Fix module path

Former-commit-id: 6b8d455aae082bde323031b7eb57268701f18c77
This commit is contained in:
Marek Nečada 2017-07-11 23:45:11 +00:00
parent 13556b210d
commit cc4815b861
2 changed files with 8 additions and 247 deletions

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@ -1,247 +0,0 @@
import numpy as np
from enum import Enum
nx = None
class LatticeType(Enum):
"""
All the five Bravais lattices in 2D
"""
OBLIQUE=1
RECTANGULAR=2
SQUARE=4
RHOMBIC=5
EQUILATERAL_TRIANGULAR=3
RIGHT_ISOSCELES=SQUARE
PARALLELOGRAMMIC=OBLIQUE
CENTERED_RHOMBIC=RECTANGULAR
RIGHT_TRIANGULAR=RECTANGULAR
CENTERED_RECTANGULAR=RHOMBIC
ISOSCELE_TRIANGULAR=RHOMBIC
RIGHT_ISOSCELE_TRIANGULAR=SQUARE
HEXAGONAL=EQUILATERAL_TRIANGULAR
def reduceBasisSingle(b1, b2):
"""
Lagrange-Gauss reduction of a 2D basis.
cf. https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch17.pdf
inputs and outputs are (2,)-shaped numpy arrays
The output shall satisfy |b1| <= |b2| <= |b2 - b1|
TODO doc
TODO perhaps have the (on-demand?) guarantee of obtuse angle between b1, b2?
TODO possibility of returning the (in-order, no-obtuse angles) b as well?
"""
b1 = np.array(b1)
b2 = np.array(b2)
if b1.shape != (2,) or b2.shape != (2,):
raise ValueError('Shape of b1 and b2 must be (2,)')
B1 = np.sum(b1 * b1, axis=-1, keepdims=True)
mu = np.sum(b1 * b2, axis=-1, keepdims=True) / B1
b2 = b2 - np.rint(mu) * b1
B2 = np.sum(b2 * b2, axis=-1, keepdims=True)
while(np.any(B2 < B1)):
b2t = b1
b1 = b2
b2 = b2t
B1 = B2
mu = np.sum(b1 * b2, axis=-1, keepdims=True) / B1
b2 = b2 - np.rint(mu) * b1
B2 = np.sum(b2*b2, axis=-1, keepdims=True)
return(b1,b2)
def shortestBase3(b1, b2):
'''
returns the "ordered shortest triple" of base vectors (each pair from
the triple is a base) and there may not be obtuse angle between b1, b2
and between b2, b3
'''
b1, b2 = reduceBasisSingle(b1,b2)
if is_obtuse(b1, b2, tolerance=0):
b3 = b2
b2 = b2 + b1
else:
b3 = b2 - b1
return (b1, b2, b3)
def shortestBase46(b1, b2, tolerance=1e-13):
b1, b2 = reduceBasisSingle(b1,b2)
b1s = np.sum(b1 ** 2)
b2s = np.sum(b2 ** 2)
b3 = b2 - b1
b3s = np.sum(b3 ** 2)
eps = tolerance * (b2s + b1s)
if abs(b3s - b2s - b1s) < eps:
return(b1, b2, -b1, -b2)
else:
if b3s - b2s - b1s > eps: #obtuse
b3 = b2
b2 = b2 + b1
return (b1, b2, b3, -b1, -b2, -b3)
def is_obtuse(b1, b2, tolerance=1e-13):
b1s = np.sum(b1 ** 2)
b2s = np.sum(b2 ** 2)
b3 = b2 - b1
b3s = np.sum(b3 ** 2)
eps = tolerance * (b2s + b1s)
return (b3s - b2s - b1s > eps)
def classifyLatticeSingle(b1, b2, tolerance=1e-13):
"""
Given two basis vectors, returns 2D Bravais lattice type.
Tolerance is relative.
TODO doc
"""
b1, b2 = reduceBasisSingle(b1, b2)
b1s = np.sum(b1 ** 2)
b2s = np.sum(b2 ** 2)
b3 = b2 - b1
b3s = np.sum(b3 ** 2)
eps = tolerance * (b2s + b1s)
# Avoid obtuse angle between b1 and b2. TODO This should be yet thoroughly tested.
# TODO use is_obtuse here?
if b3s - b2s - b1s > eps:
b3 = b2
b2 = b2 + b1
# N. B. now the assumption |b3| >= |b2| is no longer valid
#b3 = b2 - b1
b2s = np.sum(b2 ** 2)
b3s = np.sum(b3 ** 2)
if abs(b2s - b1s) < eps or abs(b2s - b3s) < eps: # isoscele
if abs(b3s - b1s) < eps:
return LatticeType.EQUILATERAL_TRIANGULAR
elif abs(b3s - 2 * b1s) < eps:
return LatticeType.SQUARE
else:
return LatticeType.RHOMBIC
elif abs(b3s - b2s - b1s) < eps:
return LatticeType.RECTANGULAR
else:
return LatticeType.OBLIQUE
def range2D(maxN, mini=1, minj=0, minN = 0):
"""
"Triangle indices"
Generates pairs of non-negative integer indices (i, j) such that
minN i + j maxN, i mini, j minj.
TODO doc and possibly different orderings
"""
for maxn in range(min(mini, minj, minN), floor(maxN+1)): # i + j == maxn
for i in range(mini, maxn + 1):
yield (i, maxn - i)
def generateLattice(b1, b2, maxlayer=5, include_origin=False, order='leaves'):
bvs = shortestBase46(b1, b2)
cc = len(bvs) # "corner count"
if order == 'leaves':
indices = np.array(list(range2D(maxlayer)))
ia = indices[:,0]
ib = indices[:,1]
cc = len(bvs) # 4 for square/rec,
