def test_Rec():
q = geo.Rec(nb.Matrix([[1, 2, 3, 0]]))
assert q.__str__() == "Rec < 1 2 3 > "
assert q.h() == 1
assert q.k() == 2
assert q.l() == 3
x = geo.Rec(nb.Matrix([[0, 0, 1.00000000, 0]]))
y = geo.Rec(nb.Matrix([[0, 0, 0.99999999, 0]]))
assert hash(x) == hash(y)
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 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 recfromstr(string):
string = string.replace('\n', ' ')
string = re.sub("\\\\| \/|\/ |[|<>]", " ", string)
# string = string.replace('\\', ' ')
# string = string.replace('/ ', ' ')
# string = string.replace(' /', ' ')
# string = string.replace('|', ' ')
# string = string.replace('<', ' ')
# string = string.replace('>', ' ')
string = removeletters(string)
words = string.split()
string = ' '.join(words)
string += " 0"
return geo.Rec(matrixfromstr(string))
def test_Skalarprodukt():
d1 = geo.Dif(nb.Matrix([[1], [2], [3], [0]]))
q1 = geo.Rec(nb.Matrix([[4, 5, 6, 0]]))
assert q1 * d1 == 32
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_Transformation():
t1 = geo.Transformation(nb.Matrix([[0, 1, 0, 0],
[1, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
assert t1.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = b\n" \
" b' = a\n" \
" c' = c"
t2 = geo.Transformation(nb.Matrix([[1, 0, 0, fr.Fraction(1, 2)],
[0, 1, 0, fr.Fraction(1, 4)],
[0, 0, 1, fr.Fraction(1, 3)],
[0, 0, 0, 1]]))
assert t2.__str__() == "Transformation O -> (-1/2, -1/4, -1/3)\n" \
" then\n" \
" a' = a\n" \
" b' = b\n" \
" c' = c"
assert isinstance(t2.inv(), geo.Transformation)
assert t2 * t2.inv() == geo.Transformation(nb.Matrix.onematrix(4))
t3 = geo.Transformation(nb.Matrix([[1.0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]))
print(t3.value)
assert t3.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = 1.0a\n" \
" b' = b\n" \
" c' = c"
q1 = geo.Rec(nb.Matrix([[1, 0, 0, 0]]))
t = geo.Transformation(nb.Matrix([[0, 1, 0, 0],
[0, 0, 1, 0],
[1, 0, 0, 0],
[0, 0, 0, 1]]))
assert isinstance(t ** q1, geo.Rec)
assert (t ** q1) == geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
q1 = geo.Rec(nb.Matrix([[1, 0, 0, 0]]))
t = geo.Transformation(nb.Matrix([[0, 1, 0, 0.3],
[0, 0, 1, 0.7],
[1, 0, 0, 100],
[0, 0, 0, 1]]))
assert isinstance(t ** q1, geo.Rec)
assert (t ** q1) == geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
q1 = geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
t = geo.Transformation(nb.Matrix([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 2, 0],
[0, 0, 0, 1]]))
assert t.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = a\n" \
" b' = b\n" \
" c' = 1/2c"
assert isinstance(t ** q1, geo.Rec)
assert (t ** q1) == \
geo.Rec(nb.Matrix([[0, 0, nb.Mixed(fr.Fraction(1, 2)), 0]]))
q1 = geo.Rec(nb.Matrix([[0, 0, 1, 0]]))
t = geo.Transformation(nb.Matrix([[1, 0, 0, 0],
[0, 0, 2, 0],
[0, -1, 0, 0],
[0, 0, 0, 1]]))
assert t.__str__() == "Transformation O -> (0, 0, 0)\n" \
" then\n" \
" a' = a\n" \
" b' = 1/2c\n" \
" c' = -b"
assert isinstance(t ** q1, geo.Rec)
print(t)
assert (t ** q1) == \
geo.Rec(nb.Matrix([[0, nb.Mixed(fr.Fraction(1, 2)), 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]]))
def test_Rec():
q = geo.Rec(nb.Matrix([[1, 2, 3, 0]]))
assert q.__str__() == "Rec < 1 2 3 > "
assert q.h() == 1
assert q.k() == 2
assert q.l() == 3
