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13-May-2025 15:25:32

lights_out_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  lights_out() examines the 5x5 Lights Out game.

  lo_initialize_random(m,n,k) randomly initializes
  the board with k lights turned on.

  Random board with 15 lights illuminated.

  * * * . *
  * . . * *
  * . . * *
  * . . * *
  * . . * .

  lo_initialize_solvable(m,n,push) randomly initializes
  the board with push = 5 button pushes.

  Solvable board with 13 lights illuminated

  * . * * *
  . * . * .
  . * * . .
  * * . * .
  . * . * .

  lo_update(L,i,j) updates the board after button
  (i,j) = (2,3) was pushed.

  Updated board with 10 lights illuminated

  * . . * *
  . . * . .
  . * . . .
  * * . * .
  . * . * .

  lo_solvability_matrices() returns matrices N1 and N2
  which test a board configuration for solvability.

  Solvability matrix N1

  . * * * .
  * . * . *
  * * . * *
  * . * . *
  . * * * .

  Solvability matrix N2

  * . * . *
  * . * . *
  . . . . .
  * . * . *
  * . * . *

  lo_dot() computes the dot product modulo 2
  of two board configurations.

  Dot product of N1 and N2 is 0

  Dot product of L1 and N1 is 0
  Dot product of L1 and N2 is 0

  Dot product of L2 and N1 is 0
  Dot product of L2 and N2 is 0

  lo_solvable(L) determines whether configuration L
  is solvable.

  Test lo_initialize_solvable() configurations
  Solvable?  true
  Solvable?  true
  Solvable?  true
  Solvable?  true
  Solvable?  true

  Test lo_initialize_random() configurations
  Solvable?  false
  Solvable?  false
  Solvable?  false
  Solvable?  false
  Solvable?  true

  lo_light_chase(L) pushes buttons to shut off all
  lights above the bottom row.

  Initial configuration L0

  . . . * .
  * * . * *
  . . . . .
  * * * . *
  . . . . *

  Light chasing required 9 button pushes.

  After light chasing:

  . . . . .
  . . . . .
  . . . . .
  . . . . .
  . . . . .

  lo_light_chase_top(L) examines a Lights Out configuration
  after the light chase algorithm has been completed.
  It reports whether the problem is completed, unsolvable,
  or solvable.
  For solvable problems, it suggests which buttons to push
  on the top row, so that restarting the light chase algorithm
  will solve the problem.

  Initial configuration L0

  * . * . *
  . * * . .
  * . . . .
  * * * * .
  . * * * *

  Light chasing required 7 button pushes.

  After light chasing:

  . . . . .
  . . . . .
  . . . . .
  . . . . .
  . * * . *

  This configuration is solvable.
  Pushing these buttons in top row:
     1     0     0     0     0

  Then do a second round of light chasing.

  After pushing top row buttons:

  * * . . .
  * . . . .
  . . . . .
  . . . . .
  . * * . *

  Light chasing required 8 button pushes.

  After second round of light chasing:

  . . . . .
  . . . . .
  . . . . .
  . . . . .
  . . . . .

  lo_matrix() returns a 25x25 matrix A which applies
  a set of button pushes P, creating the corresponding
  Lights Out configuration AP.

  Given a configuration AP, we can try to solve A*P=AP
  to get a set of button pushes creating the configuration.
  Applying them to a configuration solves the puzzle.

  The 9x9 submatrix of A:

     1     1     0     0     0     1     0     0     0
     1     1     1     0     0     0     1     0     0
     0     1     1     1     0     0     0     1     0
     0     0     1     1     1     0     0     0     1
     0     0     0     1     1     0     0     0     0
     1     0     0     0     0     1     1     0     0
     0     1     0     0     0     1     1     1     0
     0     0     1     0     0     0     1     1     1
     0     0     0     1     0     0     0     1     1


  The button pushes

     0     0     0     0     0
     0     1     0     0     0
     0     0     1     0     0
     0     0     0     0     0
     0     0     0     0     0


  The configuration after pushing button 7 and 13

     0     1     0     0     0
     1     1     0     0     0
     0     0     1     1     0
     0     0     1     0     0
     0     0     0     0     0

[Warning: Matrix is close to singular or badly scaled. Results may be
inaccurate. RCOND =  4.827057e-19.] 
[> In lights_out_test (line 235)
In run (line 91)
] 

  The button pushes deduced from the configuration
  The singular system solution may have errors.

     0     0     0     0     1
     0     1     0     1     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0


lights_out_test():
  Normal end of execution.

13-May-2025 15:25:32