Source code for eqc_models.algorithms.alm

# (C) Quantum Computing Inc., 2025.
from dataclasses import dataclass, field
from typing import Callable, Dict, List, Tuple, Optional, Sequence, Union
import numpy as np
from collections import defaultdict
from eqc_models.base.polynomial import PolynomialModel
Array = np.ndarray
PolyTerm = Tuple[Tuple[int, ...], float]
[docs]
@dataclass
class ALMConstraint:
    """One constraint family; fun returns a vector; jac returns its Jacobian."""
    kind: str                                           # "eq" or "ineq"
    fun: Callable[[Array], Array]                       # h(x) or g(x)
    jac: Optional[Callable[[Array], Array]] = None
    name: str = ""
    family: str = ""
[docs]
@dataclass
class ALMBlock:
    """Lifted discrete variable block (optional)."""
    idx: Sequence[int]                                  # indices of block in the full x
    levels: Array                                       # (k,) level values (b_i)
    enforce_sum_to_one: bool = True                     # register as equality via helper
    enforce_one_hot: bool = True                        # ALM linearization with M = 11^T - I
[docs]
@dataclass
class ALMConfig:
    # penalties
    rho_h: float = 50.0                                 # equalities
    rho_g: float = 50.0                                 # inequalities / one-hot
    rho_min: float = 1e-3
    rho_max: float = 1e3
    # per-family penalty overrides
    rho_eq_family: Dict[str, float] = field(default_factory=dict)
    rho_ineq_family: Dict[str, float] = field(default_factory=dict)
    # allow per-family adaptation toggle  (optional)
    adapt_by_family: bool = True
    # adaptation toggles
    adapt: bool = True
    tau_up_h: float = 0.90
    tau_down_h: float = 0.50
    tau_up_g: float = 0.90
    tau_down_g: float = 0.50
    gamma_up: float = 2.0
    gamma_down: float = 1.0
    # tolerances & loop
    tol_h: float = 1e-6
    tol_g: float = 1e-6
    max_outer: int = 100
    # stagnation safety net
    use_stagnation_bump: bool = True
    patience_h: int = 10
    patience_g: int = 10
    stagnation_factor: float = 1e-3
    # smoothing (optional)
    ema_alpha: float = 0.3
    # finite diff (only used if jac=None)
    fd_eps: float = 1e-6
    # activation threshold for projected ALM
    act_tol: float = 1e-10
[docs]
class ConstraintRegistry:
    """
    Holds constraints and block metadata; keeps ALMAlgorithm stateless. Register constraints and
    (optional) lifted-discrete blocks here.
    """
    def __init__(self):
        self.constraints: List[ALMConstraint] = []
        self.blocks: List[ALMBlock] = []
[docs]
    def add_equality(self, fun, jac=None, name="", family=""):
        self.constraints.append(ALMConstraint("eq", fun, jac, name, family))
[docs]
    def add_inequality(self, fun, jac=None, name="", family=""):
        self.constraints.append(ALMConstraint("ineq", fun, jac, name, family))
[docs]
    def add_block(self, idx: Sequence[int], levels: Array, sum_to_one=True, one_hot=True):
        self.blocks.append(ALMBlock(list(idx), np.asarray(levels, float), sum_to_one, one_hot))
[docs]
class ALMAlgorithm:
    """Stateless ALM outer loop. Call `run(model, registry, core, cfg, **core_kwargs)`."""
