





'''simple docstring'''

from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray







def  a__    (    lowercase :					NDArray[floataa], lowercase :					NDArray[floataa], lowercase :					list[int], lowercase :					int, )		->		list[float]:





     """simple docstring"""

     _UpperCamelCase       =	coefficient_matrix.shape
     _UpperCamelCase       =	constant_matrix.shape

     if rowsa != colsa:
          _UpperCamelCase       =	F"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
          raise ValueError(lowercase				)

     if colsa != 1:
          _UpperCamelCase       =	F"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
          raise ValueError(lowercase				)

     if rowsa != rowsa:
          _UpperCamelCase       =	(
              """Coefficient and constant matrices dimensions must be nxn and nx1 but """
              F"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
          )
          raise ValueError(lowercase				)

     if len(lowercase				) != rowsa:
          _UpperCamelCase       =	(
              """Number of initial values must be equal to number of rows in coefficient """
              F"""matrix but received {len(lowercase				)} and {rowsa}"""
          )
          raise ValueError(lowercase				)

     if iterations <= 0:
          raise ValueError('''Iterations must be at least 1'''				)

     _UpperCamelCase       =	np.concatenate(
         (coefficient_matrix, constant_matrix), axis=1				)

     _UpperCamelCase       =	table.shape

     strictly_diagonally_dominant(lowercase				)

     # Iterates the whole matrix for given number of times
     for _ in range(lowercase				):
          _UpperCamelCase       =	[]
          for row in range(lowercase				):
               _UpperCamelCase       =	0
               for col in range(lowercase				):
                    if col == row:
                         _UpperCamelCase       =	table[row][col]
                    elif col == cols - 1:
                         _UpperCamelCase       =	table[row][col]
                    else:
                         temp += (-1) * table[row][col] * init_val[col]
               _UpperCamelCase       =	(temp + val) / denom
               new_val.append(lowercase				)
          _UpperCamelCase       =	new_val

     return [float(lowercase				) for i in new_val]







def  a__    (    lowercase :					NDArray[floataa]				)		->		bool:





     """simple docstring"""

     _UpperCamelCase       =	table.shape

     _UpperCamelCase       =	True

     for i in range(0, lowercase				):
          _UpperCamelCase       =	0
          for j in range(0, cols - 1				):
               if i == j:
                    continue
               else:
                    total += table[i][j]

          if table[i][i] <= total:
               raise ValueError('''Coefficient matrix is not strictly diagonally dominant'''				)

     return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''

from cva import destroyAllWindows, imread, imshow, waitKey







def  a__    (    lowercase :					str				)		->		Optional[int]:





     """simple docstring"""

     _UpperCamelCase   ,    _UpperCamelCase       =	img.shape[0], img.shape[1]

     # converting each pixel's color to its negative
     for i in range(lowercase				):
          for j in range(lowercase				):
               _UpperCamelCase       =	[255, 255, 255] - img[i][j]

     return img


if __name__ == "__main__":
   # read original image
   lowercase__						:      Optional[int]	=    imread('image_data/lena.jpg', 1)

   # convert to its negative
   lowercase__						:      Union[str, Any]	=    convert_to_negative(img)

   # show result image
   imshow('negative of original image', img)
   waitKey(0)
   destroyAllWindows()



