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13-May-2025 19:06:25

trinity_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7.
  trinity() implements a linear programming
  approach to the trinity tiling problem.

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

  LP system computed.
  Matrix A has 148 rows, 142 columns, 5254 nonzeros

  LP information saved as "trinity.lp"

lp_generate():
  Normal end of execution.

trinity_lp_alt():
  Define the trinity puzzle and a set of tiles.
  Set up the linear system A*x=b defining the tiling problem.
  Use sparse storage for the matrix A.
  Write that information to an LP file.
  An alternative form for the objective function is to be used.

  trinity system computed.
  matrix A has 148 rows, 142 columns, 5254 nonzeros

  trinity information saved as "trinity_alt.lp"

trinity_alt_lp():
  Normal end of execution.

trinity_lpa():
  Define the trinity puzzle and a set of tiles.
  Set up the linear system A*x=b defining the tiling problem.
  Use sparse storage for the matrix A.
  Write that information to an LP file.
  An alternative form for the objective function is to be used.

  trinity system computed.
  matrix A1 has 144 rows, 142 columns, 5112 nonzeros
  matrix A2 has 4 rows, 142 columns

  trinity information saved as "trinity_lpa.lp"

trinity_lpa():
  Normal end of execution.

trinity_cplex_test():
  Examine the trinity() solution from cplex().

solution_plot():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Plot a solution generated by cplex().
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)
  Graphics saved as "trinity_cplex.png"

solution_plot():
  Normal end of execution.

solution_tikz_ij():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Make a tikz() image of a tiling solution.
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)
  tikz image saved as "trinity_cplex_ij.tex"

solution_tikz_ij():
  Normal end of execution.

solution_tikz_xy():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Make a tikz() image of a tiling solution.
  The (x,y) coordinate system is used.
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)  pxy=(3,3.4641)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)  pxy=(2.5,0.866025)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)  pxy=(1.5,0.866025)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)  pxy=(2,0)
  tikz image saved as "trinity_cplex_xy.tex"

solution_tikz_xy():
  Normal end of execution.

solution_print():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Print, for each configuration in a solution,
  the grid elements and (i,j) vertex
  coordinates covered by the configuration.
  Configuration 26 used in solution.
  Tile = 1, VAR_NUM = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Configuration 47 used in solution.
  Tile = 2, VAR_NUM = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Configuration 76 used in solution.
  Tile = 3, VAR_NUM = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Configuration 142 used in solution.
  Tile = 4, VAR_NUM = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)

solution_print():
  Normal end of execution.

trinity_cplex_test():
  Normal end of execution.

trinity_gurobi_test():
  Examine the trinity() solution from gurobi().

gurobi_solution_read():
  Extract information from GUROBI file "trinity_gurobi.sol".
  The file contains 143 lines of information.

  The file contains 4 nonzero values.
  X array size adjusted to 142

solution_plot():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Plot a solution generated by cplex().
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)
  Graphics saved as "trinity_gurobi.png"

solution_plot():
  Normal end of execution.

solution_tikz_ij():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Make a tikz() image of a tiling solution.
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)
  tikz image saved as "trinity_gurobi_ij.tex"

solution_tikz_ij():
  Normal end of execution.

solution_tikz_xy():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Make a tikz() image of a tiling solution.
  The (x,y) coordinate system is used.
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)  pxy=(3,3.4641)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)  pxy=(2.5,0.866025)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)  pxy=(1.5,0.866025)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)  pxy=(2,0)
  tikz image saved as "trinity_gurobi_xy.tex"

solution_tikz_xy():
  Normal end of execution.

solution_print():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Print, for each configuration in a solution,
  the grid elements and (i,j) vertex
  coordinates covered by the configuration.
  Configuration 26 used in solution.
  Tile = 1, VAR_NUM = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Configuration 47 used in solution.
  Tile = 2, VAR_NUM = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Configuration 76 used in solution.
  Tile = 3, VAR_NUM = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Configuration 142 used in solution.
  Tile = 4, VAR_NUM = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)

solution_print():
  Normal end of execution.

trinity_gurobi_test():
  Normal end of execution.

trinity_scip_test():
  Examine the trinity() solution from scip().

scip_solution_read():
  Extract solution information from an SCIP solution file.
  File contains 6 lines
  Number of nonzero entries in X is 4

solution_plot():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Plot a solution generated by cplex().
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)
  Graphics saved as "trinity_scip.png"

solution_plot():
  Normal end of execution.

solution_tikz_ij():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Make a tikz() image of a tiling solution.
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)
  tikz image saved as "trinity_scip_ij.tex"

solution_tikz_ij():
  Normal end of execution.

solution_tikz_xy():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Make a tikz() image of a tiling solution.
  The (x,y) coordinate system is used.
  Tile = 1, VAR = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)  pxy=(3,3.4641)
  Tile = 2, VAR = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)  pxy=(2.5,0.866025)
  Tile = 3, VAR = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)  pxy=(1.5,0.866025)
  Tile = 4, VAR = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)  pxy=(2,0)
  tikz image saved as "trinity_scip_xy.tex"

solution_tikz_xy():
  Normal end of execution.

solution_print():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  Print, for each configuration in a solution,
  the grid elements and (i,j) vertex
  coordinates covered by the configuration.
  Configuration 26 used in solution.
  Tile = 1, VAR_NUM = 26,  Rotate = 4, reflect = 0,  type = -5  pij = (12,24)
  Configuration 47 used in solution.
  Tile = 2, VAR_NUM = 47,  Rotate = 2, reflect = 0,  type = -6  pij = (10,6)
  Configuration 76 used in solution.
  Tile = 3, VAR_NUM = 76,  Rotate = 2, reflect = 0,  type = 2  pij = (6,6)
  Configuration 142 used in solution.
  Tile = 4, VAR_NUM = 142,  Rotate = 5, reflect = 1,  type = -6  pij = (8,0)

solution_print():
  Normal end of execution.

trinity_scip_test():
  Normal end of execution.

trinity_test():
  Normal end of execution.

13-May-2025 19:06:44