    # ---- helpers (static) ----
    @staticmethod
    def _finite_diff_jac(fun: Callable[[Array], Array], x: Array, eps: float) -> Array:
        y0 = fun(x)
        m = int(np.prod(y0.shape))
        y0 = y0.reshape(-1)
        n = x.size
        J = np.zeros((m, n), dtype=float)
        for j in range(n):
            xp = x.copy()
            xp[j] += eps
            J[:, j] = (fun(xp).reshape(-1) - y0) / eps
        return J
    @staticmethod
    def _pairwise_M(k: int) -> Array:
        return np.ones((k, k), dtype=float) - np.eye(k, dtype=float)
    @staticmethod
    def _sum_to_one_selector(n: int, idx: Sequence[int]) -> Array:
        S = np.zeros((1, n), dtype=float)
        S[0, np.array(list(idx), int)] = 1.0
        return S
    @staticmethod
    def _make_sum1_fun(S):
        return lambda x: S @ x - np.array([1.0])
    @staticmethod
    def _make_sum1_jac(S):
        return lambda x: S
    @staticmethod
    def _make_onehot_fun(sl, M):
        sl = np.array(sl, int)
        def _f(x):
            s = x[sl]
            return np.array([float(s @ (M @ s))])  # shape (1,)
        return _f
    @staticmethod
    def _make_onehot_jac(sl, M, n):
        sl = np.array(sl, int)
        def _J(x):
            s = x[sl]
            grad_blk = 2.0 * (M @ s)  # (k,)
            J = np.zeros((1, n), dtype=float)  # shape (1, n)
            J[0, sl] = grad_blk
            return J
        return _J
    @staticmethod
    def _poly_value(poly_terms: List[PolyTerm], x: Array) -> float:
        val = 0.0
        for inds, coeff in poly_terms:
            prod = 1.0
            for j in inds:
                if j == 0:
                    continue
                else:
                    prod *= x[j - 1]
            val += coeff * prod
        return float(val)
    @staticmethod
    def _merge_poly(poly_terms: Optional[List[PolyTerm]], Q_aug: Optional[Array],
                                c_aug: Optional[Array]) -> List[PolyTerm]:
        """
        Merge ALM's quadratic/linear increments (Q_aug, c_aug) into the base polynomial term list `poly_terms`.
        If 'poly_terms' is None, then turn x^T Q_aug x + c_aug^T x into polynomial monomials.
        Terms are of the form:
            ((0, i), w) for linear, ((i, j), w) for quadratic.
        """
        merged = list(poly_terms) if poly_terms is not None else []
        if Q_aug is not None:
            Qs = 0.5 * (Q_aug + Q_aug.T)
            n = Qs.shape[0]
            for i in range(n):
                # diagonal contributes Qii * x_i^2
                if Qs[i, i] != 0.0:
                    merged.append(((i + 1, i + 1), float(Qs[i, i])))
                for j in range(i + 1, n):
                    q = 2.0 * Qs[i, j]  # x^T Q x -> sum_{i<j} 2*Q_ij x_i x_j
                    if q != 0.0:
                        merged.append(((i + 1, j + 1), float(q)))
        if c_aug is not None:
            for i, ci in enumerate(c_aug):
                if ci != 0.0:
                    merged.append(((0, i + 1), float(ci)))
        return merged
    @staticmethod
    def _block_offsets(blocks: List[ALMBlock]) -> List[int]:
        """
        Return starting offsets (0-based) for each lifted block in the
        concatenated s-vector.
        """
        offs, pos = [], 0
        for blk in blocks:
            offs.append(pos)
            pos += len(blk.levels)     # each block contributes k lifted coordinates
        return offs
[docs]
    @staticmethod
    def lift_Qc_to_poly_terms(
            Q_native: np.ndarray,       # shape (m, m) over original discrete vars (one block per var)
            c_native: np.ndarray,       # shape (m,)
            blocks: List[ALMBlock],     # ALM blocks (in the same order as the rows/cols of Q_native, c_native)
    ) -> Tuple[List[Tuple[int, ...]], List[float]]:
        """
        Expand a quadratic/linear objective over m native discrete variables into the lifted
        (one-hot) s-space.
        Given `Q_native` and `c_native` over original m discrete vars (one block per var), and
        `blocks` (`list[ALMBlock]` in the same order as original vars), we enforce:
        - For variable i with level values b_i (length k_i), we create k_i lifted coords s_{i,a}.
        - Quadratic term: J_ij = Q_native[i,j] * (b_i b_j^T) contributes to pairs (s_{i,a}, s_{j,b})
        - Linear term: C_i = c_native[i] * b_i contributes to s_{i,a}
        Returns polynomial (indices, coeffs) over concatenated s variables.
