data_gen.py

"""
data_gen.py  —  Training / test data for the elastic mesh.

Each sample is a triple (A, B, C) where:
  A  ∈ ℝ^DIM   encodes constraints   ("what must be true")
  B  ∈ ℝ^DIM   encodes objectives    ("what we want")
  C  ∈ ℝ^DIM   is the analytic solution — the feasibility center the mesh must learn to produce

Five problem families, each with a geometrically distinct C:

  1. box_proj      — clamp B into axis-aligned box defined by A
  2. halfspace     — project B onto hyperplane defined by A
  3. sphere        — project B onto sphere surface defined by A
  4. simplex       — project B onto probability simplex (A = uniform prior signal)
  5. elastic_bal   — per-dimension weighted balance between A-center and B

These cover:
  - Bounded feasibility   (box)
  - Equality constraints  (halfspace)
  - Norm constraints      (sphere)
  - Probability/sum=1     (simplex)
  - Soft trade-offs       (elastic)

The mesh sees ONLY (A, B) during inference; C is what it must reconstruct.
"""

import numpy as np
import json, pathlib, argparse
from typing import List, Dict

DIM              = 32    # embedding dimension  (set to 768 for LLM-scale)
SAMPLES_PER_TYPE = 1000  # × 5 types = 5 000 total


# ── UTILITIES ─────────────────────────────────────────────────────────────────

def normalize(v: np.ndarray) -> np.ndarray:
    n = np.linalg.norm(v)
    return v / (n + 1e-12)

def pack(*arrays: np.ndarray, dim: int) -> np.ndarray:
    """Concatenate + trim/pad to `dim`."""
    v = np.concatenate(arrays)
    if len(v) >= dim:
        return v[:dim]
    return np.pad(v, (0, dim - len(v)))


# ── PROBLEM TYPE 1: BOX PROJECTION ────────────────────────────────────────────
#
# Constraint  A : encodes per-dimension box  [lo, hi]
#               A[:D/2] = lo[:D/2],  A[D/2:] = hi[:D/2]
# Objective   B : unconstrained target point in ℝ^D
# Solution    C : clip(B, lo, hi)   — nearest point in box to B
#
# Meaning: "stay within resource/capacity bounds while aiming for B"

def gen_box(n: int, dim: int, rng: np.random.Generator) -> List[Dict]:
    data = []
    for _ in range(n):
        center = rng.uniform(-2, 2, dim)
        half   = rng.uniform(0.3, 2.0, dim)
        lo, hi = center - half, center + half
        B = rng.uniform(-4, 4, dim)
        C = np.clip(B, lo, hi)
        A = pack(lo[:dim//2], hi[:dim//2], dim=dim)
        data.append({'A': A.tolist(), 'B': B.tolist(), 'C': C.tolist(), 'type': 'box_proj'})
    return data


# ── PROBLEM TYPE 2: HALFSPACE PROJECTION ──────────────────────────────────────
#
# Constraint  A : encodes a hyperplane  nᵀx = b
#               A = normal vector, A[0] carries the offset b
# Objective   B : unconstrained point in ℝ^D
# Solution    C : projection of B onto the hyperplane
#               C = B − (nᵀB − b) · n
#
# Meaning: "satisfy one hard equality constraint at minimum cost to B"

def gen_halfspace(n: int, dim: int, rng: np.random.Generator) -> List[Dict]:
    data = []
    for _ in range(n):
        normal = normalize(rng.standard_normal(dim))
        b      = float(rng.uniform(-1, 1))
        B      = rng.uniform(-3, 3, dim)
        C      = B - (float(np.dot(normal, B)) - b) * normal
        A      = normal.copy()
        A[0]   = b          # offset embedded in first slot
        data.append({'A': A.tolist(), 'B': B.tolist(), 'C': C.tolist(), 'type': 'halfspace'})
    return data


# ── PROBLEM TYPE 3: SPHERE SURFACE ────────────────────────────────────────────
#
# Constraint  A : encodes a sphere (center, radius)
#               A = center vector, A[0] overwritten with radius r
# Objective   B : external point
# Solution    C : point on sphere surface nearest to B
#               C = center + r · (B − center) / ‖B − center‖
#
# Meaning: "satisfy a norm/budget constraint, move toward B as far as allowed"

def gen_sphere(n: int, dim: int, rng: np.random.Generator) -> List[Dict]:
    data = []
    for _ in range(n):
        center = rng.uniform(-1.5, 1.5, dim)
        r      = float(rng.uniform(1.0, 3.0))
        B      = rng.uniform(-4, 4, dim)
        diff   = B - center
        nd     = np.linalg.norm(diff)
        if nd < 1e-10:
            diff = np.ones(dim) / np.sqrt(dim)
            nd   = 1.0
        C    = center + r * diff / nd
        A    = center.copy()
        A[0] = r          # radius in first slot
        data.append({'A': A.tolist(), 'B': B.tolist(), 'C': C.tolist(), 'type': 'sphere'})
    return data


# ── PROBLEM TYPE 4: SIMPLEX PROJECTION ────────────────────────────────────────
#
# Constraint  A : uniform-prior signal (all ones) → encodes simplex constraint Σxᵢ=1, xᵢ≥0
# Objective   B : unconstrained "belief" vector
# Solution    C : nearest point on probability simplex to B
#
# Meaning: "find a valid probability distribution closest to unconstrained belief B"
# Useful for softmax-like problems.

