def symmetryfromstr(string):
words = string.split(',')
assert len(words) == 3, \
"The following string looks like a Symmetry, but it has not "\
"three comma-separated terms: %s" % (string)
liste = []
for word in words:
row = nb.Row(str2linearterm(word, ['x', 'y', 'z']))
liste.append(row)
liste.append(
nb.Row([fromstr("0"),
fromstr("0"),
fromstr("0"),
fromstr("1")]))
return geo.Symmetry(nb.Matrix(liste))
def to_Metric(self):
a = self.a
b = self.b
c = self.c
alpha = self.alpha
beta = self.beta
gamma = self.gamma
aa = a * a
bb = b * b
cc = c * c
ab = a * b * nb.cos(nb.deg2rad(gamma))
ac = a * c * nb.cos(nb.deg2rad(beta))
bc = b * c * nb.cos(nb.deg2rad(alpha))
return Metric(
nb.Matrix([
nb.Row([aa, ab, ac, 0]),
nb.Row([ab, bb, bc, 0]),
nb.Row([ac, bc, cc, 0]),
nb.Row([0, 0, 0, 1])
]))
def __init__(self, value):
assert isinstance(value, nb.Matrix), \
"Must be created by an object of type Matrix."
assert value.shape() == (4, 4), \
"Must be created by a 4x4-Matrix."
assert value.liste[3] == nb.Row([0, 0, 0, 1]), \
"Must be created by a 4x4-Matrix of this shape: \n"\
" * * * * \n"\
" * * * * \n"\
" * * * * \n"\
" 0 0 0 1 \n"
self.value = value
def __str__(self):
result = 'Transformation '
m = self.value.inv()
Ox = m.liste[0].liste[3]
Oy = m.liste[1].liste[3]
Oz = m.liste[2].liste[3]
matrix = nb.Matrix([[1, 0, 0, Ox], [0, 1, 0, Oy], [0, 0, 1, Oz],
[0, 0, 0, 1]])
result = "Transformation O -> (%s, %s, %s)\n" \
" then\n" % \
(Ox.__str__(), Oy.__str__(), Oz.__str__())
matrix = nb.Matrix([
nb.Row([
m.liste[0].liste[0], m.liste[1].liste[0], m.liste[2].liste[0],
0
]),
nb.Row([
m.liste[0].liste[1], m.liste[1].liste[1], m.liste[2].liste[1],
0
]),
nb.Row([
m.liste[0].liste[2], m.liste[1].liste[2], m.liste[2].liste[2],
0
]),
nb.Row([
m.liste[3].liste[0], m.liste[3].liste[1], m.liste[3].liste[2],
1
])
])
terms = []
for i in range(3):
print(matrix.liste[i].liste[0], matrix.liste[i].liste[1],
matrix.liste[i].liste[2], matrix.liste[i].liste[3])
terms.append(
linearterm2str(matrix.liste[i].liste, ["a", "b", "c", '']))
return result + " a' = " + terms[0] + "\n" \
+ " b' = " + terms[1] + "\n" \
+ " c' = " + terms[2]
def __init__(self, b1, b2, b3):
assert isinstance(b1, Dif) \
and isinstance(b2, Dif) \
and isinstance(b3, Dif), \
"Arguments must be of type Dif."
self.liste = [b1, b2, b3]
m00 = b1.value.liste[0].liste[0]
m01 = b2.value.liste[0].liste[0]
m02 = b3.value.liste[0].liste[0]
m10 = b1.value.liste[1].liste[0]
m11 = b2.value.liste[1].liste[0]
m12 = b3.value.liste[1].liste[0]
m20 = b1.value.liste[2].liste[0]
m21 = b2.value.liste[2].liste[0]
m22 = b3.value.liste[2].liste[0]
self.transformation = Transformation(
nb.Matrix([
nb.Row([m00, m01, m02, 0]),
nb.Row([m10, m11, m12, 0]),
nb.Row([m20, m21, m22, 0]),
nb.Row([0, 0, 0, 1])
]))
self.transformationinv = self.transformation.inv()
def __init__(self, value):
assert isinstance(value, nb.Matrix), \
"Must be created by an object of type Matrix."
assert value.shape() == (4, 4), \
"Must be created by a 4x4-Matrix."
