def get_complex(delta, b, a):
str_min, str_plus = '', ''
min, plus, denum = -sqrt(-delta), sqrt(-delta), 2 * a
complex_min, complex_plus, real = None, None, None
if denum.is_integer():
if min.is_integer():
complex_min = irreductible(min, denum)
if plus.is_integer():
complex_plus = irreductible(plus, denum)
if float(b).is_integer():
real = irreductible(b, denum)
if complex_min == '':
complex_min = None
if complex_plus == '':
complex_plus = None
if real == '':
real = None
if complex_min != None or real != None:
if complex_min != None:
str_min += '{}i + '.format(complex_min)
if real != None:
str_min += real
else:
str_min += str(b / (2 * a))
elif real != None:
str_min = '{}i + {}'.format(min / (2 * a), real)
if complex_plus != None:
str_plus += '{}i + '.format(complex_plus)
if real != None:
str_plus += real
else:
str_plus += str(b / (2 * a))
elif real != None:
str_plus = '{}i + {}'.format(plus / (2 * a), real)
return (str_plus.strip(), str_min.strip())
def get_fraction(b, a, delta, sign):
if sign == '-':
num = -b - sqrt(delta)
else:
num = -b + sqrt(delta)
denum = 2 * a
return (irreductible(num, denum))
def test_sqrt(self):
test_sets = [
[0.0, 0.0],
[0.25, 0.5],
[1.0, 1.0],
[100.0, 10.0],
[315.2354235, 17.754870416311128],
[10 ** 10, 10 ** 5]
]
error_values = [-0.25, -0.001, -123.5325, -645634.43]
for arg, expected_result in test_sets:
assert compare_floats_with_epsilon(sqrt(arg), expected_result)
for error_value in error_values:
with pytest.raises(ValueError):
sqrt(error_value)
def rotMatrix2AxisAndAngle(R):
"""
stackoverflow.com/questions/12463487/obtain-rotation-axis-from-rotation-matrix-and-translation-vector-in-opencv
R : 3x3 rotation matrix
returns axis, angle
"""
angle = np.arccos(old_div((R[0, 0] + R[1, 1] + R[2, 2] - 1), 2))
axis = np.array([
# x
old_div((R[2, 1] - R[1, 2]), utils.sqrt((R[2, 1] - R[1, 2])
** 2 + (R[0, 2] - R[2, 0])**2 + (R[1, 0] - R[0, 1])**2)),
# y
old_div((R[0, 2] - R[2, 0]), utils.sqrt((R[2, 1] - R[1, 2])
** 2 + (R[0, 2] - R[2, 0])**2 + (R[1, 0] - R[0, 1])**2)),
# z
old_div((R[1, 0] - R[0, 1]), utils.sqrt((R[2, 1] - R[1, 2])**2 +
(R[0, 2] - R[2, 0])**2 + (R[1, 0] - R[0, 1])**2))])
return axis, angle
def solveDeg2(self, reduced):
a = reduced["2"]
b = reduced["1"]
c = reduced["0"]
delta = b * b - 4 * a * c
if delta < 0:
sqr = sqrt(-delta, 0.001)
print(
"Discriminand is strictly negative, the 2 complex solutions are:"
)
print("(", -b, " + ", sqr, "i ) /", 2 * a)
print("(", -b, " - ", sqr, "i ) /", 2 * a)
elif delta == 0:
print("Discriminant is equal to zero, the solution is:")
print(-b / (2 * a))
else:
sqr = sqrt(delta, 0.001)
print("Discriminant is strictly positive, the 2 solutions are:")
print((-b + sqr) / (2 * a))
print((-b - sqr) / (2 * a))
def solve_quadratic_equation(self) -> Tuple[Any, ...]:
discriminant: float = self.b * self.b - 4 * self.a * self.c
if compare_floats_with_epsilon(discriminant, 0.0):
x = -self.b / (2 * self.a)
if self.verbose:
print(f'Дискриминант равен нулю')
print(
f'Уравнение имеет 2 совпадающих вещественных решения:\nx0 = {x}\nx1 = {x}'
)
return x,
elif discriminant > 0:
discriminant_sqrt = sqrt(discriminant)
x0 = (-self.b + discriminant_sqrt) / (2 * self.a)
x1 = (-self.b - discriminant_sqrt) / (2 * self.a)
if self.verbose:
print(f'Дискриминант больше нуля')
print(
f'Уравнение имеет 2 вещественных решения:\nx0 = {x0}\nx1 = {x1}'
)
return x0, x1
else:
discriminant_sqrt = sqrt(-discriminant)
operand1 = -self.b / (2 * self.a)
if compare_floats_with_epsilon(operand1, 0.0):
operand1 = abs(operand1)
operand2 = discriminant_sqrt / (2 * self.a)
if operand2 > 0.0:
signs = ['+', '-']
else:
operand2 *= -1
signs = ['-', '+']
x0 = f'{operand1} {signs[0]} {operand2} * i'
x1 = f'{operand1} {signs[1]} {operand2} * i'
if self.verbose:
print(f'Дискриминант меньше нуля')
print(
f'Уравнение не имеет вещественных решений и имеет 2 мнимых решения:\nx0 = {x0}\nx1 = {x1}'
)
return x0, x1
def axisAndAngle2RotMatrix(axis, angle):
"""
http://stackoverflow.com/questions/6802577/python-rotation-of-3d-vector
Return the rotation matrix associated with counterclockwise rotation about
the given axis by angle radians.
"""
axis = np.asarray(axis)
angle = np.asarray(angle)
axis = old_div(axis, utils.sqrt(np.dot(axis, axis)))
a = utils.cos(old_div(angle, 2))
b, c, d = -axis * utils.sin(old_div(angle, 2))
aa, bb, cc, dd = a * a, b * b, c * c, d * d
bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)],
[2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],
[2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]])
def distancia(self, lat, long):
diffLat = lat - self._latitud
diffLong = long - self._longitud
return sqrt((diffLat * diffLat) + (diffLong * diffLong))