Source code for gpaw.kpt_descriptor

# Copyright (C) 2003  CAMP
# Please see the accompanying LICENSE file for further information.

"""K-point descriptor."""

import numpy as np

from ase.dft.kpoints import monkhorst_pack, get_monkhorst_pack_size_and_offset
from ase.calculators.calculator import kptdensity2monkhorstpack

from gpaw import KPointError
from gpaw.kpoint import KPoint
import gpaw.mpi as mpi
import _gpaw


def to1bz(bzk_kc, cell_cv):
    """Wrap k-points to 1. BZ.

    Return k-points wrapped to the 1. BZ.

    bzk_kc: (n,3) ndarray
        Array of k-points in units of the reciprocal lattice vectors.
    cell_cv: (3,3) ndarray
        Unit cell.
    """

    B_cv = 2.0 * np.pi * np.linalg.inv(cell_cv).T
    K_kv = np.dot(bzk_kc, B_cv)
    N_xc = np.indices((3, 3, 3)).reshape((3, 27)).T - 1
    G_xv = np.dot(N_xc, B_cv)

    bz1k_kc = bzk_kc.copy()

    # Find the closest reciprocal lattice vector:
    for k, K_v in enumerate(K_kv):
        # If a k-point has the same distance to several reciprocal
        # lattice vectors, we don't want to pick a random one on the
        # basis of numerical noise, so we round off the differences
        # between the shortest distances to 6 decimals and chose the
        # one with the lowest index.
        d = ((G_xv - K_v)**2).sum(1)
        x = (d - d.min()).round(6).argmin()
        bz1k_kc[k] -= N_xc[x]

    return bz1k_kc


def kpts2sizeandoffsets(size=None, density=None, gamma=None, even=None,
                        atoms=None):
    """Helper function for selecting k-points.

    Use either size or density.

    size: 3 ints
        Number of k-points.
    density: float
        K-point density in units of k-points per Ang^-1.
    gamma: None or bool
        Should the Gamma-point be included?  Yes / no / don't care:
        True / False / None.
    even: None or bool
        Should the number of k-points be even?  Yes / no / don't care:
        True / False / None.
    atoms: Atoms object
        Needed for calculating k-point density.

    """

    if size is None:
        if density is None:
            size = [1, 1, 1]
        else:
            size = kptdensity2monkhorstpack(atoms, density, even)

    offsets = [0, 0, 0]

    if gamma is not None:
        for i, s in enumerate(size):
            if atoms.pbc[i] and s % 2 != bool(gamma):
                offsets[i] = 0.5 / s

