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PyTorch backend (AMICATorchNG)

The natural-gradient EM backend that reaches Fortran parity (Newton, exact-EM mixture updates, symmetric-ZCA sphere, Jacobian log-likelihood). The AMICA interface delegates to this class; use it directly for lower-level control.

pyAMICA.AMICATorchNG

Natural-gradient EM AMICA, ported from pyAMICA.numpy_impl.core.AMICA.

Not an nn.Module: there are no learnable nn.Parameters and no autograd. Parameters (A, W, c, mu, alpha, beta, rho, gm) are plain tensors mutated in place by closed-form E-step/M-step updates each iteration, mirroring pyAMICA.AMICA._get_block_updates/_update_parameters.

Parameters:

Name Type Description Default
n_channels int

Number of input channels (data_dim in the NumPy/Fortran code).

required
n_models int

Number of ICA mixture models.

1
n_mix int

Number of mixture components per source.

3
block_size int

Number of samples processed per accumulation block. Peak memory during the E-step scales with this, not with the total sample count. Larger blocks give bigger tensor ops (less Python/dispatch overhead, better threading/GPU utilization) at higher memory. 512 is a fixed choice inside Fortran's do_opt_block auto-tune range (128-1024, step 128); the Fortran header default is 128 and it auto-tunes per host, so this does not track a single reference value. A single iteration's sufficient statistics are block-size-independent to ~1e-8 (test_blocking_invariance), but the (chaotic) multi-iteration trajectory shifts at the ~1e-6 level as this changes.

512
lrate float

Initial/maximum natural-gradient learning rate (lrate0 in NumPy).

0.1
minlrate float

Hard learning-rate floor: once lrate anneals to it, fit stops (stop_reason="lrate_floor").

1e-12
lratefact float

Factor by which lrate (and the ceiling lrate_cap/newtrate) are annealed when the log-likelihood decreases; see fit for the Fortran-style numdecs/maxdecs ratchet.

0.5
maxdecs int

Number of consecutive log-likelihood decreases after which the learning-rate ceiling is ratcheted down (Fortran maxdecs).

5
newt_ramp int

Denominator of the per-iteration learning-rate ramp toward the current ceiling: lrate = min(ceiling, lrate + min(1/newt_ramp, lrate)) (ceiling is lrate_cap for natural gradient, newtrate for Newton).

10
do_newton bool

Enable the Newton preconditioner for the A/W update once iteration >= newt_start. Ported from the Fortran reference (amica17.f90): natural gradient alone plateaus well short of the Fortran solution, and the Newton step (a per-source-pair 2x2 solve preconditioning the natural gradient by an approximate Hessian) is what closes the gap.

False
newt_start int

Iteration at which the Newton step switches on (natural gradient is used before it, letting the mixture parameters settle first).

20
newtrate float

Maximum learning rate the ramp climbs to while Newton is active (the natural-gradient phase is capped at lrate/lrate0).

0.5
do_reject bool

Enable Fortran-style outlier rejection: after the parameter update, samples whose total log-likelihood falls below mean - rejsig*std are permanently excluded from subsequent sufficient-statistic accumulation and from the sample count used to normalize gm and the reported log-likelihood.

False
rejsig float

Rejection threshold in standard deviations of the per-sample log-likelihood.

3.0
rejstart int

First rejection iteration, interval between rejections, and maximum number of rejection passes (matching amica17.f90:1141-1146).

2
rejint int

First rejection iteration, interval between rejections, and maximum number of rejection passes (matching amica17.f90:1141-1146).

2
maxrej int

First rejection iteration, interval between rejections, and maximum number of rejection passes (matching amica17.f90:1141-1146).

2
rho0 float

Generalized-Gaussian shape-parameter initialization, clamp bounds, and learning rate.

1.5
minrho float

Generalized-Gaussian shape-parameter initialization, clamp bounds, and learning rate.

1.5
maxrho float

Generalized-Gaussian shape-parameter initialization, clamp bounds, and learning rate.

1.5
rholrate float

Generalized-Gaussian shape-parameter initialization, clamp bounds, and learning rate.

1.5
keep_best bool

Return the highest-log-likelihood iterate instead of the last one (issue #51). The lrate schedule is non-monotone (it anneals only after an LL decrease), so a late Newton-fallback overshoot can leave the final iterate below a peak the run already reached. When the final LL falls more than a small tolerance below that peak, fit restores the peak's parameters. A monotone single-model run (issue #24 parity) is a bit-exact no-op. Automatically inactive under do_reject (the good-sample set, and thus the LL normalization, changes across iterations, making per-iteration LLs incomparable).

True
pdftype int

Source-density family (issue #26), matching Fortran amica15.f90's pdtype codes: 0 generalized Gaussian (default; rho adapts), 2 Gaussian, 3 logistic, 4 sub-Gaussian cosh+. pdftype=1 enables the extended-Infomax adaptive switcher, which flips each source between the super-Gaussian (code 1) and sub-Gaussian (code 4) cosh densities by kurtosis sign. For every non-GG family the GG shape update is frozen (Fortran dorho=.false.); the single-component families 1/4 (and the adaptive mode) require n_mix=1. pdftype=0 is byte-for-byte the pre-#26 implementation.

0
kurt_start int

Adaptive-switch schedule (only used when pdftype=1): first iteration to re-estimate kurtosis, number of switch passes, and the iteration interval between them. num_kurt=0 disables switching (the family stays at its super-Gaussian init).

3
num_kurt int

Adaptive-switch schedule (only used when pdftype=1): first iteration to re-estimate kurtosis, number of switch passes, and the iteration interval between them. num_kurt=0 disables switching (the family stays at its super-Gaussian init).

