Progress on lattices2d.py; dudom
Former-commit-id: 0b9f718ce5cfff12f1d044dbf995f51092daf76b
This commit is contained in:
Marek Nečada
parent
97648ce214
commit
f925f2163d
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@ -1,6 +1,9 @@
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import numpy as np
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import warnings
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from enum import Enum
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nx = None
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class LatticeType(Enum):
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"""
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All the five Bravais lattices in 2D
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@ -19,16 +22,19 @@ class LatticeType(Enum):
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RIGHT_ISOSCELE_TRIANGULAR=SQUARE
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HEXAGONAL=EQUILATERAL_TRIANGULAR
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def reduceBasisSingle(b1, b2):
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"""
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Lagrange-Gauss reduction of a 2D basis.
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cf. https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch17.pdf
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TODO doc
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inputs and outputs are (2,)-shaped numpy arrays
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The output shall satisfy |b1| <= |b2| <= |b2 - b1|
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TODO doc
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TODO perhaps have the (on-demand?) guarantee of obtuse angle between b1, b2?
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TODO possibility of returning the (in-order, no-obtuse angles) b as well?
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"""
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b1 = np.array(b1)
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b2 = np.array(b2)
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if b1.shape != (2,) or b2.shape != (2,):
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raise ValueError('Shape of b1 and b2 must be (2,)')
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B1 = np.sum(b1 * b1, axis=-1, keepdims=True)
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@ -43,7 +49,29 @@ def reduceBasisSingle(b1, b2):
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mu = np.sum(b1 * b2, axis=-1, keepdims=True) / B1
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b2 = b2 - np.rint(mu) * b1
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B2 = np.sum(b2*b2, axis=-1, keepdims=True)
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return (b1,b2)
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return(b1,b2)
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def orderedReducedBasis(b1, b2):
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''' blah blab blah
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|b1| is still the shortest possible basis vector,
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but if there would be obtuse angle between b1 and b2, b2 - b1 is returned
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in place of the original b2. In other words, b1, b2 and b2-b1 are
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'''
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b1, b2 = reduceBasisSingle(b1,b2)
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if b3s - b2s - b1s > eps: # obtuse angle between b1 and b2
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pass
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pass
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#-------- zde jsem skončil ------------
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def is_obtuse(b1, b2, tolerance=1e-13):
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b1s = np.sum(b1 ** 2)
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b2s = np.sum(b2 ** 2)
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b3 = b2 - b1
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b3s = np.sum(b3 ** 2)
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eps = tolerance * (b2s + b1s)
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return (b3s - b2s - b1s > eps)
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def classifyLatticeSingle(b1, b2, tolerance=1e-13):
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"""
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@ -57,15 +85,17 @@ def classifyLatticeSingle(b1, b2, tolerance=1e-13):
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b3 = b2 - b1
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b3s = np.sum(b3 ** 2)
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eps = tolerance * (b2s + b1s)
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# avoid obtuse angle between b1 and b2
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if b3s - b2s - b1s < eps:
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# Avoid obtuse angle between b1 and b2. TODO This should be yet thoroughly tested.
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# TODO use is_obtuse here?
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if b3s - b2s - b1s > eps:
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b3 = b2
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b2 = b2 + b1
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# N. B. now the assumption |b3| >= |b2| is no longer valid
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#b3 = b2 - b1
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b2s = np.sum(b2 ** 2)
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b3 = b2 - b1
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b3s = np.sum(b3 ** 2)
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# This will, however, probably not happen due to the basis reduction
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print (sys.stderr, "it happened, obtuse angle!")
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if abs(b2s - b1s) < eps: # isoscele
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warnings.warn("obtuse angle between reduced basis vectors, the lattice type identification might is not well tested.")
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if abs(b2s - b1s) < eps or abs(b2s - b3s) < eps: # isoscele
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if abs(b3s - b1s) < eps:
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return LatticeType.EQUILATERAL_TRIANGULAR
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elif abs(b3s - 2 * b1s) < eps:
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@ -73,7 +103,7 @@ def classifyLatticeSingle(b1, b2, tolerance=1e-13):
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else:
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return LatticeType.RHOMBIC
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elif abs(b3s - b2s - b1s) < eps:
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return LatticeType.SQUARE
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return LatticeType.RECTANGULAR
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else:
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return LatticeType.OBLIQUE
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@ -88,6 +118,41 @@ def range2D(maxN, mini=1, minj=0, minN = 0):
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for i in range(mini, maxn + 1):
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yield (i, maxn - i)
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def generateLattice(b1, b2, maxlayer=5, include_origin=False, order='leaves'):
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b1, b2 = reduceBasisSingle(b1, b2)
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latticeType = classifyLatticeSingle(b1, b2)
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if latticeType is LatticeType.RECTANGULAR or latticeType is LatticeType.SQUARE:
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bvs = (b1, b2, -b1, -b2)
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else:
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# Avoid obtuse angle between b1 and b2. TODO This should be yet thoroughly tested.
