[python]pycddlib使用案例
测试版本：
pycddlib==3.0.2
Examples
The following examples presume:
>>> import cdd >>> from pprint import pprint
Checking and Removing Redundancies
>>> array = [[2, 1, 2, 3], [0, 1, 2, 3], [3, 0, 1, 2], [0, -2, -4, -6]]
>>> mat = cdd.matrix_from_array(array, rep_type=cdd.RepType.INEQUALITY)
>>> cdd.redundant(mat, 0) is None
True
>>> cdd.redundant(mat, 1)
[5.0, -3.0, 0.0]
>>> cdd.redundant(mat, 2)
[8.0, -4.0, 0.0]
>>> cdd.redundant(mat, 3)
[6.4999..., -3.0, 0.0]
>>> cdd.redundant_rows(mat)
{0}
>>> cdd.matrix_canonicalize(mat)
({1, 3}, {0}, [None, 0, 1, None])
>>> pprint(mat.array)
[[0.0, 1.0, 2.0, 3.0], [3.0, 0.0, 1.0, 2.0]]
>>> mat.lin_set
{0}
Solving Linear Programs
>>> array = [ ... [4 / 3, -2, -1], # 0 <= 4/3-2x-y ... [2 / 3, 0, -1], # 0 <= 2/3-y ... [0, 1, 0], # 0 <= x ... [0, 0, 1], # 0 <= y ... [0, 3, 4], # obj func: 3x+4y ... ] >>> lp = cdd.linprog_from_array(array, obj_type=cdd.LPObjType.MAX) >>> cdd.linprog_solve(lp) >>> lp.status == cdd.LPStatusType.OPTIMAL True >>> lp.obj_value 3.666666... >>> lp.primal_solution [0.333333..., 0.666666...] >>> lp.dual_solution [(0, 1.5), (1, 2.5)]
Calculating Extreme Points / Rays
This is the sampleh1.ine example that comes with cddlib.
>>> array = [[2, -1, -1, 0], [0, 1, 0, 0], [0, 0, 1, 0]]
>>> mat = cdd.matrix_from_array(array, rep_type=cdd.RepType.INEQUALITY)
>>> poly = cdd.polyhedron_from_matrix(mat)
>>> ext = cdd.copy_generators(poly)
>>> ext.rep_type
<RepType.GENERATOR: 2>
>>> pprint(ext.array)
[[1.0, 0.0, 0.0, 0.0],[1.0, 2.0, 0.0, 0.0],[1.0, 0.0, 2.0, 0.0],[0.0, 0.0, 0.0, 1.0]]
>>> ext.lin_set # note: first row is 0, so fourth row is 3
{3}
Matrix Rank
>>> # row 3 = row 1 - row 2
>>> # col 2 = 2 * col 1
>>> array = [[1, 2, 0, 1], [1, 2, 1, 3], [0, 0, -1, -2]]
>>> mat = cdd.matrix_from_array(array)
>>> row_basis, col_basis, rank = cdd.matrix_rank(mat)
>>> row_basis
{0, 1}
>>> col_basis
{0, 2}
>>> rank
2
Matrix Adjacencies
>>> # H-representation of a square
>>> # 0 <= 1 + x1 (face 0)
>>> # 0 <= 1 + x2 (face 1)
>>> # 0 <= 1 - x1 (face 2)
>>> # 0 <= 1 - x2 (face 3)
>>> #
>>> # +---(3)---+
>>> # | |
>>> # | |
>>> # (0) (2)
>>> # | |
>>> # | |
>>> # +---(1)---+
>>> array = [[1, 1, 0], [1, 0, 1], [1, -1, 0], [1, 0, -1]]
>>> mat = cdd.matrix_from_array(array, rep_type=cdd.RepType.INEQUALITY)
>>> cdd.matrix_adjacency(mat)
[{1, 3}, {0, 2}, {1, 3}, {0, 2}]
>>> # V-representation of a square
>>> #
>>> # 1-----3
>>> # | |
>>> # | |
>>> # 0-----2
>>> array = [[1, -1, -1], [1, -1, 1], [1, 1, -1], [1, 1, 1]]
>>> mat = cdd.matrix_from_array(array, rep_type=cdd.RepType.GENERATOR)
>>> cdd.matrix_adjacency(mat)
[{1, 2}, {0, 3}, {0, 3}, {1, 2}]
Polyhedron Adjacencies and Incidences
>>> # H-representation of a square
>>> # 0 <= 1 + x1 (face 0)
>>> # 0 <= 1 + x2 (face 1)
>>> # 0 <= 1 - x1 (face 2)
>>> # 0 <= 1 - x2 (face 3)
>>> array = [[1, 1, 0], [1, 0, 1], [1, -1, 0], [1, 0, -1]]
>>> mat = cdd.matrix_from_array(array, rep_type=cdd.RepType.INEQUALITY)
>>> poly = cdd.polyhedron_from_matrix(mat)
>>> gen = cdd.copy_generators(poly)
>>> gen.rep_type
<RepType.GENERATOR: 2>