3
kurt_int int

Adaptive-switch schedule (only used when pdftype=1): first iteration to re-estimate kurtosis, number of switch passes, and the iteration interval between them. num_kurt=0 disables switching (the family stays at its super-Gaussian init).

3
invsigmin float

Clamp bounds for the mixture scale parameter beta.

0.0001
invsigmax float

Clamp bounds for the mixture scale parameter beta.

0.0001
doscaling (bool, int)

Whether/how often to rescale A columns to unit norm each iteration (with matching mu/beta rescale).

True
scalestep (bool, int)

Whether/how often to rescale A columns to unit norm each iteration (with matching mu/beta rescale).

True
share_comps bool

Enable multi-model component sharing (Fortran share_comps / identify_shared_comps, amica15.f90:1898): components that are near-collinear across different models are merged so they share one mixing column and one density. Requires n_models >= 2 (a model cannot share with itself); a no-op otherwise. OFF by default, so single-model (#24) and default multi-model (#27) results are unchanged. There is no bit-exact oracle -- the reference's similarity metric is never initialized (like do_choose_pdfs, #26) -- so this implements the intended algorithm, validated by real-data behavior.

False
share_start int

Sharing schedule: first iteration to attempt merges and the interval between attempts (Fortran share_start/share_iter). The A-update is held for the first 6 iterations of every cycle (independent of whether a merge fired) so densities can settle; share_iter must be > 6 so that window never consumes the whole cycle.

100
share_iter int

Sharing schedule: first iteration to attempt merges and the interval between attempts (Fortran share_start/share_iter). The A-update is held for the first 6 iterations of every cycle (independent of whether a merge fired) so densities can settle; share_iter must be > 6 so that window never consumes the whole cycle.

100
comp_thresh float

Cosine-similarity cutoff (in the de-sphered/sensor-space metric) above which two mixing columns are identified and merged.

0.99
do_mean bool

Preprocessing options, matching pyAMICA.AMICA._preprocess_data.

True
do_sphere bool

Preprocessing options, matching pyAMICA.AMICA._preprocess_data.

True
do_approx_sphere bool

Preprocessing options, matching pyAMICA.AMICA._preprocess_data.

True
pcakeep (int, float)

PCA dimensionality-reduction options (rarely used; see pyAMICA.AMICA._preprocess_data).

None
pcadb (int, float)

PCA dimensionality-reduction options (rarely used; see pyAMICA.AMICA._preprocess_data).

None
seed int

Seed for parameter initialization. Uses numpy.random.RandomState internally (not torch's RNG) with the exact same draw order as pyAMICA.AMICA._initialize_parameters, so the same seed produces bit-identical starting parameters to the NumPy reference.

None
device str or device

Compute device for the block loop. Preprocessing (mean/cov/eigh) is always done in float64 on CPU regardless of device, since eigh is not reliably supported on MPS.

None
dtype dtype

Parameter/computation dtype. float64 is the parity default (Fortran bit-parity) and ~4.5x on CUDA over CPU (issue #63). float32 converges on full-size data across seeds (issue #75 guarded the one float32-only divide-by-zero -- a sample rounding an activation to exactly 0 gave 0/0 in the mu denominator) and is the required precision on MPS, which has no float64. float32 is NOT bit-parity with float64 (~7 significant digits), so use float64 for Fortran-parity runs and float32 for speed / Apple-GPU.

torch.float64
Source code in pyAMICA/torch_impl/core.py
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class AMICATorchNG:
    """
    Natural-gradient EM AMICA, ported from ``pyAMICA.numpy_impl.core.AMICA``.

    Not an ``nn.Module``: there are no learnable ``nn.Parameter``s and no
    autograd. Parameters (``A``, ``W``, ``c``, ``mu``, ``alpha``, ``beta``,
    ``rho``, ``gm``) are plain tensors mutated in place by closed-form
    E-step/M-step updates each iteration, mirroring
    ``pyAMICA.AMICA._get_block_updates``/``_update_parameters``.

