from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int				,  __UpperCamelCase					: int				,  __UpperCamelCase					: float = 1 / sqrt(2			)			)							->      IIRFilter:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__    							=   tau * frequency / samplerate
		SCREAMING_SNAKE_CASE__    							=   sin(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   cos(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   _sin / (2 * q_factor)

		SCREAMING_SNAKE_CASE__    							=   (1 - _cos) / 2
		SCREAMING_SNAKE_CASE__    							=   1 - _cos

		SCREAMING_SNAKE_CASE__    							=   1 + alpha
		SCREAMING_SNAKE_CASE__    							=   -2 * _cos
		SCREAMING_SNAKE_CASE__    							=   1 - alpha

		SCREAMING_SNAKE_CASE__    							=   IIRFilter(2			)
		filt.set_coefficients([aa, aa, aa]				,  [ba, ba, ba]			)
		return filt



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int				,  __UpperCamelCase					: int				,  __UpperCamelCase					: float = 1 / sqrt(2			)			)							->      IIRFilter:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__    							=   tau * frequency / samplerate
		SCREAMING_SNAKE_CASE__    							=   sin(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   cos(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   _sin / (2 * q_factor)

		SCREAMING_SNAKE_CASE__    							=   (1 + _cos) / 2
		SCREAMING_SNAKE_CASE__    							=   -1 - _cos

		SCREAMING_SNAKE_CASE__    							=   1 + alpha
		SCREAMING_SNAKE_CASE__    							=   -2 * _cos
		SCREAMING_SNAKE_CASE__    							=   1 - alpha

		SCREAMING_SNAKE_CASE__    							=   IIRFilter(2			)
		filt.set_coefficients([aa, aa, aa]				,  [ba, ba, ba]			)
		return filt



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int				,  __UpperCamelCase					: int				,  __UpperCamelCase					: float = 1 / sqrt(2			)			)							->      IIRFilter:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__    							=   tau * frequency / samplerate
		SCREAMING_SNAKE_CASE__    							=   sin(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   cos(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   _sin / (2 * q_factor)

		SCREAMING_SNAKE_CASE__    							=   _sin / 2
		SCREAMING_SNAKE_CASE__    							=   0
		SCREAMING_SNAKE_CASE__    							=   -ba

		SCREAMING_SNAKE_CASE__    							=   1 + alpha
		SCREAMING_SNAKE_CASE__    							=   -2 * _cos
		SCREAMING_SNAKE_CASE__    							=   1 - alpha

		SCREAMING_SNAKE_CASE__    							=   IIRFilter(2			)
		filt.set_coefficients([aa, aa, aa]				,  [ba, ba, ba]			)
		return filt



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int				,  __UpperCamelCase					: int				,  __UpperCamelCase					: float = 1 / sqrt(2			)			)							->      IIRFilter:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__    							=   tau * frequency / samplerate
		SCREAMING_SNAKE_CASE__    							=   sin(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   cos(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   _sin / (2 * q_factor)

		SCREAMING_SNAKE_CASE__    							=   1 - alpha
		SCREAMING_SNAKE_CASE__    							=   -2 * _cos
		SCREAMING_SNAKE_CASE__    							=   1 + alpha

		SCREAMING_SNAKE_CASE__    							=   IIRFilter(2			)
		filt.set_coefficients([ba, ba, ba]				,  [ba, ba, ba]			)
		return filt



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int				,  __UpperCamelCase					: int				,  __UpperCamelCase					: float				,  __UpperCamelCase					: float = 1 / sqrt(2			)				,  )							->      IIRFilter:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__    							=   tau * frequency / samplerate
		SCREAMING_SNAKE_CASE__    							=   sin(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   cos(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   _sin / (2 * q_factor)
		SCREAMING_SNAKE_CASE__    							=   10 ** (gain_db / 40)

		SCREAMING_SNAKE_CASE__    							=   1 + alpha * big_a
		SCREAMING_SNAKE_CASE__    							=   -2 * _cos
		SCREAMING_SNAKE_CASE__    							=   1 - alpha * big_a
		SCREAMING_SNAKE_CASE__    							=   1 + alpha / big_a
		SCREAMING_SNAKE_CASE__    							=   -2 * _cos
		SCREAMING_SNAKE_CASE__    							=   1 - alpha / big_a

		SCREAMING_SNAKE_CASE__    							=   IIRFilter(2			)
		filt.set_coefficients([aa, aa, aa]				,  [ba, ba, ba]			)
		return filt



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int				,  __UpperCamelCase					: int				,  __UpperCamelCase					: float				,  __UpperCamelCase					: float = 1 / sqrt(2			)				,  )							->      IIRFilter:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__    							=   tau * frequency / samplerate
		SCREAMING_SNAKE_CASE__    							=   sin(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   cos(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   _sin / (2 * q_factor)
		SCREAMING_SNAKE_CASE__    							=   10 ** (gain_db / 40)
		SCREAMING_SNAKE_CASE__    							=   (big_a + 1) - (big_a - 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   (big_a + 1) + (big_a - 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   (big_a - 1) - (big_a + 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   (big_a - 1) + (big_a + 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   2 * sqrt(__UpperCamelCase			) * alpha

		SCREAMING_SNAKE_CASE__    							=   big_a * (pmc + aaa)
		SCREAMING_SNAKE_CASE__    							=   2 * big_a * mpc
		SCREAMING_SNAKE_CASE__    							=   big_a * (pmc - aaa)
		SCREAMING_SNAKE_CASE__    							=   ppmc + aaa
		SCREAMING_SNAKE_CASE__    							=   -2 * pmpc
		SCREAMING_SNAKE_CASE__    							=   ppmc - aaa