        """
        m = len(blocks)
        assert Q_native.shape == (m, m), "Q_native must match number of blocks"
        assert c_native.shape == (m,), "c_native must match number of blocks"
        offs = ALMAlgorithm._block_offsets(blocks)
        terms_acc = defaultdict(float)
        # Quadratic lift: J = kron-expansion
        for i in range(m):
            bi = blocks[i].levels[:, None]                      # (k_i, 1)
            oi = offs[i]
            for j in range(m):
                bj = blocks[j].levels[:, None]                  # (k_j, 1)
                oj = offs[j]
                J_ij = Q_native[i, j] * (bi @ bj.T)         # (k_i, k_j)
                if np.allclose(J_ij, 0.0):
                    continue
                ki, kj = bi.shape[0], bj.shape[0]
                for a in range(ki):
                    ia = oi + a + 1
                    for b in range(kj):
                        jb = oj + b + 1
                        w = float(J_ij[a, b])
                        if w == 0.0:
                            continue
                        if ia == jb:
                            terms_acc[(ia, ia)] += w
                        else:
                            # NOTE: we store each cross monomial once (i < j); for i==j block pairs,
                            # double to represent J_ab + J_ba
                            if i == j:                      # intra-block off-diagonal needs 2x
                                w *= 2.0
                            i1, i2 = (ia, jb) if ia < jb else (jb, ia)
                            terms_acc[(i1, i2)] += w
        # Linear lift: C_i = L_i * b_i
        for i in range(m):
            b = blocks[i].levels
            oi = offs[i]
            for a, val in enumerate(b):
                ia = oi + a + 1
                w = float(c_native[i] * val)
                if w != 0.0:
                    terms_acc[(0, ia)] += w
        # Pack to PolynomialModel format
        indices = [tuple(k) for k in terms_acc.keys()]
        coeffs = [float(v) for v in terms_acc.values()]
        return indices, coeffs
    # ---- main entrypoint ----
[docs]
    @staticmethod
    def run(
            base_model: PolynomialModel,
            registry: ConstraintRegistry,
            solver,
            cfg: ALMConfig = ALMConfig(),
            x0: Optional[Array] = None,
            *,
            parse_output=None,
            verbose: bool = True,
            **solver_kwargs,
    ) -> Dict[str, Union[Array, Dict[int, float], Dict]]:
        """
        Solve with ALM. Keep all ALM state local to this call (no global side-effects).
        Handles three modes:
            (A) No blocks -> continuous; use base_model as-is
            (B) Blocks + native base_model -> lift to s-space
            (C) Blocks + already-lifted base_model -> use as-is (compat)
        Returns:
             {
                "x": final iterate,
                "decoded": {start_idx_of_block: level_value, ...} for lifted blocks,
                "decoded_debug": {start_idx_of_block: native_device_value, ...},
                "hist": { "eq_inf": [...], "ineq_inf": [...], "obj": [...], "x": [...] }
             }
        """
        blocks = registry.blocks
        has_blocks = len(blocks) > 0
        # ---- choose working model + dimension n ----
        if not has_blocks:
            # (A) continuous case: use the provided model directly
            model = base_model
            # Prefer model.n, fall back to bounds; else infer from polynomial indices
            n = getattr(model, "n", None)
            if n is None:
                ub = getattr(model, "upper_bound", None)
                lb = getattr(model, "lower_bound", None)
                if ub is not None:
                    n = len(ub)
                elif lb is not None:
                    n = len(lb)
                else:
                    # infer from polynomial terms
                    n = 0
                    for inds in getattr(model, "indices", getattr(model.polynomial, "indices", [])):
                        for j in inds:
                            if j > 0:
                                n = max(n, j)
            lifted_slices: List[List[int]] = []
        else:
            # (B/C) lifted (discrete) case
            target_lifted_n = sum(len(blk.levels) for blk in blocks)
            base_n = getattr(base_model, "n", None)
            def _infer_n_from_terms(pm: PolynomialModel) -> int:
                inds_list = getattr(pm, "indices", getattr(pm.polynomial, "indices", []))
                mx = 0
                for inds in inds_list:
                    for j in inds:
                        if j > mx:
                            mx = j
                return int(mx)
            if base_n is None:
