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https://github.com/triqs/dft_tools
synced 2024-08-30 15:53:41 +02:00
![Oleg E. Peil](/assets/img/avatar_default.png)
The mapping for NORMION = True has been implemented. Also, the orthogonalization loop has been fixed. First of all, orthogonalization should be done separately for each block map 'bl_map'. Second, one has to take into account that the orbital dimensions of the block matrix can vary from block to block. To make that the overlap matrix is non-singular one, thus, has to pass to 'orthogonalize_projector_matrix()' only a view of a submatrix of 'pmat' corresponding to the current block. Two tests to check the simplest cases have been added.
286 lines
10 KiB
Python
286 lines
10 KiB
Python
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import numpy as np
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np.set_printoptions(suppress=True)
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################################################################################
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################################################################################
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#
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# class ProjectorGroup
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#
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################################################################################
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################################################################################
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class ProjectorGroup:
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"""
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Container of projectors defined within a certain energy window.
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The constructor selects a subset of projectors according to
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the parameters from the config-file (passed in `pars`).
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Parameters:
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- gr_pars (dict) : group parameters from the config-file
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- shells ([ProjectorShell]) : array of ProjectorShell objects
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- eigvals (numpy.array) : array of KS eigenvalues
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"""
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def __init__(self, gr_pars, shells, eigvals, ferw):
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"""
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Constructor
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"""
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self.emin, self.emax = gr_pars['ewindow']
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self.ishells = gr_pars['shells']
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self.ortho = gr_pars['normalize']
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self.normion = gr_pars['normion']
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self.shells = shells
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# Determine the minimum and maximum band numbers
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ib_win, ib_min, ib_max = self.select_bands(eigvals)
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self.ib_win = ib_win
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self.ib_min = ib_min
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self.ib_max = ib_max
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self.nb_max = ib_max - ib_min + 1
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# Select projectors within the energy window
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for ish in self.ishells:
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shell = self.shells[ish]
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shell.select_projectors(ib_win, ib_min, ib_max)
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################################################################################
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#
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# nelect_window
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#
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################################################################################
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def nelect_window(self, el_struct):
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"""
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Determines the total number of electrons within the window.
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"""
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self.nelect = 0
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nk, ns_band, _ = self.ib_win.shape
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rspin = 2.0 if ns_band == 1 else 1.0
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for isp in xrange(ns_band):
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for ik in xrange(nk):
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ib1 = self.ib_win[ik, isp, 0]
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ib2 = self.ib_win[ik, isp, 1]
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occ = el_struct.ferw[isp, ik, ib1:ib2]
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kwght = el_struct.kmesh['kweights'][ik]
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self.nelect += occ.sum() * kwght * rspin
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return self.nelect
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################################################################################
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#
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# orthogonalize
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#
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################################################################################
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def orthogonalize(self):
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"""
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Orthogonalize a group of projectors.
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There are two options for orthogonalizing projectors:
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1. one ensures orthogonality on each site (NORMION = True);
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2. one ensures orthogonality for subsets of sites (NORMION = False),
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as, e.g., in cluster calculations.
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In order to handle various cases the strategy is first to build a
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mapping that selects appropriate blocks of raw projectors, forms a
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matrix consisting of these blocks, orthogonalize the matrix, and use
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the mapping again to write the orthogonalized projectors back to the
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projector arrays. Note that the blocks can comprise several projector arrays
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contained in different projector shells.
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Mapping is defined as a list of 'block_maps' corresponding to subsets
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of projectors to be orthogonalized. Each subset corresponds to a subset of sites
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and spans all orbital indices. defined by 'bl_map' as
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bl_map = [((i1_start, i1_end), (i1_shell, i1_ion)),
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((i2_start, i2_end), (i2_shell, i2_ion)),
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...],
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where `iX_start`, `iX_end` is the range of indices of the block matrix
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(in Python convention `iX_end = iX_last + 1`, with `iX_last` being the last index
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of the range),
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`iX_shell` and `iX_ion` the shell and site indices. The length of the range
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should be consistent with 'nlm' dimensions of a corresponding shell, i.e.,
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`iX_end - iX_start = nlm[iX_shell]`.
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Consider particular cases:
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1. Orthogonality is ensured on each site (NORMION = True).
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For each site 'ion' we have the following mapping:
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block_maps = [bl_map[ion] for ion in xrange(shell.nion)
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for shell in shells]
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bl_map = [((i1_start, i1_end), (i1_shell, ion)),
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((i2_start, i2_end), (i2_shell, ion)),
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...],
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2. Orthogonality is ensured on all sites within the group (NORMION = False).
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The mapping:
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block_maps = [bl_map]
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bl_map = [((i1_start, i1_end), (i1_shell, i1_shell.ion1)),
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((i1_start, i1_end), (i1_shell, i1_shell.ion2)),
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...