    Parameters
    ----------
    n_channels : int
        Number of input channels (``data_dim`` in the NumPy/Fortran code).
    n_models : int, default=1
        Number of ICA mixture models.
    n_mix : int, default=3
        Number of mixture components per source.
    block_size : int, default=512
        Number of samples processed per accumulation block. Peak memory
        during the E-step scales with this, not with the total sample count.
        Larger blocks give bigger tensor ops (less Python/dispatch overhead,
        better threading/GPU utilization) at higher memory. 512 is a fixed
        choice inside Fortran's ``do_opt_block`` auto-tune range (128-1024, step
        128); the Fortran *header* default is 128 and it auto-tunes per host, so
        this does not track a single reference value. A single iteration's
        sufficient statistics are block-size-independent to ~1e-8
        (``test_blocking_invariance``), but the (chaotic) multi-iteration
        trajectory shifts at the ~1e-6 level as this changes.
    lrate : float, default=0.1
        Initial/maximum natural-gradient learning rate (``lrate0`` in NumPy).
    minlrate : float, default=1e-12
        Hard learning-rate floor: once ``lrate`` anneals to it, ``fit`` stops
        (``stop_reason="lrate_floor"``).
    lratefact : float, default=0.5
        Factor by which ``lrate`` (and the ceiling ``lrate_cap``/``newtrate``)
        are annealed when the log-likelihood decreases; see ``fit`` for the
        Fortran-style ``numdecs``/``maxdecs`` ratchet.
    maxdecs : int, default=5
        Number of consecutive log-likelihood decreases after which the
        learning-rate *ceiling* is ratcheted down (Fortran ``maxdecs``).
    newt_ramp : int, default=10
        Denominator of the per-iteration learning-rate ramp toward the current
        ceiling: ``lrate = min(ceiling, lrate + min(1/newt_ramp, lrate))``
        (ceiling is ``lrate_cap`` for natural gradient, ``newtrate`` for
        Newton).
    do_newton : bool, default=False
        Enable the Newton preconditioner for the ``A``/``W`` update once
        ``iteration >= newt_start``. Ported from the Fortran reference
        (``amica17.f90``): natural gradient alone plateaus well short of the
        Fortran solution, and the Newton step (a per-source-pair 2x2 solve
        preconditioning the natural gradient by an approximate Hessian) is
        what closes the gap.
    newt_start : int, default=20
        Iteration at which the Newton step switches on (natural gradient is
        used before it, letting the mixture parameters settle first).
    newtrate : float, default=0.5
        Maximum learning rate the ramp climbs to while Newton is active
        (the natural-gradient phase is capped at ``lrate``/``lrate0``).
    do_reject : bool, default=False
        Enable Fortran-style outlier rejection: after the parameter update,
        samples whose total log-likelihood falls below
        ``mean - rejsig*std`` are permanently excluded from subsequent
        sufficient-statistic accumulation and from the sample count used to
        normalize ``gm`` and the reported log-likelihood.
    rejsig : float, default=3.0
        Rejection threshold in standard deviations of the per-sample
        log-likelihood.
    rejstart, rejint, maxrej : int
        First rejection iteration, interval between rejections, and maximum
        number of rejection passes (matching ``amica17.f90:1141-1146``).
    rho0, minrho, maxrho, rholrate : float
        Generalized-Gaussian shape-parameter initialization, clamp bounds,
        and learning rate.
    keep_best : bool, default=True
        Return the highest-log-likelihood iterate instead of the last one
        (issue #51). The lrate schedule is non-monotone (it anneals only after
        an LL *decrease*), so a late Newton-fallback overshoot can leave the
        final iterate below a peak the run already reached. When the final LL
        falls more than a small tolerance below that peak, ``fit`` restores the
        peak's parameters. A monotone single-model run (issue #24 parity) is a
        bit-exact no-op. Automatically inactive under ``do_reject`` (the
        good-sample set, and thus the LL normalization, changes across
        iterations, making per-iteration LLs incomparable).
    pdftype : int, default=0
        Source-density family (issue #26), matching Fortran ``amica15.f90``'s
        ``pdtype`` codes: 0 generalized Gaussian (default; rho adapts), 2
        Gaussian, 3 logistic, 4 sub-Gaussian cosh+. ``pdftype=1`` enables the
        extended-Infomax adaptive switcher, which flips each source between the
        super-Gaussian (code 1) and sub-Gaussian (code 4) cosh densities by
        kurtosis sign. For every non-GG family the GG shape update is frozen
        (Fortran ``dorho=.false.``); the single-component families 1/4 (and the
        adaptive mode) require ``n_mix=1``. ``pdftype=0`` is byte-for-byte the
        pre-#26 implementation.
    kurt_start, num_kurt, kurt_int : int
        Adaptive-switch schedule (only used when ``pdftype=1``): first iteration
        to re-estimate kurtosis, number of switch passes, and the iteration
        interval between them. ``num_kurt=0`` disables switching (the family
        stays at its super-Gaussian init).
    invsigmin, invsigmax : float
        Clamp bounds for the mixture scale parameter ``beta``.
    doscaling, scalestep : bool, int
        Whether/how often to rescale ``A`` columns to unit norm each
        iteration (with matching ``mu``/``beta`` rescale).
    share_comps : bool, default=False
        Enable multi-model component sharing (Fortran ``share_comps`` /
        ``identify_shared_comps``, amica15.f90:1898): components that are
        near-collinear across different models are merged so they share one
        mixing column and one density. Requires ``n_models >= 2`` (a model
        cannot share with itself); a no-op otherwise. OFF by default, so
        single-model (#24) and default multi-model (#27) results are unchanged.
        There is no bit-exact oracle -- the reference's similarity metric is
        never initialized (like ``do_choose_pdfs``, #26) -- so this implements
        the intended algorithm, validated by real-data behavior.
    share_start, share_iter : int
        Sharing schedule: first iteration to attempt merges and the interval
        between attempts (Fortran ``share_start``/``share_iter``). The A-update
        is held for the first 6 iterations of every cycle (independent of whether
        a merge fired) so densities can settle; ``share_iter`` must be ``> 6`` so
        that window never consumes the whole cycle.
    comp_thresh : float, default=0.99
        Cosine-similarity cutoff (in the de-sphered/sensor-space metric) above
        which two mixing columns are identified and merged.
    do_mean, do_sphere, do_approx_sphere : bool
        Preprocessing options, matching ``pyAMICA.AMICA._preprocess_data``.
    pcakeep, pcadb : int, float, optional
        PCA dimensionality-reduction options (rarely used; see
        ``pyAMICA.AMICA._preprocess_data``).
    seed : int, optional
        Seed for parameter initialization. Uses ``numpy.random.RandomState``
        internally (not ``torch``'s RNG) with the exact same draw order as
        ``pyAMICA.AMICA._initialize_parameters``, so the same seed produces
        bit-identical starting parameters to the NumPy reference.
    device : str or torch.device, optional
        Compute device for the block loop. Preprocessing (mean/cov/eigh) is
        always done in float64 on CPU regardless of device, since eigh is
        not reliably supported on MPS.
    dtype : torch.dtype, default=torch.float64
        Parameter/computation dtype. float64 is the parity default (Fortran
        bit-parity) and ~4.5x on CUDA over CPU (issue #63). float32 converges on
        full-size data across seeds (issue #75 guarded the one float32-only
        divide-by-zero -- a sample rounding an activation to exactly 0 gave
        ``0/0`` in the mu denominator) and is the required precision on MPS,
        which has no float64. float32 is NOT bit-parity with float64 (~7
        significant digits), so use float64 for Fortran-parity runs and float32
        for speed / Apple-GPU.
    """

