



from typing import Any

import numpy as np


class 	a__       :


					"""simple docstring"""



					def __init__(		self     :str      ,  lowercase__     :np.ndarray      ,  lowercase__     :int    ):
										# Check if RHS is negative
										if np.any(tableau[:, -1]      ,  where=tableau[:, -1] < 0    ):
															raise ValueError('RHS must be > 0'    )

										lowercase						   =       tableau
										lowercase   ,      lowercase						   =       tableau.shape

										# Number of decision variables x1, x2, x3...
										lowercase						   =       n_vars

										# Number of artificial variables to be minimised
										lowercase						   =       len(np.where(tableau[self.n_vars : -1] == -1    )[0]    )

										# 2 if there are >= or == constraints (nonstandard), 1 otherwise (std)
										lowercase						   =       (self.n_art_vars > 0) + 1

										# Number of slack variables added to make inequalities into equalities
										lowercase						   =       self.n_rows - self.n_stages

										# Objectives for each stage
										lowercase						   =       ['max']

										# In two stage simplex, first minimise then maximise
										if self.n_art_vars:
															self.objectives.append('min'    )

										lowercase						   =       ['']

										# Index of current pivot row and column
										lowercase						   =       None
										lowercase						   =       None

										# Does objective row only contain (non)-negative values?
										lowercase						   =       False

					@staticmethod
					def 				__UpperCAmelCase		(		*lowercase__     :int    ):
										if len(_lowerCAmelCase    ) != 3:
															raise ValueError('Must provide n_vars, n_slack, and n_art_vars'    )

										if not all(x >= 0 and isinstance(_lowerCAmelCase      ,  _lowerCAmelCase    ) for x in args    ):
															raise ValueError('All arguments must be non-negative integers'    )

										# decision | slack | artificial
										lowercase						   =       ['x', 's', 'a']
										lowercase						   =       []
										for i in range(3    ):
															for j in range(args[i]    ):
																				titles.append(string_starts[i] + str(j + 1    )    )
										titles.append('RHS'    )
										return titles

					def 				__UpperCAmelCase		(		self     :List[str]      ,  lowercase__     :np.ndarray    ):
										lowercase						   =       self.objectives[-1]

										# Find entries of highest magnitude in objective rows
										lowercase						   =       (objective == 'min') - (objective == 'max')
										lowercase						   =       np.argmax(sign * tableau[0, : self.n_vars]    )

										# Choice is only valid if below 0 for maximise, and above for minimise
										if sign * self.tableau[0, col_idx] <= 0:
															lowercase						   =       True
															return 0, 0

										# Pivot row is chosen as having the lowest quotient when elements of
										# the pivot column divide the right-hand side

										# Slice excluding the objective rows
										lowercase						   =       slice(self.n_stages      ,  self.n_rows    )

										# RHS
										lowercase						   =       tableau[s, -1]

										# Elements of pivot column within slice
										lowercase						   =       tableau[s, col_idx]

										# Array filled with nans
										lowercase						   =       np.full(self.n_rows - self.n_stages      ,  np.nan    )

										# If element in pivot column is greater than zeron_stages, return
										# quotient or nan otherwise
										lowercase						   =       np.divide(_lowerCAmelCase      ,  _lowerCAmelCase      ,  out=_lowerCAmelCase      ,  where=divisor > 0    )

										# Arg of minimum quotient excluding the nan values. n_stages is added
										# to compensate for earlier exclusion of objective columns
										lowercase						   =       np.nanargmin(_lowerCAmelCase    ) + self.n_stages
										return row_idx, col_idx

					def 				__UpperCAmelCase		(		self     :Optional[Any]      ,  lowercase__     :np.ndarray      ,  lowercase__     :int      ,  lowercase__     :int    ):
										lowercase						   =       tableau[row_idx].copy()

										lowercase						   =       piv_row[col_idx]

