13-Jun-2022 18:43:29

t_puzzle_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  t_puzzle() analyzes four versions of the T tiling puzzle.

object_elements_test():
  object_elements() returns information about the
  triangular elements and nodes forming an object.

  #  (X,Y)

  1: (-1,3)
  2: (-0.5,3.5)
  3: (0,0)
  4: (0,1)
  5: (0,2)
  6: (0,3)
  7: (0,4)
  8: (0.5,0.5)
  9: (0.5,1.5)
  10: (0.5,2.5)
  11: (0.5,3.5)
  12: (0.5,4.5)
  13: (1,1)
  14: (1,2)
  15: (1,3)
  16: (1,4)
  17: (1,5)
  18: (1.5,1.5)
  19: (1.5,2.5)
  20: (1.5,3.5)
  21: (1.5,4.5)
  22: (1.5,5.5)
  23: (2,2)
  24: (2,3)
  25: (2,4)
  26: (2,5)
  27: (2,6)
  28: (2.5,2.5)
  29: (2.5,3.5)
  30: (2.5,4.5)
  31: (2.5,5.5)
  32: (3,3)
  33: (3,4)
  34: (3,5)
  35: (3,6)
  36: (3.5,3.5)
  37: (3.5,4.5)
  38: (3.5,5.5)
  39: (4,4)
  40: (4,5)
  41: (4,6)
  42: (4.5,4.5)
  43: (4.5,5.5)
  44: (5,5)
  45: (5,6)
  46: (5.5,5.5)
  47: (6,6)

  #  Type  (N1,N2,N3)

  1: 1  (1,6,2)
  2: 2  (6,7,2)
  3: 3  (13,4,8)
  4: 4  (4,3,8)
  5: 1  (4,13,9)
  6: 2  (13,14,9)
  7: 3  (14,5,9)
  8: 4  (5,4,9)
  9: 1  (5,14,10)
  10: 2  (14,15,10)
  11: 3  (15,6,10)
  12: 4  (6,5,10)
  13: 1  (6,15,11)
  14: 2  (15,16,11)
  15: 3  (16,7,11)
  16: 4  (7,6,11)
  17: 1  (7,16,12)
  18: 2  (16,17,12)
  19: 3  (23,14,18)
  20: 4  (14,13,18)
  21: 1  (14,23,19)
  22: 2  (23,24,19)
  23: 3  (24,15,19)
  24: 4  (15,14,19)
  25: 1  (15,24,20)
  26: 2  (24,25,20)
  27: 3  (25,16,20)
  28: 4  (16,15,20)
  29: 1  (16,25,21)
  30: 2  (25,26,21)
  31: 3  (26,17,21)
  32: 4  (17,16,21)
  33: 1  (17,26,22)
  34: 2  (26,27,22)
  35: 3  (32,24,28)
  36: 4  (24,23,28)
  37: 1  (24,32,29)
  38: 2  (32,33,29)
  39: 3  (33,25,29)
  40: 4  (25,24,29)
  41: 1  (25,33,30)
  42: 2  (33,34,30)
  43: 3  (34,26,30)
  44: 4  (26,25,30)
  45: 1  (26,34,31)
  46: 2  (34,35,31)
  47: 3  (35,27,31)
  48: 4  (27,26,31)
  49: 3  (39,33,36)
  50: 4  (33,32,36)
  51: 1  (33,39,37)
  52: 2  (39,40,37)
  53: 3  (40,34,37)
  54: 4  (34,33,37)
  55: 1  (34,40,38)
  56: 2  (40,41,38)
  57: 3  (41,35,38)
  58: 4  (35,34,38)
  59: 3  (44,40,42)
  60: 4  (40,39,42)
  61: 1  (40,44,43)
  62: 2  (44,45,43)
  63: 3  (45,41,43)
  64: 4  (41,40,43)
  65: 3  (47,45,46)
  66: 4  (45,44,46)

object_elements_test():
  Normal end of execution.

rectangle_elements_test():
  rectangle_elements() returns information about the
  triangular elements forming a rectangle.

  #  Type  (N1,N2,N3)

  1: 1  (1,8,5)
  2: 2  (8,9,5)
  3: 3  (9,2,5)
  4: 4  (2,1,5)
  5: 1  (2,9,6)
  6: 2  (9,10,6)
  7: 3  (10,3,6)
  8: 4  (3,2,6)
  9: 1  (3,10,7)
  10: 2  (10,11,7)
  11: 3  (11,4,7)
  12: 4  (4,3,7)
  13: 1  (8,15,12)
  14: 2  (15,16,12)
  15: 3  (16,9,12)
  16: 4  (9,8,12)
  17: 1  (9,16,13)
  18: 2  (16,17,13)
  19: 3  (17,10,13)
  20: 4  (10,9,13)
  21: 1  (10,17,14)
  22: 2  (17,18,14)
  23: 3  (18,11,14)
  24: 4  (11,10,14)
  25: 1  (15,22,19)
  26: 2  (22,23,19)
  27: 3  (23,16,19)
  28: 4  (16,15,19)
  29: 1  (16,23,20)
  30: 2  (23,24,20)
  31: 3  (24,17,20)
  32: 4  (17,16,20)
  33: 1  (17,24,21)
  34: 2  (24,25,21)
  35: 3  (25,18,21)
  36: 4  (18,17,21)
  37: 1  (22,29,26)
  38: 2  (29,30,26)
  39: 3  (30,23,26)
  40: 4  (23,22,26)
  41: 1  (23,30,27)
  42: 2  (30,31,27)
  43: 3  (31,24,27)
  44: 4  (24,23,27)
  45: 1  (24,31,28)
  46: 2  (31,32,28)
  47: 3  (32,25,28)
  48: 4  (25,24,28)

rectangle_elements_test():
  Normal end of execution.

