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lattices2d.py ready for (basic) use 

Former-commit-id: f1fbc9a7e44be5a3b3c5c69a6aae35562741c440
This commit is contained in:
Marek Nečada 2017-07-12 02:09:52 +03:00
parent f925f2163d
commit d2b3851da5
1 changed files with 69 additions and 41 deletions
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108
qpms/lattices2d.py
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@ -1,5 +1,4 @@
import numpy as np
import warnings
from enum import Enum
nx = None
@ -51,18 +50,34 @@ def reduceBasisSingle(b1, b2):
B2 = np.sum(b2*b2, axis=-1, keepdims=True)
return(b1,b2)
def orderedReducedBasis(b1, b2):
''' blah blab blah
|b1| is still the shortest possible basis vector,
but if there would be obtuse angle between b1 and b2, b2 - b1 is returned
in place of the original b2. In other words, b1, b2 and b2-b1 are
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)
if b3s - b2s - b1s > eps: # obtuse angle between b1 and b2
pass
pass
#-------- zde jsem skončil ------------
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):
@ -94,7 +109,6 @@ def classifyLatticeSingle(b1, b2, tolerance=1e-13):
#b3 = b2 - b1
b2s = np.sum(b2 ** 2)
b3s = np.sum(b3 ** 2)
warnings.warn("obtuse angle between reduced basis vectors, the lattice type identification might is not well tested.")
if abs(b2s - b1s) < eps or abs(b2s - b3s) < eps: # isoscele
if abs(b3s - b1s) < eps:
return LatticeType.EQUILATERAL_TRIANGULAR
@ -114,28 +128,13 @@ def range2D(maxN, mini=1, minj=0, minN = 0):
minN ≤ i + j ≤ maxN, i ≥ mini, j ≥ minj.
TODO doc and possibly different orderings
"""
for maxn in range(min(mini, minj, minN), maxN+1): # i + j == maxn
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'):
b1, b2 = reduceBasisSingle(b1, b2)
latticeType = classifyLatticeSingle(b1, b2)
if latticeType is LatticeType.RECTANGULAR or latticeType is LatticeType.SQUARE:
bvs = (b1, b2, -b1, -b2)
else:
# Avoid obtuse angle between b1 and b2. TODO This should be yet thoroughly tested.
if is_obtuse(b1,b2):
b3 = b2
b2 = b2 + b1
# N. B. now the assumption |b3| >= |b2| is no longer valid
warnings.warn("obtuse angle between reduced basis vectors, the lattice generation might is not well tested.")
else:
b3 = b2 - b1
bvs = (b1, b2, b3, -b1, -b2, -b3)
bvs = shortestBase46(b1, b2)
cc = len(bvs) # "corner count"
if order == 'leaves':
@ -169,7 +168,7 @@ def cellCornersWS(b1, b2,):
t = np.linalg.solve(lsm, rs)
return np.array(v1)/2 + t[0]*np.array((v1y, -v1x))
b1, b2 = reduceBasisSingle(b1, b2)
latticeType = classifyLaticeSingle(b1, b2)
latticeType = classifyLatticeSingle(b1, b2)
if latticeType is LatticeType.RECTANGULAR or latticeType is LatticeType.SQUARE:
return np.array( (
(+b1+b2),
@ -178,22 +177,19 @@ def cellCornersWS(b1, b2,):
(-b2+b1),
)) / 2
else:
b3 = b2 - b1
bvs = (b1, b2, b3, -b1, -b2, -b3)
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.):
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?
b1, b2 = reduceBasisSingle(b1, b2)
b3 = b2 - b1
bvs = (b1, b2, b3, -b1, -b2, -b3)
bvs = shortestBase46(b1, b2)
points = np.array(points)
for b in bvs:
mask = (np.tensordot(points, b, axes=(-1, 0)) <= np.linalg.norm(b, ord=2) * scale/2)
mask = (np.tensordot(points, b, axes=(-1, 0)) <= (scale * (1+tolerance) / 2) *np.linalg.norm(b, ord=2)**2 )
points = points[mask]
return points
@ -202,10 +198,42 @@ def filledWS(b1, b2, density=10, scale=1.):
TODO doc
TODO more intelligent generation, anisotropy balancing etc.
"""
b1, b2 = reduceBasisSingle(b1, b2)
pass
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):
pass
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).
"""