def extract_basepoint_for_parametrization(self):
"""计算基点"""
num_variables = self.dimension
pivot_indices = self.indices_of_first_nonzero_terms_in_each_row()
basepoint_coords = [0] * num_variables
for i, p in enumerate(self.planes):
pivot_var = pivot_indices[i]
if pivot_var < 0:
break
basepoint_coords[pivot_var] = p.constant_term
return Vector(basepoint_coords)
def __init__(self, normal_vector=None, constant_term=None):
self.dimension = 3
if not normal_vector:
all_zeros = ["0"] * self.dimension
normal_vector = Vector(all_zeros)
self.normal_vector = normal_vector
if not constant_term:
constant_term = Decimal("0")
self.constant_term = Decimal(constant_term)
self.set_basepoint()
def set_basepoint(self):
try:
n = self.normal_vector
c = self.constant_term
basepoint_coords = ['0'] * self.dimension
initial_index = Plane.first_nonzero_index(n)
initial_coefficient = n[initial_index]
basepoint_coords[initial_index] = c / initial_coefficient
self.basepoint = Vector(basepoint_coords)
except Exception as e:
if str(e) == Plane.NO_NONZERO_ELTS_FOUND_MSG:
self.basepoint = None
else:
raise e
def __init__(self, dimension=None, normal_vector=None, constant_term=None):
if not dimension and not normal_vector:
raise Exception(self.EITHER_DIM_OR_NORMAL_VEC_MUST_BE_PROVIDED_MSG)
elif not normal_vector:
self.dimension = dimension
all_zeros = ["0"] * self.dimension
normal_vector = Vector(all_zeros)
else:
self.dimension = normal_vector.dimension
self.normal_vector = normal_vector
if not constant_term:
constant_term = Decimal("0")
self.constant_term = Decimal(constant_term)
self.set_basepoint()
def extract_direction_vectors_for_parametrization(self):
"""计算自由变量"""
num_variables = self.dimension
pivot_indices = self.indices_of_first_nonzero_terms_in_each_row()
# 找自由变量
free_variable_indices = set(range(num_variables)) - set(pivot_indices)
direction_vectors = []
for free_var in free_variable_indices:
vector_coords = [0] * num_variables
vector_coords[free_var] = 1
for i, p in enumerate(self.planes):
pivot_var = pivot_indices[i]
if pivot_var < 0:
break
vector_coords[pivot_var] = -p.normal_vector[free_var]
direction_vectors.append(Vector(vector_coords))
return direction_vectors
def intersection_with(self, ell):
"""找到两条直线的交点"""
try:
A, B = self.normal_vector.coordinates
C, D = ell.normal_vector.coordinates
k1 = self.constant_term
k2 = ell.constant_term
x_numerator = D * k1 - B * k2
y_numerator = -C * k1 + A * k2
one_over_denom = Decimal("1") / (A * D - B * C)
return Vector([x_numerator,
y_numerator]).times_scalar(one_over_denom)
except ZeroDivisionError:
if self == ell:
return self
else:
return None
output += ' = {}'.format(constant)
return output
@staticmethod
def first_nonzero_index(iterable):
for k, item in enumerate(iterable):
if not MyDecimal(item).is_near_zero():
return k
raise Exception(Plane.NO_NONZERO_ELTS_FOUND_MSG)
class MyDecimal(Decimal):
def is_near_zero(self, eps=1e-10):
return abs(self) < eps
if __name__ == "__main__":
plane1 = Plane(Vector(["-0.412", "3.806", "0.728"]), "-3.46")
plane2 = Plane(Vector(["1.03", "-9.515", "-1.82"]), "8.65")
print(plane1.is_parallel_to(plane2))