rectangle_nodes_test():
  rectangle_nodes() returns coordinates of the
  nodes forming a rectangle.

  #  (X,Y)

  1: (0,0)
  2: (0,1)
  3: (0,2)
  4: (0,3)
  5: (0.5,0.5)
  6: (0.5,1.5)
  7: (0.5,2.5)
  8: (1,0)
  9: (1,1)
  10: (1,2)
  11: (1,3)
  12: (1.5,0.5)
  13: (1.5,1.5)
  14: (1.5,2.5)
  15: (2,0)
  16: (2,1)
  17: (2,2)
  18: (2,3)
  19: (2.5,0.5)
  20: (2.5,1.5)
  21: (2.5,2.5)
  22: (3,0)
  23: (3,1)
  24: (3,2)
  25: (3,3)
  26: (3.5,0.5)
  27: (3.5,1.5)
  28: (3.5,2.5)
  29: (4,0)
  30: (4,1)
  31: (4,2)
  32: (4,3)

rectangle_nodes_test():
  Normal end of execution.

t_configuration_test():
  This is a simple program to illustrate how a tile
  configuration can be "good" (completely inside the grid) or
  "bad" (not completely inside the grid).

label =

  0x0 empty char array

  Graphics saved as "configuration_bad.png"

label =

  0x0 empty char array

  Graphics saved as "configuration_good.png"

t_grid_word_test():
  t_grid_word() returns the boundary word of a grid.

  "The T"
  boundary word:  "AAACCCCCCCCCAAACCCEEEEEEEEEGGGAAAGGGGGGGGG"
  base point   :  [ 0, 0 ]

  "The Arrow"
  boundary word:  "AAACCCCCCAAAADDDDDDFFFFFFAAAAAGGGGGG"
  base point   :  [ 0, 0 ]

  "The Rhombus"
  boundary word:  "AAAAAAAAABBBBBBEEEEEEEEEFFFFFF"
  base point   :  [ 0, 0 ]

  "The Fat Arrow"
  boundary word:  "AAAAAACCCAAADDDDDDFFFFFFAAAGGG"
  base point   :  [ 0, 0 ]

t_grid_word_test():
  Normal end of execution.

t_gurobi_test():
  Examine a t solution from gurobi().

gurobi_solution_read():
  Extract information from GUROBI file "t_gurobi.sol".
  The file contains 219 lines of information.

  The file contains 4 nonzero values.
  X array size adjusted to 218

t_solution_plot():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Plot a T-puzzle solution.
  Tile = 1, VAR = 15,  Rotate = 2, reflect = 1,  type = 1  pij = (3,0)
  Tile = 2, VAR = 22,  Rotate = 2, reflect = 1,  type = 2  pij = (3,6)
  Tile = 3, VAR = 61,  Rotate = 2, reflect = 1,  type = 2  pij = (6,9)
  Tile = 4, VAR = 114,  Rotate = 1, reflect = 0,  type = 1  pij = (-3,12)
  Graphics saved as "t_gurobi.png"

t_solution_plot():
  Normal end of execution.

t_gurobi_test():
  Normal end of execution.

t_gurobi_test():
  Examine a arrow solution from gurobi().

gurobi_solution_read():
  Extract information from GUROBI file "arrow_gurobi.sol".
  The file contains 221 lines of information.

  The file contains 4 nonzero values.
  X array size adjusted to 220

t_solution_plot():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Plot a T-puzzle solution.
  Tile = 1, VAR = 8,  Rotate = 2, reflect = 1,  type = 1  pij = (3,0)
  Tile = 2, VAR = 12,  Rotate = 0, reflect = 1,  type = 2  pij = (1,12)
  Tile = 3, VAR = 44,  Rotate = 2, reflect = 0,  type = 1  pij = (0,9)
  Tile = 4, VAR = 82,  Rotate = 0, reflect = 0,  type = 1  pij = (-2,9)
  Graphics saved as "arrow_gurobi.png"

t_solution_plot():
  Normal end of execution.

t_gurobi_test():
  Normal end of execution.

t_gurobi_test():
  Examine a rhombus solution from gurobi().

gurobi_solution_read():
  Extract information from GUROBI file "rhombus_gurobi.sol".
  The file contains 281 lines of information.