										# Entry becomes 1
										piv_row *= 1 / piv_val

										# Variable in pivot column becomes basic, ie the only non-zero entry
										for idx, coeff in enumerate(tableau[:, col_idx]    ):
															tableau[idx] += -coeff * piv_row
										lowercase						   =       piv_row
										return tableau

					def 				__UpperCAmelCase		(		self     :int      ,  lowercase__     :np.ndarray    ):
										self.objectives.pop()

										if not self.objectives:
															return tableau

										# Slice containing ids for artificial columns
										lowercase						   =       slice(-self.n_art_vars - 1      ,  -1    )

										# Delete the artificial variable columns
										lowercase						   =       np.delete(_lowerCAmelCase      ,  _lowerCAmelCase      ,  axis=1    )

										# Delete the objective row of the first stage
										lowercase						   =       np.delete(_lowerCAmelCase      ,  0      ,  axis=0    )

										lowercase						   =       1
										self.n_rows -= 1
										lowercase						   =       0
										lowercase						   =       False
										return tableau

					def 				__UpperCAmelCase		(		self     :Optional[int]    ):
										# Stop simplex algorithm from cycling.
										for _ in range(100    ):
															# Completion of each stage removes an objective. If both stages
															# are complete, then no objectives are left
															if not self.objectives:
																				lowercase						   =       self.generate_col_titles(
																				    self.n_vars      ,  self.n_slack      ,  self.n_art_vars    )

																				# Find the values of each variable at optimal solution
																				return self.interpret_tableau(self.tableau      ,  self.col_titles    )

															lowercase   ,      lowercase						   =       self.find_pivot(self.tableau    )

															# If there are no more negative values in objective row
															if self.stop_iter:
																				# Delete artificial variable columns and rows. Update attributes
																				lowercase						   =       self.change_stage(self.tableau    )
															else:
																				lowercase						   =       self.pivot(self.tableau      ,  _lowerCAmelCase      ,  _lowerCAmelCase    )
										return {}



					def 				__UpperCAmelCase		(		self     :Any      ,  lowercase__     :np.ndarray      ,  lowercase__     :list[str]    ):
										lowercase						   =       {'P': abs(tableau[0, -1]    )}

										for i in range(self.n_vars    ):
															# Gives ids of nonzero entries in the ith column
															lowercase						   =       np.nonzero(tableau[:, i]    )
															lowercase						   =       len(nonzero[0]    )

															# First entry in the nonzero ids
															lowercase						   =       nonzero[0][0]
															lowercase						   =       tableau[nonzero_rowidx, i]

															# If there is only one nonzero value in column, which is one
															if n_nonzero == nonzero_val == 1:
																				lowercase						   =       tableau[nonzero_rowidx, -1]
																				lowercase						   =       rhs_val

        # Check for basic variables
										for title in col_titles:
															# Don't add RHS or slack variables to output dict
															if title[0] not in "R-s-a":
																				output_dict.setdefault(_lowerCAmelCase      ,  0    )
										return output_dict


if __name__ == "__main__":
		import doctest

		doctest.testmod()








import cva
import numpy as np

from digital_image_processing.filters.convolve import img_convolve
from digital_image_processing.filters.sobel_filter import sobel_filter

_UpperCamelCase:					Tuple     =180



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[Any]		,				__SCREAMING_SNAKE_CASE					:  int    ):






  """simple docstring"""




  _lowerCAmelCase						=		k_size // 2
  _lowerCAmelCase	,       _lowerCAmelCase						=		np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
  _lowerCAmelCase						=		(
      1
      / (2 * np.pi * sigma)
      * np.exp(-(np.square(__SCREAMING_SNAKE_CASE    ) + np.square(__SCREAMING_SNAKE_CASE    )) / (2 * np.square(__SCREAMING_SNAKE_CASE    ))    )
  )
  return g



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  Optional[Any]    ):






  """simple docstring"""