		SCREAMING_SNAKE_CASE__    							=   IIRFilter(2			)
		filt.set_coefficients([aa, aa, aa]				,  [ba, ba, ba]			)
		return filt






def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int				,  __UpperCamelCase					: int				,  __UpperCamelCase					: float				,  __UpperCamelCase					: float = 1 / sqrt(2			)				,  )							->      IIRFilter:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__    							=   tau * frequency / samplerate
		SCREAMING_SNAKE_CASE__    							=   sin(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   cos(__UpperCamelCase			)
		SCREAMING_SNAKE_CASE__    							=   _sin / (2 * q_factor)
		SCREAMING_SNAKE_CASE__    							=   10 ** (gain_db / 40)
		SCREAMING_SNAKE_CASE__    							=   (big_a + 1) - (big_a - 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   (big_a + 1) + (big_a - 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   (big_a - 1) - (big_a + 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   (big_a - 1) + (big_a + 1) * _cos
		SCREAMING_SNAKE_CASE__    							=   2 * sqrt(__UpperCamelCase			) * alpha

		SCREAMING_SNAKE_CASE__    							=   big_a * (ppmc + aaa)
		SCREAMING_SNAKE_CASE__    							=   -2 * big_a * pmpc
		SCREAMING_SNAKE_CASE__    							=   big_a * (ppmc - aaa)
		SCREAMING_SNAKE_CASE__    							=   pmc + aaa
		SCREAMING_SNAKE_CASE__    							=   2 * mpc
		SCREAMING_SNAKE_CASE__    							=   pmc - aaa

		SCREAMING_SNAKE_CASE__    							=   IIRFilter(2			)
		filt.set_coefficients([aa, aa, aa]				,  [ba, ba, ba]			)
		return filt

# Logistic Regression from scratch

# In[62]:

# In[63]:

# importing all the required libraries

import numpy as np
from matplotlib import pyplot as plt
from sklearn import datasets



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: Tuple			)							->      int:







  """simple docstring"""





  return 1 / (1 + np.exp(-z			))



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[Any]				,  __UpperCamelCase					: Union[str, Any]			)							->      Optional[Any]:







  """simple docstring"""





  return (-y * np.log(__UpperCamelCase			) - (1 - y) * np.log(1 - h			)).mean()



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[Any]				,  __UpperCamelCase					: List[Any]				,  __UpperCamelCase					: Union[str, Any]			)							->      int:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__    							=   np.dot(__UpperCamelCase				,  __UpperCamelCase			)
  return np.sum(y * scores - np.log(1 + np.exp(__UpperCamelCase			)			)			)



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: Tuple				,  __UpperCamelCase					: Optional[int]				,  __UpperCamelCase					: Tuple				,  __UpperCamelCase					: Any=7_00_00			)							->      Optional[int]:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__    							=   np.zeros(x.shape[1]			)

  for iterations in range(__UpperCamelCase			):
    SCREAMING_SNAKE_CASE__    							=   np.dot(__UpperCamelCase				,  __UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   sigmoid_function(__UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   np.dot(x.T				,  h - y			) / y.size
    SCREAMING_SNAKE_CASE__    							=   theta - alpha * gradient  # updating the weights
    SCREAMING_SNAKE_CASE__    							=   np.dot(__UpperCamelCase				,  __UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   sigmoid_function(__UpperCamelCase			)
    SCREAMING_SNAKE_CASE__    							=   cost_function(__UpperCamelCase				,  __UpperCamelCase			)
    if iterations % 1_00 == 0:
      print(f"""loss: {j} \t"""			)  # printing the loss after every 100 iterations
  return theta


# In[68]:

if __name__ == "__main__":
   __lowerCamelCase    :				List[Any]							     =	datasets.load_iris()
   __lowerCamelCase    :				List[Any]							     =	iris.data[:, :2]
   __lowerCamelCase    :				Dict							     =	(iris.target != 0) * 1

   __lowerCamelCase    :				List[str]							     =	0.1
   __lowerCamelCase    :				str							     =	logistic_reg(alpha, x, y, max_iterations=7_0000)
   print('''theta: ''', theta)  # printing the theta i.e our weights vector



   def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: List[str]			)							->      Tuple:







     """simple docstring"""





     return sigmoid_function(
         np.dot(__UpperCamelCase				,  __UpperCamelCase			)			)  # predicting the value of probability from the logistic regression algorithm

   plt.figure(figsize=(10, 6))
   plt.scatter(x[y == 0][:, 0], x[y == 0][:, 1], color='''b''', label='''0''')
   plt.scatter(x[y == 1][:, 0], x[y == 1][:, 1], color='''r''', label='''1''')
   ((__lowerCamelCase)     ,		(__lowerCamelCase))    :				int							     =	(x[:, 0].min(), x[:, 0].max())
   ((__lowerCamelCase)     ,		(__lowerCamelCase))    :				List[Any]							     =	(x[:, 1].min(), x[:, 1].max())
   ((__lowerCamelCase)     ,		(__lowerCamelCase))    :				List[Any]							     =	np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
   __lowerCamelCase    :				Optional[int]							     =	np.c_[xxa.ravel(), xxa.ravel()]
   __lowerCamelCase    :				Optional[int]							     =	predict_prob(grid).reshape(xxa.shape)
   plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='''black''')

   plt.legend()






   plt.show()
