



"""simple docstring"""






from __future__ import annotations

import math


def      _lowercase							(    __snake_case   ,__snake_case      )		->  list:
			if len(__snake_case      ) != 2 or len(a[0]      ) != 2 or len(__snake_case      ) != 2 or len(b[0]      ) != 2:
						raise Exception("Matrices are not 2x2"      )
			__lowerCAmelCase :    str				=			[
			    [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
			    [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
			]
			return new_matrix


def      _lowercase							(    __snake_case   ,__snake_case      )		->  str:
			return [
			    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]      )      )]
			    for row in range(len(__snake_case      )      )
			]


def      _lowercase							(    __snake_case   ,__snake_case      )		->  Optional[int]:
			return [
			    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]      )      )]
			    for row in range(len(__snake_case      )      )
			]


def      _lowercase							(    __snake_case      )		->  tuple[list, list, list, list]:
			if len(__snake_case      ) % 2 != 0 or len(a[0]      ) % 2 != 0:
						raise Exception("Odd matrices are not supported!"      )

			__lowerCAmelCase :    str				=			len(__snake_case      )
			__lowerCAmelCase :    Optional[Any]				=			matrix_length // 2

			__lowerCAmelCase :    List[str]				=			[[a[i][j] for j in range(__snake_case   ,__snake_case      )] for i in range(__snake_case      )]
			__lowerCAmelCase :    List[Any]				=			[
			    [a[i][j] for j in range(__snake_case   ,__snake_case      )] for i in range(__snake_case   ,__snake_case      )
			]

			__lowerCAmelCase :    Any				=			[[a[i][j] for j in range(__snake_case      )] for i in range(__snake_case      )]
			__lowerCAmelCase :    Union[str, Any]				=			[[a[i][j] for j in range(__snake_case      )] for i in range(__snake_case   ,__snake_case      )]

			return top_left, top_right, bot_left, bot_right


def      _lowercase							(    __snake_case      )		->  tuple[int, int]:
			return len(__snake_case      ), len(matrix[0]      )


def      _lowercase							(    __snake_case      )		->  None:
			print("\n".join(str(__snake_case      ) for line in matrix      )      )


def      _lowercase							(    __snake_case   ,__snake_case      )		->  list:
			if matrix_dimensions(__snake_case      ) == (2, 2):
						return default_matrix_multiplication(__snake_case   ,__snake_case      )

			__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    Optional[int]				=			split_matrix(__snake_case      )
			__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    int				=			split_matrix(__snake_case      )

			__lowerCAmelCase :    Any				=			actual_strassen(__snake_case   ,matrix_subtraction(__snake_case   ,__snake_case      )      )
			__lowerCAmelCase :    int				=			actual_strassen(matrix_addition(__snake_case   ,__snake_case      )   ,__snake_case      )
			__lowerCAmelCase :    Dict				=			actual_strassen(matrix_addition(__snake_case   ,__snake_case      )   ,__snake_case      )
			__lowerCAmelCase :    str				=			actual_strassen(__snake_case   ,matrix_subtraction(__snake_case   ,__snake_case      )      )
			__lowerCAmelCase :    int				=			actual_strassen(matrix_addition(__snake_case   ,__snake_case      )   ,matrix_addition(__snake_case   ,__snake_case      )      )
			__lowerCAmelCase :    int				=			actual_strassen(matrix_subtraction(__snake_case   ,__snake_case      )   ,matrix_addition(__snake_case   ,__snake_case      )      )
			__lowerCAmelCase :    Dict				=			actual_strassen(matrix_subtraction(__snake_case   ,__snake_case      )   ,matrix_addition(__snake_case   ,__snake_case      )      )

			__lowerCAmelCase :    Optional[Any]				=			matrix_addition(matrix_subtraction(matrix_addition(__snake_case   ,__snake_case      )   ,__snake_case      )   ,__snake_case      )
			__lowerCAmelCase :    Union[str, Any]				=			matrix_addition(__snake_case   ,__snake_case      )
			__lowerCAmelCase :    List[str]				=			matrix_addition(__snake_case   ,__snake_case      )
			__lowerCAmelCase :    List[Any]				=			matrix_subtraction(matrix_subtraction(matrix_addition(__snake_case   ,__snake_case      )   ,__snake_case      )   ,__snake_case      )

