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https://github.com/triqs/dft_tools
synced 2024-07-25 12:17:37 +02:00
Fixed 'plotools.py' and restructured 'proj_group.py'
Added missing import of ProjectorGroup and ProjectorShell to 'plotools.py'. Moved separate routines 'orthogonalize_projector_matrix()' and 'select_bands()' into class ProjectorGroup because these routines are anyway not used elsewhere outside this class.
This commit is contained in:
Oleg E. Peil
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61395b12fa
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401d416d4d
1
c/vasp/.gitignore
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c/vasp/.gitignore
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@ -0,0 +1 @@
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*.pyc
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@ -1,6 +1,8 @@
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import itertools as it
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import numpy as np
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from proj_group import ProjectorGroup
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from proj_shell import ProjectorShell
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np.set_printoptions(suppress=True)
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@ -18,37 +20,6 @@ def issue_warning(message):
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print " !!! WARNING !!!: " + message
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print
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class Projector:
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"""
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Class describing a local-orbital projector.
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"""
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def __init__(self, matrix, ib1=1, ib2=None, nion=1):
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self.p_matrix = matrix.astype(np.complex128)
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self.norb, self.nb = matrix.shape
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self.nion = nion
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self.ib1 = ib1 - 1
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if not ib2 is None:
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self.ib2 = ib2 - 1
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else:
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self.ib2 = self.nb - 1
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def project_up(self, mat):
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return np.dot(self.p_matrix.conj().T, np.dot(mat, self.p_matrix))
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def project_down(self, mat):
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assert mat.shape == (self.nb, self.nb), " Matrix must match projector in size"
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return np.dot(self.p_matrix, np.dot(mat, self.p_matrix.conj().T))
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def orthogonalize(self):
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"""
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Orthogonalizes a projector.
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Returns an overlap matrix and its eigenvalues for initial projectors.
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"""
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self.p_matrix, overlap, over_eig = orthogonalize_projector(self.p_matrix)
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return (overlap, over_eig)
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################################################################################
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# check_data_consistency()
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################################################################################
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@ -3,95 +3,6 @@ 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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# orthogonalize_projector_matrix()
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#
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################################################################################
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def orthogonalize_projector_matrix(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(eigvals, emin, emax):
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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 emin > eigvals.max() or 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 >= 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 > 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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################################################################################
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################################################################################
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#
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@ -125,7 +36,7 @@ class ProjectorGroup:
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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 = select_bands(eigvals, self.emin, self.emax)
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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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@ -254,7 +165,7 @@ class ProjectorGroup:
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i1, i2 = blocks[ion]
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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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p_orth, overl, eig = orthogonalize_projector_matrix(p_mat)
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p_orth, overl, eig = self.orthogonalize_projector_matrix(p_mat)
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# print "ik = ", ik
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# print overl.real
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# Distribute back projectors in the same order
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@ -265,5 +176,93 @@ class ProjectorGroup:
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i1, i2 = blocks[ion]
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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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