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if is_obtuse(b1,b2):
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b3 = b2
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b2 = b2 + b1
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# N. B. now the assumption |b3| >= |b2| is no longer valid
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warnings.warn("obtuse angle between reduced basis vectors, the lattice generation might is not well tested.")
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else:
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b3 = b2 - b1
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bvs = (b1, b2, b3, -b1, -b2, -b3)
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cc = len(bvs) # "corner count"
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if order == 'leaves':
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indices = np.array(list(range2D(maxlayer)))
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ia = indices[:,0]
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ib = indices[:,1]
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cc = len(bvs) # 4 for square/rec,
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leaves = list()
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if include_origin: leaves.append(np.array([[0,0]]))
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for c in range(cc):
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ba = bvs[c]
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bb = bvs[(c+1)%cc]
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leaves.append(ia[:,nx]*ba + ib[:,nx]*bb)
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return np.concatenate(leaves)
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else:
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raise ValueError('Lattice point order not implemented: ', order)
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def cellCornersWS(b1, b2,):
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"""
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Given basis vectors, returns the corners of the Wigner-Seitz unit cell
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@ -115,38 +180,32 @@ def cellCornersWS(b1, b2,):
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else:
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b3 = b2 - b1
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bvs = (b1, b2, b3, -b1, -b2, -b3)
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return np.array([solveWS(bvs[i], bvs[(i+1)%6]] for i in range(6)])
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return np.array([solveWS(bvs[i], bvs[(i+1)%6]) for i in range(6)])
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def cutWS(points, b1, b2, scale=1.):
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"""
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From given points, return only those that are inside (or on the edge of)
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the Wigner-Seitz cell of a (scale*b1, scale*b2)-based lattice.
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"""
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# TODO check input dimensions?
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b1, b2 = reduceBasisSingle(b1, b2)
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b3 = b2 - b1
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bvs = (b1, b2, b3, -b1, -b2, -b3)
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points = np.array(points)
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for b in bvs:
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mask = (np.tensordot(points, b, axes=(-1, 0)) <= np.linalg.norm(b, ord=2) * scale/2)
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points = points[mask]
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return points
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def filledWS(b1, b2, density=10, scale=1.):
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"""
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TODO doc
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TODO more intelligent generation, anisotropy balancing etc.
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"""
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b1, b2 = reduceBasisSingle(b1, b2)
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pass
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"""
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TODO pro všechny rozptylové a modální simulace
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Implementovat podporu následujících parametrů (v závorce implicitní hodnota):
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--bz_coverage (1.):
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základní rozsah rovnoběžné části vlnového vektoru relativně k „délce“ 1. BZ.
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Ve výchozím nastavení právě 1. BZ (tj. Wignerova-Seitzova
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buňka v převráceném prostoru)
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--k_density (50.):
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základní počet bodů mezi středem a okrajem 1. BZ
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--bz_edge_width (0.):
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poloměr (relativně k vzdáleností mezi okrajem a středem 1. BZ) zhuštěného pásu kolem okraje 1. BZ
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--bz_edge_factor (8.):
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relativní hustota zhuštěného pásu (vzhledem k k_density)
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--bz_corner_width (0.):
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velikost zhuštěné oblasti kolem vrcholů 1. BZ (relativně k velikosti BZ)
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--bz_corner_factor (16.):
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relativní hustota zhuštěné „buněčky“ kolem 1. BZ (vzhledem k k_density)
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--bz_centre_width (0.):
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totéž kolem středu BZ
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--bz_centre_factor (8):
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totéž kolem středu BZ
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--bz_edge_twoside (?),
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--bz_corner_twoside (?):
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zda s pásem zasahovat přes okraj 1. BZ, nebo jen dovnitř
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(nehoří) výhledově pořešit problém „hodně anisotropních“ mřížek (tj. kompensovat
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rozdílné délky základních vektorů).
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"""
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def reciprocalBasis(a1, a2):
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pass
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