  _lowerCAmelCase						=		np.zeros(__SCREAMING_SNAKE_CASE    )

  for row in range(1		,				image_shape[0] - 1    ):
    for col in range(1		,				image_shape[1] - 1    ):
      _lowerCAmelCase						=		gradient_direction[row, col]

      if (
          0 <= direction < PI / 8
          or 15 * PI / 8 <= direction <= 2 * PI
          or 7 * PI / 8 <= direction <= 9 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row, col - 1]
        _lowerCAmelCase						=		sobel_grad[row, col + 1]
        if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
          _lowerCAmelCase						=		sobel_grad[row, col]

      elif (
          PI / 8 <= direction < 3 * PI / 8
          or 9 * PI / 8 <= direction < 11 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row + 1, col - 1]
        _lowerCAmelCase						=		sobel_grad[row - 1, col + 1]
        if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
          _lowerCAmelCase						=		sobel_grad[row, col]

      elif (
          3 * PI / 8 <= direction < 5 * PI / 8
          or 11 * PI / 8 <= direction < 13 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row - 1, col]
        _lowerCAmelCase						=		sobel_grad[row + 1, col]
        if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
          _lowerCAmelCase						=		sobel_grad[row, col]

      elif (
          5 * PI / 8 <= direction < 7 * PI / 8
          or 13 * PI / 8 <= direction < 15 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row - 1, col - 1]
        _lowerCAmelCase						=		sobel_grad[row + 1, col + 1]
        if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
          _lowerCAmelCase						=		sobel_grad[row, col]

  return destination



def 	_a  (					__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  Union[str, Any]		,				__SCREAMING_SNAKE_CASE					:  Dict		,				__SCREAMING_SNAKE_CASE					:  List[Any]    ):






  """simple docstring"""




  for row in range(1		,				image_shape[0] - 1    ):
    for col in range(1		,				image_shape[1] - 1    ):
      if destination[row, col] >= threshold_high:
        _lowerCAmelCase						=		strong
      elif destination[row, col] <= threshold_low:
        _lowerCAmelCase						=		0
      else:
        _lowerCAmelCase						=		weak



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[Any]		,				__SCREAMING_SNAKE_CASE					:  Optional[int]		,				__SCREAMING_SNAKE_CASE					:  Optional[int]		,				__SCREAMING_SNAKE_CASE					:  Union[str, Any]    ):






  """simple docstring"""




  for row in range(1		,				image_shape[0]    ):
    for col in range(1		,				image_shape[1]    ):
      if destination[row, col] == weak:
        if 255 in (
            destination[row, col + 1],
            destination[row, col - 1],
            destination[row - 1, col],
            destination[row + 1, col],
            destination[row - 1, col - 1],
            destination[row + 1, col - 1],
            destination[row - 1, col + 1],
            destination[row + 1, col + 1],
        ):
          _lowerCAmelCase						=		strong
        else:
          _lowerCAmelCase						=		0



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  int=15		,				__SCREAMING_SNAKE_CASE					:  int=30		,				__SCREAMING_SNAKE_CASE					:  Tuple=128		,				__SCREAMING_SNAKE_CASE					:  List[Any]=255    ):






  """simple docstring"""




  _lowerCAmelCase						=		img_convolve(__SCREAMING_SNAKE_CASE		,				gen_gaussian_kernel(9		,				sigma=1.4    )    )
  # get the gradient and degree by sobel_filter
  _lowerCAmelCase	,       _lowerCAmelCase						=		sobel_filter(__SCREAMING_SNAKE_CASE    )
  _lowerCAmelCase						=		PI + np.radadeg(__SCREAMING_SNAKE_CASE    )

  _lowerCAmelCase						=		suppress_non_maximum(image.shape		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE    )

  detect_high_low_threshold(
      image.shape		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE    )

  track_edge(image.shape		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE    )

  return destination


if __name__ == "__main__":
       # read original image in gray mode
       _UpperCamelCase:					Optional[Any]     =cva.imread(R'../image_data/lena.jpg', 0)
       # canny edge detection
       _UpperCamelCase:					Tuple     =canny(lena)
       cva.imshow('canny', canny_destination)
       cva.waitKey(0)
