cbb
6de085fd37
- Kin.cert_lever 用三角不等式给全姿态位移界（替代 JS 随机采样×1.05），界量级 5.93–48.86 mm/整步 - Kin.certify_segments 批量前沿二分+每根查询预算：48 固定段中预算32判安全37/碰撞1/未知拒10， 第180题1.08–1.10s漏检段以5次查询判碰撞；未知只拒不放 - 修 seg_seg_dist 第二条退化成点不投影（模型内退化胶囊686受影响）；但7586个加密点的组最小间隙 逐位不变、2000样本JS对拍仍 PASS → 不解释轮次30漏检、不改既有成绩 - 负结论：B=1 单段认证 P50 22.93/P90 58.43/P99 101.57 ms，432次中225次>20ms； 自适应宽相位 cap 交错复测耗时无收益，先前1.6×为GPU顺序漂移，已在日志撤回 - 成本模型 L=ceil(log2(bound/(ga+gb)))、查询=2^L+1 与实测对齐（安全段2–17次，未知段33–65次） - 新增8项段认证测试+1项回放测试（14→23项通过）；变异实测证明张量 max_depth 回绕会误放行
334 lines
18 KiB
Python
334 lines
18 KiB
Python
"""PyTorch 批量运动学 + 可微胶囊间隙（与 webapp/js/ik-solver.js 同口径）。
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数据来自 ml/assets/kin.json（node ml/prep/export_kin.cjs 生成）：
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- cum_xf / fk / orient：与 JS cumXf / fk(q,0) / orient(q) 一致（角度制输入）
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- gaps(q, cap)：所有 |Δg|≥2 胶囊对的 间隙 = 线段距离 − (r_i + r_j + margin)。
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宽相位复刻 JS 的簇球筛选（被筛掉的对间隙必 > cap），故 min(gap, cap) 与 JS gapMatrix 逐位同口径；
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筛选在 no_grad 下做，幸存对的精确距离保留梯度（APG / FK 损失用）。
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"""
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import json, math, os
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import torch
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HERE = os.path.dirname(os.path.abspath(__file__))
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DEFAULT_KIN = os.path.join(HERE, '..', 'assets', 'kin.json')
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D2R = math.pi / 180.0
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def rot_axis(d, a):
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"""d: [3] 单位轴；a: [...] 弧度 → [..., 3, 3]（Rodrigues，右手）"""
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c, s = torch.cos(a), torch.sin(a)
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x, y, z = float(d[0]), float(d[1]), float(d[2])
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C = 1 - c
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row0 = torch.stack([c + x * x * C, x * y * C - z * s, x * z * C + y * s], -1)
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row1 = torch.stack([y * x * C + z * s, c + y * y * C, y * z * C - x * s], -1)
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row2 = torch.stack([z * x * C - y * s, z * y * C + x * s, c + z * z * C], -1)
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return torch.stack([row0, row1, row2], -2)
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def seg_seg_dist(p1, q1, p2, q2, eps=1e-12):
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"""两线段最近距离（Ericson, Real-Time Collision Detection §5.1.9），[..., 3] → [...]"""
