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22-Apr-2023 15:26:33

variomino_test():
  MATLAB/Octave version 9.14.0.2206163 (R2023a)
  variomino() analyzes polyominoes with numeric variety.

cplex_solution_read_test():
  MATLAB/Octave version 9.14.0.2206163 (R2023a)
  cplex_solution_read() reads the cplex() XML file "reid.sol"

  10x4 solution data:
  Number of nonzero entries per column:
  4  4  4  4
  Sum of entries per column:
  4  4  4  4

   1:    1  1  0  0
   2:    0  0  1  1
   3:    0  1  0  0
   4:    0  0  0  1
   5:    1  0  0  0
   6:    0  0  1  0
   7:    0  1  1  1
   8:    0  0  0  1
   9:    1  0  0  0
  10:    1  1  1  0

  Wrote the ASCII file "reid.txt"

variomino_area_test():
  variomino_area() returns the area of a variomino.

  variomino #1:

  1212
  Area is 4

  variomino #2:

  21.
  .2.
  .12
  Area is 5

  variomino #3:

  2..
  123
  Area is 4

  variomino #4:

  ....3.
  1...23
  3.231.
  2.1.3.
  12312.
  Area is 16

variomino_condense_test():
  variomino_condense() "cleans up" a matrix that
  represents a variomino by eliminating initial and final:
  rows and columns of zeros.

  The initial (3,3) variomino P:

  .12
  23.
  .2.

  The condensed (3,3) variomino Q:

  .12
  23.
  .2.

  The initial (4,4) variomino P:

  ....
  .23.
  .12.
  ....

  The condensed (2,2) variomino Q:

  23
  12

  The initial (3,4) variomino P:

  31.3
  ....
  12.1

  The condensed (3,4) variomino Q:

  31.3
  ....
  12.1

  The initial (2,4) variomino P:

  ....
  ....

  The condensed (0,0) variomino Q:

  [ Null matrix ]

variomino_embed_list_test():
  variomino_embed_list() lists the offsets used
  to embed a fixed variomino in a region.

  region R:

  .231
  31.3
  2312
  1.31

  variomino P:

  231
  1..

  P can be embedded in R in 2 ways

  Embedding number 1:

  0***
  3*03
  2312
  1031

  Embedding number 2:

  0231
  3103
  ***2
  *031

variomino_embed_number_test():
  variomino_embed_number() reports the number of ways a
  fixed variomino can be embedded in a region.

  Region R:

  .231
  31.3
  2312
  1.31

  variomino P:

  .1
  .3
  12

  P can be embedded in R in 1 ways

  variomino P:

  231
  1..

  P can be embedded in R in 2 ways

variomino_equal_test():
  variomino_equal() determines if variominoes are equal.

  The variomino P1:

  3.23
  231.
  .23.

  The variomino P2:

  3.23
  231.
  .23.

  The variomino P3:

  3.23.
  231..
  .23..

  The variomino P4:

  3.23
  231.
  .23.

  P1 == P1? true
  P1 == P2? false
  P1 == P3? false
  P1 == P4? true

variomino_index_test():
  variomino_index() assigns an index to each nonzero entry
  of a variomino.

  The variomino P:

  3.23
  231.
  .23.

  PIN: Index vector for P:

 1 0 5 8
 2 3 6 0
 0 4 7 0

variomino_lp_write_test():
  variomino_lp_write() writes an LP file associated
  with an integer linear programming problem for tiling
  a region with copies of three variominoes.

  variomino_lp_write() created the LP file "reid.lp"

variomino_matrix_test():
  variomino_matrix() sets up the linear system
  associated with a variomino tiling problem.

  Region R:

  31.
  231
  123

  variomino N:

  12

  variomino O:

  23

  variomino P:

  13

  Linear system has order (11,10) = 
  System matrix A and right hand side B:

   1:   0 0 0 0 1 0 1 0 0 0   1
   2:   0 1 1 0 1 0 0 0 0 0   1
   3:   1 1 0 0 0 0 0 0 0 0   1
   4:   0 0 0 0 0 0 1 0 1 0   1
   5:   0 0 1 0 0 1 0 1 1 0   1
   6:   1 0 0 1 0 1 0 0 0 0   1
   7:   0 0 0 0 0 0 0 1 0 1   1
   8:   0 0 0 1 0 0 0 0 0 1   1
   9:   1 1 0 0 0 0 0 0 0 0   1
  10:   0 0 1 1 1 1 0 0 0 0   1
  11:   0 0 0 0 0 0 1 1 1 1   2

  Linear system saved in LP file:"reid.lp"

variomino_matrix_reid_test():
  variomino_matrix_reid() sets up the linear system
  associated with the Reid variomino tiling problem.