assert (value.liste[3] == nb.Row([0, 0, 0, 1])) \
and (value.liste[0].liste[3] == 0) \
and (value.liste[1].liste[3] == 0) \
and (value.liste[2].liste[3] == 0), \
"Argument must be a Matrix of this shape:\n" \
" * * * 0\n" \
" * * * 0\n" \
" * * * 0\n" \
" 0 0 0 1"
self.value = value
self.valueinv = value.inv()
self.schmidttransformation = self.calculate_schmidttransformation()
def matrixfromstr(string):
string = string.replace('|', '\\')
string = re.sub('\/ | \/|[<>]', ' ', string)
# string = string.replace('/ ', ' ')
# string = string.replace('<', ' ')
# string = string.replace('>', ' ')
# string = string.replace(' /', ' ')
string = string.replace('\n', '\\')
# string = re.sub('\\\\ +\\\\', '\\', string)
for i in range(4):
string = string.replace('\\ \\', '\\')
string = string.replace('\\ \\', '\\')
string = string.replace('\\ \\', '\\')
rowwords = string.split('\\')
rowliste = []
for rowword in rowwords:
words = rowword.split()
liste = []
for word in words:
liste.append(mixedfromstr(word))
rowliste.append(nb.Row(liste))
return nb.Matrix(rowliste)
def transformationfromstr(string):
if len(string.split("then")) > 1:
# The string respresents not an elementar transformation,
# i.e. the string represents a transformation which is
# a composition of elementar transformations.
result = geo.Transformation(nb.Matrix.onematrix(4))
for word in string.split("\nthen\n"):
result = transformationfromstr(word) * result
return result
else:
# The string represents an elementar transformation,
# i.e. either a pure translation of the origin or a
# pure change of the axes.
if ('O' in string) or ("->" in string):
# The string represents a pure translation of the origin.
words = string.split("->")
word = words[1]
word = word.replace('\n', ' ')
word = word.replace('(', ' ').replace(')', ' ').replace(',', ' ')
threenumbers = fromstr(word)
matrix = nb.Matrix([[1, 0, 0, -threenumbers.liste[0].liste[0]],
[0, 1, 0, -threenumbers.liste[0].liste[1]],
[0, 0, 1, -threenumbers.liste[0].liste[2]],
[0, 0, 0, 1]])
return geo.Transformation(matrix)
elif ('a' in string) or ('b' in string) or ('c' in string):
# The string represents a pure change of the axes
lines = string.split('\n')
assert len(lines) == 3, \
"The following string looks like a Transformation, " \
"but it has not exactly three lines: %s" % (string)
liste = []
i = 0
for line in lines:
if len(line.split(' ')) > 0:
i += 1
words = line.split(' ')
assert ( ((i == 1) and (words[0] == "a'"))
or ((i == 2) and (words[0] == "b'"))
or ((i == 3) and (words[0] == "c'")) )\
and (words[1] == '='), \
"The Transformation must have the following form: \n" \
"a' = ... \n" \
"b' = ... \n" \
"c' = ... \n" \
"in this Order!"
words = line.split('=')
row = nb.Row(str2linearterm(words[1], ['a', 'b', 'c']))
liste.append(row)
liste.append(
nb.Row(
[fromstr("0"),
fromstr("0"),
fromstr("0"),
fromstr("1")]))
m = nb.Matrix(liste)
matrix = nb.Matrix([
nb.Row([
m.liste[0].liste[0], m.liste[1].liste[0],
m.liste[2].liste[0], 0
]),
nb.Row([
m.liste[0].liste[1], m.liste[1].liste[1],
m.liste[2].liste[1], 0
]),
nb.Row([
m.liste[0].liste[2], m.liste[1].liste[2],
m.liste[2].liste[2], 0
]),
nb.Row([0, 0, 0, 1])
])
return geo.Transformation(matrix.inv())
def test_Row():
# Create
e = uc.ufloat(1.2, 0.1)
