


from __future__ import annotations

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



def 				UpperCamelCase_(      lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_							, )    ->						list[float]:
    _lowercase		,				_lowercase       :							Union[str, Any]      		=		coefficient_matrix.shape
    _lowercase		,				_lowercase       :							Any      		=		constant_matrix.shape

    if rowsa != colsa:
        _lowercase       :							Any      		=		F'''Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'''
        raise ValueError(lowerCamelCase_ )

    if colsa != 1:
        _lowercase       :							List[str]      		=		F'''Constant matrix must be nx1 but received {rowsa}x{colsa}'''
        raise ValueError(lowerCamelCase_ )

    if rowsa != rowsa:
        _lowercase       :							Any      		=		(
            '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:
        _lowercase       :							Optional[Any]      		=		(
            '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' )

    _lowercase       :							NDArray[floataa]      		=		np.concatenate(
        (coefficient_matrix, constant_matrix)							, axis=1 )

    _lowercase		,				_lowercase       :							Optional[int]      		=		table.shape

    strictly_diagonally_dominant(lowerCamelCase_ )

    # Iterates the whole matrix for given number of times
    for _ in range(lowerCamelCase_ ):
        _lowercase       :							List[str]      		=		[]
        for row in range(lowerCamelCase_ ):
            _lowercase       :							List[str]      		=		0
            for col in range(lowerCamelCase_ ):
                if col == row:
                    _lowercase       :							Union[str, Any]      		=		table[row][col]
                elif col == cols - 1:
                    _lowercase       :							Optional[int]      		=		table[row][col]
                else:
                    temp += (-1) * table[row][col] * init_val[col]
            _lowercase       :							Union[str, Any]      		=		(temp + val) / denom
            new_val.append(lowerCamelCase_ )
        _lowercase       :							Any      		=		new_val

    return [float(lowerCamelCase_ ) for i in new_val]



def 				UpperCamelCase_(      lowerCamelCase_ )    ->						bool:
    _lowercase		,				_lowercase       :							Any      		=		table.shape

    _lowercase       :							List[Any]      		=		True

    for i in range(0							, lowerCamelCase_ ):
        _lowercase       :							Optional[Any]      		=		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()







from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros

def        a						(      _UpperCAmelCase							:					Tuple ,   _UpperCAmelCase							:					Optional[int]						):







		'''simple docstring'''





		__UpperCAmelCase    :     Union[str, Any]													=	k_size // 2
		__UpperCAmelCase							,					__UpperCAmelCase    :     Optional[Any]													=	mgrid[0 - center : k_size - center, 0 - center : k_size - center]
		__UpperCAmelCase    :     Any													=	1 / (2 * pi * sigma) * exp(-(square(_UpperCAmelCase						) + square(_UpperCAmelCase						)) / (2 * square(_UpperCAmelCase						))						)
		return g

def        a						(      _UpperCAmelCase							:					Optional[int] ,   _UpperCAmelCase							:					Any ,   _UpperCAmelCase							:					List[Any]						):







		'''simple docstring'''





		__UpperCAmelCase							,					__UpperCAmelCase    :     Union[str, Any]													=	image.shape[0], image.shape[1]
		# dst image height and width
		__UpperCAmelCase    :     str													=	height - k_size + 1
		__UpperCAmelCase    :     Optional[int]													=	width - k_size + 1

		# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
		__UpperCAmelCase    :     str													=	zeros((dst_height * dst_width, k_size * k_size)						)
		__UpperCAmelCase    :     Optional[Any]													=	0
		for i, j in product(range(_UpperCAmelCase						) ,   range(_UpperCAmelCase						)						):
				__UpperCAmelCase    :     int													=	ravel(image[i : i + k_size, j : j + k_size]						)
				__UpperCAmelCase    :     Union[str, Any]													=	window
				row += 1

		#  turn the kernel into shape(k*k, 1)
		__UpperCAmelCase    :     Tuple													=	gen_gaussian_kernel(_UpperCAmelCase ,   _UpperCAmelCase						)
		__UpperCAmelCase    :     List[Any]													=	ravel(_UpperCAmelCase						)

		# reshape and get the dst image
		__UpperCAmelCase    :     Optional[Any]													=	dot(_UpperCAmelCase ,   _UpperCAmelCase						).reshape(_UpperCAmelCase ,   _UpperCAmelCase						).astype(_UpperCAmelCase						)

		return dst


if __name__ == "__main__":
				# read original image
				__A   			=imread(R"../image_data/lena.jpg")
				# turn image in gray scale value
				__A   			=cvtColor(img, COLOR_BGR2GRAY)

				# get values with two different mask size
				__A   			=gaussian_filter(gray, 3, sigma=1)
				__A   			=gaussian_filter(gray, 5, sigma=0.8)

				# show result images
				imshow("gaussian filter with 3x3 mask", gaussianaxa)
				imshow("gaussian filter with 5x5 mask", gaussianaxa)
				waitKey()





