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_Pos():
x = geo.Pos(nb.Matrix([[1], [2], [3], [1]]))
assert x.__str__() == "Pos / 1 \ \n | 2 |\n \ 3 / "
assert x.x() == 1
assert x.y() == 2
assert x.z() == 3
x = geo.origin
assert x == geo.Pos(nb.Matrix([[0], [0], [0], [1]]))
def test_add_and_sub():
x1 = geo.Pos(nb.Matrix([[1], [2], [3], [1]]))
x2 = geo.Pos(nb.Matrix([[2], [3], [4], [1]]))
d1 = geo.Dif(nb.Matrix([[4], [5], [6], [0]]))
d2 = geo.Dif(nb.Matrix([[5], [5], [5], [0]]))
assert (x1 + d1) == geo.Pos(nb.Matrix([[5], [7], [9], [1]]))
assert (d1 + d2) == geo.Dif(nb.Matrix([[9], [10], [11], [0]]))
assert (d1 - d2) == geo.Dif(nb.Matrix([[-1], [0], [1], [0]]))
assert (x1 - d1) == geo.Pos(nb.Matrix([[-3], [-3], [-3], [1]]))
assert (x1 - x2) == geo.Dif(nb.Matrix([[-1], [-1], [-1], [0]]))
q1 = geo.Rec(nb.Matrix([[1, 2, 3, 0]]))
q2 = geo.Rec(nb.Matrix([[4, 5, 6, 0]]))
assert (q1 + q2) == geo.Rec(nb.Matrix([[5, 7, 9, 0]]))
assert (q1 - q2) == geo.Rec(nb.Matrix([[-3, -3, -3, 0]]))
assert -d1 == geo.Dif(nb.Matrix([[-4], [-5], [-6], [0]]))
assert -q1 == geo.Rec(nb.Matrix([[-1, -2, -3, 0]]))
def posfromstr(string):
string = re.sub('\\\\| \/|\/ |\|', ' ', string)
string = string.replace('\n', ' ')
# string = string.replace('\\', ' ')
# string = string.replace('/ ', ' ')
# string = string.replace(' /', ' ')
# string = string.replace('|', ' ')
string = removeletters(string)
words = string.split()
string = '\n'.join(words)
string += "\n 1"
return geo.Pos(matrixfromstr(string))
def test_eq():
r1 = geo.Pos(nb.Matrix([[1], [2], [3], [1]]))
r2 = geo.Pos(nb.Matrix([[1], [2], [3], [1]]))
r3 = geo.Pos(nb.Matrix([[1], [2], [4], [1]]))
d1 = geo.Dif(nb.Matrix([[4], [5], [6], [0]]))
d2 = geo.Dif(nb.Matrix([[4], [5], [6], [0]]))
d3 = geo.Dif(nb.Matrix([[3], [5], [6], [0]]))
q1 = geo.Rec(nb.Matrix([[1, 2, 3, 0]]))
q2 = geo.Rec(nb.Matrix([[1, 2, 3, 0]]))
q3 = geo.Rec(nb.Matrix([[2, 3, 4, 0]]))
assert not (r1 == d1)
assert (r1 == r1)
assert (r1 == r2)
assert not (r1 == r3)
assert (d1 == d1)
assert (d1 == d2)
assert not (d1 == d3)
assert not (r1 == q1)
assert not (d1 == q1)
assert (q1 == q1)
assert (q1 == q2)
assert not (q1 == q3)
def test_Symmetry():
g = geo.Symmetry(nb.Matrix([[1, 0, 2, -1],
[0, -2, 0, 0],
[0, 0, 1, fr.Fraction(1, 3)],
[0, 0, 0, 1]]))
assert g.__str__() == "x+2z-1,-2y,z+1/3"
assert isinstance(g.inv(), geo.Symmetry)
assert g * g.inv() == geo.Symmetry(nb.Matrix.onematrix(4))
g = geo.Symmetry(nb.Matrix([[0,-1, 0, 0],
[1, -1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
print(g)
assert g.__str__() == "-y,x-y,z"
x = uc.ufloat(0.4, 0.1)
p = geo.Pos(nb.Matrix([[x], [x], [0], [1]]))
print(p)
print((g*g*g)**p)
assert (g*g*g)**p == p
def test_centre_of_gravity():
p1 = geo.Pos(nb.Matrix([[1], [0], [0], [1]]))
p2 = geo.Pos(nb.Matrix([[3], [0], [0], [1]]))
assert geo.centre_of_gravity([p1, p2]) == geo.Pos(nb.Matrix([[2], [0], [0], [1]]))