    def __init__(
        self,
        n_channels: int,
        n_models: int = 1,
        n_mix: int = 3,
        block_size: int = 512,
        lrate: float = 0.1,
        minlrate: float = 1e-12,
        lratefact: float = 0.5,
        maxdecs: int = 5,
        newt_ramp: int = 10,
        do_newton: bool = False,
        newt_start: int = 20,
        newtrate: float = 0.5,
        do_reject: bool = False,
        rejsig: float = 3.0,
        rejstart: int = 2,
        rejint: int = 3,
        maxrej: int = 1,
        rho0: float = 1.5,
        minrho: float = 1.0,
        maxrho: float = 2.0,
        rholrate: float = 0.05,
        rholratefact: float = 0.1,
        keep_best: bool = True,
        pdftype: int = 0,
        kurt_start: int = 3,
        num_kurt: int = 5,
        kurt_int: int = 1,
        invsigmin: float = 1e-4,
        invsigmax: float = 1000.0,
        doscaling: bool = True,
        scalestep: int = 1,
        share_comps: bool = False,
        share_start: int = 100,
        share_iter: int = 100,
        comp_thresh: float = 0.99,
        do_mean: bool = True,
        do_sphere: bool = True,
        do_approx_sphere: bool = True,
        pcakeep: Optional[int] = None,
        pcadb: Optional[float] = None,
        seed: Optional[int] = None,
        device: Optional[Union[str, torch.device]] = None,
        dtype: torch.dtype = torch.float64,
    ):
        self.n_channels = n_channels
        self.n_models = n_models
        self.n_mix = n_mix
        self.n_comps = n_channels * n_models
        self.block_size = block_size

        self.lrate0 = lrate
        self.lrate = lrate
        self.minlrate = minlrate
        self.lratefact = lratefact
        self.maxdecs = maxdecs
        self.newt_ramp = newt_ramp

        self.do_newton = do_newton
        self.newt_start = newt_start
        self.newtrate = newtrate
        self.newtrate0 = newtrate

        self.do_reject = do_reject
        self.rejsig = rejsig
        self.rejstart = rejstart
        self.rejint = rejint
        self.maxrej = maxrej
        if do_reject:
            if rejint < 1:
                raise ValueError(f"rejint must be >= 1, got {rejint}")
            if rejsig <= 0:
                raise ValueError(f"rejsig must be > 0, got {rejsig}")
            if maxrej < 0:
                raise ValueError(f"maxrej must be >= 0, got {maxrej}")

        self.rho0 = rho0
        self.minrho = minrho
        self.maxrho = maxrho
        self.rholrate = rholrate
        self.rholrate0 = rholrate
        self.rholratefact = rholratefact

        # Best-iterate safeguard (issue #51). When True, fit() restores the
        # highest-log-likelihood iterate if the run ends more than _KEEP_BEST_TOL
        # below it (a late Newton-fallback overshoot). Disabled automatically
        # under do_reject, where the good-sample set (and the LL normalization)
        # changes across iterations, so per-iteration LLs are not comparable.
        self.keep_best = keep_best

        # Source-density family selection (Fortran ``pdftype``, amica15.f90). Values
        # match Fortran's per-source ``pdtype`` codes: 0 generalized Gaussian (the
        # default, GG-mixture with adaptive rho), 2 Gaussian mixture, 3 logistic
        # (sech^2) mixture, 4 sub-Gaussian cosh+ (single component). pdftype=1 enables
        # the extended-Infomax adaptive switcher (Fortran's do_choose_pdfs trigger),
        # which flips each source between the super-Gaussian (code 1) and sub-Gaussian
        # (code 4) cosh densities by kurtosis sign on the kurt_start/num_kurt/kurt_int
        # schedule. Families 1 and 4 are single-component (no alpha mixture).
        if pdftype not in (0, 1, 2, 3, 4):
            raise ValueError(f"pdftype must be one of 0,1,2,3,4; got {pdftype}")
        self.pdftype = pdftype
        # Fortran freezes the GG shape update for every non-GG family (amica15.f90:
        # `if (pdftype /= 0) dorho = .false.`, line 3682).
        self.dorho = pdftype == 0
        # pdftype==1 is Fortran's adaptive trigger (amica15.f90:594).
        self.do_choose_pdfs = pdftype == 1
        self.kurt_start = kurt_start
        self.num_kurt = num_kurt
        self.kurt_int = kurt_int
        # Families 1/4 (and the adaptive mode, which uses only codes 1 and 4) are
        # single-component densities: Fortran's z0 references only mixture component
        # j=1 and omits log(alpha). They are meaningful only with n_mix == 1.
        if pdftype in (1, 4) and n_mix != 1:
            raise ValueError(
                f"pdftype={pdftype} is a single-component density (adaptive mode "
                f"uses codes 1 and 4); it requires n_mix=1, got n_mix={n_mix}."
            )
        # Validate the adaptive-switch schedule up front (mirrors the do_reject
        # checks below): kurt_int==0 would otherwise raise a bare ZeroDivisionError
        # deep in fit(), and a negative kurt_int silently changes the schedule.
        if self.do_choose_pdfs:
            if kurt_int < 1:
                raise ValueError(f"kurt_int must be >= 1, got {kurt_int}")
            if kurt_start < 1:
                raise ValueError(f"kurt_start must be >= 1, got {kurt_start}")
            if num_kurt < 0:
                raise ValueError(f"num_kurt must be >= 0, got {num_kurt}")