  System matrix A and right hand side B:

   0 0 0 0 1 0 1 0 0 0   1
   0 1 1 0 1 0 0 0 0 0   1
   1 1 0 0 0 0 0 0 0 0   1
   0 0 0 0 0 0 1 0 1 0   1
   0 0 1 0 0 1 0 1 1 0   1
   1 0 0 1 0 1 0 0 0 0   1
   0 0 0 0 0 0 0 1 0 1   1
   0 0 0 1 0 0 0 0 0 1   1
   1 1 0 0 0 0 0 0 0 0   1
   0 0 1 1 1 1 0 0 0 0   1
   0 0 0 0 0 0 1 1 1 1   2

variomino_print_test():
  variomino_print() prints a variomino.

  variomino #1:

  1231

  variomino #2:

  31.
  .3.
  .23

  variomino #3:

  2..
  123

  variomino #4:

  ....3.
  1...21
  3.231.
  2.1.3.
  12312.

variomino_tiling_print_test
  MATLAB/Octave version 9.14.0.2206163 (R2023a)
  Given a solutions for the Reid variomino
  tiling problem, print corresponding tilings.

  Region R:

  31.
  231
  123

  variomino N:

  12

  variomino O:

  23

  variomino P:

  13
DEBUG: A*x
     1
     1
     1
     1
     1
     1
     1
     1
     1
     1
     2

DEBUG: xi
     1
     0
     0
     0
     2
     0
     0
     0
     3
     4

DEBUG: axi
     2
     2
     1
     3
     3
     1
     4
     4


  Reid variomino tiling
  Numeric Labels

  2 3 0
  2 3 4
  1 1 4

  Reid variomino tiling
  "Colors"

  2 3 0
  2 3 4
  1 1 4

variomino_transform_test():
  variomino_transform() transforms a variomino.
  Generate all 8 combinations of rotation and reflection
  applied to a variomino.

  The given variomino P:

  .31
  12.
  .1.

  P after 0 reflections and 0 rotations:

  .31
  12.
  .1.

  P after 0 reflections and 1 rotations:

  1..
  321
  .1.

  P after 0 reflections and 2 rotations:

  .1.
  .21
  13.

  P after 0 reflections and 3 rotations:

  .1.
  123
  ..1

  P after 1 reflections and 0 rotations:

  13.
  .21
  .1.

  P after 1 reflections and 1 rotations:

  .1.
  321
  1..

  P after 1 reflections and 2 rotations:

  .1.
  12.
  .31

  P after 1 reflections and 3 rotations:

  ..1
  123
  .1.

variomino_variants_test01():
  variomino_variants() determines variants
  of an array of variominoes.

  Region in which variominoes must fit:

  3x5 array of 1 variominoes:

  variomino #1

  31231
  23123
  12312

  Array of variominoes to be analyzed:

  3x5 array of 3 variominoes:

  variomino #1

  1231

  variomino #2

  31.
  .3.
  .23

  variomino #3

  3..
  231

  The variominoes have 18 variants that fit the region

  Variant 1 of variomino 1

  1231

  Variant 2 of variomino 1

  1321

  Variant 3 of variomino 2

  31.
  .3.
  .23

  Variant 4 of variomino 2

  ..3
  132
  3..

  Variant 5 of variomino 2

  32.
  .3.
  .13

  Variant 6 of variomino 2

  ..3
  231
  3..

  Variant 7 of variomino 2

  .13
  .3.
  32.

  Variant 8 of variomino 2

  3..
  132
  ..3

  Variant 9 of variomino 2

  .23
  .3.
  31.

  Variant 10 of variomino 2

  3..
  231
  ..3

  Variant 11 of variomino 3

  3..
  231

  Variant 12 of variomino 3

  .1
  .3
  32

  Variant 13 of variomino 3

  132
  ..3

  Variant 14 of variomino 3

  23
  3.
  1.

  Variant 15 of variomino 3

  ..3
  132

  Variant 16 of variomino 3

  32
  .3
  .1

  Variant 17 of variomino 3

  231
  3..

  Variant 18 of variomino 3

  1.
  3.
  23

variomino_variants_test02():
  variomino_variants() determines variants
  of an array of variominoes.

  Region in which variominoes must fit:

  2312
  1231

  Array of variominoes to be analyzed:

  2x4 array of 3 variominoes:

  variomino #1

  1

  variomino #2

  231

  variomino #3

  ..2
  231

  The variominoes have 7 variants that fit the region

  Variant 1 of variomino 1

  1

  Variant 2 of variomino 2

  231

  Variant 3 of variomino 2

  132

  Variant 4 of variomino 3

  ..2
  231

  Variant 5 of variomino 3

  132
  2..

  Variant 6 of variomino 3

  2..
  132

  Variant 7 of variomino 3

  231
  ..2

variomino_variety_test():
  variomino_variety() returns the variety of a variomino.

  variomino #1:

  1212
  variety: 2  2  0

  variomino #2:

  21.
  .2.
  .12
  variety: 2  3  0

  variomino #3:

  2..
  123
  variety: 1  2  1

  variomino #4:

  ....3.
  1...23
  3.231.
  2.1.3.
  12312.
  variety: 5  5  6

variominoes_print_test():
  variominoes_print() prints an array of variominoes.

  Array of variominoes to be analyzed:

  3x5 array of 3 variominoes:

  variomino #1

  1231

  variomino #2

  31.
  .3.
  .23

  variomino #3

  2..
  123

variomino_test():
  Normal end of execution.
22-Apr-2023 15:26:33