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d1, d2, r = q1 - p1, q2 - p2, p1 - p2
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a = (d1 * d1).sum(-1); e = (d2 * d2).sum(-1); f = (d2 * r).sum(-1)
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c = (d1 * r).sum(-1); b = (d1 * d2).sum(-1)
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denom = a * e - b * b
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s = torch.where(denom > eps, ((b * f - c * e) / denom.clamp_min(eps)).clamp(0, 1), torch.zeros_like(a))
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t = (b * s + f) / e.clamp_min(eps)
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# t 越界：夹回 [0,1] 并重算 s
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t_lo, t_hi = t < 0, t > 1
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s = torch.where(t_lo, (-c / a.clamp_min(eps)).clamp(0, 1), s)
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s = torch.where(t_hi, ((b - c) / a.clamp_min(eps)).clamp(0, 1), s)
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t = t.clamp(0, 1)
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# 第二条退化成点时，仍须在第一条上投影，而不是固定取其起点。
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s = torch.where(e <= eps, (-c / a.clamp_min(eps)).clamp(0, 1), s)
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s = torch.where(a <= eps, torch.zeros_like(s), s)
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t = torch.where(e <= eps, torch.zeros_like(t), t)
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c1 = p1 + d1 * s.unsqueeze(-1)
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c2 = p2 + d2 * t.unsqueeze(-1)
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return ((c1 - c2).pow(2).sum(-1) + 1e-18).sqrt()
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class Kin:
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def __init__(self, path=DEFAULT_KIN, device='cpu', dtype=torch.float32):
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with open(path, 'r', encoding='utf-8') as f:
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K = json.load(f)
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self.fp = K['fp']
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self.device, self.dtype = device, dtype
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T = lambda x, dt=dtype: torch.tensor(x, dtype=dt, device=device)
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self.P = T(K['P']); self.D = [list(map(float, d)) for d in K['D']]
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lim = K['lim']
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self.lo = T([l[0] for l in lim]); self.hi = T([l[1] for l in lim]); self.cont = T([l[2] for l in lim]).bool()
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self.tcp0 = T(K['tcp0']); self.capm = float(K['capm'])
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caps = K['caps']
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self.cap_g = torch.tensor([c['g'] for c in caps], device=device)
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self.cap_a = T([c['a'] for c in caps]); self.cap_b = T([c['b'] for c in caps]); self.cap_r = T([c['r'] for c in caps])
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cl = K['clusters']
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self.cl_g = torch.tensor([c['g'] for c in cl], device=device)
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self.cl_c = T([c['c'] for c in cl])
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cp = K['cpairs']
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self.cp_a = torch.tensor([p[0] for p in cp], device=device)
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self.cp_b = torch.tensor([p[1] for p in cp], device=device)
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self.cp_lim = T([p[2] + p[3] + self.capm for p in cp])
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# 每个簇对展开成胶囊对（全组合），按簇对连续存放
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ci, cj, start, cnt = [], [], [], []
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for p in cp:
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A, B = cl[p[0]]['caps'], cl[p[1]]['caps']
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start.append(len(ci)); cnt.append(len(A) * len(B))
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for i in A:
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for j in B:
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ci.append(i); cj.append(j)
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self.pi = torch.tensor(ci, device=device, dtype=torch.long)
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self.pj = torch.tensor(cj, device=device, dtype=torch.long)
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self.cp_start = torch.tensor(start, device=device, dtype=torch.long)
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self.cp_cnt = torch.tensor(cnt, device=device, dtype=torch.long)