R = nb.Row([nb.Mixed(fr.Fraction(1, 2)),
nb.Mixed(e),
nb.Mixed(1),
nb.Mixed(0.5)])
assert isinstance(R.liste, list)
assert isinstance(R.liste[0], nb.Mixed)
assert isinstance(R.liste[0].value, fr.Fraction)
assert R.liste[0] == nb.Mixed(fr.Fraction(1, 2))
assert isinstance(R.liste[1], nb.Mixed)
assert isinstance(R.liste[1].value, uc.UFloat)
assert R.liste[1] == nb.Mixed(e)
assert isinstance(R.liste[2], nb.Mixed)
assert isinstance(R.liste[2].value, int)
assert R.liste[2] == nb.Mixed(1)
assert isinstance(R.liste[3], nb.Mixed)
assert isinstance(R.liste[3].value, float)
assert approx(R.liste[3].value, 0.5)
R = nb.Row([fr.Fraction(1, 2),
e,
1,
0.5])
assert isinstance(R.liste, list)
assert isinstance(R.liste[0], nb.Mixed)
assert isinstance(R.liste[0].value, fr.Fraction)
assert R.liste[0] == nb.Mixed(fr.Fraction(1, 2))
assert isinstance(R.liste[1], nb.Mixed)
assert isinstance(R.liste[1].value, uc.UFloat)
assert R.liste[1] == nb.Mixed(e)
assert isinstance(R.liste[2], nb.Mixed)
assert isinstance(R.liste[2].value, int)
assert R.liste[2] == nb.Mixed(1)
assert isinstance(R.liste[3], nb.Mixed)
assert isinstance(R.liste[3].value, float)
assert approx(R.liste[3].value, 0.5)
# len
R = nb.Row([fr.Fraction(1, 2),
uc.ufloat(1.2, 0.1),
1,
0.5])
assert len(R) == 4
assert R.__str__() == "( 1/2 1.20(10) 1 0.5 )"
# Equal
e = uc.ufloat(1.2, 0.1)
R1 = nb.Row([fr.Fraction(1, 2),
e,
1,
0.5])
R2 = nb.Row([fr.Fraction(1, 2),
e,
1,
0.5])
R2wrong = nb.Row([fr.Fraction(1, 2),
uc.ufloat(1.2, 0.1),
1,
0.5])
R3 = nb.Row([fr.Fraction(1, 2),
e,
1,
fr.Fraction(1, 2)])
R4 = nb.Row([fr.Fraction(1, 2),
e,
1])
assert R1 == R2
assert (R1 == R2wrong) == False
assert (R1 == R3) == False
assert (R1 == R4) == False
assert (R1 == 5) == False
# Hash
R1 = nb.Row([0, 0, 1.00000000])
R2 = nb.Row([0, 0, 0.99999999])
assert hash(R1) == hash(R2)
e1 = uc.ufloat(1.2, 0.1)
R1 = nb.Row([0, 0, e1])
R2 = nb.Row([0, 0, e1])
R3 = nb.Row([0, 0, uc.ufloat(1.2, 0.1)])
assert hash(R1) == hash(R2)
assert (hash(R1) == hash(R3)) == False
# canonical
assert nb.Row.canonical(5, 3) == nb.Row([0, 0, 0, 1, 0])
# block
R = nb.Row([1, 2, 3, 4])
assert R.block(1, 3) == nb.Row([2, 3])
# Addition
R1 = nb.Row([1, 2, fr.Fraction(1, 2)])
R2 = nb.Row([2, 3, 4])
assert R1 + R2 == nb.Row([3, 5, fr.Fraction(9, 2)])
# Subtraction
R1 = nb.Row([1, 2, fr.Fraction(1, 2)])
R2 = nb.Row([2, 3, 4])
assert R1 - R2 == nb.Row([-1, -1, fr.Fraction(-7, 2)])
# Multiplication
R1 = nb.Row([1, 2, fr.Fraction(1, 2)])
assert R1 * nb.Mixed(2) == nb.Row([2, 4, 1])
assert nb.Mixed(2) * R1 == nb.Row([2, 4, 1])
assert R1 * 2 == nb.Row([2, 4, 1])
assert 2 * R1 == nb.Row([2, 4, 1])
# neg
R1 = nb.Row([1, 2, 3])
assert -R1 == nb.Row([-1, -2, -3])
def test_Matrix():
# create and shape
M1 = nb.Matrix([nb.Row([1, 2, 3]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([[1, 2, 3], [4, 5, 6]])
assert M1.shape() == (2, 3)
assert M2.shape() == (2, 3)
# Equal
M1 = nb.Matrix([nb.Row([1, 2, 3]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([[1, 2, 3], [4, 5, 6]])
M3 = nb.Matrix([[1, 2, 3], [4, 5.1, 6]])
M4 = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
M5 = nb.Matrix([[1, 2], [4, 5]])
M6 = nb.Matrix([[1, 2, 3], [4, 5.0, 6]])
M7 = nb.Matrix([[1, 2, 3], [4, fr.Fraction(5, 1), 6]])
assert M1 == M2
assert (M1 == M3) == False