                base_n = _infer_n_from_terms(base_model)
            # detect "already-lifted" native input (compat path)
            already_lifted = (base_n == target_lifted_n)
            if already_lifted:
                # (C) use provided model directly; assume bounds already sensible
                model = base_model
                n = target_lifted_n
            else:
                # (B) lift from native space
                # base_model must expose coefficients/indices compatible with this call
                c_base, Q_base = base_model._quadratic_polynomial_to_qubo_coefficients(
                    getattr(base_model, "coefficients", getattr(base_model.polynomial, "coefficients", [])),
                    getattr(base_model, "indices", getattr(base_model.polynomial, "indices", [])),
                    getattr(base_model, "n")
                )
                assert Q_base.shape[0] == Q_base.shape[1]
                assert c_base.shape[0] == Q_base.shape[0]
                indices_lifted, coeffs_lifted = ALMAlgorithm.lift_Qc_to_poly_terms(Q_base, c_base, blocks)
                model = PolynomialModel(coeffs_lifted, indices_lifted)
                n = target_lifted_n
                # set canonical [0,1] bounds for lifted s
                setattr(model, "lower_bound", np.zeros(n, float))
                setattr(model, "upper_bound", np.ones(n, float))
            # ---- n and lifted_slices ----
            lifted_slices = []
            pos = 0
            for blk in blocks:
                k = len(blk.levels)                                 # number of lifted coords for this block
                lifted_slices.append(list(range(pos, pos + k)))     # 0-based in lifted x
                pos += k
        # Algorithm initial solution and bounds
        lb = getattr(model, "lower_bound", None)
        ub = getattr(model, "upper_bound", None)
        if x0 is not None:
            x = np.asarray(x0, float).copy()
        else:
            # default init
            if (lb is not None) and (ub is not None) and np.all(np.isfinite(lb)) and np.all(np.isfinite(ub)):
                x = 0.5 * (np.asarray(lb, float) + np.asarray(ub, float))
            else:
                x = np.zeros(n, float)
        # ---- collect constraints ----
        problem_eqs = [c for c in registry.constraints if c.kind == "eq"]
        problem_ineqs = [c for c in registry.constraints if c.kind == "ineq"]
        # auto-install sum-to-one and one-hot as equalities
        # (One-hot: s^T (11^T - I) s = 0))
        def _install_block_equalities() -> List[ALMConstraint]:
            if not has_blocks:
                return []
            eqs: List[ALMConstraint] = []
            for blk, lift_idx in zip(registry.blocks, lifted_slices):
                if blk.enforce_sum_to_one:
                    S = ALMAlgorithm._sum_to_one_selector(n, lift_idx)
                    eqs.append(ALMConstraint(
                        "eq",
                        fun=ALMAlgorithm._make_sum1_fun(S),
                        jac=ALMAlgorithm._make_sum1_jac(S),
                        name=f"sum_to_one_block_{lift_idx[0]}",
                        family="block_sum1",
                    ))
                if blk.enforce_one_hot:
                    k = len(lift_idx)
                    M = ALMAlgorithm._pairwise_M(k)
                    eqs.append(ALMConstraint(
                        "eq",
                        fun=ALMAlgorithm._make_onehot_fun(lift_idx, M),
                        jac=ALMAlgorithm._make_onehot_jac(lift_idx, M, n),
                        name=f"onehot_block_{lift_idx[0]}",
                        family="block_onehot",
                    ))
            return eqs
        block_eqs = _install_block_equalities()
        # Unified equality list (order is fixed for whole run)
        full_eqs = problem_eqs + block_eqs
        # Allocate multipliers for every equality in full_eqs
        lam_eq = []
        for csp in full_eqs:
            r0 = csp.fun(x).reshape(-1)
            lam_eq.append(np.zeros_like(r0, dtype=float))
        # Inequality multipliers per user inequality
        mu_ineq = []
        for csp in problem_ineqs:
            r0 = csp.fun(x).reshape(-1)
            mu_ineq.append(np.zeros_like(r0, dtype=float))
        rho_eq_family = dict(getattr(cfg, "rho_eq_family", {}) or {})
        rho_ineq_family = dict(getattr(cfg, "rho_ineq_family", {}) or {})
        def _rho_for(csp_k: ALMConstraint) -> float:
            fam = getattr(csp_k, "family", "") or ""
            if csp_k.kind == "eq":
                return float(rho_eq_family.get(fam, rho_h))
            else:
                return float(rho_ineq_family.get(fam, rho_g))
        # -------- running stats for adaptive penalties --------
