def is_parallel(self, v):
self_magnitude = self.magnitude()
v_magnitude = v.magnitude()
if float_is_zero(self_magnitude) or float_is_zero(v_magnitude):
return True
else:
return float_is_zero(
abs(abs(self.dot(v)) - abs(self_magnitude * v_magnitude)))
def clear_all_terms_above_with_non_zero_coefficient(
self, from_row, variable_no, coefficient=1):
for row in reversed(range(from_row)):
coefficient_to_clear = self.planes[row].normal_vector.coordinates[
variable_no]
if not float_is_zero(coefficient_to_clear):
self.add_multiple_times_row_to_row(
-coefficient_to_clear / coefficient, from_row, row)
def compute_rref(self):
tf = self.compute_triangular_form()
for i in reversed(range(len(tf.planes))):
plane = tf.planes[i]
for j in range(tf.dimension):
coefficient = plane.normal_vector.coordinates[j]
if float_is_zero(coefficient):
continue
if coefficient != 1:
new_normal_vector = plane.normal_vector.times_scalar(
1 / coefficient)
new_constant_term = plane.constant_term / coefficient
tf.planes[i] = Plane(new_normal_vector, new_constant_term)
tf.clear_all_terms_above_with_non_zero_coefficient(i, j)
break
return tf
def compute_triangular_form(self):
system = deepcopy(self)
num_planes = len(system.planes)
j = 0
for i in range(num_planes):
while j < system.dimension:
plane = system.planes[i]
c = plane.normal_vector.coordinates[j]
if float_is_zero(c):
r = system.get_first_row_below_with_non_zero_coefficient(
i, j)
if r is None:
j += 1
continue
else:
system.swap_rows(i, r)
plane = system.planes[i]
c = plane.normal_vector.coordinates[j]
system.clear_all_terms_below_with_non_zero_coefficient(i, j, c)
j += 1
break
return system
def is_orthogonal(self, v):
return float_is_zero(abs(self.dot(v)))
def is_zero(self):
return float_is_zero(self.magnitude())
def get_first_row_below_with_non_zero_coefficient(self, i, j):
for row in range(i + 1, len(self.planes)):
if not float_is_zero(
self.planes[row].normal_vector.coordinates[j]):
return row
return None
def first_nonzero_index(iterable):
for k, item in enumerate(iterable):
if not float_is_zero(item):
return k
raise Exception(Line.NO_NONZERO_ELTS_FOUND_MSG)