assert (M1 == M4) == False
assert (M1 == M5) == False
assert (M1 == M6) == False
assert M1 == M7
M1 = nb.Matrix([nb.Row([1, 2, 3.0]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([nb.Row([1, 2, 2.999999999999]), nb.Row([4, 5, 6])])
print(hash(M1))
print(hash(M2))
assert hash(M1) == hash(M2)
e = uc.ufloat(1.2, 0.1)
M1 = nb.Matrix([nb.Row([1, 2, e]), nb.Row([4, 5, 6])])
M2 = nb.Matrix([nb.Row([1, 2, e]), nb.Row([4, 5, 6])])
M3 = nb.Matrix([nb.Row([1, 2, uc.ufloat(1.2, 0.1)]), nb.Row([4, 5, 6])])
assert M1 == M2
assert (M1 == M3) == False
assert hash(M1) == hash(M2)
assert (hash(M1) == hash(M3)) == False
# print
assert nb.Matrix([[1, 2]]).__str__() == " < 1 2 > "
assert nb.Matrix([[1, 2], [3, 4]]).__str__() == " / 1 2 \ \n" \
" \ 3 4 / "
assert nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 800, 9]]).__str__() == \
" / 1 2 3 \ \n" \
"| 4 5 6 |\n" \
" \ 7 800 9 / "
# Addition
assert nb.Matrix([[1, 2], [3, 4]]) + nb.Matrix([[5, 6], [7, 8]]) == \
nb.Matrix([[6, 8], [10, 12]])
assert nb.Matrix([[1, 2], [3, 4], [5, 6]]) + \
nb.Matrix([[1, 1], [1, 1], [1, 1]]) == \
nb.Matrix([[2, 3], [4, 5], [6, 7]])
# Subtraction
assert nb.Matrix([[1, 2], [3, 4]]) - nb.Matrix([[5, 6], [7, 8]]) == \
nb.Matrix([[-4, -4], [-4, -4]])
assert nb.Matrix([[1, 2], [3, 4], [5, 6]]) - \
nb.Matrix([[1, 1], [1, 1], [1, 1]]) == \
nb.Matrix([[0, 1], [2, 3], [4, 5]])
# neg
M1 = nb.Matrix([[1, 2, 3], [4, 5, 6]])
assert -M1 == nb.Matrix([[-1, -2, -3], [-4, -5, -6]])
# Multiplication "Matrix * Matrix"
M1 = nb.Matrix([[1, 2], [3, 4]])
M2 = nb.Matrix([[5, 6], [7, 8]])
assert isinstance(M1 * M2, nb.Matrix)
assert M1 * M2 == nb.Matrix([[19, 22], [43, 50]])
M1 = nb.Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
M2 = nb.Matrix([[uc.ufloat(1.2, 0.1)], [1], [2]])
print(M2)
print(M1*M2)
assert (M1 * M2).liste[1].liste[0] == M2.liste[1].liste[0]
assert M1 * M2 == M2
# Multiplication "Scalar * Matrix"
M1 = nb.Matrix([[1, 2], [3, 4]])
assert M1 * nb.Mixed(fr.Fraction(1, 2)) == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
assert M1 * fr.Fraction(1, 2) == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
assert nb.Mixed(fr.Fraction(1, 2)) * M1 == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
assert fr.Fraction(1, 2) * M1 == \
nb.Matrix([[fr.Fraction(1, 2), 1], [fr.Fraction(3, 2), 2]])
M = M1 * nb.Mixed(uc.ufloat(1.2, 0.1))
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
M = M1 * uc.ufloat(1.2, 0.1)
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
M = nb.Mixed(uc.ufloat(1.2, 0.1)) * M1
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
M = uc.ufloat(1.2, 0.1) * M1
assert approx(M.liste[0].liste[0].value.n, 1.2)
assert approx(M.liste[0].liste[0].value.s, 0.1)
assert approx(M.liste[0].liste[1].value.n, 2.4)
assert approx(M.liste[0].liste[1].value.s, 0.2)
assert approx(M.liste[1].liste[0].value.n, 3.6)
assert approx(M.liste[1].liste[0].value.s, 0.3)
assert approx(M.liste[1].liste[1].value.n, 4.8)
assert approx(M.liste[1].liste[1].value.s, 0.4)
assert M1 * nb.Mixed(2) == nb.Matrix([[2, 4], [6, 8]])
assert M1 * 2 == nb.Matrix([[2, 4], [6, 8]])
assert nb.Mixed(2) * M1 == nb.Matrix([[2, 4], [6, 8]])
assert 2 * M1 == nb.Matrix([[2, 4], [6, 8]])
M = M1 * nb.Mixed(2.5)
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
