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complex.py
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import math
from numbers import Complex
from .exception import CalculatorException
class Complex(Complex):
def __init__(self, real=0.0, imag=0.0):
self.real=real
self.imag=imag
def imag(self):
return self.imag
def real(self):
return self.real
def __abs__(self):
x = abs(self.real)
y = abs(self.imag)
if x == 0.0:
return y
elif y == 0.0:
return x
elif x > y:
temp = y / x
return x * math.sqrt(1.0 + (temp * temp))
else:
temp = x / y
return y * math.sqrt(1.0 + (temp * temp))
def __add__(self,b):
r= self.real+b.real
i= self.imag + b.imag
return Complex(r,i)
def __complex__(self):
return complex(self.real,self.imag)
def __eq__(self):
raise NotImplementedError
def __mul__(self,c):
r = (self.real * c.real) - (self.imag * c.imag)
i = (self.imag * c.real) + (self.real * c.imag)
return Complex(r,i)
def __neg__(self):
return Complex(-self.real, -self.imag)
def __pos__(self):
raise NotImplementedError
def __pow__(self,exp):
a = self.__log__()
a = self.mul(exp, a)
return a.__exp__()
def __radd__(self,real):
r= real+ self.real
return Complex(r,self.imag)
def __rmul__(self, real):
r = self.real * real
i = self.imag * real
return Complex(r,i)
def __rpow__(self,exp):
a = self.__log__()
a = self.rmul(exp, a)
return a.__exp__()
def __rsub__(self, real):
r= self.real-real
return Complex(r,self.imag)
def __div__(self,cmpx):
if cmpx.real == 0 and cmpx.imag == 0:
raise CalculatorException("The complex number b is 0")
c = math.pow(cmpx.real, 2)
d = math.pow(cmpx.imag, 2)
r = (self.real * cmpx.real) + (self.imag * cmpx.imag)
r /= (c + d)
i = (self.imag * cmpx.real) - (self.real * cmpx.imag)
i /= (c + d)
return Complex(r,i)
def __rdiv__(self, real):
if real == 0:
raise CalculatorException("scalar is 0")
r = self.real / real
i = self.imag / real
return Complex(r,i)
def __rtruediv__(self):
raise NotImplementedError
def __truediv__(self):
raise NotImplementedError
def conjugate(self):
return Complex(self.real, -self.imag)
def __inverse__(self):
a = self.real * self.real
b = self.imag * self.imag
if a == 0.0 and b == 0.0:
return Complex()
else:
r= self.real / (a + b)
i= self.imag / (a + b)
return Complex(r,i)
def __log__(self):
return Complex(math.log(self.abs(self)), math.atan2(self.imag, self.real))
#E^c
def __exp__(self):
exp_x = math.exp(self.real)
return Complex(exp_x * math.cos(self.imag), exp_x * math.sin(self.imag))
def __module__(self):
return math.sqrt((self.real * self.real) + (self.imag * self.imag))
def __arg__(self):
angle = math.atan2(self.imag, self.real)
print (angle)
if angle < 0.0:
angle = (2 * math.pi) + angle
return (angle * 180) / math.pi
def __log10__(self):
rpart = math.sqrt((self.real * self.real) + (self.imag * self.imag))
ipart = math.atan2(self.imag,self.real)
if ipart > math.pi:
ipart = ipart - (2.0 * math.pi)
return Complex(math.log10(rpart), (1 /math.log(10)) * ipart)
def __sqrt__(self):
r = math.sqrt((self.real * self.real) + (self.imag * self.imag))
rpart = math.sqrt(0.5 * (r + self.real))
ipart = math.sqrt(0.5 * (r - self.real))
if self.imag < 0.0:
ipart = -ipart
return Complex(rpart, ipart)
def __sin__(self):
return Complex(math.sin(self.real) * math.cosh(self.imag), math.cos(self.real) * math.sinh(self.imag))
def __cos__(self):