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hl = 0.5 * (self.cap_b - self.cap_a).norm(dim=-1)
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self.pair_need = self.cap_r[self.pi] + self.cap_r[self.pj] + self.capm
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self.pair_bl = hl[self.pi] + hl[self.pj] + self.cap_r[self.pi] + self.cap_r[self.pj] + self.capm
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gi, gj = self.cap_g[self.pi], self.cap_g[self.pj]
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self.pair_gp = torch.minimum(gi, gj) * 7 + torch.maximum(gi, gj)
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self.lever = T(K['lever'])
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table = [[0.0] * 7 for _ in range(6)]
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for group in range(1, 7):
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endpoints = [c[key] for c in caps if c['g'] == group for key in ('a', 'b')]
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if not endpoints:
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continue
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pivot, axis = K['P'][group - 1], K['D'][group - 1]
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unit = [v / math.hypot(*axis) for v in axis]
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relative = [[e[j] - pivot[j] for j in range(3)] for e in endpoints]
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radius = max(math.hypot(*v) for v in relative)
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radial = max(math.hypot(v[1] * unit[2] - v[2] * unit[1],
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v[2] * unit[0] - v[0] * unit[2],
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v[0] * unit[1] - v[1] * unit[0]) for v in relative)
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for joint in range(group):
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chain = sum(math.dist(K['P'][j], K['P'][j + 1]) for j in range(joint, group - 1))
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table[joint][group] = (chain + (radial if joint == group - 1 else radius)) * D2R
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self.cert_groups = torch.tensor([a * 7 + b for a in range(7) for b in range(a + 2, 7)], device=device)
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# 三角不等式给出全姿态界，不用随机姿态最大值冒充上界。
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self.cert_lever = T([[table[k][b] if a <= k < b else 0.0 for k in range(6)]
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for a in range(7) for b in range(a + 2, 7)])
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# ---------------- 运动学 ----------------
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def cum_xf(self, q):
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"""q: [B,6] 度 → Rs [B,7,3,3], Ts [B,7,3]"""
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B = q.shape[0]
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R = torch.eye(3, dtype=q.dtype, device=q.device).expand(B, 3, 3)
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Tt = torch.zeros(B, 3, dtype=q.dtype, device=q.device)
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Rs, Ts = [R], [Tt]
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for k in range(6):
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Rk = rot_axis(self.D[k], q[:, k] * D2R)
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Pk = self.P[k].to(q.dtype)
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tk = Pk - torch.einsum('bij,j->bi', Rk, Pk)
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Tt = torch.einsum('bij,bj->bi', R, tk) + Tt
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R = R @ Rk
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Rs.append(R); Ts.append(Tt)
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return torch.stack(Rs, 1), torch.stack(Ts, 1)
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def fk(self, q, xf=None):
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Rs, Ts = xf if xf is not None else self.cum_xf(q)
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return torch.einsum('bij,j->bi', Rs[:, 6], self.tcp0.to(q.dtype)) + Ts[:, 6]
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def orient(self, q, xf=None):
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Rs, _ = xf if xf is not None else self.cum_xf(q)
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return Rs[:, 6]
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def jac(self, q, xf=None):
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"""几何雅可比（对度）：返回 (Jv [B,3,6] mm/deg, Jw [B,3,6] 单位轴/deg)"""
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Rs, Ts = xf if xf is not None else self.cum_xf(q)
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p = self.fk(q, (Rs, Ts))
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Jv, Jw = [], []
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for k in range(6):
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d = torch.tensor(self.D[k], dtype=q.dtype, device=q.device)
