def test_Coset():
g = geo.Symmetry(nb.Matrix([[1, 0, 2, -1],
[0, -2, 0, 0],
[0, 0, 1, 1],
[0, 0, 0, 1]]))
tg = geo.Transgen(geo.Dif(nb.Matrix([[1], [0], [0], [0]])),
geo.Dif(nb.Matrix([[0], [1], [0], [0]])),
geo.Dif(nb.Matrix([[0], [0], [2], [0]])))
tg1 = geo.Transgen(geo.Dif(nb.Matrix([[1], [0], [0], [0]])),
geo.Dif(nb.Matrix([[0], [1], [0], [0]])),
geo.Dif(nb.Matrix([[0], [0], [2], [0]])))
assert tg == tg1
c = geo.Coset(g, tg)
assert c.__str__() == \
"{x+2z,-2y,z+1}\n"\
" 1 0 0 \n"\
" 0 1 0 \n"\
" 0 0 2 "
c = geo.Coset(g, geo.canonical)
assert c.__str__() == "{x+2z,-2y,z}"
g = geo.Symmetry(nb.Matrix([[ 1, 0, 0, 0.5],
[ 0, 1, 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1]]))
c = geo.Coset(g, geo.canonical)
g2 = geo.Symmetry(nb.Matrix([[ 1, 0, 0, -0.5],
[ 0, 1, 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, 0, 1]]))
p1 = geo.Pos(nb.Matrix([[0.3], [0], [0], [1]]))
p2 = geo.Pos(nb.Matrix([[0.8], [0], [0], [1]]))
assert c.coset_representant_for_pos(p1) == g
assert c.coset_representant_for_pos(p2) == g2
def test_Spacegroup():
transgen = geo.canonical
c1 = geo.Coset(geo.Symmetry(nb.Matrix.onematrix(4)), transgen)
c2 = geo.Coset(
geo.Symmetry(
nb.Matrix([[-1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0],
[0, 0, 0, 1]])), transgen)
sg = geo.Spacegroup(transgen, [c1, c2])
assert sg.__str__() == \
"Spacegroup \n"\
"---------- \n"\
" canonical \n"\
" x,y,z\n"\
" -x,-y,-z"
transgen = geo.Transgen(geo.Dif(nb.Matrix([[1], [0], [0], [0]])),
geo.Dif(nb.Matrix([[0], [1], [0], [0]])),
geo.Dif(nb.Matrix([[0], [0], [2], [0]])))
c1 = geo.Coset(geo.Symmetry(nb.Matrix.onematrix(4)), transgen)
c2 = geo.Coset(
geo.Symmetry(
nb.Matrix([[-1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0],
[0, 0, 0, 1]])), transgen)
sg = geo.Spacegroup(transgen, [c1, c2])
assert sg.__str__() == \
" Spacegroup \n"\
" ---------- \n"\
"Transgen / 1 \ / 0 \ / 0 \ \n"\
" | 0 | | 1 | | 0 | \n"\
" \ 0 / \ 0 / \ 2 / \n"\
" x,y,z\n"\
" -x,-y,-z"
sg = geo.Spacegroup(geo.canonical, [
geo.Coset(geo.Symmetry(nb.Matrix.onematrix(4)), geo.canonical),
geo.Coset(
geo.Symmetry(
nb.Matrix([[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]])), geo.canonical)
])
transformation = geo.Transformation(
nb.Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]))
sg1 = transformation**sg
sg2 = geo.Spacegroup(transformation**geo.canonical, [
geo.Coset(geo.Symmetry(nb.Matrix.onematrix(4)), geo.canonical),
geo.Coset(
geo.Symmetry(
nb.Matrix([[-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]])), geo.canonical)
])
assert sg.is_really_a_spacegroup() == True
sg_error = geo.Spacegroup(geo.canonical, [
geo.Coset(geo.Symmetry(nb.Matrix.onematrix(4)), geo.canonical),
geo.Coset(
geo.Symmetry(
nb.Matrix([[1, 0, 0, fr.Fraction(1, 4)], [0, 1, 0, 0],
[0, 0, 1, 0], [0, 0, 0, 1]])), geo.canonical)
])
assert sg_error.is_really_a_spacegroup() == False
def test_Transgen():
tg = geo.Transgen(geo.Dif(nb.Matrix([[1], [0], [0], [0]])),
geo.Dif(nb.Matrix([[0], [0], [2], [0]])),
geo.Dif(nb.Matrix([[0], [3], [0], [0]])))
assert tg.__str__() == "Transgen / 1 \ / 0 \ / 0 \ \n"\
" | 0 | | 0 | | 3 |\n"\
" \ 0 / \ 2 / \ 0 / "
def test_Atom():
atom1 = cr.Atom("Cs1", "Cs", fs("p 0 0 0"))
assert atom1.has_color == False
assert atom1.__str__() == \