        self.invsigmin = invsigmin
        self.invsigmax = invsigmax

        self.doscaling = doscaling
        self.scalestep = scalestep

        # Component sharing (Fortran share_comps / identify_shared_comps trigger
        # amica15.f90:1838, subroutine :1898-1945): periodically merge mixing
        # columns near-collinear across DIFFERENT models so they share one
        # density and one mixing column. Multi-model only (a model cannot share
        # with itself); OFF by default so single-model (#24) and default
        # multi-model (#27) parity stay byte-for-byte. No bit-exact oracle -- the
        # reference's Spinv2 metric is declared but never allocated, so its
        # reassignment is unrunnable (the do_choose_pdfs situation, #26); this is
        # the intended algorithm, validated by real-data behavior.
        self.share_comps = share_comps
        self.share_start = share_start
        self.share_iter = share_iter
        self.comp_thresh = comp_thresh
        self._spinv = None  # cached de-sphering metric, built on first share
        if share_comps:
            if share_start < 1:
                raise ValueError(f"share_start must be >= 1, got {share_start}")
            if share_iter <= 6:
                # The A-freeze settle window is 6 iterations; a smaller cycle
                # would freeze A permanently (never leaving room to update it).
                raise ValueError(f"share_iter must be > 6, got {share_iter}")
            if not 0.0 < comp_thresh <= 1.0:
                raise ValueError(f"comp_thresh must be in (0, 1], got {comp_thresh}")
            if pcakeep is not None or pcadb is not None:
                # PCA reduction makes the sphere rank-deficient, so the
                # de-sphering metric used for the merge decision is not
                # invertible. Reject up front rather than crash mid-fit.
                raise ValueError(
                    "share_comps is incompatible with PCA reduction "
                    "(pcakeep/pcadb): the de-sphering similarity metric requires "
                    "a full-rank sphere."
                )

        self.do_mean = do_mean
        self.do_sphere = do_sphere
        self.do_approx_sphere = do_approx_sphere
        self.pcakeep = pcakeep
        self.pcadb = pcadb

        self.seed = seed

        if device is None:
            device = setup_device()
        elif isinstance(device, str):
            device = torch.device(device)
        self.device = device
        self.dtype = dtype

        if self.device.type == "mps" and self.dtype == torch.float64:
            raise ValueError(
                "MPS does not support float64. Use dtype=torch.float32 for "
                "device='mps', or device='cpu'/'cuda' for float64 parity runs."
            )

        self.iteration = 0
        self.ll_history: list[float] = []
        # Log-likelihood of the *returned* parameters (issue #51). With
        # keep_best, ``ll_history`` stays the true per-iteration trajectory
        # (which can include a late overshoot), while ``final_ll_`` is the LL of
        # the iterate fit() actually kept -- use this, not ``ll_history[-1]``, as
        # the model's fitted log-likelihood. Set by fit().
        self.final_ll_: Optional[float] = None

        # Outlier-rejection bookkeeping (set up in fit()).
        self.numrej = 0
        self.good_idx: Optional[torch.Tensor] = None

        # Set by fit(): why fitting stopped ("max_iter", "nan_ll", "lrate_floor")
        # and how many iterations reverted Newton to natural gradient (Fortran
        # prints this; here it is exposed for parity debugging, see issue #21).
        self.stop_reason: Optional[str] = None
        self.n_newton_fallbacks = 0

        # Populated by fit()/_initialize_parameters().
        self.A: Optional[torch.Tensor] = None
        self.W: Optional[torch.Tensor] = None
        self.c: Optional[torch.Tensor] = None
        self.mu: Optional[torch.Tensor] = None
        self.alpha: Optional[torch.Tensor] = None
        self.beta: Optional[torch.Tensor] = None
        self.rho: Optional[torch.Tensor] = None
        # Per-source density-family codes (n_channels, n_models); set in
        # _initialize_parameters and mutated by the adaptive switcher.
        self.pdtype: Optional[torch.Tensor] = None
        # Number of adaptive-switch passes already performed (Fortran numchpdf).
        self.n_kurt_done = 0
        self.gm: Optional[torch.Tensor] = None
        self.comp_list: Optional[torch.Tensor] = None
        self.mean: Optional[torch.Tensor] = None
        self.sphere: Optional[torch.Tensor] = None
        self.sldet = 0.0

    # ------------------------------------------------------------------
    # Preprocessing
    # ------------------------------------------------------------------
    def _preprocess(self, X: np.ndarray) -> torch.Tensor:
        """Mean-removal + sphering, matching ``pyAMICA.AMICA._preprocess_data``.