>>> pprint(gen.array, width=40)
[[1.0, 1.0, -1.0],[1.0, 1.0, 1.0],[1.0, -1.0, 1.0],[1.0, -1.0, -1.0]]
>>> gen.lin_set
set()
>>> # V-representation of this square
>>> #
>>> # 2---(3)---1
>>> # | |
>>> # | |
>>> # (0) (2)
>>> # | |
>>> # | |
>>> # 3---(1)---0
>>> #
>>> # vertex 0 is adjacent to vertices 1 and 3
>>> # vertex 1 is adjacent to vertices 0 and 2
>>> # vertex 2 is adjacent to vertices 1 and 3
>>> # vertex 3 is adjacent to vertices 0 and 2
>>> cdd.copy_adjacency(poly)
[{1, 3}, {0, 2}, {1, 3}, {0, 2}]
>>> # vertex 0 is the intersection of faces (1) and (2)
>>> # vertex 1 is the intersection of faces (2) and (3)
>>> # vertex 2 is the intersection of faces (0) and (3)
>>> # vertex 3 is the intersection of faces (0) and (1)
>>> cdd.copy_incidence(poly)
[{1, 2}, {2, 3}, {0, 3}, {0, 1}]
>>> # face (0) is adjacent to faces (1) and (3)
>>> # face (1) is adjacent to faces (0) and (2)
>>> # face (2) is adjacent to faces (1) and (3)
>>> # face (3) is adjacent to faces (0) and (2)
>>> cdd.copy_input_adjacency(poly)
[{1, 3}, {0, 2}, {1, 3}, {0, 2}, set()]
>>> # face (0) intersects with vertices 2 and 3
>>> # face (1) intersects with vertices 0 and 3
>>> # face (2) intersects with vertices 0 and 1
>>> # face (3) intersects with vertices 1 and 2
>>> cdd.copy_input_incidence(poly)
[{2, 3}, {0, 3}, {0, 1}, {1, 2}, set()]
>>> # add a vertex, and construct new polyhedron
>>> cdd.matrix_append_to(gen, cdd.matrix_from_array([[1, 0, 2]]))
>>> vpoly = cdd.polyhedron_from_matrix(gen)
>>> vmat = cdd.copy_inequalities(vpoly)
>>> vmat.rep_type
<RepType.INEQUALITY: 1>
>>> pprint(vmat.array)
[[1.0, 0.0, 1.0],[2.0, 1.0, -1.0],[1.0, 1.0, 0.0],[2.0, -1.0, -1.0],[1.0, -1.0, 0.0]]
>>> vmat.lin_set
set()
>>> # so now we have:
>>> # 0 <= 1 + x2
>>> # 0 <= 2 + x1 - x2
>>> # 0 <= 1 + x1
>>> # 0 <= 2 - x1 - x2
>>> # 0 <= 1 - x1
>>> #
>>> # graphical depiction of vertices and faces:
>>> #
>>> # 4
>>> # / \
>>> # / \
>>> # (1) (3)
>>> # / \
>>> # 2 1
>>> # | |
>>> # | |
>>> # (2) (4)
>>> # | |
>>> # | |
>>> # 3---(0)---0
>>> #
>>> # for each face, list adjacent faces
>>> cdd.copy_adjacency(vpoly)
[{2, 4}, {2, 3}, {0, 1}, {1, 4}, {0, 3}]
>>> # for each face, list adjacent vertices
>>> cdd.copy_incidence(vpoly)
[{0, 3}, {2, 4}, {2, 3}, {1, 4}, {0, 1}]
>>> # for each vertex, list adjacent vertices
>>> cdd.copy_input_adjacency(vpoly)
[{1, 3}, {0, 4}, {3, 4}, {0, 2}, {1, 2}]
>>> # for each vertex, list adjacent faces
>>> cdd.copy_input_incidence(vpoly)
[{0, 4}, {3, 4}, {1, 2}, {0, 2}, {1, 3}]
Fourier and Block Elimination
The next example is taken from Wikipedia.
>>> array = [
... [10, -2, 5, -4], # 2x-5y+4z<=10
... [9, -3, 6, -3], # 3x-6y+3z<=9
... [-7, 1, -5, 2], # -x+5y-2z<=-7
... [12, 3, -2, -6], # -3x+2y+6z<=12
... ]
>>> mat = cdd.matrix_from_array(array, rep_type=cdd.RepType.INEQUALITY)
>>> cdd.fourier_elimination(mat).array
[[-1.0, 0.0, -1.25], [-1.0, -1.0, -1.0], [-1.5, 1.0, -2.833333...]]
>>> cdd.block_elimination(mat, {3}).array
[[-4.0, 0.0, -5.0], [-1.5, -1.5, -1.5], [-9.0, 6.0, -17.0]]
案例来自：Examples — pycddlib 3.0.2 documentation