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a = Rs[:, k] @ d
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o = torch.einsum('bij,j->bi', Rs[:, k], self.P[k].to(q.dtype)) + Ts[:, k]
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Jv.append(torch.linalg.cross(a, p - o, dim=-1) * D2R)
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Jw.append(a * D2R)
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return torch.stack(Jv, -1), torch.stack(Jw, -1)
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def caps_world(self, q, xf=None):
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Rs, Ts = xf if xf is not None else self.cum_xf(q)
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Rg, Tg = Rs[:, self.cap_g], Ts[:, self.cap_g] # [B,C,3,3], [B,C,3]
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a = torch.einsum('bcij,cj->bci', Rg, self.cap_a.to(q.dtype)) + Tg
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b = torch.einsum('bcij,cj->bci', Rg, self.cap_b.to(q.dtype)) + Tg
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return a, b
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# ---------------- 间隙 ----------------
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# 2026-10-19（用户实测 dagger/诊断吃满 24 GB 显存）：本模型 1936 条胶囊 / 491 组 / 67256 粗对 / 104.7 万细对。
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# 显存有两段峰值，都随点数线性涨：
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# 粗筛段 cc[:,cp_a]-cc[:,cp_b] 的广播中间量 ≈ 36 B × 点数 × 粗对数（4096 点实测 9.3 GiB，与 cap 无关）；
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# 精算段 ≈ 每对几百字节 × 幸存细对数（4096 点 cap 40 幸存 2.4 亿对；旧版不分块实测 36.9 GiB）。
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# 所以先按 COARSE_ENTRIES 把点切块（粗筛每块 ≤ ~1 GiB），块内再按幸存细对数 PAIR_BUDGET 切（精算每块 ≤ ~1 GiB）。
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# 两段不同时存在，峰值与调用方 batch 大小无关。结果与不分块逐位一致（梯度经 cat 保留）。
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COARSE_ENTRIES = 30_000_000
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PAIR_BUDGET = 2_000_000
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@staticmethod
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def _cat_gaps(parts, starts):
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out = {'gm': torch.cat([p.pop('gm') for p in parts], 0)}
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if 'b' in parts[0]:
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# 非 in-place：b 会被 autograd 的索引反向图引用（APG 的碰撞铰链梯度路径），+= 会让 backward 报 version 错
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for p, s in zip(parts, starts): p['b'] = p['b'] + s
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for k in ('b', 'i', 'j', 'gap'): out[k] = torch.cat([p.pop(k) for p in parts]) # 逐键拼、拼完即释放
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return out
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def gaps(self, q, cap=40.0, xf=None, max_pairs=None, pairs=False):
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"""返回 dict：
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gm [B,49]：组对最小间隙 min(gap, cap)（gA*7+gB，gA<gB；其余为 cap）
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pairs=True 时另有 b, i, j, gap：幸存胶囊对（gap 可微；只有 APG 的 hinge 与 check_parity 需要）
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2026-10-19（用户实测 4096 点 cap 40 峰值 4.46 GiB 全在拼接 8.6e7 对的 b/i/j/gap）：
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默认只返回 gm，每块算完就丢掉胶囊对，峰值只剩单块。
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"""
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xf = xf if xf is not None else self.cum_xf(q)
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Rs, Ts = xf
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B = q.shape[0]
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step = max(1, self.COARSE_ENTRIES // int(self.cp_a.shape[0]))
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if B <= step:
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return self._gaps_split(q, cap, xf, pairs)
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st = list(range(0, B, step))
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return self._cat_gaps([self._gaps_split(q[s:s + step], cap, (Rs[s:s + step], Ts[s:s + step]), pairs) for s in st], st)
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def _coarse(self, q, cap, xf):
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Rs, Ts = xf
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cc = torch.einsum('bkij,kj->bki', Rs[:, self.cl_g], self.cl_c.to(q.dtype)) + Ts[:, self.cl_g]
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d2 = (cc[:, self.cp_a] - cc[:, self.cp_b]).pow(2).sum(-1) # [B,M]
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del cc
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return d2 <= (self.cp_lim + cap).pow(2)
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def _gaps_split(self, q, cap, xf, pairs):
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"""粗筛已在显存预算内：按幸存细对数再切块做精算"""