M = M1 * 2.5
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
M = nb.Mixed(2.5) * M1
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
M = 2.5 * M1
assert approx(M.liste[0].liste[0].value, 2.5)
assert approx(M.liste[0].liste[1].value, 5.0)
assert approx(M.liste[1].liste[0].value, 7.5)
assert approx(M.liste[1].liste[1].value, 10.0)
# onematrix
assert nb.Matrix.onematrix(2) == nb.Matrix([[1, 0], [0, 1]])
assert nb.Matrix.onematrix(3) == nb.Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
# block
M = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert M.block(0, 2, 0, 2) == nb.Matrix([[1, 2], [4, 5]])
assert M.block(1, 2, 0, 3) == nb.Matrix([[4, 5, 6]])
M = nb.Matrix([[1, 2, 3, 4]])
assert M.block(0, 1, 0, 3) == nb.Matrix([[1, 2, 3]])
# swap_rows
M = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert M.swap_rows(0, 1) == nb.Matrix([[4, 5, 6], [1, 2, 3], [7, 8, 9]])
# vglue
M1 = nb.Matrix([[1, 2, 3]])
M2 = nb.Matrix([[4, 5, 6]])
assert nb.Matrix.vglue(M1, M2) == nb.Matrix([[1, 2, 3], [4, 5, 6]])
# subtract_x_times_rowj_from_rowi
M = nb.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert M.subtract_x_times_rowj_from_rowi(2, 2, 0) == \
nb.Matrix([[1, 2, 3], [4, 5, 6], [5, 4, 3]])
# inv
assert nb.Matrix([[2, 3],
[4, 5]]).inv() == \
nb.Matrix([[-fr.Fraction(5, 2), fr.Fraction(3, 2)],
[2, -1]])
assert nb.Matrix([[0, 1, 1],
[1, 0, 0],
[0, 0, -1]]).inv() == \
nb.Matrix([[0, 1, 0],
[1, 0, 1],
[0, 0, -1]])
assert nb.Matrix([[0, 0, 1, 0],
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 1]]).inv() == \
nb.Matrix([[0, 1, 0, 0],
[0, 0, 1, 0],
[1, 0, 0, 0],
[0, 0, 0, 1]])
# transpose
assert nb.Matrix([[1, 2, 3], [4, 5, 6]]).transpose() == \
nb.Matrix([[1, 4], [2, 5], [3, 6]])
# delete_ith_row_and_first_column
M = nb.Matrix([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12]])
assert M.delete_ith_row_and_first_column(1) == nb.Matrix([[2, 3, 4],
[10, 11, 12]])
# det
M = nb.Matrix([[3]])
assert M.det() == 3
M = nb.Matrix([[1, 2],
[3, 4]])
assert M.det() == -2
M = nb.Matrix([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
assert M.det() == 0
M = nb.Matrix([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 8, 11, 12],
[13, 14, 15, 17]])
assert M.det() == -16
# delete_translation
M = nb.Matrix([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[0, 0, 0, 1]])
assert M.delete_translation() == nb.Matrix([[1, 2, 3, 0],
[5, 6, 7, 0],
[9, 10, 11, 0],
[0, 0, 0, 1]])
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"))
return Dif(
nb.Matrix([[right * self.x()], [right * self.y()],
[right * self.z()], [0]]))
else:
return NotImplemented
def to_Symmetry(self):
# Returns the symmetry operation that is a translation with
# the Dif-Vector.
return Symmetry(
nb.Matrix([[1, 0, 0, self.x()], [0, 1, 0, self.y()],
[0, 0, 1, self.z()], [0, 0, 0, 1]]))
canonical_e0 = Dif(
nb.Matrix([nb.Row([1]), nb.Row([0]),
nb.Row([0]), nb.Row([0])]))
canonical_e1 = Dif(
nb.Matrix([nb.Row([0]), nb.Row([1]),
nb.Row([0]), nb.Row([0])]))
canonical_e2 = Dif(
nb.Matrix([nb.Row([0]), nb.Row([0]),
nb.Row([1]), nb.Row([0])]))
# **** class Rec ****
# An object of this class represents a vector in 3D reciprocal space.
# It is constructed via a 1x4-numbers.Matrix, wherein the last
# entry must be a 0.
