for n in range(self.bd.nbands):
                        psit_G = self.get_wave_function_array(n, k, s)
                        writer.fill(psit_G, s, k, n)

    def read(self, reader, hdf5):
        if ((not hdf5 and self.bd.comm.size == 1)
                or (hdf5 and self.world.size == 1)):
            # We may not be able to keep all the wave
            # functions in memory - so psit_nG will be a special type of
            # array that is really just a reference to a file:
            for kpt in self.kpt_u:
                kpt.psit_nG = reader.get_reference('PseudoWaveFunctions',
                                                   (kpt.s, kpt.k))
        else:
            for kpt in self.kpt_u:
                kpt.psit_nG = self.empty(self.bd.mynbands)
                if hdf5:
                    indices = [kpt.s, kpt.k]
                    indices.append(self.bd.get_slice())
                    indices += self.gd.get_slice()
                    reader.get('PseudoWaveFunctions',
                               out=kpt.psit_nG,
                               parallel=(self.world.size > 1),
                               *indices)
                else:
                    # Read band by band to save memory
                    for myn, psit_G in enumerate(kpt.psit_nG):
                        n = self.bd.global_index(myn)
                        if self.gd.comm.rank == 0:
                            big_psit_G = np.array(
                                reader.get('PseudoWaveFunctions', kpt.s, kpt.k,
                                           n), self.dtype)
                        else:
                            big_psit_G = None
                        self.gd.distribute(big_psit_G, psit_G)

    def initialize_from_lcao_coefficients(self, basis_functions, mynbands):
        for kpt in self.kpt_u:
            kpt.psit_nG = self.gd.zeros(self.bd.mynbands, self.dtype)
            basis_functions.lcao_to_grid(kpt.C_nM, kpt.psit_nG[:mynbands],
                                         kpt.q)
            kpt.C_nM = None
            if use_mic:
                kpt.psit_nG_mic = stream.bind(kpt.psit_nG)
                stream.sync()

    def random_wave_functions(self, nao):
        """Generate random wave functions."""

        gpts = self.gd.N_c[0] * self.gd.N_c[1] * self.gd.N_c[2]

        if self.bd.nbands < gpts / 64:
            gd1 = self.gd.coarsen()
            gd2 = gd1.coarsen()

            psit_G1 = gd1.empty(dtype=self.dtype)
            psit_G2 = gd2.empty(dtype=self.dtype)

            interpolate2 = Transformer(gd2, gd1, 1, self.dtype).apply
            interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply

            shape = tuple(gd2.n_c)
            scale = np.sqrt(12 / abs(np.linalg.det(gd2.cell_cv)))

            old_state = np.random.get_state()

            np.random.seed(4 + self.world.rank)

            for kpt in self.kpt_u:
                for psit_G in kpt.psit_nG[nao:]:
                    if self.dtype == float:
                        psit_G2[:] = (np.random.random(shape) - 0.5) * scale
                    else:
                        psit_G2.real = (np.random.random(shape) - 0.5) * scale
                        psit_G2.imag = (np.random.random(shape) - 0.5) * scale

                    interpolate2(psit_G2, psit_G1, kpt.phase_cd)
                    interpolate1(psit_G1, psit_G, kpt.phase_cd)
            np.random.set_state(old_state)

        elif gpts / 64 <= self.bd.nbands < gpts / 8:
            gd1 = self.gd.coarsen()

            psit_G1 = gd1.empty(dtype=self.dtype)

            interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply

            shape = tuple(gd1.n_c)
            scale = np.sqrt(12 / abs(np.linalg.det(gd1.cell_cv)))

            old_state = np.random.get_state()

            np.random.seed(4 + self.world.rank)

            for kpt in self.kpt_u:
                for psit_G in kpt.psit_nG[nao:]:
                    if self.dtype == float:
                        psit_G1[:] = (np.random.random(shape) - 0.5) * scale
                    else:
                        psit_G1.real = (np.random.random(shape) - 0.5) * scale
                        psit_G1.imag = (np.random.random(shape) - 0.5) * scale

                    interpolate1(psit_G1, psit_G, kpt.phase_cd)
            np.random.set_state(old_state)

        else:
            shape = tuple(self.gd.n_c)
            scale = np.sqrt(12 / abs(np.linalg.det(self.gd.cell_cv)))

            old_state = np.random.get_state()

            np.random.seed(4 + self.world.rank)

            for kpt in self.kpt_u:
                for psit_G in kpt.psit_nG[nao:]:
                    if self.dtype == float:
                        psit_G[:] = (np.random.random(shape) - 0.5) * scale
                    else:
                        psit_G.real = (np.random.random(shape) - 0.5) * scale
                        psit_G.imag = (np.random.random(shape) - 0.5) * scale

            np.random.set_state(old_state)

    def estimate_memory(self, mem):
        FDPWWaveFunctions.estimate_memory(self, mem)
Esempio n. 7
0
    def get_projections(self, locfun, spin=0):
        """Project wave functions onto localized functions

        Determine the projections of the Kohn-Sham eigenstates
        onto specified localized functions of the format::

          locfun = [[spos_c, l, sigma], [...]]

        spos_c can be an atom index, or a scaled position vector. l is
        the angular momentum, and sigma is the (half-) width of the
        radial gaussian.

