def _f(m: Block):
m.lmbda = Var(vertices, domain=NonNegativeReals) # 非负
m.y = Var(simplices, domain=Binary) # 二进制
m.a0 = Constraint(dimensions, rule=lambda m, d: sum(m.lmbda[v] * pointsT[d][v] for v in vertices) == input[d])
if bound == 'eq':
m.a1 = Constraint(expr=output == sum(m.lmbda[v] * values[v] for v in vertices))
elif bound == 'lb':
m.a1 = Constraint(expr=output <= sum(m.lmbda[v] * values[v] for v in vertices))
elif bound == 'ub':
m.a1 = Constraint(expr=output >= sum(m.lmbda[v] * values[v] for v in vertices))
else:
raise RuntimeError("bound值错误！bound=" + bound)
m.b = Constraint(expr=sum(m.lmbda[v] for v in vertices) == 1)
# generate a map from vertex index to simplex index,
# which avoids an n^2 lookup when generating the
# constraint
vertex_to_simplex = [[] for _ in vertices]
for s, simplex in enumerate(tri.simplices):
for v in simplex:
vertex_to_simplex[v].append(s)
m.c0 = Constraint(vertices, rule=lambda m, v: m.lmbda[v] <= sum(m.y[s] for s in vertex_to_simplex[v]))
m.c1 = Constraint(expr=sum(m.y[s] for s in simplices) == 1)
return m
def dlog(m: Block,
tri: qhull.Delaunay,
values: List[float],
input: List[SimpleVar] = None,
output: SimpleVar = None,
bound: str = 'eq',
**kw):
values = np.array(values).tolist()
ndim = len(input)
nsimplices = len(tri.simplices)
npoints = len(tri.points)
pointsT = list(zip(*tri.points))
# create index objects
dimensions = list(range(ndim))
simplices = list(range(nsimplices)) # 跟单纯形 数量一致
vertices = list(range(npoints))
bound = bound.lower()
L = int(math.ceil(math.log2(nsimplices)))
L_Range = list(range(L))
vp = [0, 1, 2]
#
m.lmbda = Var(simplices, vp, domain=NonNegativeReals) # 非负
m.a0 = Constraint(
dimensions,
rule=lambda m, d: sum(m.lmbda[s, v] * pointsT[d][tri.simplices[s][v]]
for s in simplices for v in vp) == input[d])
if bound == 'eq':
m.a1 = Constraint(expr=output == sum(
m.lmbda[s, v] * values[tri.simplices[s][v]] for s in simplices
for v in vp))
elif bound == 'lb':
m.a1 = Constraint(
expr=output <= sum(m.lmbda[s, v] * values[tri.simplices[s][v]]
for s in simplices for v in vp))
elif bound == 'ub':
m.a1 = Constraint(
expr=output >= sum(m.lmbda[s, v] * values[tri.simplices[s][v]]
for s in simplices for v in vp))
else:
raise RuntimeError("bound值错误！bound=" + bound)
m.b1 = Constraint(expr=sum(m.lmbda[s, v] for s in simplices
for v in vp) == 1)
m.y = Var(L_Range, domain=Binary) # 二进制
m.c0 = Constraint(L_Range,
rule=lambda m, l: sum(m.lmbda[s, v] for s in simplices
if bin(s)[2:].zfill(L)[l] == '1'
for v in vp) <= m.y[l])
m.c1 = Constraint(L_Range,
rule=lambda m, l: sum(m.lmbda[s, v] for s in simplices
if bin(s)[2:].zfill(L)[l] == '0'
for v in vp) <= 1 - m.y[l])
return m
def cc(m: Block,
tri: qhull.Delaunay,
values: List[float],
input: List[SimpleVar] = None,
output: SimpleVar = None,
bound: str = 'eq',
**kw):
values = np.array(values).tolist()
ndim = len(input)
nsimplices = len(tri.simplices)
npoints = len(tri.points)
pointsT = list(zip(*tri.points))
# create index objects
dimensions = list(range(ndim))
simplices = list(range(nsimplices)) # 跟单纯形 数量一致
vertices = list(range(npoints))
bound = bound.lower()
m.lmbda = Var(vertices, domain=NonNegativeReals) # 非负
m.y = Var(simplices, domain=Binary) # 二进制
# m.y = Var(simplices, domain=NonNegativeReals, bounds=(0, 1)) # 二进制
m.a0 = Constraint(dimensions,
rule=lambda m, d: sum(m.lmbda[v] * pointsT[d][v]
