





'''simple docstring'''




# 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 	_lowerCAmelCase      (  __snake_case  :			List[str]      )					->					Optional[Any]:
     return 1 / (1 + np.exp(-z      ))






def 	_lowerCAmelCase      (  __snake_case  :			Optional[Any]			,							__snake_case  :			Tuple      )					->					int:
     return (-y * np.log(_snake_case      ) - (1 - y) * np.log(1 - h      )).mean()






def 	_lowerCAmelCase      (  __snake_case  :			Tuple			,							__snake_case  :			List[Any]			,							__snake_case  :			int      )					->					Optional[Any]:
     __A						:			Any								=	np.dot(_snake_case			,							_snake_case      )
     return np.sum(y * scores - np.log(1 + np.exp(_snake_case      )      )      )






def 	_lowerCAmelCase      (  __snake_case  :			Tuple			,							__snake_case  :			Optional[Any]			,							__snake_case  :			Optional[int]			,							__snake_case  :			List[Any]=7_00_00      )					->					List[Any]:
     __A						:			Optional[Any]								=	np.zeros(x.shape[1]      )

     for iterations in range(_snake_case      ):
          __A						:			Dict								=	np.dot(_snake_case			,							_snake_case      )
          __A						:			Tuple								=	sigmoid_function(_snake_case      )
          __A						:			List[str]								=	np.dot(x.T			,							h - y      ) / y.size
          __A						:			Union[str, Any]								=	theta - alpha * gradient  # updating the weights
          __A						:			Optional[Any]								=	np.dot(_snake_case			,							_snake_case      )
          __A						:			List[Any]								=	sigmoid_function(_snake_case      )
          __A						:			Tuple								=	cost_function(_snake_case			,							_snake_case      )
          if iterations % 1_00 == 0:
               print(f'loss: {j} \t'      )  # printing the loss after every 100 iterations
     return theta


# In[68]:

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

  lowercase__      =   0.1
  lowercase__      =   logistic_reg(alpha, x, y, max_iterations=7_00_00)
  print('''theta: ''', theta)  # printing the theta i.e our weights vector






  def 	_lowerCAmelCase      (  __snake_case  :			Dict      )					->					Dict:
       return sigmoid_function(
           np.dot(_snake_case			,							_snake_case      )      )  # 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''')
  (lowercase__)      =   (x[:, 0].min(), x[:, 0].max())
  (lowercase__)      =   (x[:, 1].min(), x[:, 1].max())
  (lowercase__)      =   np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
  lowercase__      =   np.c_[xxa.ravel(), xxa.ravel()]
  lowercase__      =   predict_prob(grid).reshape(xxa.shape)
  plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='''black''')

  plt.legend()







  plt.show()






'''simple docstring'''




from math import pi, sqrt, tan






def 	_lowerCAmelCase      (  __snake_case  :			float      )					->					float:
     if side_length < 0:
          raise ValueError('surface_area_cube() only accepts non-negative values'      )
     return 6 * side_length**2






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if length < 0 or breadth < 0 or height < 0:
          raise ValueError('surface_area_cuboid() only accepts non-negative values'      )
     return 2 * ((length * breadth) + (breadth * height) + (length * height))






def 	_lowerCAmelCase      (  __snake_case  :			float      )					->					float:
     if radius < 0:
          raise ValueError('surface_area_sphere() only accepts non-negative values'      )
     return 4 * pi * radius**2






def 	_lowerCAmelCase      (  __snake_case  :			float      )					->					float:
     if radius < 0:
          raise ValueError('surface_area_hemisphere() only accepts non-negative values'      )
     return 3 * pi * radius**2






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if radius < 0 or height < 0:
          raise ValueError('surface_area_cone() only accepts non-negative values'      )
     return pi * radius * (radius + (height**2 + radius**2) ** 0.5)






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if radius_a < 0 or radius_a < 0 or height < 0:
          raise ValueError(
              'surface_area_conical_frustum() only accepts non-negative values'      )
     __A						:			Union[str, Any]								=	(height**2 + (radius_a - radius_a) ** 2) ** 0.5
     return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if radius < 0 or height < 0:
          raise ValueError('surface_area_cylinder() only accepts non-negative values'      )
     return 2 * pi * radius * (height + radius)