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((i2_start, i2_end), (i2_shell, i2_shell.ion1)),
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((i2_start, i2_end), (i2_shell, i2_shell.ion2)),
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...],
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"""
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# Quick exit if no normalization is requested
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if not self.ortho:
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return
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# Determine the dimension of the projector matrix
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# and map the blocks to the big matrix
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if self.normion:
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block_maps = []
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ndim = 0
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for ish in self.ishells:
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_shell = self.shells[ish]
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nion, ns, nk, nlm, nb_max = _shell.proj_win.shape
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ndim = max(ndim, nlm)
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for ion in xrange(nion):
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i1_bl = 0
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i2_bl = nlm
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block = {'bmat_range': (i1_bl, i2_bl)}
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block['shell_ion'] = (ish, ion)
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bl_map = [block]
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block_maps.append(bl_map)
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else:
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block_maps = []
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bl_map = []
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i1_bl = 0
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for ish in self.ishells:
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_shell = self.shells[ish]
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nion, ns, nk, nlm, nb_max = _shell.proj_win.shape
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for ion in xrange(nion):
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i2_bl = i1_bl + nlm
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block = {'bmat_range': (i1_bl, i2_bl)}
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block['shell_ion'] = (ish, ion)
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bl_map.append(block)
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i1_bl = i2_bl
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ndim = i2_bl
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block_maps.append(bl_map)
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print block_maps
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p_mat = np.zeros((ndim, nb_max), dtype=np.complex128)
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# Note that 'ns' and 'nk' are the same for all shells
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for isp in xrange(ns):
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for ik in xrange(nk):
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nb = self.ib_win[ik, isp, 1] - self.ib_win[ik, isp, 0] + 1
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# Combine all projectors of the group to one block projector
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for bl_map in block_maps:
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p_mat[:, :] = 0.0j # !!! Clean-up from the last k-point and block!
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for ibl, block in enumerate(bl_map):
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i1, i2 = block['bmat_range']
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ish, ion = block['shell_ion']
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shell = self.shells[ish]
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p_mat[i1:i2, :nb] = shell.proj_win[ion, isp, ik, :nlm, :nb]
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# Now orthogonalize the obtained block projector
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ibl_max = i2
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p_orth, overl, eig = self.orthogonalize_projector_matrix(p_mat[:ibl_max, :nb])
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# Distribute projectors back using the same mapping
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for ibl, block in enumerate(bl_map):
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i1, i2 = block['bmat_range']
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ish, ion = block['shell_ion']
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shell = self.shells[ish]
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shell.proj_win[ion, isp, ik, :nlm, :nb] = p_orth[i1:i2, :nb]
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################################################################################
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#
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# orthogonalize_projector_matrix()
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#
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################################################################################
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def orthogonalize_projector_matrix(self, p_matrix):
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"""
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Orthogonalizes a projector defined by a rectangular matrix `p_matrix`.
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Parameters
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----------
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p_matrix (numpy.array[complex]) : matrix `Nm x Nb`, where `Nm` is
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the number of orbitals, `Nb` number of bands
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Returns
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-------
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Orthogonalized projector matrix, initial overlap matrix and its eigenvalues.
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"""
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# Overlap matrix O_{m m'} = \sum_{v} P_{m v} P^{*}_{v m'}
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overlap = np.dot(p_matrix, p_matrix.conj().T)
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# Calculate [O^{-1/2}]_{m m'}
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eig, eigv = np.linalg.eigh(overlap)
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assert np.all(eig > 0.0), ("Negative eigenvalues of the overlap matrix:"
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"projectors are ill-defined")
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sqrt_eig = np.diag(1.0 / np.sqrt(eig))
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shalf = np.dot(eigv, np.dot(sqrt_eig, eigv.conj().T))
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# Apply \tilde{P}_{m v} = \sum_{m'} [O^{-1/2}]_{m m'} P_{m' v}
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p_ortho = np.dot(shalf, p_matrix)
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return (p_ortho, overlap, eig)
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################################################################################
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#
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# select_bands()
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#
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################################################################################
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def select_bands(self, eigvals):
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"""
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Select a subset of bands lying within a given energy window.
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The band energies are assumed to be sorted in an ascending order.
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Parameters
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----------
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eigvals (numpy.array) : all eigenvalues
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emin, emax (float) : energy window
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Returns
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-------
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ib_win, nb_min, nb_max :
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"""
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# Sanity check
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if self.emin > eigvals.max() or self.emax < eigvals.min():
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raise Exception("Energy window does not overlap with the band structure")
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nk, nband, ns_band = eigvals.shape
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ib_win = np.zeros((nk, ns_band, 2), dtype=np.int32)
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ib_min = 10000000
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ib_max = 0
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for isp in xrange(ns_band):
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for ik in xrange(nk):
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for ib in xrange(nband):
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en = eigvals[ik, ib, isp]
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if en >= self.emin:
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break
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ib1 = ib
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for ib in xrange(ib1, nband):
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en = eigvals[ik, ib, isp]
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if en > self.emax:
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break
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else:
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# If we reached the last band add 1 to get the correct bound
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ib += 1
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ib2 = ib - 1
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assert ib1 <= ib2, "No bands inside the window for ik = %s"%(ik)
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ib_win[ik, isp, 0] = ib1
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ib_win[ik, isp, 1] = ib2
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ib_min = min(ib_min, ib1)
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ib_max = max(ib_max, ib2)
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return ib_win, ib_min, ib_max
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