        rho_h, rho_g = cfg.rho_h, cfg.rho_g
        best_eq, best_ineq = np.inf, np.inf
        no_imp_eq = no_imp_ineq = 0
        prev_eq_inf, prev_ineq_inf = np.inf, np.inf
        eps = 1e-12
        prev_eq_inf_by_family, prev_ineq_inf_by_family = {}, {}
        # ---- per-family stagnation tracking (only used when cfg.adapt_by_family=True)
        best_eq_by_family: Dict[str, float] = {}
        best_ineq_by_family: Dict[str, float] = {}
        no_imp_eq_by_family: Dict[str, int] = {}
        no_imp_ineq_by_family: Dict[str, int] = {}
        hist = {"eq_inf": [], "ineq_inf": [], "obj": [], "x": [],
                # per-iteration logs for parameters/multipliers
                "rho_h": [], "rho_g": [],
                "rho_eq_family": [], "rho_ineq_family": [],
                "eq_inf_by_family": [], "ineq_inf_by_family": [],
                # critical for debugging hardware compatibility (per-iteration)
                "dynamic_range": [],
                }
        for k_idx, csp in enumerate(full_eqs):
            if csp.kind != "eq":
                continue
            hist[f"lam_eq_max_idx{k_idx}"] = []
            hist[f"lam_eq_min_idx{k_idx}"] = []
        for k_idx, csp in enumerate(problem_ineqs):
            if csp.kind != "ineq":
                continue
            hist[f"mu_ineq_max_idx{k_idx}"] = []
            hist[f"mu_ineq_min_idx{k_idx}"] = []
        for it in range(cfg.max_outer):
            # -------- base polynomial (does not include fixed penalties here) --------
            base_terms: List[PolyTerm] = list(zip(model.polynomial.indices, model.polynomial.coefficients))
            # -------- ALM quadratic/linear pieces (assembled here, kept separate) --------
            Q_aug = np.zeros((n, n), dtype=float)
            c_aug = np.zeros(n, dtype=float)
            have_aug = False
            # (A) Equalities: linearize h near x^t => (rho/2)||A x - b||^2 + lam^T(Ax - b)
            for k_idx, csp in enumerate(full_eqs):
                if csp.kind != "eq":
                    continue
                h = csp.fun(x).reshape(-1)
                A = csp.jac(x) if csp.jac is not None else ALMAlgorithm._finite_diff_jac(csp.fun, x, cfg.fd_eps)
                A = np.atleast_2d(A)
                assert A.shape[1] == n, f"A has {A.shape[1]} cols, expected {n}"
                # linearization about current x: residual model r(x) = A x - b, with b = A x - h
                b = A @ x - h
                rho_k = _rho_for(csp)
                Qk = 0.5 * rho_k * (A.T @ A)
                ck = (A.T @ lam_eq[k_idx]) - rho_k * (A.T @ b)
                Q_aug += Qk
                c_aug += ck
                have_aug = True
            # (B) Inequalities: projected ALM. Linearize g near x^t.
            for k_idx, csp in enumerate(problem_ineqs):
                if csp.kind != "ineq":
                    continue
                g = csp.fun(x).reshape(-1)
                G = csp.jac(x) if csp.jac is not None else ALMAlgorithm._finite_diff_jac(csp.fun, x, cfg.fd_eps)
                G = np.atleast_2d(G)
                assert G.shape[1] == n, f"G has {G.shape[1]} cols, expected {n}"
                d = G @ x - g
                rho_k = _rho_for(csp)
                # Activation measure at current iterate; meaning, the current violating inequality components:
                # g(x) + mu/rho; Powell-Hestenes-Rockafellar shifted residual
                y = G @ x - d + mu_ineq[k_idx] / rho_k
                active = (y > cfg.act_tol)
                if np.any(active):
                    GA = G[active, :]
                    muA = mu_ineq[k_idx][active]
                    gA = g[active]
                    # Q += (rho/2) * GA^T GA
                    Qk = 0.5 * rho_k * (GA.T @ GA)
                    # c += GA^T mu - rho * GA^T (GA x - gA); where GA x - gA is active measures of d = G @ x - g
                    ck = (GA.T @ muA) - rho_k * (GA.T @ (GA @ x - gA))
                    Q_aug += Qk
                    c_aug += ck
                    have_aug = True
            # -------- build merged polynomial for the core solver --------
            all_terms = ALMAlgorithm._merge_poly(base_terms, Q_aug if have_aug else None,
                                                 c_aug if have_aug else None)
            idxs, coeffs = zip(*[(inds, w) for (inds, w) in all_terms]) if all_terms else ([], [])
            poly_model = PolynomialModel(list(coeffs), list(idxs))
            if lb is not None and hasattr(poly_model, "lower_bound"):
                poly_model.lower_bound = np.asarray(lb, float)
            if ub is not None and hasattr(poly_model, "upper_bound"):
                poly_model.upper_bound = np.asarray(ub, float)
            x_ws = x.copy()