for v in vertices) == input[d])
if bound == 'eq':
m.a1 = Constraint(expr=output == sum(m.lmbda[v] * values[v]
for v in vertices))
elif bound == 'lb':
m.a1 = Constraint(expr=output <= sum(m.lmbda[v] * values[v]
for v in vertices))
elif bound == 'ub':
m.a1 = Constraint(expr=output >= sum(m.lmbda[v] * values[v]
for v in vertices))
else:
raise RuntimeError("bound值错误！bound=" + bound)
m.b = Constraint(expr=sum(m.lmbda[v] for v in vertices) == 1)
# generate a map from vertex index to simplex index,
# which avoids an n^2 lookup when generating the
# constraint
vertex_to_simplex = [[] for _ in vertices]
for s, simplex in enumerate(tri.simplices):
for v in simplex:
vertex_to_simplex[v].append(s)
m.c0 = Constraint(
vertices,
rule=lambda m, v: m.lmbda[v] <= sum(m.y[s]
for s in vertex_to_simplex[v]))
m.c1 = Constraint(expr=sum(m.y[s] for s in simplices) == 1)
return m
def log_lp(m: Block, tri: qhull.Delaunay,
values: List[float],
input: List[SimpleVar] = None,
output: SimpleVar = None,
bound: str = 'eq', **kw):
num = kw["num"]
values = np.array(values).tolist()
ndim = len(input)
npoints = len(tri.points)
pointsT = list(zip(*tri.points))
dims = list(range(ndim))
vertices = list(range(npoints))
bound = bound.lower()
# 与 npoints 匹配的索引
# vertices_idx = list(zip(*generate_points([list(range(num)) for _ in range(ndim)])))
vertices_idx = generate_points([list(range(num)) for _ in range(ndim)]).tolist()
if len(vertices_idx) != len(vertices):
raise RuntimeError("生成的的tri需要是米字形！")
# (9a)
m.lmbda = Var(vertices, domain=NonNegativeReals) # 非负
m.a0 = Constraint(dims, rule=lambda m, d: sum(m.lmbda[v] * pointsT[d][v] for v in vertices) == input[d])
m.a_sum = Expression(expr=sum(m.lmbda[v] * values[v] for v in vertices))
if bound == 'eq':
m.a1 = Constraint(expr=output == m.a_sum)
elif bound == 'lb':
m.a1 = Constraint(expr=output <= m.a_sum)
elif bound == 'ub':
m.a1 = Constraint(expr=output >= m.a_sum)
else:
raise RuntimeError("bound值错误！bound=" + bound)
# (9b)
m.b = Constraint(expr=sum(m.lmbda[v] for v in vertices) == 1)
# (9c)
# 约束a和b与cc方法是一样的
K = num - 1 # K 必须是偶数
N = list(range(1, ndim + 1))
log2K = math.ceil(math.log2(K))
L = list(range(1, log2K + 1))
G = generate_gray_code(log2K)
def O(l, b):
# k == 0 或者 k == K 的意思是不能是第一个和最后一个，避免越界
res = []
for k in range(K + 1):
if (k == 0 or G[k - 1][l - 1] == b) and (k == K or G[k][l - 1] == b):
res.append(k)
return res
# return [k for k in range(K + 1) if (k == 0 or G[k][l] == b) and (k == K or G[k + 1][l] == b)]
m.y_s1 = Var(N, L, domain=NonNegativeReals, bounds=(0, 1)) # 二进制
m.c1_s1 = Constraint(N, L, rule=lambda m, s1, s2: sum(
m.lmbda[v] for v, idx in zip(vertices, vertices_idx) if idx[s1 - 1] in O(s2, 1)
) <= m.y_s1[s1, s2])
m.c2_s1 = Constraint(N, L, rule=lambda m, s1, s2: sum(
m.lmbda[v] for v, idx in zip(vertices, vertices_idx) if idx[s1 - 1] in O(s2, 0)
) <= 1 - m.y_s1[s1, s2])
S2 = [(s1, s2) for s1 in N for s2 in N if s1 < s2]
S2_idx = list(range(len(S2)))
m.y_s2 = Var(S2_idx, domain=NonNegativeReals, bounds=(0, 1))
m.c1_s2 = Constraint(S2_idx, rule=lambda m, i: sum(
m.lmbda[v] for v, idx in zip(vertices, vertices_idx) if
idx[S2[i][0] - 1] % 2 == 0 and idx[S2[i][1] - 1] % 2 == 1
) <= m.y_s2[i])
m.c2_s2 = Constraint(S2_idx, rule=lambda m, i: sum(
m.lmbda[v] for v, idx in zip(vertices, vertices_idx) if
idx[S2[i][0] - 1] % 2 == 1 and idx[S2[i][1] - 1] % 2 == 0
) <= 1 - m.y_s2[i])
return m