        Done in float64 on CPU (eigh is not reliably supported on MPS and
        this is a one-time O(n_channels^3) cost, not the per-block hot
        path), then cast/moved to ``self.device``/``self.dtype``.
        """
        X_cpu = torch.from_numpy(np.ascontiguousarray(X)).to(torch.float64)
        data_dim = X_cpu.shape[0]

        if self.do_mean:
            mean = X_cpu.mean(dim=1, keepdim=True)
            X_cpu = X_cpu - mean
        else:
            mean = torch.zeros(data_dim, 1, dtype=torch.float64)

        if self.do_sphere:
            # Population covariance (divide by N), matching Fortran's DSYRK
            # scatter/N -- NOT torch.cov's default sample covariance (/(N-1)).
            # The two differ by a pure scalar sqrt(N/(N-1)); using /(N-1) leaves
            # a ~5e-6 sphere mismatch vs the reference (issue #24, check [1] of
            # .context/issue-24/root_cause_Aupdate.py).
            cov = torch.cov(X_cpu, correction=0)
            evals, evecs = torch.linalg.eigh(cov)
            order = torch.argsort(evals, descending=True)
            evals = evals[order]
            evecs = evecs[:, order]

            if self.pcakeep is not None:
                n_comp = min(self.pcakeep, evals.shape[0])
            elif self.pcadb is not None:
                db = 10.0 * torch.log10(evals / evals[0])
                n_comp = int((db > -self.pcadb).sum().item())
            else:
                n_comp = evals.shape[0]

            V = evecs[:, :n_comp]
            inv_sqrt = torch.diag(1.0 / torch.sqrt(evals[:n_comp]))
            if self.do_approx_sphere:
                # Symmetric ZCA sphere V diag(1/sqrt(eval)) V^T (Fortran
                # do_approx_sphere=True, amica17.f90:480-481). This is the
                # Fortran default and the parity-validated form; the old
                # diag(1/sqrt)@V^T (PCA whitening) is a different, non-symmetric
                # transform that breaks activation parity.
                sphere = V @ inv_sqrt @ V.T
            else:
                # Non-symmetric PCA whitening D^-1/2 V^T (Fortran
                # do_approx_sphere=False path, amica17.f90:495).
                sphere = inv_sqrt @ V.T

            X_cpu = sphere @ X_cpu
            # Sphering log-determinant term of the data log-likelihood
            # (Fortran ``sldet``, amica17.f90:474): sum over the kept
            # eigenvalues of -0.5*log(eval). For the PCA-reduced-rank case
            # this is a pseudo-determinant, matching Fortran which sums over
            # numeigs kept eigenvalues regardless of full rank.
            sldet = float(-0.5 * torch.log(evals[:n_comp]).sum().item())
        else:
            sphere = torch.eye(data_dim, dtype=torch.float64)
            sldet = 0.0

        self.mean = mean.to(device=self.device, dtype=self.dtype)
        self.sphere = sphere.to(device=self.device, dtype=self.dtype)
        self.sldet = sldet

        return X_cpu.to(device=self.device, dtype=self.dtype)

    # ------------------------------------------------------------------
    # Initialization
    # ------------------------------------------------------------------
    def _initialize_parameters(self):
        """Initialize parameters, mirroring ``pyAMICA.AMICA._initialize_parameters``
        exactly (same RNG draws, same order) so the same seed gives
        bit-identical starting parameters to the NumPy reference.
        """
        rng = np.random.RandomState(self.seed)
        n, m, ncomp, nmix = self.n_channels, self.n_models, self.n_comps, self.n_mix

        A_np = np.zeros((n, ncomp), dtype=np.float64)
        for h in range(m):
            A_np[:, h * n : (h + 1) * n] = np.eye(n) + 0.01 * (0.5 - rng.rand(n, n))

        comp_list_np = np.zeros((n, m), dtype=np.int64)
        for h in range(m):
            comp_list_np[:, h] = np.arange(h * n, (h + 1) * n)

        mu_np = np.zeros((nmix, ncomp), dtype=np.float64)
        for k in range(ncomp):
            mu_np[:, k] = np.linspace(-1, 1, nmix)
            mu_np[:, k] += 0.05 * (1 - 2 * rng.rand(nmix))

        alpha_np = np.ones((nmix, ncomp), dtype=np.float64) / nmix

        beta_np = np.ones((nmix, ncomp), dtype=np.float64)
        beta_np += 0.1 * (0.5 - rng.rand(nmix, ncomp))

        rho_np = self.rho0 * np.ones((nmix, ncomp), dtype=np.float64)
        gm_np = np.ones(m, dtype=np.float64) / m
        c_np = np.zeros((n, m), dtype=np.float64)

        self.A = torch.from_numpy(A_np).to(self.device, self.dtype)
        self.comp_list = torch.from_numpy(comp_list_np).to(self.device)
        self.mu = torch.from_numpy(mu_np).to(self.device, self.dtype)
        self.alpha = torch.from_numpy(alpha_np).to(self.device, self.dtype)
        self.beta = torch.from_numpy(beta_np).to(self.device, self.dtype)
        self.rho = torch.from_numpy(rho_np).to(self.device, self.dtype)
        self.gm = torch.from_numpy(gm_np).to(self.device, self.dtype)
        self.c = torch.from_numpy(c_np).to(self.device, self.dtype)

        # Per-source density-family codes, Fortran ``pdtype = pdftype`` (amica15.f90:
        # 593). In adaptive mode (pdftype==1) every source starts as the
        # super-Gaussian code 1 and the switcher may flip it to 4.
        self.pdtype = torch.full(
            (n, m), self.pdftype, dtype=torch.long, device=self.device
        )
        self.n_kurt_done = 0

