From b4ca0610918ce703bcc5714a7719ec13e553c6cc Mon Sep 17 00:00:00 2001
From: Anton Akhmerov <anton.akhmerov@gmail.com>
Date: Wed, 21 Dec 2016 18:05:33 +0100
Subject: [PATCH] add `subgroup` method to symmetries
---
kwant/builder.py | 27 +++++++++++++++++++++++++++
kwant/lattice.py | 32 ++++++++++++++++++++++++++++++++
kwant/tests/test_builder.py | 16 ++++++++++++++++
kwant/tests/test_lattice.py | 25 +++++++++++++++++++++++++
4 files changed, 100 insertions(+)
diff --git a/kwant/builder.py b/kwant/builder.py
index f60a7712..89e4377e 100644
--- a/kwant/builder.py
+++ b/kwant/builder.py
@@ -317,6 +317,22 @@ class Symmetry(metaclass=abc.ABCMeta):
return False
return True
+ @abc.abstractmethod
+ def subgroup(self, *generators):
+ """Return the subgroup generated by a sequence of group elements."""
+ pass
+
+ @abc.abstractmethod
+ def isstrictsupergroup(self, other):
+ """Test whether other symmetry is a strict supergroup."""
+ pass
+
+ def issubgroup(self, other):
+ """Test whether other symmetry is a subgroup."""
+ return other.isstrictsupergroup(self)
+
+ __le__ = issubgroup
+
class NoSymmetry(Symmetry):
"""A symmetry with a trivial symmetry group."""
@@ -334,6 +350,8 @@ class NoSymmetry(Symmetry):
def num_directions(self):
return 0
+ periods = ()
+
_empty_array = ta.array((), int)
def which(self, site):
@@ -350,6 +368,15 @@ class NoSymmetry(Symmetry):
def in_fd(self, site):
return True
+ def subgroup(self, *generators):
+ if any(generators):
+ raise ValueError('Generators must be empty for NoSymmetry.')
+ return NoSymmetry(generators)
+
+ def isstrictsupergroup(self, other):
+ return False
+
+
################ Hopping kinds
diff --git a/kwant/lattice.py b/kwant/lattice.py
index 5bc1e88f..5b2ac3d9 100644
--- a/kwant/lattice.py
+++ b/kwant/lattice.py
@@ -542,6 +542,38 @@ class TranslationalSymmetry(builder.Symmetry):
self.site_family_data = {}
self.is_reversed = False
+ def subgroup(self, *generators):
+ """Return the subgroup generated by a sequence of group elements.
+
+ Parameters
+ ----------
+ *generators: sequence of int
+ Each generator must have length ``self.num_directions``.
+ """
+ generators = ta.array(generators)
+ if generators.dtype != int:
+ raise ValueError('Generators must be sequences of integers.')
+ return TranslationalSymmetry(*ta.dot(generators, self.periods))
+
+ def isstrictsupergroup(self, other):
+ if isinstance(other, builder.NoSymmetry):
+ return True
+ elif not isinstance(other, TranslationalSymmetry):
+ raise ValueError("Unknown symmetry type.")
+
+ if other.periods.shape[1] != self.periods.shape[1]:
+ return False # Mismatch of spatial dimensionalities.
+
+ inv = np.linalg.pinv(self.periods)
+ factors = np.dot(other.periods, inv)
+ # Absolute tolerance is correct in the following since we want an error
+ # relative to the closest integer.
+ if not (np.allclose(factors, np.round(factors), rtol=0, atol=1e-8) and
+ np.allclose(ta.dot(factors, self.periods), other.periods)):
+ return False
+ else:
+ return True
+
def add_site_family(self, fam, other_vectors=None):
"""
Select a fundamental domain for site family and cache associated data.
diff --git a/kwant/tests/test_builder.py b/kwant/tests/test_builder.py
index 65dcf150..bfe757ed 100644
--- a/kwant/tests/test_builder.py
+++ b/kwant/tests/test_builder.py
@@ -125,6 +125,22 @@ class VerySimpleSymmetry(builder.Symmetry):
def num_directions(self):
return 1
+ def isstrictsupergroup(self, other):
+ if isinstance(other, builder.NoSymmetry):
+ return True
+ elif isinstance(other, VerySimpleSymmetry):
+ return not other.period % self.period
+ else:
+ return False
+
+ def subgroup(self, *generators):
+ generators = ta.array(generators)
+ assert generators.shape == (1, 1)
+ if generators.dtype != int:
+ raise ValueError('Generators must be sequences of integers.')
+ g = generators[0, 0]
+ return VerySimpleSymmetry(g * self.period)
+
def which(self, site):
return ta.array((site.tag[0] // self.period,), int)
diff --git a/kwant/tests/test_lattice.py b/kwant/tests/test_lattice.py
index fa4196dc..45337c10 100644
--- a/kwant/tests/test_lattice.py
+++ b/kwant/tests/test_lattice.py
@@ -229,3 +229,28 @@ def test_norbs():
assert lat != lat1
assert lat != lat2
assert lat1 != lat2
+
+
+def test_symmetry_subgroup():
+ rng = np.random.RandomState(0)
+ ## test whether actual subgroups are detected as such
+ vecs = rng.randn(3, 3)
+ sym1 = lattice.TranslationalSymmetry(*vecs)
+ assert sym1 >= sym1
+ assert sym1 >= builder.NoSymmetry()
+ assert sym1 >= lattice.TranslationalSymmetry(2 * vecs[0],
+ 3 * vecs[1] + 4 * vecs[2])
+ assert not sym1 <= lattice.TranslationalSymmetry(*(0.8 * vecs))
+
+ ## test subgroup creation
+ for dim in range(1, 4):
+ generators = rng.randint(10, size=(dim, 3))
+ assert sym1.subgroup(*generators) <= sym1
+
+ # generators are not linearly independent
+ with raises(ValueError):
+ sym1.subgroup(*rng.randint(10, size=(4, 3)))
+
+ # generators are not integer sequences
+ with raises(ValueError):
+ sym1.subgroup(*rng.rand(1, 3))
--
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