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_
def test_Metric():
M = nb.Matrix([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
metric = geo.Metric(M)
t = metric.schmidttransformation
assert t ** geo.canonical_e0 == geo.Dif(nb.Matrix([[1], [0], [0], [0]]))
assert t ** geo.canonical_e1 == geo.Dif(nb.Matrix([[0], [1], [0], [0]]))
assert t ** geo.canonical_e2 == geo.Dif(nb.Matrix([[0], [0], [1], [0]]))
metric = geo.Cellparameters(1, 1, 1, 90, 90, 45).to_Metric()
t = metric.schmidttransformation
assert t ** geo.canonical_e0 == geo.Dif(nb.Matrix([[1], [0], [0], [0]]))
e1 = t ** geo.canonical_e1
assert abs(e1.x() - 0.70710678).value < 0.000001
assert abs(e1.y() - 0.70710678).value < 0.000001
assert abs(e1.z() - 0).value < 0.000001
e2 = t ** geo.canonical_e2
assert abs(e2.x() - 0).value < 0.000001
assert abs(e2.y() - 0).value < 0.000001
assert abs(e2.z() - 1).value < 0.000001
t = metric.schmidttransformation.inv()
M = nb.Matrix([[9, 0, 0, 0],
[0, 4, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
metric = geo.Metric(M)
assert metric.__str__() == "Metric / 9 0 0 0 \ \n" \
" | 0 4 0 0 |\n" \
" | 0 0 1 0 |\n" \
" \ 0 0 0 1 / "
o = geo.Pos(nb.Matrix([[0], [0], [0], [1]]))
p1 = geo.Pos(nb.Matrix([[1], [0], [0], [1]]))
p2 = geo.Pos(nb.Matrix([[0], [1], [0], [1]]))
q1 = geo.Rec(nb.Matrix([[1, 0, 0, 0]]))
q2 = geo.Rec(nb.Matrix([[0, 1, 0, 0]]))
q3 = geo.Rec(nb.Matrix([[1, 1, 0, 0]]))
assert metric.dot(p1 - o, p1 - o).__str__() == "9"
assert metric.dot(p1 - o, p2 - o).__str__() == "0"
assert metric.dot(q1, q1).__str__() == "1/9"
assert metric.dot(q2, q2).__str__() == "1/4"
assert metric.dot(q3, q3).__str__() == "13/36"
assert metric.length(p1 - o) == 3
assert np.abs(float(metric.angle(p1 - o, p2 - o)) - 1.5707963) < 0.0001
assert metric.dangle(p1 - o, p2 - o) == 90
assert metric.length(q1).__str__() == "1/3"
assert np.abs(float(metric.angle(q1, q2)) - 1.5707963) < 0.0001
assert metric.dangle(q1, q2) == 90
assert metric.angle(p1 - o, p1 - o).__str__() == "0.0"
assert metric.dangle(p1 - o, p1 - o).__str__() == "0"
assert metric.angle(q1, q1).__str__() == "0.0"
assert metric.dangle(q1, q1).__str__() == "0"
metric = geo.Cellparameters(4.15, 4.15, 28.64, 90, 90, 120).to_Metric()
M = nb.Matrix([[9, 0, 0, 0],
[0, 4, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
metric = geo.Metric(M)
cell = metric.to_Cellparameters()
assert cell.__str__() == \
geo.Cellparameters(3, 2, 1, 90, 90, 90).__str__()
t = geo.Transformation(nb.Matrix([[0, 1, 0, 0],
[1, 0, 0, 0],
[0, 0, 1, 0.5],
[0, 0, 0, 1]]))
assert t ** metric == geo.Metric(nb.Matrix([[4, 0, 0, 0],
[0, 9, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
metric = geo.Cellparameters(fs("8.534(5)"), fs("8.556(5)"), fs("7.015(5)"),
fs("101.53(8)"), fs("114.97(8)"),
fs("103.38(8)")).to_Metric()
assert np.abs(metric.cellvolume().value.n - 425.24239) < 0.0001
metric = geo.Cellparameters(fs("1.0(1)"), 1, 1, 90, 90, 90).to_Metric()