def _proj_simplex(v: np.ndarray) -> np.ndarray:
    n  = len(v)
    u  = np.sort(v)[::-1]
    cs = np.cumsum(u) - 1.0
    rho = int(np.where(u * np.arange(1, n + 1) > cs)[0][-1])
    theta = cs[rho] / (rho + 1.0)
    return np.maximum(v - theta, 0.0)

def gen_simplex(n: int, dim: int, rng: np.random.Generator) -> List[Dict]:
    data = []
    for _ in range(n):
        A = np.ones(dim)                     # simplex constraint signal
        B = rng.uniform(-1.0, 3.0, dim)      # unconstrained belief
        C = _proj_simplex(B)
        data.append({'A': A.tolist(), 'B': B.tolist(), 'C': C.tolist(), 'type': 'simplex'})
    return data


# ── PROBLEM TYPE 5: ELASTIC BALANCE ───────────────────────────────────────────
#
# Constraint  A : encodes soft constraint center + per-dimension tightness weight w ∈ [0,1]
#               A[:D/2] = constraint centers,  A[D/2:] = tightness weights
# Objective   B : desired goal point
# Solution    C : per-dimension elastic balance
#               C[j] = w[j] · a_center[j] + (1 − w[j]) · B[j]
#
# Meaning: "each dimension is pulled between constraint center and objective,
#           with w[j] controlling how hard the constraint is in that dimension"
# This is the natural problem for the elastic mesh.

def gen_elastic(n: int, dim: int, rng: np.random.Generator) -> List[Dict]:
    data = []
    for _ in range(n):
        a_center = rng.uniform(-2, 2, dim)
        w        = rng.uniform(0.05, 0.95, dim)   # per-dim tightness
        B        = rng.uniform(-3, 3, dim)
        C        = w * a_center + (1.0 - w) * B
        A        = pack(a_center[:dim//2], w[:dim//2], dim=dim)
        data.append({'A': A.tolist(), 'B': B.tolist(), 'C': C.tolist(), 'type': 'elastic'})
    return data


# ── ASSEMBLY ──────────────────────────────────────────────────────────────────

GENERATORS = {
    'box_proj':  gen_box,
    'halfspace': gen_halfspace,
    'sphere':    gen_sphere,
    'simplex':   gen_simplex,
    'elastic':   gen_elastic,
}

def generate_all(n_per_type: int = SAMPLES_PER_TYPE,
                 dim: int       = DIM,
                 seed: int      = 42) -> List[Dict]:
    rng  = np.random.default_rng(seed)
    data = []
    for fn in GENERATORS.values():
        data.extend(fn(n_per_type, dim, rng))
    idx = rng.permutation(len(data))
    return [data[i] for i in idx]


# ── MAIN ──────────────────────────────────────────────────────────────────────

if __name__ == '__main__':
    parser = argparse.ArgumentParser(description='Generate elastic mesh training data')
    parser.add_argument('--dim', type=int, default=DIM,              help='embedding dimension')
    parser.add_argument('--n',   type=int, default=SAMPLES_PER_TYPE, help='samples per problem type')
    parser.add_argument('--out', type=str, default='data',           help='output directory')
    args = parser.parse_args()

    print(f"\n{'─'*50}")
    print(f"  Generating {5 * args.n} samples  |  dim={args.dim}")
    print(f"{'─'*50}")

    data  = generate_all(args.n, args.dim)
    split = int(len(data) * 0.9)
    train, test = data[:split], data[split:]

    out = pathlib.Path(args.out)
    out.mkdir(exist_ok=True)
    with open(out / 'train.json', 'w') as f: json.dump(train, f)
    with open(out / 'test.json',  'w') as f: json.dump(test,  f)

    # Per-type statistics
    from collections import Counter
    train_types = Counter(d['type'] for d in train)
    test_types  = Counter(d['type'] for d in test)

    print(f"\n  Train : {len(train)}")
    print(f"  Test  : {len(test)}\n")
    print(f"  {'Type':<14} {'Train':>8} {'Test':>7}  C-norm (mean)")
    print(f"  {'─'*14} {'─'*8} {'─'*7}  {'─'*14}")
    for t in GENERATORS:
        subset = [d for d in data if d['type'] == t]
        norms  = [np.linalg.norm(d['C']) for d in subset]
        print(f"  {t:<14} {train_types[t]:>8} {test_types[t]:>7}  "
              f"{np.mean(norms):.3f} ± {np.std(norms):.3f}")

    # Sanity check one sample per type
    print(f"\n  Sanity check (first sample per type):")
    seen = set()
    for d in data:
        if d['type'] in seen: continue
        seen.add(d['type'])
        A, B, C = map(np.array, [d['A'], d['B'], d['C']])
        err = np.linalg.norm(A - B)
        print(f"  [{d['type']:<12}]  "
              f"‖A‖={np.linalg.norm(A):.2f}  ‖B‖={np.linalg.norm(B):.2f}  "
              f"‖C‖={np.linalg.norm(C):.2f}  ‖A-B‖={err:.2f}")

    print(f"\n  Saved → {out}/train.json  {out}/test.json\n")