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Rs, Ts = xf
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B = q.shape[0]
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with torch.no_grad():
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per = (self._coarse(q, cap, xf).long() * self.cp_cnt).sum(1) # [B] 每点幸存细对数
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if B <= 1 or int(per.sum()) <= self.PAIR_BUDGET:
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bounds = [0, B]
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else:
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cs = torch.cumsum(per, 0).tolist(); bounds = [0]; base = 0
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for k, c in enumerate(cs):
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if c - base > self.PAIR_BUDGET and k > bounds[-1]:
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bounds.append(k); base = cs[k - 1]
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bounds.append(B)
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del per
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if len(bounds) == 2:
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return self._gaps_one(q, cap, xf, pairs)
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return self._cat_gaps([self._gaps_one(q[s:e], cap, (Rs[s:e], Ts[s:e]), pairs) for s, e in zip(bounds[:-1], bounds[1:])], bounds[:-1])
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def _gaps_one(self, q, cap, xf, pairs):
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Rs, Ts = xf
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B = q.shape[0]
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with torch.no_grad():
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keep = self._coarse(q, cap, xf)
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bb, mm = keep.nonzero(as_tuple=True)
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del keep
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cnt = self.cp_cnt[mm]
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rep_b = torch.repeat_interleave(bb, cnt)
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off = torch.repeat_interleave(self.cp_start[mm] - torch.cumsum(cnt, 0) + cnt, cnt) + torch.arange(int(cnt.sum()), device=q.device)
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pidx = off
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a, b = self.caps_world(q, xf)
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with torch.no_grad():
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pi, pj = self.pi[pidx], self.pj[pidx]
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mid = 0.5 * (a[rep_b, pi] + b[rep_b, pi] - a[rep_b, pj] - b[rep_b, pj])
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k2 = mid.pow(2).sum(-1) <= (self.pair_bl[pidx] + cap).pow(2)
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rep_b, pidx, pi, pj = rep_b[k2], pidx[k2], pi[k2], pj[k2]
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d = seg_seg_dist(a[rep_b, pi], b[rep_b, pi], a[rep_b, pj], b[rep_b, pj])
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gap = d - self.pair_need[pidx].to(q.dtype)
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gm = torch.full((B * 49,), float(cap), dtype=q.dtype, device=q.device)
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gm = gm.scatter_reduce(0, rep_b * 49 + self.pair_gp[pidx], gap.clamp(max=cap), reduce='amin', include_self=True)
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if not pairs: return {'gm': gm.view(B, 49)}
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return {'gm': gm.view(B, 49), 'b': rep_b, 'i': pi, 'j': pj, 'gap': gap}
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def gm_groups(self, q, gp, cap=40.0):
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"""只算指定组对 gp=[(a,b),...] 的最小间隙 [B,len(gp)]（特征用，避免 49 组全量）。
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数值与 gaps(q,cap)['gm'][:, a*7+b] 一致；组对在碰撞粗对里不存在时返回 cap。"""
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key = tuple(gp)
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if getattr(self, '_gp_key', None) != key:
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m = torch.full((49,), -1, dtype=torch.long, device=q.device)
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for i, (a_, b_) in enumerate(gp): m[min(a_, b_) * 7 + max(a_, b_)] = i
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ga, gb = self.cl_g[self.cp_a], self.cl_g[self.cp_b]
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cg = torch.minimum(ga, gb) * 7 + torch.maximum(ga, gb) # 簇对 → 7 连杆组对
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sel = torch.isin(cg, torch.tensor([min(a, b) * 7 + max(a, b) for a, b in gp], device=q.device))
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self._gp = (m, sel, sel.nonzero(as_tuple=True)[0]); self._gp_key = key
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self._gp49, sel, idx = self._gp
