




from math import atan, cos, radians, sin, tan

from .haversine_distance import haversine_distance

_lowerCamelCase      :  Tuple      						=						6_3_7_8_1_3_7.0
_lowerCamelCase      :  Dict      						=						6_3_5_6_7_5_2.3_1_4_2_4_5
_lowerCamelCase      :  int      						=						6_3_7_8_1_3_7




def 							_UpperCAmelCase  (UpperCamelCase_ : float      ,    UpperCamelCase_ : float      ,    UpperCamelCase_ : float      ,    UpperCamelCase_ : float       ):
				'''simple docstring'''
				_lowerCAmelCase    :    Optional[Any]										=      (AXIS_A - AXIS_B) / AXIS_A
				# Parametric latitudes
				# https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
				_lowerCAmelCase    :    List[str]										=      atan((1 - flattening) * tan(radians(UpperCamelCase_       )       )       )
				_lowerCAmelCase    :    int										=      atan((1 - flattening) * tan(radians(UpperCamelCase_       )       )       )

				# Compute central angle between two points
				# using haversine theta. sigma =  haversine_distance / equatorial radius
				_lowerCAmelCase    :    str										=      haversine_distance(UpperCamelCase_      ,    UpperCamelCase_      ,    UpperCamelCase_      ,    UpperCamelCase_       ) / EQUATORIAL_RADIUS

				# Intermediate P and Q values
				_lowerCAmelCase    :    Union[str, Any]										=      (b_lata + b_lata) / 2
				_lowerCAmelCase    :    List[Any]										=      (b_lata - b_lata) / 2

				# Intermediate X value
				# X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
				_lowerCAmelCase    :    Optional[Any]										=      (sin(UpperCamelCase_       ) ** 2) * (cos(UpperCamelCase_       ) ** 2)
				_lowerCAmelCase    :    Optional[Any]										=      cos(sigma / 2       ) ** 2
				_lowerCAmelCase    :    Optional[int]										=      (sigma - sin(UpperCamelCase_       )) * (x_numerator / x_demonimator)

				# Intermediate Y value
				# Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
				_lowerCAmelCase    :    Optional[int]										=      (cos(UpperCamelCase_       ) ** 2) * (sin(UpperCamelCase_       ) ** 2)
				_lowerCAmelCase    :    Optional[int]										=      sin(sigma / 2       ) ** 2
				_lowerCAmelCase    :    Dict										=      (sigma + sin(UpperCamelCase_       )) * (y_numerator / y_denominator)

				return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (x_value + y_value)))


if __name__ == "__main__":
	import doctest

	doctest.testmod()







import pandas as pd
from matplotlib import pyplot as plt
from sklearn.linear_model import LinearRegression

# Splitting the dataset into the Training set and Test set
from sklearn.model_selection import train_test_split

# Fitting Polynomial Regression to the dataset
from sklearn.preprocessing import PolynomialFeatures

# Importing the dataset
_lowerCamelCase      :  Dict      						=						pd.read_csv(
    "https://s3.us-west-2.amazonaws.com/public.gamelab.fun/dataset/"
    "position_salaries.csv"
)
_lowerCamelCase      :  Union[str, Any]      						=						dataset.iloc[:, 1:2].values
_lowerCamelCase      :  Any      						=						dataset.iloc[:, 2].values


_lowerCamelCase						, _lowerCamelCase						, _lowerCamelCase						, _lowerCamelCase      :  Optional[int]      						=						train_test_split(X, y, test_size=0.2, random_state=0)


_lowerCamelCase      :  Optional[Any]      						=						PolynomialFeatures(degree=4)
_lowerCamelCase      :  Optional[Any]      						=						poly_reg.fit_transform(X)
_lowerCamelCase      :  Dict      						=						LinearRegression()
pol_reg.fit(X_poly, y)




def 							_UpperCAmelCase  ():
				'''simple docstring'''
				plt.scatter(UpperCamelCase_      ,    UpperCamelCase_      ,    color="""red"""       )
				plt.plot(UpperCamelCase_      ,    pol_reg.predict(poly_reg.fit_transform(UpperCamelCase_       )       )      ,    color="""blue"""       )
				plt.title("""Truth or Bluff (Linear Regression)"""       )
				plt.xlabel("""Position level"""       )
				plt.ylabel("""Salary"""       )
				plt.show()


if __name__ == "__main__":
	viz_polymonial()

	# Predicting a new result with Polymonial Regression
	pol_reg.predict(poly_reg.fit_transform([[5.5]]))
	# output should be 132148.43750003

