class TestCGA3D(_TestBase):
layout, blades, stuff = clifford.conformalize(clifford.Cl(3)[0])
e1 = blades['e1']
e2 = blades['e2']
e3 = blades['e3']
@pytest.fixture(params=[
layout.scalar,
e1,
e1^e2,
e1^e2^e3,
])
def direction(self, request):
return request.param
@pytest.fixture(params=[
layout.scalar * 0,
3*e1,
])
def location(self, request):
return request.param
def test_inferred_dims(self):
""" Test that the appropriate subclass is inferred from arguments """
e1, e2, e3 = self.e1, self.e2, self.e3
C = Round(location=e1, direction=e2^e3, radius=1)
assert isinstance(C, Circle)
S = Round(location=e1, direction=e1^e2^e3, radius=1)
assert isinstance(S, Sphere)
# wrong grade
with pytest.raises(ValueError):
Sphere(location=e1, direction=e1^e2, radius=1)
with pytest.raises(ValueError):
Circle(location=e1, direction=e1^e2^e3, radius=1)
def __init__(self, dimensions) -> None:
self.dimensions = dimensions
self.layout, self.blades = cf.Cl(dimensions)
for name in self.blades:
setattr(self, name, self.blades[name])
self.unitvectors = self.layout.blades_of_grade(1)
def test_hitzer_inverse(self, p, q):
Ntests = 100
layout, blades = cf.Cl(p, q)
for i in range(Ntests):
mv = layout.randomMV()
mv_inv = mv.hitzer_inverse()
np.testing.assert_almost_equal((mv * mv_inv).value,
layout.scalar.value)
def test_hitzer_inverse(self, p, q, r, rng): # noqa: F811
Ntests = 10
layout, blades = cf.Cl(p, q, r)
for i in range(Ntests):
mv = layout.randomMV(rng=rng)
mv_inv = mv.hitzer_inverse()
np.testing.assert_allclose((mv * mv_inv).value,
layout.scalar.value,
rtol=1E-5,
atol=1E-6)
def __init__(self, dimensions) -> None:
"""
Creates Geometric Algebra Rotations class for n-dimensions
Args:
dimensions (int): number of dimensions
"""
self.dimensions = dimensions
self.layout, self.blades = clifford.Cl(dimensions)
for name in self.blades:
setattr(self, name, self.blades[name])
self.unitvectors = self.layout.blades_of_grade(1)
def test_shirokov_inverse(self, p, q, r, rng): # noqa: F811
Ntests = 5
layout, blades = cf.Cl(p, q, r)
if p + q + r > 7:
# This is perhaps a little extreme but algorithm really does struggle
# with larger algebras
atol = 0.15
else:
atol = 1E-6
for i in range(Ntests):
mv = layout.randomMV(rng=rng)
mv_inv = mv.shirokov_inverse()
np.testing.assert_allclose((mv * mv_inv).value,
layout.scalar.value,
rtol=1E-5,
atol=atol)
class TestCGA2D(_TestBase):
layout, blades, stuff = clifford.conformalize(clifford.Cl(2)[0])
e1 = blades['e1']
e2 = blades['e2']
@pytest.fixture(params=[
layout.scalar,
e1,
e1^e2,
])
def direction(self, request):
return request.param
@pytest.fixture(params=[
layout.scalar * 0,
3*e1,
])
def location(self, request):
return request.param
for k in range(1, N):
Ck = (Decimal(N) / Decimal(k)) * Uk.value[0]
adjU = +Uk
adjU.value[0] = adjU.value[0] - Ck
# adjU = (Uk - Ck)
Uk = U * adjU
if Uk.value[0] == 0:
raise ValueError('Multivector has no inverse')
return adjU / Uk.value[0]
return shirokov_inverse
rng = np.random.default_rng(1)
layout, blades = cf.Cl(8, 0, 1)
sinv = get_shirokov_inverse(layout)
sinv_dec = get_shirokov_inverse_decimal(layout)
# for i in range(10):
# avalue = rng.standard_normal(layout.gaDims)
# a = layout.MultiVector(avalue)
# ainv = sinv(a)
# print(np.linalg.norm((1 - a * ainv).value))
#
#
# rng = np.random.default_rng(1)
# for i in range(10):
# avalue = np.array([Decimal(x) for x in rng.standard_normal(layout.gaDims)], dtype=object)
# a = layout.MultiVector(avalue)
import clifford as cf layout, blades = cf.Cl(2) # creates a 2-dimensional clifford algebra e1 = blades['e1'] e2 = blades['e2'] e12 = blades['e12'] (e1^e2) - e12 abs((e1^e2) - e12) 2^e1^e2 - 7^e12 (2^e1^e2) - (7^e12)