leaves = list()
if include_origin: leaves.append(np.array([[0,0]]))
for c in range(cc):
ba = bvs[c]
bb = bvs[(c+1)%cc]
leaves.append(ia[:,nx]*ba + ib[:,nx]*bb)
return np.concatenate(leaves)
else:
raise ValueError('Lattice point order not implemented: ', order)
def generateLatticeDisk(b1, b2, r, include_origin=False, order='leaves'):
b1, b2 = reduceBasisSingle(b1,b2)
blen = np.linalg.norm(b1, ord=2)
maxlayer = 2*r/blen # FIXME kanon na vrabce? Nestačí odmocnina ze 2?
points = generateLattice(b1,b2, maxlayer=maxlayer, include_origin=include_origin, order=order)
mask = (np.linalg.norm(points, axis=-1, ord=2) <= r)
return points[mask]
def cellCornersWS(b1, b2,):
"""
Given basis vectors, returns the corners of the Wigner-Seitz unit cell
(w1, w2, -w1, w2) for rectangular and square lattice or
(w1, w2, w3, -w1, -w2, -w3) otherwise
"""
def solveWS(v1, v2):
v1x = v1[0]
v1y = v1[1]
v2x = v2[0]
v2y = v2[1]
lsm = ((-v1y, v2y), (v1x, -v2x))
rs = ((v1x-v2x)/2, (v1y - v2y)/2)
t = np.linalg.solve(lsm, rs)
return np.array(v1)/2 + t[0]*np.array((v1y, -v1x))
b1, b2 = reduceBasisSingle(b1, b2)
latticeType = classifyLatticeSingle(b1, b2)
if latticeType is LatticeType.RECTANGULAR or latticeType is LatticeType.SQUARE:
return np.array( (
(+b1+b2),
(+b2-b1),
(-b1-b2),
(-b2+b1),
)) / 2
else:
bvs = shortestBase46(b1,b2,tolerance=0)
return np.array([solveWS(bvs[i], bvs[(i+1)%6]) for i in range(6)])
def cutWS(points, b1, b2, scale=1., tolerance=1e-13):
"""
From given points, return only those that are inside (or on the edge of)
the Wigner-Seitz cell of a (scale*b1, scale*b2)-based lattice.
"""
# TODO check input dimensions?
bvs = shortestBase46(b1, b2)
points = np.array(points)
for b in bvs:
mask = (np.tensordot(points, b, axes=(-1, 0)) <= (scale * (1+tolerance) / 2) *np.linalg.norm(b, ord=2)**2 )
points = points[mask]
return points
def filledWS(b1, b2, density=10, scale=1.):
"""
TODO doc
TODO more intelligent generation, anisotropy balancing etc.
"""
points = generateLattice(b1,b2,maxlayer=density*scale, include_origin=True)
points = cutWS(points/density, np.array(b1)*scale, np.array(b2)*scale)
return points
rot90_ = np.array([[0,1],[-1,0]])
def reciprocalBasis(a1, a2):
a1, a2 = reduceBasisSingle(a1,a2) # this can be replaced with the vector version of reduceBasis when it is made
prefac = 2*np.pi/np.sum(np.tensordot(a1, rot90_, axes=[-1,0]) * a2, axis=-1)
b1 = np.tensordot(rot90_, a2, axes=[-1,-1]) * prefac
b2 = np.tensordot(rot90_, a1, axes=[-1,-1]) * prefac
return (b1, b2)
# TODO fill it with "points from reciprocal space" instead
def filledWS2(b1,b2, density=10, scale=1.):
b1, b2 = reduceBasisSingle(b1,b2)
b1r, b2r = reciprocalBasis(b1,b2)
b1l = np.linalg.norm(b1, ord=2)
b2l = np.linalg.norm(b2, ord=2)
b1rl = np.linalg.norm(b1r, ord=2)
b2rl = np.linalg.norm(b2r, ord=2)
# Black magick. Think later.™ Really. FIXME
sicher_ratio = np.maximum(b1rl/b2rl, b2rl/b1rl) * np.maximum(b1l/b2l, b2l/b1l) # This really has to be adjusted
points = generateLattice(b1r,b2r,maxlayer=density*scale*sicher_ratio, include_origin=True)
points = cutWS(points*b1l/b1rl/density, b1*scale, b2*scale)
return points
"""
TODO
====
- DOC!!!!!
- (nehoří) výhledově pořešit problém hodně anisotropních mřížek (tj. kompensovat
rozdílné délky základních vektorů).
"""

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@ -151,6 +151,14 @@ def generateLattice(b1, b2, maxlayer=5, include_origin=False, order='leaves'):
return np.concatenate(leaves)
else:
raise ValueError('Lattice point order not implemented: ', order)
def generateLatticeDisk(b1, b2, r, include_origin=False, order='leaves'):
b1, b2 = reduceBasisSingle(b1,b2)
blen = np.linalg.norm(b1, ord=2)
maxlayer = 2*r/blen # FIXME kanon na vrabce? Nestačí odmocnina ze 2?
points = generateLattice(b1,b2, maxlayer=maxlayer, include_origin=include_origin, order=order)
mask = (np.linalg.norm(points, axis=-1, ord=2) <= r)
return points[mask]
def cellCornersWS(b1, b2,):
"""