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xf = self.cum_xf(q); Rs, Ts = xf; B = q.shape[0]
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with torch.no_grad():
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cc = torch.einsum('bkij,kj->bki', Rs[:, self.cl_g], self.cl_c.to(q.dtype)) + Ts[:, self.cl_g]
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d2 = (cc[:, self.cp_a[idx]] - cc[:, self.cp_b[idx]]).pow(2).sum(-1)
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keep = d2 <= (self.cp_lim[idx] + cap).pow(2)
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bb, mm = keep.nonzero(as_tuple=True)
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del keep, d2, cc
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cnt = self.cp_cnt[idx][mm]
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rep_b = torch.repeat_interleave(bb, cnt)
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off = torch.repeat_interleave(self.cp_start[idx][mm] - torch.cumsum(cnt, 0) + cnt, cnt) + torch.arange(int(cnt.sum()), device=q.device)
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pidx = off
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a, b = self.caps_world(q, xf)
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with torch.no_grad():
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pi, pj = self.pi[pidx], self.pj[pidx]
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mid = 0.5 * (a[rep_b, pi] + b[rep_b, pi] - a[rep_b, pj] - b[rep_b, pj])
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k2 = mid.pow(2).sum(-1) <= (self.pair_bl[pidx] + cap).pow(2)
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rep_b, pidx, pi, pj = rep_b[k2], pidx[k2], pi[k2], pj[k2]
|
||
d = seg_seg_dist(a[rep_b, pi], b[rep_b, pi], a[rep_b, pj], b[rep_b, pj])
|
||
gap = d - self.pair_need[pidx].to(q.dtype)
|
||
gm = torch.full((B * len(gp),), float(cap), dtype=q.dtype, device=q.device)
|
||
gm = gm.scatter_reduce(0, rep_b * len(gp) + self._gp49[self.pair_gp[pidx]], gap.clamp(max=cap), reduce='amin', include_self=True)
|
||
return gm.view(B, len(gp))
|
||
|
||
@torch.no_grad()
|
||
def certify_segments(self, a, b, max_queries=32, max_depth=12, eps=1e-4, cap=20.0, adaptive_cap=True):
|
||
if self.dtype != torch.float64 or a.dtype != torch.float64 or b.dtype != torch.float64:
|
||
raise ValueError('segment certification requires float64')
|
||
# 预算给成张量时 max_depth + 1 会在 uint8 这类窄类型上回绕成 0，循环整个跳过，把碰撞段当安全返回。
|
||
if type(max_queries) is not int or type(max_depth) is not int:
|
||
raise ValueError('certification budgets must be plain ints')
|
||
if max_queries < 2 or max_depth < 0 or eps <= 0 or cap <= eps:
|
||
raise ValueError('invalid certification budget or tolerance')
|
||
count = a.shape[0]
|
||
status = torch.zeros(count, dtype=torch.long, device=a.device)
|
||
inside = (((a >= self.lo) & (a <= self.hi) & (b >= self.lo) & (b <= self.hi)) | self.cont).all(-1)
|
||
status[~inside] = 3
|
||
root = torch.arange(count, device=a.device)
|
||
gaps = self.gaps(torch.cat([a, b]), cap)['gm'][:, self.cert_groups]
|
||
ga, gb = gaps[:count], gaps[count:]
|
||
queries = torch.full((count,), 2, dtype=torch.long, device=a.device)
|
||
bound = (b - a).abs() @ self.cert_lever.T
|
||
for depth in range(max_depth + 1):
|
||
finite = torch.isfinite(ga).all(-1) & torch.isfinite(gb).all(-1)
|
||
collision = (ga <= 0).any(-1) | (gb <= 0).any(-1)
|
||
status[root[~finite]] = 2
|
||
status[root[collision]] = 1
|
||
positive = (ga > eps).all(-1) & (gb > eps).all(-1)
|
||
proven = positive & (ga + gb > bound + 2 * eps).all(-1)
|
||
pending = (status[root] == 0) & ~proven
|
||
if not bool(pending.any()):
|
||
break
|
||
a, b, ga, gb, root, bound = a[pending], b[pending], ga[pending], gb[pending], root[pending], bound[pending]
|
||
if depth == max_depth:
|
||
status[root] = 2
|
||
break
|
||
requested = torch.bincount(root, minlength=count)
|
||
status[(status == 0) & (queries + requested > max_queries)] = 2
|
||
keep = status[root] == 0
|
||
a, b, ga, gb, root, bound = (t[keep] for t in (a, b, ga, gb, root, bound))
|
||
if not root.numel():
|
||
break
|
||
mid = a + 0.5 * (b - a)
|
||
# 子段的界是父段一半；宽相位只需覆盖到能被证明的最小间隙，层越深筛得越狠。
|
||
qc = min(cap, float(bound.max()) / 2 + eps) if adaptive_cap else cap
|
||
gm = self.gaps(mid, qc)['gm'][:, self.cert_groups]
|
||
queries += torch.bincount(root, minlength=count)
|
||
a, b = torch.cat([a, mid]), torch.cat([mid, b])
|
||
ga, gb = torch.cat([ga, gm]), torch.cat([gm, gb])
|
||
root = torch.cat([root, root])
|
||
bound = torch.cat([bound, bound]) / 2
|
||
return {'safe': status == 0, 'collision': status == 1, 'unresolved': status == 2,
|
||
'outside_box': status == 3, 'queries': queries}
|
||
|
||
def min_gap(self, q, cap=40.0):
|
||
return self.gaps(q, cap)['gm'].min(-1).values
|
||
|
||
def unwrap_to(self, a, b):
|
||
"""连续轴取离 a 最近的等价角（与 JS unwrapTo 同口径）"""
|
||
d = b - a
|
||
dw = torch.remainder(d + 180.0, 360.0) - 180.0
|
||
return torch.where(self.cont, a + dw, b)
|
||
|
||
def clamp_box(self, q):
|
||
return torch.where(self.cont, q, torch.maximum(torch.minimum(q, self.hi), self.lo))
|