"""
finite size scaling tools
"""
from typing import List, Tuple, Optional
import numpy as np
[文档]def data_collapse(
n: List[int],
p: List[float],
obs: List[List[float]],
pc: float,
nu: float,
beta: float = 0,
obs_type: int = 1,
fit_type: int = 0,
dobs: Optional[List[List[float]]] = None,
) -> Tuple[List[float], List[List[float]], List[List[float]], float]:
xL: List[List[float]] = [] # x=(p-pc)L^(1/\nv)
yL: List[List[float]] = [] # y=S(p,L)-S(pc,L) or S(p,L)
pc_list = []
if not isinstance(p[0], list):
p = [p for _ in n] # type: ignore
for n0 in range(len(n)):
xL.append([])
yL.append([])
for p0 in range(len(p[n0])): # type: ignore
xL[n0].append((p[n0][p0] - pc) * (n[n0] ** (1 / nu))) # type: ignore
pc_L = pc_linear_interpolation(p[n0], obs[n0], pc) # type: ignore
if obs_type == 0:
yL[n0].append((obs[n0][p0] - pc_L) * n[n0] ** beta)
# entanglement with only collapse and no crossing
else:
yL[n0].append(obs[n0][p0] * n[n0] ** beta)
# tripartite mutual information
pc_list.append(pc_L)
if fit_type == 0:
xL_all = []
for i in range(len(xL)):
xL_all.extend(xL[i])
yL_ave = []
loss = []
for x0 in range(len(xL_all)):
ybar_list = []
for n0 in range(len(n)):
if xL_all[x0] >= xL[n0][0] and xL_all[x0] <= xL[n0][-1]:
yinsert = pc_linear_interpolation(xL[n0], yL[n0], xL_all[x0])
ybar_list.append(yinsert)
ybar = np.mean(ybar_list)
mean_squared = [(ybar_list[i] - ybar) ** 2 for i in range(len(ybar_list))]
loss.append(np.sum(mean_squared))
yL_ave.append(ybar)
loss = np.sum(loss)
return pc_list, xL, yL, loss # type: ignore
# fit_type == 1
if dobs is None:
raise ValueError("uncertainty of each y has to be specified in `dobs`")
datas = []
for n0 in range(len(n)):
for i in range(len(xL[n0])):
datas.append([xL[n0][i], yL[n0][i], dobs[n0][i]])
datas = sorted(datas, key=lambda x: x[0])
loss = _quality_objective_v2(datas) # type: ignore
return pc_list, xL, yL, loss # type: ignore
def _quality_objective_v2(datas: List[List[float]]) -> float:
# https://journals.aps.org/prb/supplemental/10.1103/PhysRevB.101.060301/Supplement.pdf
loss = []
for i in range(len(datas) - 2):
# i, i+1, i+2
x, y, d = datas[i + 1]
x1, y1, d1 = datas[i]
x2, y2, d2 = datas[i + 2]
if np.abs(x - x1) < 1e-4 or np.abs(x - x2) < 1e-4:
continue
ybar = ((x2 - x) * y1 - (x1 - x) * y2) / (x2 - x1)
delta = (
d**2
+ d1**2 * (x2 - x) ** 2 / (x2 - x1) ** 2
+ d2**2 * (x1 - x) ** 2 / (x2 - x1) ** 2
)
w = (y - ybar) ** 2 / delta
loss.append(w)
return np.mean(loss) # type: ignore
[文档]def pc_linear_interpolation(p: List[float], SA: List[float], pc_input: float) -> float:
if pc_input in p:
pc_index = p.index(pc_input)
pc = SA[pc_index]
else:
pr_index = 0
for p0 in range(len(p)):
if p[p0] > pc_input:
pr_index = p0
break
x = [p[pr_index - 1], p[pr_index]]
y = [SA[pr_index - 1], SA[pr_index]]
linear_model = np.polyfit(x, y, 1)
linear_model_fn = np.poly1d(linear_model)
pc = linear_model_fn(pc_input)
return pc