print(metric.cellvolume())
assert np.abs(metric.cellvolume().value.n - 1) < 0.00000001
assert np.abs(metric.cellvolume().value.s - 0.1) < 0.00000001
a = fs("1.0(1)")
metric = geo.Cellparameters(a, a, a, 90, 90, 90).to_Metric()
m00 = metric.value.liste[0].liste[0]
m11 = metric.value.liste[1].liste[1]
assert (m00 - m11).value.n == 0.0
assert (m00 - m11).value.s == 0.0
def test_fromstr():
string = "1/2"
assert isinstance(fs(string), nb.Mixed)
assert fs(string) == nb.Mixed(fr.Fraction(1, 2))
string = "1.2+/-0.1"
assert fs(string).value.n == nb.Mixed(uc.ufloat(1.2, 0.1)).value.n
assert fs(string).value.s == nb.Mixed(uc.ufloat(1.2, 0.1)).value.s
string = "1.2(1)"
assert fs(string).value.n == nb.Mixed(uc.ufloat(1.2, 0.1)).value.n
assert fs(string).value.s == nb.Mixed(uc.ufloat(1.2, 0.1)).value.s
string = "4"
assert fs(string) == nb.Mixed(fr.Fraction(4, 1))
string = "4.5"
assert fs(string) == nb.Mixed(4.5)
string = "1 2 3"
assert fromstr.typefromstr(string) == nb.Matrix
assert fs(string) == nb.Matrix([[1, 2, 3]])
string = "/ 1 2 \ \n \ 3 4 /"
assert fs(string) == \
nb.Matrix([nb.Row([nb.Mixed(1), nb.Mixed(2)]),
nb.Row([nb.Mixed(3), nb.Mixed(4)])])
string = "1 2 \n 3 4"
assert fs(string) == \
nb.Matrix([nb.Row([nb.Mixed(1), nb.Mixed(2)]),
nb.Row([nb.Mixed(3), nb.Mixed(4)])])
string = "x+y,y - x +1/3,2z"
g = fs(string)
assert g == geo.Symmetry(
fs("/ 1 1 0 0 \n"
" -1 1 0 1/3 \n"
" 0 0 2 0 \n"
" 0 0 0 1"))
string = "O->(0,0,0)\n" \
"then\n" \
"a' = a-b \n" \
"b' = b+a \n" \
"c' = 2c"
g = fs(string)
assert g == geo.Transformation(
fs(" 1 1 0 0 \n"
"-1 1 0 0 \n"
" 0 0 2 0 \n"
" 0 0 0 1").inv())
string = "O->(0,0,0) \n" \
"then\n" \
"a' = c \n" \
"b' = a \n" \
"c' = b"
g = fs(string)
assert g == geo.Transformation(
fs("0 1 0 0 \n"
"0 0 1 0 \n"
"1 0 0 0 \n"
"0 0 0 1").inv())
string = "O -> (1/2, 0, 0) \n" \
"then\n" \
"a' = a \n" \
"b' = b \n" \
"c' = c"
g = fs(string)
assert g == geo.Transformation(
fs("1 0 0 -1/2 \n"
"0 1 0 0 \n"
"0 0 1 0 \n"
"0 0 0 1"))
string1 = "O -> (1/2, 0, 0) \n" \
"then\n" \
"a' = a \n" \
"b' = b \n" \
"c' = c"
string2 = "O -> (0,0,0) \n" \
"then\n" \
"a' = b\n" \
"b' = a\n" \
"c' = c"
string = "O -> (1/2, 0, 0) \n" \
"then\n"\
"a' = b\n"\
"b' = a\n"\
"c' = c"
g1 = fs(string1)
g2 = fs(string2)
g = fs(string)
assert g == g2 * g1
string = "O -> (1/2, 0, 0) \n" \
"then\n" \
"a' = a + b\n" \
"b' = b\n" \
"c' = c"
print("--------")
g = fs(string)
print(g.value)
assert g**fs("p 1/2 0 0") == fs("p 0 0 0")
assert g**fs("p 1/2 1/3 0") == fs("p 0 1/3 0")
assert g**fs("p 0 0 0") == fs("p -1/2 1/2 0")
assert g * g.inv() == geo.Transformation(nb.Matrix.onematrix(4))
string = "p0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = "P0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = "r0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = "R0 0 0"
p = fs(string)
assert p == geo.Pos(fs("0 \n 0 \n 0 \n 1"))
string = p.__str__()