			# construct the new matrix from our 4 quadrants
			__lowerCAmelCase :    Any				=			[]
			for i in range(len(__snake_case      )      ):
						new_matrix.append(top_left[i] + top_right[i]      )
			for i in range(len(__snake_case      )      ):
						new_matrix.append(bot_left[i] + bot_right[i]      )
			return new_matrix


def      _lowercase							(    __snake_case   ,__snake_case      )		->  list:
			if matrix_dimensions(__snake_case      )[1] != matrix_dimensions(__snake_case      )[0]:
						__lowerCAmelCase :    Tuple				=			(
						    "Unable to multiply these matrices, please check the dimensions.\n"
						    F"""Matrix A: {matrixa}\n"""
						    F"""Matrix B: {matrixa}"""
						)
						raise Exception(__snake_case      )
			__lowerCAmelCase :    Tuple				=			matrix_dimensions(__snake_case      )
			__lowerCAmelCase :    Optional[Any]				=			matrix_dimensions(__snake_case      )

			if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
						return [matrixa, matrixa]

			__lowerCAmelCase :    List[str]				=			max(*__snake_case   ,*__snake_case      )
			__lowerCAmelCase :    Dict				=			int(math.pow(2   ,math.ceil(math.loga(__snake_case      )      )      )      )
			__lowerCAmelCase :    str				=			matrixa
			__lowerCAmelCase :    Optional[Any]				=			matrixa

			# Adding zeros to the matrices so that the arrays dimensions are the same and also
			# power of 2
			for i in range(0   ,__snake_case      ):
						if i < dimensiona[0]:
									for _ in range(dimensiona[1]   ,__snake_case      ):
												new_matrixa[i].append(0      )
						else:
									new_matrixa.append([0] * maxim      )
						if i < dimensiona[0]:
									for _ in range(dimensiona[1]   ,__snake_case      ):
												new_matrixa[i].append(0      )
						else:
									new_matrixa.append([0] * maxim      )

			__lowerCAmelCase :    Dict				=			actual_strassen(__snake_case   ,__snake_case      )

			# Removing the additional zeros
			for i in range(0   ,__snake_case      ):
						if i < dimensiona[0]:
									for _ in range(dimensiona[1]   ,__snake_case      ):
												final_matrix[i].pop()
						else:
									final_matrix.pop()
			return final_matrix


if __name__ == "__main__":
	__snake_case				:  Optional[Any] =       [
	    [2, 3, 4, 5],
	    [6, 4, 3, 1],
	    [2, 3, 6, 7],
	    [3, 1, 2, 4],
	    [2, 3, 4, 5],
	    [6, 4, 3, 1],
	    [2, 3, 6, 7],
	    [3, 1, 2, 4],
	    [2, 3, 4, 5],
	    [6, 2, 3, 1],
	]
	__snake_case				:  Optional[Any] =       [[0, 2, 1, 1], [16, 2, 3, 3], [2, 2, 7, 7], [13, 11, 22, 4]]
	print(strassen(matrixa, matrixa))




"""simple docstring"""






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
__snake_case				:  Optional[Any] =       pd.read_csv(
    'https://s3.us-west-2.amazonaws.com/public.gamelab.fun/dataset/'
    'position_salaries.csv'
)
__snake_case				:  int =       dataset.iloc[:, 1:2].values
__snake_case				:  Tuple =       dataset.iloc[:, 2].values


__snake_case ,						__snake_case ,						__snake_case ,						__snake_case				:  int =       train_test_split(X, y, test_size=0.2, random_state=0)


__snake_case				:  Tuple =       PolynomialFeatures(degree=4)
__snake_case				:  Any =       poly_reg.fit_transform(X)
__snake_case				:  List[str] =       LinearRegression()
pol_reg.fit(X_poly, y)


def      _lowercase							(    )		->  List[Any]:
			plt.scatter(__snake_case   ,__snake_case   ,color="red"      )
			plt.plot(__snake_case   ,pol_reg.predict(poly_reg.fit_transform(__snake_case      )      )   ,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