"Atom Cs1 Cs Pos / 0 \ \n" \
" | 0 |\n" \
" \ 0 / "
assert (atom1 + "hallo").name == atom1.name + "hallo"
atom2 = cr.Atom("Cs2", "Cs", fs("p 0 0 0"))
assert atom2 == atom1
assert hash(atom2) == hash(atom1)
assert {atom2} == {atom1}
atom3 = cr.Atom("Cs3", "Cs", fs("p0.1 0 0"))
assert atom3 != atom1
atom4 = cr.Atom("Cs1", "Fe", fs("p 0 0 0"))
assert atom4 != atom1
atom5 = cr.Atom("Cs1", "Cs", fs("p 0.1234 0 0"))
atom6 = cr.Atom("Cs2", "Cs", fs("p 0.1234000000001 0 0"))
assert hash(atom5) == hash(atom6)
assert atom5 == atom6
atom = cr.Atom("Cl1", "Cl", fs("p 1/2 1/2 1/2"))
transformation = fs("O->(0,0,0) \n"
"then\n"
"a' = a \n"
"b' = 2b \n"
"c' = c")
atom_trans = cr.Atom("Cl1", "Cl", fs("p 1/2 1/4 1/2"))
assert (transformation ** atom).__str__() == atom_trans.__str__()
sym = fs("-x+1/2,-y+1/2, z")
atom_sym = cr.Atom("Cl1", "Cl", fs("p0 0 1/2"))
assert (sym ** atom).__str__() == atom_sym.__str__()
coset = fs("{x, -y, z+1}")
atom = cr.Atom("Cl1", "Cl", fs("p 1/2 1/4 1/2"))
atom1 = coset ** atom
atom2 = cr.Atom("Cl1", "Cl", fs("p 1/2 3/4 1/2"))
assert atom1.__str__() == atom2.__str__()
transgen = geo.Transgen(fs("d 1 0 0"),
fs("d 0 1 0"),
fs("d 0 0 2"))
atom = cr.Atom("Cl1", "Cl", fs("p 1/2 5/4 -1/2"))
atom1 = atom % transgen
atom2 = cr.Atom("Cl1", "Cl", fs("p 1/2 1/4 3/2"))
assert atom1 == atom2
d = fs("d 1/2 0 0")
atom1 = cr.Atom("Cl1", "Cl", fs("p 0 0 0"))
atom2 = cr.Atom("Cl1", "Cl", fs("p 1/2 0 0"))
atom3 = atom1 + d
assert atom2 == atom3
def test_operations():
# Here I want to test all operations between equal and different types.
# It shall be as follows:
#
# * | Symmetry Transformation Transgen Coset Pos Dif Metric Spacegroup
# ----------------------------------------------------------------------------------------------
# Symmetry | Symmetry - - - - - - -
# Transformation | - Transformation - - - - - -
# Transgen | - - - - - - - -
# Coset | - - - Coset - - - -
# Pos | - - - - - - - -
# Dif | - - - - - - - -
# Metric | - - - - - - - -
# Spacegroup | - - - - - - - -
#
#
# ** | Symmetry Transformation Transgen Coset Pos Dif Metric Spacegroup
# -----------------------------------------------------------------------------------------------
# Symmetry | - - - - Pos Dif - -
# Transformation | Symmetry - Transgen Coset Pos Dif Metric Spacegroup
# Transgen | - - - - - - - -
# Coset | - - - - Pos Dif - -
# Pos | - - - - - - - -
# Dif | - - - - - - - -
# Metric | - - - - - - - -
# Spacegroup | - - - - - - - -
#
#
# % | Symmetry Transformation Transgen Coset Pos Dif Metric Spacegroup
# ---------------------------------------------------------------------------------------------
# Symmetry | - - Symmetry - - - - -
# Transformation | - - - - - - - -
# Transgen | - - - - - - - -
# Coset | - - Coset - - - - -
# Pos | - - Pos - - - - -
# Dif | - - Dif - - - - -
# Metric | - - - - - - - -
# Spacegroup | - - Spacegroup - - - - -
# Coset needs some pow()-declarations, so first I test everything else:
symmetry = geo.Symmetry(nb.Matrix([[-1, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
transformation = geo.Transformation(nb.Matrix([[0, 1, 0, 0],
[1, 0, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 1]]))
transgen = geo.canonical
pos = geo.Pos(nb.Matrix([[1], [2], [3], [1]]))
dif = geo.Dif(nb.Matrix([[4], [5], [6], [0]]))