        Return format is::

          f_kni = <psi_kn | f_i>

        where psi_kn are the wave functions, and f_i are the specified
        localized functions.

        As a special case, locfun can be the string 'projectors', in which
        case the bound state projectors are used as localized functions.
        """

        wfs = self.wfs
        
        if locfun == 'projectors':
            f_kin = []
            for kpt in wfs.kpt_u:
                if kpt.s == spin:
                    f_in = []
                    for a, P_ni in kpt.P_ani.items():
                        i = 0
                        setup = wfs.setups[a]
                        for l, n in zip(setup.l_j, setup.n_j):
                            if n >= 0:
                                for j in range(i, i + 2 * l + 1):
                                    f_in.append(P_ni[:, j])
                            i += 2 * l + 1
                    f_kin.append(f_in)
            f_kni = np.array(f_kin).transpose(0, 2, 1)
            return f_kni.conj()

        from gpaw.lfc import LocalizedFunctionsCollection as LFC
        from gpaw.spline import Spline
        from gpaw.utilities import _fact

        nkpts = len(wfs.ibzk_kc)
        nbf = np.sum([2 * l + 1 for pos, l, a in locfun])
        f_kni = np.zeros((nkpts, wfs.nbands, nbf), wfs.dtype)

        spos_ac = self.atoms.get_scaled_positions() % 1.0
        spos_xc = []
        splines_x = []
        for spos_c, l, sigma in locfun:
            if isinstance(spos_c, int):
                spos_c = spos_ac[spos_c]
            spos_xc.append(spos_c)
            alpha = .5 * Bohr**2 / sigma**2
            r = np.linspace(0, 6. * sigma, 500)
            f_g = (_fact[l] * (4 * alpha)**(l + 3 / 2.) *
                   np.exp(-alpha * r**2) /
                   (np.sqrt(4 * np.pi) * _fact[2 * l + 1]))
            splines_x.append([Spline(l, rmax=r[-1], f_g=f_g, points=61)])
            
        lf = LFC(wfs.gd, splines_x, wfs.kpt_comm, dtype=wfs.dtype)
        if not wfs.gamma:
            lf.set_k_points(wfs.ibzk_qc)
        lf.set_positions(spos_xc)

        k = 0
        f_ani = lf.dict(wfs.nbands)
        for kpt in wfs.kpt_u:
            if kpt.s != spin:
                continue
            lf.integrate(kpt.psit_nG[:], f_ani, kpt.q)
            i1 = 0
            for x, f_ni in f_ani.items():
                i2 = i1 + f_ni.shape[1]
                f_kni[k, :, i1:i2] = f_ni
                i1 = i2
            k += 1

        return f_kni.conj()
Esempio n. 8
0
gd = GridDescriptor(N_c=[16, 20, 20],
                    cell_cv=[a, a + 1, a + 2],
                    pbc_c=(0, 1, 1))
spos_ac = np.array([[0.25, 0.15, 0.35], [0.5, 0.5, 0.5]])
kpts_kc = None
s = Spline(l=0, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
p = Spline(l=1, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
spline_aj = [[s], [s, p]]
c = LFC(gd, spline_aj, cut=True, forces=True)
c.set_positions(spos_ac)
C_ani = c.dict(3, zero=True)
if 1 in C_ani:
    C_ani[1][:, 1:] = np.eye(3)
psi = gd.zeros(3)
c.add(psi, C_ani)
c.integrate(psi, C_ani)
if 1 in C_ani:
    d = C_ani[1][:, 1:].diagonal()
    assert d.ptp() < 4e-6
    C_ani[1][:, 1:] -= np.diag(d)
    assert abs(C_ani[1]).max() < 5e-17
d_aniv = c.dict(3, derivative=True)
c.derivative(psi, d_aniv)
if 1 in d_aniv:
    for v in range(3):
        assert abs(d_aniv[1][v - 1, 0, v] + 0.2144) < 5e-5
        d_aniv[1][v - 1, 0, v] = 0
    assert abs(d_aniv[1]).max() < 3e-16
eps = 0.0001
pos_av = np.dot(spos_ac, gd.cell_cv)
for v in range(3):
Esempio n. 9
0
 if mode == 'fd':
     pt = LFC(gd, [setup.pt_j for setup in setups],
                       KPointDescriptor(bzk_kc),
                       dtype=calc.wfs.dtype)
     pt.set_positions(spos_ac)
 
     for spin in range(nspins):
         for k in range(len(bzk_kc)):
             ibzk = k  # since no symmetry
             u = kd.get_rank_and_index(spin, ibzk)[1]
             kpt = calc.wfs.kpt_u[u]
             for n in range(nbands):
                 P_ai = pt.dict()
                 psit_G = calc.wfs.get_wave_function_array(n, ibzk,
                                                           spin)
                 pt.integrate(psit_G, P_ai, ibzk)
                     
                 for a in range(len(P_ai)):
                     assert np.abs(
                         P_ai[a] -
                         calc.wfs.kpt_u[u].P_ani[a][n]).sum() < 1e-8
                     assert np.abs(
                         P_ai[a] -
                         df.get_P_ai(k, n, spin)[a]).sum() < 1e-8
 
 else:
     pt = PWLFC([setup.pt_j for setup in setups], calc.wfs.pd)
     pt.set_positions(spos_ac)
 
     for spin in range(nspins):
         for k in range(len(bzk_kc)):