print(plane1 == plane2)
plane1 = Plane(Vector(["2.611", "5.528", "0.283"]), "4.6")
plane2 = Plane(Vector(["7.715", "8.306", "5.342"]), "3.76")
print(plane1.is_parallel_to(plane2))
print(plane1 == plane2)
plane1 = Plane(Vector(["-7.926", "8.625", "-7.212"]), "-7.952")
plane2 = Plane(Vector(["-2.642", "2.875", "-2.404"]), "2.443")
print(plane1.is_parallel_to(plane2))
print(plane1 == plane2)
constant = round(self.constant_term, num_decimal_places)
if constant % 1 == 0:
constant = int(constant)
output += ' = {}'.format(constant)
return output
@staticmethod
def first_nonzero_index(iterable):
for k, item in enumerate(iterable):
if not MyDecimal(item).is_near_zero():
return k
raise Exception(Line.NO_NONZERO_ELTS_FOUND_MSG)
class MyDecimal(Decimal):
def is_near_zero(self, eps=1e-10):
return abs(self) < eps
if __name__ == "__main__":
line1 = Line(Vector(["4.046", "2.836"]), "1.21")
line2 = Line(Vector(["10.115", "7.09"]), "3.025")
print(line1.intersection_with(line2))
line1 = Line(Vector(["7.204", "3.182"]), "8.68")
line2 = Line(Vector(["8.172", "4.114"]), "9.883")
print(line1.intersection_with(line2))
line1 = Line(Vector(["1.182", "5.562"]), "6.744")
line2 = Line(Vector(["1.773", "8.343"]), "9.525")
print(line1.intersection_with(line2))
temp = []
for i in range(self.dimension):
s = "x{} = ".format(i + 1)
s += str(round(self.basepoint[i], num_decimal_places))
for j, direction in enumerate(self.direction_vectors):
c = round(direction[i], num_decimal_places)
if c == 0:
continue
s += " + {}t{}".format(c, j + 1)
temp.append(s)
ret = "\n".join(temp)
return ret
if __name__ == "__main__":
p1 = Hyperplane(normal_vector=Vector(['0.786', '0.786']),
constant_term='-0.714')
p2 = Hyperplane(normal_vector=Vector(['-0.138', '-0.138']),
constant_term='0.319')
print(p1.is_parallel_to(p2))
s = LinearSystem([p1, p2])
r = s.compute_solution()
print(r)
p1 = Hyperplane(normal_vector=Vector(['8.631', '5.112', '-1.816']),
constant_term='-5.113')
p2 = Hyperplane(normal_vector=Vector(['4.315', '11.132', '-5.27']),
constant_term='-6.775')
p3 = Hyperplane(normal_vector=Vector(['-2.158', '3.01', '-1.727']),
constant_term='-0.831')
s = LinearSystem([p1, p2, p3])
@staticmethod
def first_nonzero_index(iterable):
for k, item in enumerate(iterable):
if not MyDecimal(item).is_near_zero():
return k
raise Exception(Hyperplane.NO_NONZERO_ELTS_FOUND_MSG)
class MyDecimal(Decimal):
def is_near_zero(self, eps=1e-10):
return abs(self) < eps
if __name__ == "__main__":
plane1 = Hyperplane(normal_vector=Vector(
["-0.412", "3.806", "0.728", "5.23"]),
constant_term="-3.46")
plane2 = Hyperplane(normal_vector=Vector(
["1.03", "-9.515", "-1.82", "1.2"]),
constant_term="8.65")
print(plane1.is_parallel_to(plane2))
# plane1 = Hyperplane(Vector(["2.611", "5.528", "0.283"]), "4.6")
# plane2 = Hyperplane(Vector(["7.715", "8.306", "5.342"]), "3.76")
# print(plane1.is_parallel_to(plane2))
# print(plane1 == plane2)
# plane1 = Hyperplane(Vector(["-7.926", "8.625", "-7.212"]), "-7.952")
# plane2 = Hyperplane(Vector(["-2.642", "2.875", "-2.404"]), "2.443")
# print(plane1.is_parallel_to(plane2))
# print(plane1 == plane2)