metric = geo.Metric(nb.Matrix([[4, 0, 0, 0],
[0, 9, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
spacegroup = geo.Spacegroup(geo.canonical,
[geo.Coset(geo.Symmetry(nb.Matrix.onematrix(4)), geo.canonical),
geo.Coset(geo.Symmetry(nb.Matrix([[-1, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, -1, 0],
[0, 0, 0, 1]])), geo.canonical)])
# * :
#====
# symmetry * symmetry:
assert isinstance(symmetry * symmetry, geo.Symmetry)
# transformation * transformation
assert isinstance(transformation * transformation, geo.Transformation)
# **:
#====
# symmetry ** pos:
assert isinstance(symmetry ** pos, geo.Pos)
# symmetry ** dif:
assert isinstance(symmetry ** dif, geo.Dif)
# transformation ** symmetry:
assert isinstance(transformation ** symmetry, geo.Symmetry)
# transformation ** transgen:
assert isinstance(transformation ** transgen, geo.Transgen)
# transformation ** pos:
assert isinstance(transformation ** pos, geo.Pos)
# transformation ** dif:
assert isinstance(transformation ** dif, geo.Dif)
# transformation ** metric:
assert isinstance(transformation ** metric, geo.Metric)
# transformation ** spacegroup:
assert isinstance(transformation ** spacegroup, geo.Spacegroup)
# %:
#===
# symmetry % transgen:
assert isinstance(symmetry % transgen, geo.Symmetry)
# pos % transgen:
assert isinstance(pos % transgen, geo.Pos)
transgen1 = geo.Transgen(geo.Dif(nb.Matrix([[1], [0], [0], [0]])),
geo.Dif(nb.Matrix([[0], [1], [0], [0]])),
geo.Dif(nb.Matrix([[0], [0], [2], [0]])))
pos1 = geo.Pos(nb.Matrix([[0], [0], [fr.Fraction(3, 2)], [1]]))
pos1_ = geo.Pos(nb.Matrix([[0], [0], [fr.Fraction(3, 2)], [1]]))
assert pos1 % transgen1 == pos1_
transgen1 = geo.Transgen(geo.Dif(nb.Matrix([[0], [0], [2], [0]])),
geo.Dif(nb.Matrix([[0], [1], [0], [0]])),
geo.Dif(nb.Matrix([[1], [0], [0], [0]])))
pos1 = geo.Pos(nb.Matrix([[0], [0], [fr.Fraction(3, 2)], [1]]))
pos1_ = geo.Pos(nb.Matrix([[0], [0], [fr.Fraction(3, 2)], [1]]))
assert pos1 % transgen1 == pos1_
# dif % transgen:
assert isinstance(dif % transgen, geo.Dif)
transgen1 = geo.Transgen(geo.Dif(nb.Matrix([[0], [0], [2], [0]])),
geo.Dif(nb.Matrix([[0], [1], [0], [0]])),
geo.Dif(nb.Matrix([[1], [0], [0], [0]])))
dif1 = geo.Dif(nb.Matrix([[0], [0], [fr.Fraction(3, 2)], [0]]))
dif1_ = geo.Dif(nb.Matrix([[0], [0], [fr.Fraction(3, 2)], [0]]))
assert dif1 % transgen1 == dif1_
# spacegroup % transgen:
assert isinstance(spacegroup % transgen, geo.Spacegroup)
# Here comes Coset:
#==================
coset = geo.Coset(symmetry, transgen)
# coset * coset:
assert isinstance(coset * coset, geo.Coset)
# coset ** pos:
assert isinstance(coset ** pos, geo.Pos)
# coset ** dif:
assert isinstance(coset ** dif, geo.Dif)
# coset % transgen:
assert isinstance(coset % transgen, geo.Coset)
transgen1 = geo.Transgen(geo.Dif(nb.Matrix([[0], [0], [2], [0]])),
geo.Dif(nb.Matrix([[0], [1], [0], [0]])),
geo.Dif(nb.Matrix([[1], [0], [0], [0]])))
coset1 = geo.Coset(geo.Symmetry(nb.Matrix([[1, 0, 0, fr.Fraction(3, 2)],
[0, 1, 0, fr.Fraction(3, 2)],
[0, 0, 1, fr.Fraction(7, 2)],
[0, 0, 0, 1]])), transgen1)
coset1_ = geo.Coset(geo.Symmetry(nb.Matrix([[1, 0, 0, fr.Fraction(1, 2)],
[0, 1, 0, fr.Fraction(1, 2)],
[0, 0, 1, fr.Fraction(3, 2)],
[0, 0, 0, 1]])), transgen1)
assert coset1 % transgen1 == coset1_