
'''simple docstring'''



from __future__ import annotations

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


def A (__lowerCamelCase :NDArray[floataa]					,      __lowerCamelCase :NDArray[floataa]					,      __lowerCamelCase :list[int]					,      __lowerCamelCase :int					,      ):
						_lowerCAmelCase		,       _lowerCAmelCase    		=					coefficient_matrix.shape
						_lowerCAmelCase		,       _lowerCAmelCase    		=					constant_matrix.shape

						if rowsa != colsa:
												_lowerCAmelCase    		=					f'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
												raise ValueError(__lowerCamelCase						)

						if colsa != 1:
												_lowerCAmelCase    		=					f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
												raise ValueError(__lowerCamelCase						)

						if rowsa != rowsa:
												_lowerCAmelCase    		=					(
												    """Coefficient and constant matrices dimensions must be nxn and nx1 but """
												    f'received {rowsa}x{colsa} and {rowsa}x{colsa}'
												)
												raise ValueError(__lowerCamelCase						)

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

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

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

						_lowerCAmelCase		,       _lowerCAmelCase    		=					table.shape

						strictly_diagonally_dominant(__lowerCamelCase						)

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

						return [float(__lowerCamelCase						) for i in new_val]


def A (__lowerCamelCase :NDArray[floataa]						):
						_lowerCAmelCase		,       _lowerCAmelCase    		=					table.shape

						_lowerCAmelCase    		=					True

						for i in range(0					,      __lowerCamelCase						):
												_lowerCAmelCase    		=					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 manim import *




class     UpperCAmelCase_	(						_SCREAMING_SNAKE_CASE					):






						'''simple docstring'''






						def    _lowercase      (   self ):

												"""simple docstring"""



												_lowerCAmelCase    		=					Rectangle(height=0.5       ,  width=0.5 )
												_lowerCAmelCase    		=					Rectangle(height=0.46       ,  width=0.46 ).set_stroke(width=0 )

												_lowerCAmelCase    		=					[mem.copy() for i in range(6 )]
												_lowerCAmelCase    		=					[mem.copy() for i in range(6 )]
												_lowerCAmelCase    		=					VGroup(*_lowercase ).arrange(_lowercase       ,  buff=0 )
												_lowerCAmelCase    		=					VGroup(*_lowercase ).arrange(_lowercase       ,  buff=0 )
												_lowerCAmelCase    		=					VGroup(_lowercase       ,  _lowercase ).arrange(_lowercase       ,  buff=0 )
												_lowerCAmelCase    		=					Text("""CPU"""       ,  font_size=24 )
												_lowerCAmelCase    		=					Group(_lowercase       ,  _lowercase ).arrange(_lowercase       ,  buff=0.5       ,  aligned_edge=_lowercase )
												cpu.move_to([-2.5, -0.5, 0] )
												self.add(_lowercase )

												_lowerCAmelCase    		=					[mem.copy() for i in range(1 )]
												_lowerCAmelCase    		=					VGroup(*_lowercase ).arrange(_lowercase       ,  buff=0 )
												_lowerCAmelCase    		=					Text("""GPU"""       ,  font_size=24 )
												_lowerCAmelCase    		=					Group(_lowercase       ,  _lowercase ).arrange(_lowercase       ,  buff=0.5       ,  aligned_edge=_lowercase )
												gpu.align_to(_lowercase       ,  _lowercase )
												gpu.set_x(gpu.get_x() - 1 )

												self.add(_lowercase )

												_lowerCAmelCase    		=					[mem.copy() for i in range(6 )]
												_lowerCAmelCase    		=					VGroup(*_lowercase ).arrange(_lowercase       ,  buff=0 )

												_lowerCAmelCase    		=					Text("""Model"""       ,  font_size=24 )
												_lowerCAmelCase    		=					Group(_lowercase       ,  _lowercase ).arrange(_lowercase       ,  buff=0.5       ,  aligned_edge=_lowercase )
												model.move_to([3, -1.0, 0] )

												self.play(
												    Create(_lowercase       ,  run_time=1 )       ,  Create(_lowercase       ,  run_time=1 )       ,  Create(_lowercase       ,  run_time=1 )       ,  )

												_lowerCAmelCase    		=					MarkupText(
												    F'First, an empty model skeleton is loaded\ninto <span fgcolor=\'{YELLOW}\'>memory</span> without using much RAM.'       ,  font_size=24       ,  )

												_lowerCAmelCase    		=					Square(side_length=2.2 )
												key.move_to([-5, 2, 0] )

												_lowerCAmelCase    		=					MarkupText(
												    F'<b>Key:</b>\n\n<span fgcolor=\'{YELLOW}\'>●</span> Empty Model'       ,  font_size=18       ,  )

												key_text.move_to([-5, 2.4, 0] )

												step_a.move_to([2, 2, 0] )
												self.play(Write(_lowercase       ,  run_time=2.5 )       ,  Write(_lowercase )       ,  Write(_lowercase ) )

												self.add(_lowercase )

												_lowerCAmelCase    		=					[]
												_lowerCAmelCase    		=					[]
												_lowerCAmelCase    		=					[]
												for i, rect in enumerate(_lowercase ):
																		_lowerCAmelCase    		=					Rectangle(height=0.46       ,  width=0.46 ).set_stroke(width=0.0 ).set_fill(_lowercase       ,  opacity=0.7 )
																		cpu_target.move_to(_lowercase )
																		cpu_target.generate_target()
																		_lowerCAmelCase    		=					0.46 / 4
																		_lowerCAmelCase    		=					0.46 / 3

																		if i == 0:
																								cpu_target.target.next_to(cpu_left_col_base[0].get_corner(DOWN + LEFT )       ,  buff=0.02       ,  direction=_lowercase )
																								cpu_target.target.set_x(cpu_target.target.get_x() + 0.1 )
																		elif i == 3:
																								cpu_target.target.next_to(cpu_targs[0].target       ,  direction=_lowercase       ,  buff=0.0 )
																		else:
																								cpu_target.target.next_to(cpu_targs[i - 1].target       ,  direction=_lowercase       ,  buff=0.0 )
																		cpu_targs.append(_lowercase )

																		first_animations.append(rect.animate(run_time=0.5 ).set_stroke(_lowercase ) )
																		second_animations.append(MoveToTarget(_lowercase       ,  run_time=1.5 ) )

												self.play(*_lowercase )
												self.play(*_lowercase )

												self.wait()