    return size, offsets


[docs]class KPointDescriptor: """Descriptor-class for k-points.""" def __init__(self, kpts, nspins: int = 1): """Construct descriptor object for kpoint/spin combinations (ks-pair). Parameters: kpts: None, sequence of 3 ints, or (n,3)-shaped array Specification of the k-point grid. None=Gamma, list of ints=Monkhorst-Pack, ndarray=user specified. nspins: int Number of spins. Attributes =================== ================================================= ``N_c`` Number of k-points in the different directions. ``nspins`` Number of spins in total. ``mynspins`` Number of spins on this CPU. ``nibzkpts`` Number of irreducible kpoints in 1st BZ. ``mynks`` Number of k-point/spin combinations on this CPU. ``gamma`` Boolean indicator for gamma point calculation. ``comm`` MPI-communicator for kpoint distribution. ``weight_k`` Weights of each k-point ``ibzk_kc`` Unknown ``ibzk_qc`` Unknown ``sym_k`` Unknown ``time_reversal_k`` Unknown ``bz2ibz_k`` Unknown ``ibz2bz_k`` Unknown ``bz2bz_ks`` Unknown ``symmetry`` Object representing symmetries =================== ================================================= """ if kpts is None: self.bzk_kc = np.zeros((1, 3)) self.N_c = np.array((1, 1, 1), dtype=int) self.offset_c = np.zeros(3) else: kpts = np.asarray(kpts) if kpts.ndim == 1: self.N_c = np.array(kpts, dtype=int) self.bzk_kc = monkhorst_pack(self.N_c) self.offset_c = np.zeros(3) else: self.bzk_kc = np.array(kpts, dtype=float) try: self.N_c, self.offset_c = \ get_monkhorst_pack_size_and_offset(self.bzk_kc) except ValueError: self.N_c = None self.offset_c = None self.nspins = nspins self.nbzkpts = len(self.bzk_kc) # Gamma-point calculation? self.gamma = self.nbzkpts == 1 and np.allclose(self.bzk_kc, 0) # Point group and time-reversal symmetry neglected: self.weight_k = np.ones(self.nbzkpts) / self.nbzkpts self.ibzk_kc = self.bzk_kc.copy() self.sym_k = np.zeros(self.nbzkpts, int) self.time_reversal_k = np.zeros(self.nbzkpts, bool) self.bz2ibz_k = np.arange(self.nbzkpts) self.ibz2bz_k = np.arange(self.nbzkpts) self.bz2bz_ks = np.arange(self.nbzkpts)[:, np.newaxis] self.nibzkpts = self.nbzkpts self.refine_info = None self.monkhorst = (self.N_c is not None) self.set_communicator(mpi.serial_comm) def __str__(self): s = str(self.symmetry) if self.refine_info is not None: s += '\n' + str(self.refine_info) if -1 in self.bz2bz_ks: s += 'Note: your k-points are not as symmetric as your crystal!\n' if self.gamma: s += '\n1 k-point (Gamma)' else: s += '\n%d k-points' % self.nbzkpts if self.monkhorst: s += ': %d x %d x %d Monkhorst-Pack grid' % tuple(self.N_c) if self.offset_c.any(): s += ' + [' for x in self.offset_c: if x != 0 and abs(round(1 / x) - 1 / x) < 1e-12: s += '1/%d,' % round(1 / x) else: s += '%f,' % x s = s[:-1] + ']' s += ('\n%d k-point%s in the irreducible part of the Brillouin zone\n' % (self.nibzkpts, ' s'[1:self.nibzkpts])) if self.monkhorst: w_k = self.weight_k * self.nbzkpts assert np.allclose(w_k, w_k.round()) w_k = w_k.round() s += ' k-points in crystal coordinates weights\n' for k in range(self.nibzkpts): if k < 10 or k == self.nibzkpts - 1: if self.monkhorst: s += ('%4d: %12.8f %12.8f %12.8f %6d/%d\n' % ((k,) + tuple(self.ibzk_kc[k]) + (w_k[k], self.nbzkpts))) else: s += ('%4d: %12.8f %12.8f %12.8f %12.8f\n' % ((k,) + tuple(self.ibzk_kc[k]) + (self.weight_k[k],))) elif k == 10: s += ' ...\n' return s
[docs] def set_symmetry(self, atoms, symmetry, comm=None): """Create symmetry object and construct irreducible Brillouin zone. atoms: Atoms object Defines atom positions and types and also unit cell and boundary conditions. symmetry: Symmetry object Symmetry object. """ self.symmetry = symmetry # XXX we pass the whole atoms object just to complain if its PBCs # are not how we like them for c, periodic in enumerate(atoms.pbc): if not periodic and not np.allclose(self.bzk_kc[:, c], 0.0): raise ValueError('K-points can only be used with PBCs!') if symmetry.time_reversal or symmetry.point_group: (self.ibzk_kc, self.weight_k, self.sym_k, self.time_reversal_k, self.bz2ibz_k, self.ibz2bz_k, self.bz2bz_ks) = symmetry.reduce(self.bzk_kc, comm) # Number of irreducible k-points and k-point/spin combinations. self.nibzkpts = len(self.ibzk_kc)