        # Reset the mutable optimization state to the pristine constructor
        # values (lrate_cap, newtrate, rholrate are ratcheted down during
        # fit; restore them so a re-fit starts fresh).
        self.lrate = self.lrate0
        self.lrate_cap = self.lrate0
        self.newtrate = self.newtrate0
        self.rholrate = self.rholrate0
        self.iteration = 0
        self._update_unmixing_matrices()

    def _update_unmixing_matrices(self):
        """Recompute W from A via direct (batched) inversion -- never pinv."""
        assert self.A is not None and self.comp_list is not None
        A_stack = torch.stack(
            [self.A[:, self.comp_list[:, h]] for h in range(self.n_models)], dim=0
        )
        W_stack = torch.linalg.inv(A_stack)
        self.W = W_stack.permute(1, 2, 0).contiguous()

    def _pdtype_h(self, h: int) -> Optional[torch.Tensor]:
        """Per-source density-family codes for model ``h``, shaped for
        broadcasting against ``(batch, n_channels, num_mix)`` tensors, or
        ``None`` on the default ``pdftype=0`` (GG-only) fast path so the E-step
        stays bit-identical to the pre-#26 implementation.
        """
        if self.pdftype == 0:
            return None
        assert self.pdtype is not None
        return self.pdtype[:, h].view(1, -1, 1)

    # ------------------------------------------------------------------
    # E-step / M-step sufficient statistics (the hot path)
    # ------------------------------------------------------------------
    def _forward(self, X: torch.Tensor):
        """Run the E-step forward pass for one data block.

        Computes, for every model ``h``, the activations ``b``, scaled
        activations ``y``, normalized mixture responsibilities ``z``, the power
        ``|y|^rho`` (reused by the rho update), and the per-sample per-model
        log-likelihood ``logV`` (including the ``log|det W|`` and ``sldet``
        Jacobian terms, matching Fortran's ``Ptmp`` seed, amica17.f90:1273).
        Shared by ``_get_block_updates`` (which reduces it into sufficient
        statistics) and ``_block_sample_ll`` (which only needs ``logV``).

        Returns
        -------
        logV : torch.Tensor of shape (batch, n_models)
        b_list, z_list, y_list, azrho_list : lists (one entry per model) of
            per-model tensors (``b``: (batch, n_channels); ``z``/``y``/``azrho``:
            (batch, n_channels, n_mix)).
        """
        assert (
            self.comp_list is not None
            and self.c is not None
            and self.W is not None
            and self.mu is not None
            and self.beta is not None
            and self.rho is not None
            and self.alpha is not None
            and self.gm is not None
        )
        batch_size = X.shape[1]
        num_models = self.n_models
        b_list, z_list, y_list, azrho_list = [], [], [], []
        logV = torch.empty(batch_size, num_models, dtype=self.dtype, device=self.device)

        for h in range(num_models):
            idx = self.comp_list[:, h]
            # Activation b = W(x - c): c is the per-model data-space center.
            # Fortran subtracts wc in the E-step (amica17.f90:1280-1292), where
            # wc = W@c is precomputed in get_unmixing_matrices (amica17.f90:2178).
            # Subtracting c in data space before W is equivalent and keeps c's
            # semantics identical to Fortran's. For n_models=1, c == 0, so this is
            # bit-identical to the old X.T @ W.
            b = (X - self.c[:, h].unsqueeze(1)).T @ self.W[:, :, h]  # (batch, n_ch)

            mu_h = self.mu[:, idx].T.unsqueeze(0)  # (1, n_channels, num_mix)
            beta_h = self.beta[:, idx].T.unsqueeze(0)
            rho_h = self.rho[:, idx].T.unsqueeze(0)
            alpha_h = self.alpha[:, idx].T.unsqueeze(0)

            y = beta_h * (b.unsqueeze(-1) - mu_h)  # (batch, n_channels, num_mix)
            # Only log_pdf is needed here; the score fp (and drho's |y|^rho) are
            # reused in _get_block_updates. az_rho = |y|^rho is threaded through
            # so the rho-update does not recompute it (issue #63).
            log_pdf, az_rho = _log_pdf_only(y, rho_h, self._pdtype_h(h))

            # z0 = log(alpha) + log(beta) + log_pdf. For the single-component
            # families (codes 1/4) n_mix==1 so alpha==1 and log(alpha)==0, which
            # reproduces Fortran's alpha-free z0 (amica15.f90:1340/1352).
            z0 = torch.log(alpha_h) + torch.log(beta_h) + log_pdf
            ll_i = torch.logsumexp(
                z0, dim=-1
            )  # (batch, n_channels) -- per-source log-density
            z = torch.softmax(z0, dim=-1)  # normalized responsibilities

            logdet_W = torch.linalg.slogdet(self.W[:, :, h])[1]
            logV[:, h] = (
                torch.log(self.gm[h]) + logdet_W + self.sldet + ll_i.sum(dim=-1)
            )

            b_list.append(b)
            z_list.append(z)
            y_list.append(y)
            azrho_list.append(az_rho)

        return logV, b_list, z_list, y_list, azrho_list

    def _block_sample_ll(self, X: torch.Tensor) -> torch.Tensor:
        """Per-sample total log-likelihood for a data block (the rejection
        statistic; Fortran ``P``/``loglik``, amica17.f90:1372)."""
        logV, *_ = self._forward(X)
        return torch.logsumexp(logV, dim=1)  # (batch,)

    def _get_block_updates(self, X: torch.Tensor) -> Dict[str, torch.Tensor]:
        """Compute sufficient-statistic accumulators for one data block.

        Fortran-faithful exact-EM statistics (amica17.f90:1437-1592), validated
        against the reference binary to machine precision (issue #24). Unlike a
        first-order gradient M-step, the mixture updates use exact-EM numerator/
        denominator pairs and the score ``fp = rho*sign(y)*|y|^(rho-1)`` (``_score``,
        Fortran ``fp``) rather than the density derivative ``dpdf``:

        * ``dmu_n = sum(u*fp)``, ``dmu_d = sbeta*sum(u*fp/y)``   (mu += dmu_n/dmu_d)
        * ``dbeta_n = sum(u)``, ``dbeta_d = sum(u*fp*y)``        (beta *= sqrt(n/d))
        * ``drho_n = rho*sum(u*|y|^rho*ln|y|)``                  (rho digamma update)
        * ``dWtmp = g^T b`` with ``g = sum_j sbeta*u*fp``        (natural gradient)

        where ``u = v*z`` (model x mixture responsibility). ``ll`` is the correct
        pre-normalization ``logsumexp`` (see module docstring).