            # Convention: many cores look for one of these fields if present.
            # Use one or more to be future-proof; harmless if ignored.
            setattr(poly_model, "initial_guess", x_ws)
            setattr(poly_model, "warm_start", x_ws)
            setattr(poly_model, "x0", x_ws)
            # -------- inner solve --------
            out = solver.solve(poly_model, **solver_kwargs)
            # -------- parse --------
            if parse_output:
                x = parse_output(out)
            else:
                # default: support (value, x) or `.x` or raw x
                if isinstance(out, tuple) and len(out) == 2:
                    _, x = out
                elif isinstance(out, dict) and "results" in out and "solutions" in out["results"]:
                    x = out["results"]["solutions"][0]
                elif isinstance(out, dict) and "x" in out:
                    x = out["x"]
                else:
                    x = getattr(out, "x", out)
                x = np.asarray(x, float)
            # ---- multiplier tracking ----
            for k_idx, csp in enumerate(full_eqs):
                if csp.kind != "eq": continue
                hist[f"lam_eq_max_idx{k_idx}"].append(float(np.max(lam_eq[k_idx])))
                hist[f"lam_eq_min_idx{k_idx}"].append(float(np.min(lam_eq[k_idx])))
            for k_idx, csp in enumerate(problem_ineqs):
                if csp.kind != "ineq": continue
                hist[f"mu_ineq_max_idx{k_idx}"].append(float(np.max(mu_ineq[k_idx])))
                hist[f"mu_ineq_min_idx{k_idx}"].append(float(np.min(mu_ineq[k_idx])))
            # -------- residuals + multiplier updates --------
            eq_infs = []
            for k_idx, csp in enumerate(full_eqs):
                if csp.kind != "eq": continue
                r = csp.fun(x).reshape(-1)
                rho_k = _rho_for(csp)
                lam_eq[k_idx] = lam_eq[k_idx] + rho_k * r
                if r.size:
                    eq_infs.append(np.max(np.abs(r)))
            eq_inf = float(np.max(eq_infs)) if eq_infs else 0.0
            ineq_infs = []
            for k_idx, csp in enumerate(problem_ineqs):
                if csp.kind != "ineq": continue
                r = csp.fun(x).reshape(-1)
                rho_k = _rho_for(csp)
                mu_ineq[k_idx] = np.maximum(0.0, mu_ineq[k_idx] + rho_k * r)
                if r.size:
                    ineq_infs.append(np.max(np.maximum(0.0, r)))
            ineq_inf = float(np.max(ineq_infs)) if ineq_infs else 0.0
            assert len(lam_eq) == len(full_eqs)
            assert len(mu_ineq) == len(problem_ineqs)
            # ---- per-family residual telemetry ----
            eq_inf_by_family = {}
            for k_idx, csp in enumerate(full_eqs):
                if csp.kind != "eq": continue
                fam = getattr(csp, "family", "") or ""
                r = csp.fun(x).reshape(-1)
                v = float(np.max(np.abs(r))) if r.size else 0.0
                eq_inf_by_family[fam] = max(eq_inf_by_family.get(fam, 0.0), v)
            ineq_inf_by_family = {}
            for k_idx, csp in enumerate(problem_ineqs):
                if csp.kind != "ineq": continue
                fam = getattr(csp, "family", "") or ""
                r = csp.fun(x).reshape(-1)
                v = float(np.max(np.maximum(0.0, r))) if r.size else 0.0
                ineq_inf_by_family[fam] = max(ineq_inf_by_family.get(fam, 0.0), v)
            # evaluate base polynomial only (ca add aug value if want to track full L_A)
            f_val = ALMAlgorithm._poly_value(base_terms, x)
            # evaluate dynamic range
            dynamic_range = poly_model.dynamic_range
            hist["eq_inf"].append(eq_inf); hist["ineq_inf"].append(ineq_inf)
            hist["obj"].append(float(f_val)); hist["x"].append(x.copy())
            hist["dynamic_range"].append(float(dynamic_range))
            # parameter tracking
            hist["rho_h"].append(float(rho_h)); hist["rho_g"].append(float(rho_g))
            hist["rho_eq_family"].append(dict(rho_eq_family))
            hist["rho_ineq_family"].append(dict(rho_ineq_family))
            hist["eq_inf_by_family"].append(dict(eq_inf_by_family))
            hist["ineq_inf_by_family"].append(dict(ineq_inf_by_family))
            if verbose:
                # show worst 3 equality families by residual, with their rhos
                eq_items = sorted(eq_inf_by_family.items(), key=lambda kv: kv[1], reverse=True)
                eq_top = eq_items[:3]
                eq_str = ",".join([
                    f"{fam or 'eq'}:{val:.2e}@"
                    f"{_rho_for(next(c for c in full_eqs if (getattr(c,'family','') or '')==fam and c.kind=='eq')):.1g}"
                    for fam, val in eq_top
                ])
                # show worst 3 inequality families by residual, with their rhos
                ineq_items = sorted(ineq_inf_by_family.items(), key=lambda kv: kv[1], reverse=True)
                ineq_top = ineq_items[:3]
                ineq_str = ",".join([
                    f"{fam or 'ineq'}:{val:.2e}@"
                    f"{_rho_for(next(c for c in problem_ineqs if (getattr(c, 'family', '') or '') == fam and c.kind == 'ineq')):.1g}"
                    for fam, val in ineq_top
                ])
                print(f"[ALM {it:02d}] f={f_val:.6g} | eq_inf={eq_inf:.2e} | ineq_inf={ineq_inf:.2e} "
                      f"| rho_h={rho_h:.2e} | rho_g={rho_g:.2e} | eq_fam[{eq_str}] | ineq_fam[{ineq_str}] "
                      f"| dynamic_range={dynamic_range:.4g}")
            # stopping
            if eq_inf <= cfg.tol_h and ineq_inf <= cfg.tol_g:
                if verbose:
                    print(f"[ALM] converged at iter {it}")
                break
            # EMA smoothing to reduce jitter
            if it == 0:
                eq_inf_smooth = eq_inf
                ineq_inf_smooth = ineq_inf
            else:
                eq_inf_smooth = cfg.ema_alpha * eq_inf + (1 - cfg.ema_alpha) * eq_inf_smooth
                ineq_inf_smooth = cfg.ema_alpha * ineq_inf + (1 - cfg.ema_alpha) * ineq_inf_smooth
            # -------- Residual-ratio controller --------
            if cfg.adapt and it > 0:
                # per-family rho adaptation for equalities
                if getattr(cfg, "adapt_by_family", False):
                    # Equality family
                    for fam, cur in eq_inf_by_family.items():
                        prev = max(prev_eq_inf_by_family.get(fam, cur), eps)
                        # rho value for family: if absent, start at rho_h
                        rho_f = float(rho_eq_family.get(fam, rho_h))
                        if cur > cfg.tau_up_h * prev:
                            rho_f = min(cfg.gamma_up * rho_f, cfg.rho_max)
                        elif cur < cfg.tau_down_h * prev:
                            rho_f = max(cfg.gamma_down * rho_f, cfg.rho_min)
                        rho_eq_family[fam] = rho_f
                    # update prev map
                    prev_eq_inf_by_family = dict(eq_inf_by_family)
                    # Inequality family
                    for fam, cur in ineq_inf_by_family.items():
                        prev = max(prev_ineq_inf_by_family.get(fam, cur), eps)
                        # rho value for family: if absent, start at rho_g
                        rho_f = float(rho_ineq_family.get(fam, rho_g))
                        if cur > cfg.tau_up_g * prev:
                            rho_f = min(cfg.gamma_up * rho_f, cfg.rho_max)
                        elif cur < cfg.tau_down_g * prev:
                            rho_f = max(cfg.gamma_down * rho_f, cfg.rho_min)
                        rho_ineq_family[fam] = rho_f
                    # update prev map
                    prev_ineq_inf_by_family = dict(ineq_inf_by_family)
                else:
                    # Equality group
                    if eq_inf_smooth > cfg.tau_up_h * max(prev_eq_inf, eps):          # stalled or not shrinking
                        rho_h = min(cfg.gamma_up * rho_h, cfg.rho_max)
                    elif eq_inf_smooth < cfg.tau_down_h * max(prev_eq_inf, eps):      # fast progress, allow relaxation
                        rho_h = max(cfg.gamma_down * rho_h, cfg.rho_min)
                    # Inequality group
                    if ineq_inf_smooth > cfg.tau_up_g * max(prev_ineq_inf, eps):
                        rho_g = min(cfg.gamma_up * rho_g, cfg.rho_max)
                    elif ineq_inf_smooth < cfg.tau_down_g * max(prev_ineq_inf, eps):
                        rho_g = max(cfg.gamma_down * rho_g, cfg.rho_min)
            else:
                # per-family rho adaptation for equalities