  The file contains 4 nonzero values.
  X array size adjusted to 280

t_solution_plot():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Plot a T-puzzle solution.
  Tile = 1, VAR = 5,  Rotate = 3, reflect = 1,  type = 1  pij = (9,3)
  Tile = 2, VAR = 14,  Rotate = 0, reflect = 0,  type = 1  pij = (9,0)
  Tile = 3, VAR = 30,  Rotate = 0, reflect = 0,  type = 1  pij = (6,3)
  Tile = 4, VAR = 262,  Rotate = 3, reflect = 1,  type = 1  pij = (6,6)
  Graphics saved as "rhombus_gurobi.png"

t_solution_plot():
  Normal end of execution.

t_gurobi_test():
  Normal end of execution.

t_gurobi_test():
  Examine a fatarrow solution from gurobi().

gurobi_solution_read():
  Extract information from GUROBI file "fatarrow_gurobi.sol".
  The file contains 305 lines of information.

  The file contains 4 nonzero values.
  X array size adjusted to 304

t_solution_plot():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Plot a T-puzzle solution.
  Tile = 1, VAR = 1,  Rotate = 0, reflect = 0,  type = 1  pij = (0,0)
  Tile = 2, VAR = 11,  Rotate = 3, reflect = 0,  type = 2  pij = (9,3)
  Tile = 3, VAR = 97,  Rotate = 3, reflect = 0,  type = 1  pij = (6,0)
  Tile = 4, VAR = 277,  Rotate = 3, reflect = 1,  type = 1  pij = (0,6)
  Graphics saved as "fatarrow_gurobi.png"

t_solution_plot():
  Normal end of execution.

t_gurobi_test():
  Normal end of execution.

t_puzzle_lp():
  Define the T puzzle and a set of tiles.
  Set up the linear system A*x=b for the tiling problem.
  Use sparse storage for the matrix A.
  Write that information to an LP file.

  Tile configuration counts:

  1  20
  2  2
  3  56
  4  70

  linear programming system computed.
  matrix A1 has 216 rows, 148 columns, 5544 nonzeros
  matrix A2 has 4 rows, 148 columns, 148 nonzeros

  The lp file has been saved as "t.lp"

t_puzzle_lp():
  Normal end of execution.

t_puzzle_lp():
  Define the T puzzle and a set of tiles.
  Set up the linear system A*x=b for the tiling problem.
  Use sparse storage for the matrix A.
  Write that information to an LP file.

  Tile configuration counts:

  1  11
  2  2
  3  59
  4  74

  linear programming system computed.
  matrix A1 has 216 rows, 146 columns, 4932 nonzeros
  matrix A2 has 4 rows, 146 columns, 146 nonzeros

  The lp file has been saved as "arrow.lp"

t_puzzle_lp():
  Normal end of execution.

t_puzzle_lp():
  Define the T puzzle and a set of tiles.
  Set up the linear system A*x=b for the tiling problem.
  Use sparse storage for the matrix A.
  Write that information to an LP file.

  Tile configuration counts:

  1  8
  2  12
  3  84
  4  88

  linear programming system computed.
  matrix A1 has 216 rows, 192 columns, 6624 nonzeros
  matrix A2 has 4 rows, 192 columns, 192 nonzeros

  The lp file has been saved as "rhombus.lp"

t_puzzle_lp():
  Normal end of execution.

t_puzzle_lp():
  Define the T puzzle and a set of tiles.
  Set up the linear system A*x=b for the tiling problem.
  Use sparse storage for the matrix A.
  Write that information to an LP file.

  Tile configuration counts:

  1  4
  2  8
  3  100
  4  96

  linear programming system computed.
  matrix A1 has 216 rows, 208 columns, 6816 nonzeros
  matrix A2 has 4 rows, 208 columns, 208 nonzeros

  The lp file has been saved as "fatarrow.lp"

t_puzzle_lp():
  Normal end of execution.

t_tile_word_test():
  t_tile_word() returns the boundary word of a tile.

  "T puzzle tile #1"
  boundary word:  "AAACCCCCCCCCFFFGGGGGG"
  base point   :  [ 0, 0 ]

  "T puzzle tile #2"
  boundary word:  "BBBBBBEEEEFFFAGGG"
  base point   :  [ 0, 0 ]

  "T puzzle tile #3"
  boundary word:  "AABBBEEEEEGGG"
  base point   :  [ 0, 0 ]

  "T puzzle tile #4"
  boundary word:  "AAACCCFFF"
  base point   :  [ 0, 0 ]

t_tile_word_test():
  Normal end of execution.

word_plot_test():
  word_plot() plots a polyabolo from its boundary word.
  Graphics saved as "word_plot_t.png"
  Graphics saved as "word_plot_arrow.png"
  Graphics saved as "word_plot_rhombus.png"
  Graphics saved as "word_plot_fatarrow.png"
  Graphics saved as "word_plot_tile1.png"
  Graphics saved as "word_plot_tile2.png"
  Graphics saved as "word_plot_tile3.png"
  Graphics saved as "word_plot_tile4.png"

word_plot_test():
  Normal end of execution.

t_puzzle_test():
  Normal end of execution.

13-Jun-2022 18:44:23