[docs] def set_communicator(self, comm): """Set k-point communicator.""" # Ranks < self.rank0 have mynks0 k-point/spin combinations and # ranks >= self.rank0 have mynks0+1 k-point/spin combinations. mynk0, x = divmod(self.nibzkpts, comm.size) self.rank0 = comm.size - x self.comm = comm # My number and offset of k-point/spin combinations self.mynk = self.get_count() self.k0 = self.get_offset() self.ibzk_qc = self.ibzk_kc[self.k0:self.k0 + self.mynk] self.weight_q = self.weight_k[self.k0:self.k0 + self.mynk]
[docs] def copy(self, comm=mpi.serial_comm): """Create a copy with shared symmetry object.""" kd = KPointDescriptor(self.bzk_kc, self.nspins) kd.weight_k = self.weight_k kd.ibzk_kc = self.ibzk_kc kd.sym_k = self.sym_k kd.time_reversal_k = self.time_reversal_k kd.bz2ibz_k = self.bz2ibz_k kd.ibz2bz_k = self.ibz2bz_k kd.bz2bz_ks = self.bz2bz_ks kd.symmetry = self.symmetry kd.nibzkpts = self.nibzkpts kd.set_communicator(comm) return kd
[docs] def create_k_points(self, sdisp_cd, collinear): """Return a list of KPoints.""" kpt_qs = [] for k in range(self.k0, self.k0 + self.mynk): q = k - self.k0 weightk = self.weight_k[k] weight = weightk * 2 / self.nspins if self.gamma: phase_cd = np.ones((3, 2), complex) else: phase_cd = np.exp(2j * np.pi * sdisp_cd * self.ibzk_kc[k, :, np.newaxis]) if collinear: spins = range(self.nspins) else: spins = [None] weight *= 0.5 kpt_qs.append([KPoint(weightk, weight, s, k, q, phase_cd) for s in spins]) return kpt_qs
[docs] def collect(self, a_ux, broadcast: bool): """Collect distributed data to all.""" xshape = a_ux.shape[1:] a_qsx = a_ux.reshape((-1, self.nspins) + xshape) if self.comm.rank == 0 or broadcast: a_ksx = np.empty((self.nibzkpts, self.nspins) + xshape, a_ux.dtype) if self.comm.rank > 0: self.comm.send(a_qsx, 0) else: k1 = self.get_count(0) a_ksx[0:k1] = a_qsx requests = [] for rank in range(1, self.comm.size): k2 = k1 + self.get_count(rank) requests.append(self.comm.receive(a_ksx[k1:k2], rank, block=False)) k1 = k2 assert k1 == self.nibzkpts self.comm.waitall(requests) if broadcast: self.comm.broadcast(a_ksx, 0) if self.comm.rank == 0 or broadcast: return a_ksx.transpose((1, 0, 2))
[docs] def transform_wave_function(self, psit_G, k, index_G=None, phase_G=None): """Transform wave function from IBZ to BZ. k is the index of the desired k-point in the full BZ. """ s = self.sym_k[k] time_reversal = self.time_reversal_k[k] op_cc = np.linalg.inv(self.symmetry.op_scc[s]).round().astype(int) # Identity if (np.abs(op_cc - np.eye(3, dtype=int)) < 1e-10).all(): if time_reversal: return psit_G.conj() else: return psit_G # General point group symmetry else: ik = self.bz2ibz_k[k] kibz_c = self.ibzk_kc[ik] b_g = np.zeros_like(psit_G) kbz_c = np.dot(self.symmetry.op_scc[s], kibz_c) if index_G is not None: assert index_G.shape == psit_G.shape == phase_G.shape _gpaw.symmetrize_with_index(psit_G, b_g, index_G, phase_G) else: _gpaw.symmetrize_wavefunction(psit_G, b_g, op_cc.copy(), np.ascontiguousarray(kibz_c), kbz_c) if time_reversal: return b_g.conj() else: return b_g
[docs] def get_transform_wavefunction_index(self, nG, k): """Get the "wavefunction transform index". This is a permutation of the numbers 1, 2, .. N which associates k + q to some k, and where N is the total number of grid points as specified by nG which is a 3D tuple. Returns index_G and phase_G which are one-dimensional arrays on the grid.""" s = self.sym_k[k] op_cc = np.linalg.inv(self.symmetry.op_scc[s]).round().astype(int) # General point group symmetry if (np.abs(op_cc - np.eye(3, dtype=int)) < 1e-10).all(): nG0 = np.prod(nG) index_G = np.arange(nG0).reshape(nG) phase_G = np.ones(nG) else: ik = self.bz2ibz_k[k] kibz_c = self.ibzk_kc[ik] index_G = np.zeros(nG, dtype=int) phase_G = np.zeros(nG, dtype=complex) kbz_c = np.dot(self.symmetry.op_scc[s], kibz_c) _gpaw.symmetrize_return_index(index_G, phase_G, op_cc.copy(), np.ascontiguousarray(kibz_c), kbz_c) return index_G, phase_G