assert string == "Pos / 0 \ \n" \
" | 0 |\n" \
" \ 0 / "
p1 = fs(string)
assert p == p1
string = "R1/2 1/2 1/2"
p = fs(string)
assert p == geo.Pos(fs("1/2 \n 1/2 \n 1/2 \n 1"))
q = fs("k1 2 3")
assert q == geo.Rec(fs("1 2 3 0"))
q = fs("K 1 2 3")
assert q == geo.Rec(fs("1 2 3 0"))
q = fs("q 1/2 1/2 0")
assert q == geo.Rec(fs("1/2 1/2 0 0"))
q = fs("Q0 0 0")
assert q == geo.Rec(fs("0 0 0 0"))
q = fs("Rec < 1 2 3 > ")
assert q == geo.Rec(fs("1 2 3 0"))
def test_Metric():
M = nb.Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
metric = geo.Metric(M)
t = metric.schmidttransformation
assert t**geo.canonical_e0 == geo.Dif(nb.Matrix([[1], [0], [0], [0]]))
assert t**geo.canonical_e1 == geo.Dif(nb.Matrix([[0], [1], [0], [0]]))
assert t**geo.canonical_e2 == geo.Dif(nb.Matrix([[0], [0], [1], [0]]))
metric = geo.Cellparameters(1, 1, 1, 90, 90, 45).to_Metric()
t = metric.schmidttransformation
assert t**geo.canonical_e0 == geo.Dif(nb.Matrix([[1], [0], [0], [0]]))
e1 = t**geo.canonical_e1
assert abs(e1.x() - 0.70710678).value < 0.000001
assert abs(e1.y() - 0.70710678).value < 0.000001
assert abs(e1.z() - 0).value < 0.000001
e2 = t**geo.canonical_e2
assert abs(e2.x() - 0).value < 0.000001
assert abs(e2.y() - 0).value < 0.000001
assert abs(e2.z() - 1).value < 0.000001
t = metric.schmidttransformation.inv()
M = nb.Matrix([[9, 0, 0, 0], [0, 4, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
metric = geo.Metric(M)
assert metric.__str__() == "Metric / 9 0 0 0 \ \n" \
" | 0 4 0 0 |\n" \
" | 0 0 1 0 |\n" \
" \ 0 0 0 1 / "
o = geo.Pos(nb.Matrix([[0], [0], [0], [1]]))
p1 = geo.Pos(nb.Matrix([[1], [0], [0], [1]]))
p2 = geo.Pos(nb.Matrix([[0], [1], [0], [1]]))
q1 = geo.Rec(nb.Matrix([[1, 0, 0, 0]]))
q2 = geo.Rec(nb.Matrix([[0, 1, 0, 0]]))
q3 = geo.Rec(nb.Matrix([[1, 1, 0, 0]]))
assert metric.dot(p1 - o, p1 - o).__str__() == "9"
assert metric.dot(p1 - o, p2 - o).__str__() == "0"
assert metric.dot(q1, q1).__str__() == "1/9"
assert metric.dot(q2, q2).__str__() == "1/4"
assert metric.dot(q3, q3).__str__() == "13/36"
assert metric.length(p1 - o) == 3
assert abs(float(
(metric.angle(p1 - o, p2 - o) - nb.deg2rad(90)))) < 0.00001
assert metric.length(q1).__str__() == "1/3"
assert abs(float((metric.angle(q1, q2) - nb.deg2rad(90)))) < 0.00001
assert metric.angle(p1 - o, p1 - o).__str__() == "0.0"
assert metric.angle(q1, q1).__str__() == "0.0"
metric = geo.Cellparameters(4.15, 4.15, 28.64, 90, 90, 120).to_Metric()
M = nb.Matrix([[9, 0, 0, 0], [0, 4, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
metric = geo.Metric(M)
cell = metric.to_Cellparameters()
assert cell.__str__() == \
geo.Cellparameters(3, 2, 1, 90.0, 90.0, 90.0).__str__()
t = geo.Transformation(
nb.Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 1, 0.5], [0, 0, 0, 1]]))
assert t**metric == geo.Metric(
nb.Matrix([[4, 0, 0, 0], [0, 9, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]))