return Complex(math.cos(self.real) * math.cosh(self.imag), -math.sin(self.real) * math.sinh(self.imag))
def __tan__(self):
return self.div(self.__sin__(), self.__cos__())
def __asin__(self):
im = Complex(0.0, -1.0)
zp = self.mul(self, im)
zm = self.add((self.sub(Complex(1.0, 0.0), self.mul(self, self))).__sqrt__(), zp)
return self.mul(zm.__log__(), Complex(0.0, 1.0))
def __acos__(self):
im = Complex(0.0, -1.0)
zm = self.add(self.mul((self.sub(Complex(1.0, 0.0), self.mul(self, self))).__sqrt__(), im), self)
return self.mul(zm.__log__(), Complex(0.0, 1.0))
def __atan__(self):
im = Complex(0.0, -1.0);
zp= Complex(self.real, self.imag - 1.0);
zm = Complex(-self.real, -self.imag - 1.0);
aux = self.div(zp, zm).__log__()
aux2 = self.mul(im, aux)
return self.rdiv(2.0, aux2)
def __sinh__(self):
return Complex(math.sinh(self.real) * math.cos(self.imag), math.cosh(self.real) * math.sin(self.imag))
def __cosh__(self):
return Complex(math.cosh(self.real) * math.cos(self.imag), math.sinh(self.real) * math.sin(self.imag))
def __tanh__(self):
return self.div(self.__sinh__(), self.__cosh__())
def __atanh__(self):
#aux1 = self.add(1.0, self).__log__()
#aux21 = self.rsub(1.0, self)
#aux22 = aux21.__neg__()
#aux2 = self.rdiv(2.0, aux22.__log__())
#return self.sub(aux1,aux2)
raise NotImplementedError
@staticmethod
def add(a, b):
r= a.real+b.real
i= a.imag + b.imag
return Complex(r,i)
# @staticmethod
#def cbrt(self,c):
# if c.imag != 0.0:
# real = math.cbrt(self.abs(c)) * math.cos(c.__arg__() / 3.0)
# imag = math.cbrt(self.abs(c)) * math.sin(c.__arg__() / 3.0)
# return Complex(real,imag)
# else:
# return Complex(math.cbrt(c.real), 0)
@staticmethod
def radd(real, c):
r= c.real+ real
return Complex(r,c.imag)
@staticmethod
def sub(a, b):
r= a.real-b.real
i= a.imag - b.imag
return Complex(r,i)
@staticmethod
def rsub(real, c):
r= c.real-real
return Complex(r,c.imag)
@staticmethod
def mul(a, b):
r = (a.real * b.real) - (a.imag * b.imag)
i = (a.imag * b.real) + (a.real * b.imag)
return Complex(r,i)
@staticmethod
def rmul(real, c):
r = c.real * real
i = c.imag * real
return Complex(r,i)
@staticmethod
def sconjugate(c):
return Complex(c.real, -c.imag)
@staticmethod
def div(a, b):
if b.real == 0 and b.imag == 0:
raise CalculatorException("The complex number b is 0")
c = math.pow(b.real, 2)
d = math.pow(b.imag, 2)
r = (a.real * b.real) + (a.imag * b.imag)
r /= (c + d)
i = (a.imag * b.real) - (a.real * b.imag)
i /= (c + d)
return Complex(r,i)
@staticmethod
def rdiv(real, c):
if real == 0:
raise CalculatorException("scalar is 0")
r = c.real / real
i = c.imag / real
return Complex(r,i)
@staticmethod
def abs(c):
x = abs(c.real)
y = abs(c.imag)
if x == 0.0:
return y
elif y == 0.0:
return x
elif x > y:
temp = y / x
return x * math.sqrt(1.0 + (temp * temp))
else:
temp = x / y
return y * math.sqrt(1.0 + (temp * temp))
@staticmethod
def sqrt(c):
if c.real == 0.0 and c.imag == 0.0:
return Complex()
else:
x = abs(c.real)
y = abs(c.imag)
r = 0.0
w = 0.0
real = 0.0
imag = 0.0
if x >= y:
r = y / x
w = math.sqrt(x) * math.sqrt(0.5 * (1.0 + math.sqrt(1.0 + (r * r))))
else:
r = x / y
w = math.sqrt(y) * math.sqrt(0.5 * (r + math.sqrt(1.0 + (r * r))))
if c.real >= 0.0:
real = w
imag = c.imag / (2.0 * w)
else:
imag = w if c.imag >=0 else -w
real = c.imag / (2.0 * imag)
Complex(real, imag)
@staticmethod
def rpow(c, exp):
return c.__rpow__(exp)
@staticmethod
def pow(c, exp):
return c.__pow__(exp)