[docs] def find_k_plus_q(self, q_c, kpts_k=None): """Find the indices of k+q for all kpoints in the Brillouin zone. In case that k+q is outside the BZ, the k-point inside the BZ corresponding to k+q is given. Parameters: q_c: ndarray Coordinates for the q-vector in units of the reciprocal lattice vectors. kpts_k: list of ints Restrict search to specified k-points. """ k_x = kpts_k if k_x is None: return self.find_k_plus_q(q_c, range(self.nbzkpts)) i_x = [] for k in k_x: kpt_c = self.bzk_kc[k] + q_c d_kc = kpt_c - self.bzk_kc d_k = abs(d_kc - d_kc.round()).sum(1) i = d_k.argmin() if d_k[i] > 1e-8: raise KPointError('Could not find k+q!') i_x.append(i) return i_x
[docs] def get_bz_q_points(self, first=False): """Return the q=k1-k2. q-mesh is always Gamma-centered.""" shift_c = 0.5 * ((self.N_c + 1) % 2) / self.N_c bzq_qc = monkhorst_pack(self.N_c) + shift_c if first: return to1bz(bzq_qc, self.symmetry.cell_cv) else: return bzq_qc
[docs] def get_ibz_q_points(self, bzq_qc, op_scc): """Return ibz q points and the corresponding symmetry operations that work for k-mesh as well.""" ibzq_qc_tmp = [] ibzq_qc_tmp.append(bzq_qc[-1]) weight_tmp = [0] for i, op_cc in enumerate(op_scc): if np.abs(op_cc - np.eye(3)).sum() < 1e-8: identity_iop = i break ibzq_q_tmp = {} iop_q = {} timerev_q = {} diff_qc = {} for i in range(len(bzq_qc) - 1, -1, -1): # loop opposite to kpoint try: ibzk, iop, timerev, diff_c = self.find_ibzkpt( op_scc, ibzq_qc_tmp, bzq_qc[i]) find = False for ii, iop1 in enumerate(self.sym_k): if iop1 == iop and self.time_reversal_k[ii] == timerev: find = True break if not find: raise ValueError('cant find k!') ibzq_q_tmp[i] = ibzk weight_tmp[ibzk] += 1. iop_q[i] = iop timerev_q[i] = timerev diff_qc[i] = diff_c except ValueError: ibzq_qc_tmp.append(bzq_qc[i]) weight_tmp.append(1.) ibzq_q_tmp[i] = len(ibzq_qc_tmp) - 1 iop_q[i] = identity_iop timerev_q[i] = False diff_qc[i] = np.zeros(3) # reverse the order. nq = len(ibzq_qc_tmp) ibzq_qc = np.zeros((nq, 3)) ibzq_q = np.zeros(len(bzq_qc), dtype=int) for i in range(nq): ibzq_qc[i] = ibzq_qc_tmp[nq - i - 1] for i in range(len(bzq_qc)): ibzq_q[i] = nq - ibzq_q_tmp[i] - 1 self.q_weights = np.array(weight_tmp[::-1]) / len(bzq_qc) return ibzq_qc, ibzq_q, iop_q, timerev_q, diff_qc
[docs] def find_ibzkpt(self, symrel, ibzk_kc, bzk_c): """Find index in IBZ and related symmetry operations.""" find = False ibzkpt = 0 iop = 0 timerev = False for sign in (1, -1): for ioptmp, op in enumerate(symrel): for i, ibzk in enumerate(ibzk_kc): diff_c = bzk_c - sign * np.dot(op, ibzk) if (np.abs(diff_c - diff_c.round()) < 1e-8).all(): ibzkpt = i iop = ioptmp find = True if sign == -1: timerev = True break if find: break if find: break if not find: raise ValueError('Cant find corresponding IBZ kpoint!') return ibzkpt, iop, timerev, diff_c.round()
[docs] def where_is_q(self, q_c, bzq_qc): """Find the index of q points in BZ.""" d_qc = q_c - bzq_qc d_q = abs(d_qc - d_qc.round()).sum(1) q = d_q.argmin() if d_q[q] > 1e-8: raise KPointError('Could not find q!') return q
[docs] def get_count(self, rank=None): """Return the number of ks-pairs which belong to a given rank.""" if rank is None: rank = self.comm.rank assert rank in range(self.comm.size) mynk0 = self.nibzkpts // self.comm.size mynk = mynk0 if rank >= self.rank0: mynk += 1 return mynk
[docs] def get_offset(self, rank=None): """Return the offset of the first ks-pair on a given rank.""" if rank is None: rank = self.comm.rank assert rank in range(self.comm.size) mynk0 = self.nibzkpts // self.comm.size k0 = rank * mynk0 if rank >= self.rank0: k0 += rank - self.rank0 return k0
[docs] def get_rank_and_index(self, k): """Find rank and local index of k-point/spin combination.""" rank, q = self.who_has(k) return rank, q
[docs] def get_indices(self, rank=None): """Return the global ks-pair indices which belong to a given rank.""" k1 = self.get_offset(rank) k2 = k1 + self.get_count(rank) return np.arange(k1, k2)
[docs] def who_has(self, k): """Convert global index to rank information and local index.""" mynk0 = self.nibzkpts // self.comm.size if k < mynk0 * self.rank0: rank, q = divmod(k, mynk0) else: rank, q = divmod(k - mynk0 * self.rank0, mynk0 + 1) rank += self.rank0 return rank, q
def write(self, writer): writer.write('ibzkpts', self.ibzk_kc) writer.write('bzkpts', self.bzk_kc) writer.write('bz2ibz', self.bz2ibz_k) writer.write('weights', self.weight_k) writer.write('rotations', self.symmetry.op_scc) writer.write('translations', self.symmetry.ft_sc) writer.write('atommap', self.symmetry.a_sa)