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if torus_radius < 0 or tube_radius < 0:
          raise ValueError('surface_area_torus() only accepts non-negative values'      )
     if torus_radius < tube_radius:
          raise ValueError(
              'surface_area_torus() does not support spindle or self intersecting tori'      )
     return 4 * pow(__snake_case			,							2      ) * torus_radius * tube_radius






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if length < 0 or width < 0:
          raise ValueError('area_rectangle() only accepts non-negative values'      )
     return length * width






def 	_lowerCAmelCase      (  __snake_case  :			float      )					->					float:
     if side_length < 0:
          raise ValueError('area_square() only accepts non-negative values'      )
     return side_length**2






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if base < 0 or height < 0:
          raise ValueError('area_triangle() only accepts non-negative values'      )
     return (base * height) / 2






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if sidea < 0 or sidea < 0 or sidea < 0:
          raise ValueError('area_triangle_three_sides() only accepts non-negative values'      )
     elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
          raise ValueError('Given three sides do not form a triangle'      )
     __A						:			int								=	(sidea + sidea + sidea) / 2
     __A						:			Tuple								=	sqrt(
         semi_perimeter
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)      )
     return area






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if base < 0 or height < 0:
          raise ValueError('area_parallelogram() only accepts non-negative values'      )
     return base * height






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if basea < 0 or basea < 0 or height < 0:
          raise ValueError('area_trapezium() only accepts non-negative values'      )
     return 1 / 2 * (basea + basea) * height






def 	_lowerCAmelCase      (  __snake_case  :			float      )					->					float:
     if radius < 0:
          raise ValueError('area_circle() only accepts non-negative values'      )
     return pi * radius**2






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if radius_x < 0 or radius_y < 0:
          raise ValueError('area_ellipse() only accepts non-negative values'      )
     return pi * radius_x * radius_y






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if diagonal_a < 0 or diagonal_a < 0:
          raise ValueError('area_rhombus() only accepts non-negative values'      )
     return 1 / 2 * diagonal_a * diagonal_a






def 	_lowerCAmelCase      (  __snake_case  :			int			,							__snake_case  :			float      )					->					float:
     if not isinstance(__snake_case			,							__snake_case      ) or sides < 3:
          raise ValueError(
              'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'      )
     elif length < 0:
          raise ValueError(
              'area_reg_polygon() only accepts non-negative values as \
length of a side'      )
     return (sides * length**2) / (4 * tan(pi / sides      ))
     return (sides * length**2) / (4 * tan(pi / sides      ))


if __name__ == "__main__":
  import doctest

  doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

  print('''[DEMO] Areas of various geometric shapes: \n''')
  print(f"""Rectangle: {area_rectangle(10, 20) = }""")
  print(f"""Square: {area_square(10) = }""")
  print(f"""Triangle: {area_triangle(10, 10) = }""")
  print(f"""Triangle: {area_triangle_three_sides(5, 12, 13) = }""")
  print(f"""Parallelogram: {area_parallelogram(10, 20) = }""")
  print(f"""Rhombus: {area_rhombus(10, 20) = }""")
  print(f"""Trapezium: {area_trapezium(10, 20, 30) = }""")
  print(f"""Circle: {area_circle(20) = }""")
  print(f"""Ellipse: {area_ellipse(10, 20) = }""")
  print('''\nSurface Areas of various geometric shapes: \n''')
  print(f"""Cube: {surface_area_cube(20) = }""")
  print(f"""Cuboid: {surface_area_cuboid(10, 20, 30) = }""")
  print(f"""Sphere: {surface_area_sphere(20) = }""")
  print(f"""Hemisphere: {surface_area_hemisphere(20) = }""")
  print(f"""Cone: {surface_area_cone(10, 20) = }""")
  print(f"""Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }""")
  print(f"""Cylinder: {surface_area_cylinder(10, 20) = }""")
  print(f"""Torus: {surface_area_torus(20, 10) = }""")
  print(f"""Equilateral Triangle: {area_reg_polygon(3, 10) = }""")
  print(f"""Square: {area_reg_polygon(4, 10) = }""")
  print(f"""Reqular Pentagon: {area_reg_polygon(5, 10) = }""")