                if getattr(cfg, "adapt_by_family", False):
                    # update prev map
                    prev_eq_inf_by_family = dict(eq_inf_by_family)
                    prev_ineq_inf_by_family = dict(ineq_inf_by_family)
            # -------- Stagnation bump (safety net) --------
            if cfg.use_stagnation_bump:
                if getattr(cfg, "adapt_by_family", False):
                    # ---- Equality families ----
                    for fam, cur in eq_inf_by_family.items():
                        # initialize
                        if fam not in best_eq_by_family:
                            best_eq_by_family[fam] = float(cur)
                            no_imp_eq_by_family[fam] = 0
                        if cur <= best_eq_by_family[fam] * (1 - cfg.stagnation_factor):
                            best_eq_by_family[fam] = float(cur)
                            no_imp_eq_by_family[fam] = 0
                        else:
                            no_imp_eq_by_family[fam] += 1
                            if no_imp_eq_by_family[fam] >= cfg.patience_h:
                                rho_f = float(rho_eq_family.get(fam, rho_h))
                                rho_eq_family[fam] = min(2.0 * rho_f, cfg.rho_max)
                                no_imp_eq_by_family[fam] = 0
                    # ---- Inequality families ----
                    for fam, cur in ineq_inf_by_family.items():
                        # initialize
                        if fam not in best_ineq_by_family:
                            best_ineq_by_family[fam] = float(cur)
                            no_imp_ineq_by_family[fam] = 0
                        if cur <= best_ineq_by_family[fam] * (1 - cfg.stagnation_factor):
                            best_ineq_by_family[fam] = float(cur)
                            no_imp_ineq_by_family[fam] = 0
                        else:
                            no_imp_ineq_by_family[fam] += 1
                            if no_imp_ineq_by_family[fam] >= cfg.patience_g:
                                rho_f = float(rho_ineq_family.get(fam, rho_g))
                                rho_ineq_family[fam] = min(2.0 * rho_f, cfg.rho_max)
                                no_imp_ineq_by_family[fam] = 0
                else:
                    # Equality stagnation
                    if eq_inf <= best_eq * (1 - cfg.stagnation_factor):
                        best_eq = eq_inf; no_imp_eq = 0
                    else:
                        no_imp_eq += 1
                        if no_imp_eq >= cfg.patience_h:
                            rho_h = min(2.0 * rho_h, cfg.rho_max); no_imp_eq = 0
                    # Inequality stagnation
                    if ineq_inf <= best_ineq * (1 - cfg.stagnation_factor):
                        best_ineq = ineq_inf; no_imp_ineq = 0
                    else:
                        no_imp_ineq += 1
                        if no_imp_ineq >= cfg.patience_g:
                            rho_g = min(2.0 * rho_g, cfg.rho_max); no_imp_ineq = 0
            # -------- finalize for next iteration --------
            prev_eq_inf = max(eq_inf_smooth, eps)
            prev_ineq_inf = max(ineq_inf_smooth, eps)
        # ---- decoding back to native levels (only if blocks) ----
        decoded_native: Dict[int, float] = {}           # maps original var anchor -> chosen level value
        decoded_lifted: Dict[int, int] = {}             # maps lifted start index -> argmax position (optional)
        if has_blocks:
            for blk, lift_idx in zip(registry.blocks, lifted_slices):
                if not lift_idx:
                    continue
                sl = np.array(lift_idx, int)
                if len(sl) == 0:
                    continue
                sblk = x[sl]
                j = int(np.argmax(sblk))                    # which level got selected in the block
                orig_anchor = int(blk.idx[0])               # anchor original var id for this block
                decoded_native[orig_anchor] = float(blk.levels[j])
                decoded_lifted[sl[0]] = j                   # optional: lifted index -> chosen slot
        return {
            "x": x,
            "decoded": decoded_native if has_blocks else {},
            "decoded_debug": decoded_lifted if has_blocks else {},
            "hist": hist,
        }