        Assumes ``rho <= 2`` (the ``maxrho`` default); the ``rho > 2`` denominator
        branches of Fortran (:1539/:1551) are unreachable and not implemented.

        Returns
        -------
        updates : dict with ``dgm`` (n_models,), ``dalpha_n``/``dmu_n``/``dmu_d``/
            ``dbeta_n``/``dbeta_d``/``drho_n`` (n_mix, n_comps), ``dWtmp``
            (n_channels, n_channels, n_models), ``dc_numer`` (n_channels,
            n_models; the data-space bias numerator ``sum_t v_h*x``, issue #27),
            ``ll`` (scalar), and -- when ``do_newton`` -- ``dsigma2_numer``,
            ``dkappa_numer``, ``dlambda_numer`` (see ``_finalize_newton_stats``).
        """
        assert (
            self.comp_list is not None
            and self.beta is not None
            and self.rho is not None
        )
        num_mix, num_models = self.n_mix, self.n_models
        dev, dt = self.device, self.dtype

        logV, b_list, z_list, y_list, azrho_list = self._forward(X)
        block_ll = torch.logsumexp(logV, dim=1).sum()
        v = torch.softmax(logV, dim=1)  # (batch, num_models)

        def zeros(*shape):
            return torch.zeros(*shape, dtype=dt, device=dev)

        dgm = zeros(num_models)
        dalpha_n = zeros(num_mix, self.n_comps)
        dmu_n = zeros(num_mix, self.n_comps)
        dmu_d = zeros(num_mix, self.n_comps)
        dbeta_n = zeros(num_mix, self.n_comps)
        dbeta_d = zeros(num_mix, self.n_comps)
        drho_n = zeros(num_mix, self.n_comps)
        dWtmp = zeros(self.n_channels, self.n_channels, num_models)
        dc_numer = zeros(self.n_channels, num_models)
        do_newton = self.do_newton
        if do_newton:
            dsigma2_numer = zeros(self.n_channels, num_models)
            dkappa_numer = zeros(num_mix, self.n_channels, num_models)
            dlambda_numer = zeros(num_mix, self.n_channels, num_models)
        tiny = torch.finfo(dt).tiny

        for h in range(num_models):
            idx = self.comp_list[:, h]
            b, zr, y = b_list[h], z_list[h], y_list[h]
            v_h = v[:, h]
            beta_h = self.beta[:, idx].T.unsqueeze(0)  # sbeta, (1, n_ch, num_mix)
            rho_h = self.rho[:, idx].T  # (n_ch, num_mix)
            # score fp; the family select-case is amica15.f90:1449-1473 (amica17
            # is GG-only, so cite the binary's source explicitly here).
            fp = _score(y, rho_h.unsqueeze(0), self._pdtype_h(h))
            u = v_h.unsqueeze(-1).unsqueeze(-1) * zr  # u = v*z (:1439)
            ufp = u * fp  # (:1485)

            dgm[h] = v_h.sum()
            dalpha_n.index_add_(1, idx, u.sum(0).T)  # sum(u) (:1524)
            dmu_n.index_add_(1, idx, ufp.sum(0).T)  # sum(ufp) (:1532)
            # mu denominator sbeta*sum(ufp/y) (:1537). In float32 a sample sitting
            # on a mixture mean can round y to *exactly* 0; the score fp(0)=0 (for
            # the supported rho>=1), so the raw ufp/y is 0/0 = NaN -- the sole
            # trigger of the full-data float32 divergence (issue #75; NOT a
            # summation-precision problem, so compensated accumulation does not
            # help). The true term ufp/y = u*rho*|y|^(rho-2) is NOT 0 in the limit:
            # a nonzero constant at rho==2, and an integrable singularity that
            # diverges as y->0 for rho<2 -- so once y underflows to exactly 0 the
            # real contribution is unrepresentable. Substituting 0 (ufp==0 there,
            # so 0/1) drops that one sample instead of poisoning all of dmu_d with a
            # NaN: a bounded, empirically negligible bias (it fires <=1 sample per
            # iteration on the sample EEG, and float32 still matches the float64 LL
            # to ~5 sig digits). float64 never rounds y to exactly 0, so the guard
            # is a bit-identical no-op there (single-model #24 parity preserved),
            # and it needs no float64, so it also stabilizes the MPS/float32 path.
            safe_y = torch.where(y == 0, torch.ones_like(y), y)
            dmu_d.index_add_(
                1, idx, (beta_h.squeeze(0) * (ufp / safe_y).sum(0)).T
            )  # (:1537)
            dbeta_n.index_add_(1, idx, u.sum(0).T)  # sum(u) (:1550)
            dbeta_d.index_add_(1, idx, (ufp * y).sum(0).T)  # sum(ufp*y) (:1556)

            # drho_numer = rho * sum(u*|y|^rho*ln|y|)  (:1560-1578). The leading
            # rho comes from ln(|y|^rho)=rho*ln|y| in the Fortran logab chain
            # (issue #24 Bug 1). Guard only the per-sample underflow (:1570) --
            # no per-component (rho!=1&rho!=2) mask (Bug 2): |y|^rho*ln|y| is 0 at
            # y=0, and clamping the log input makes the product collapse there.
            ay = y.abs()
            ayrho = azrho_list[h]  # |y|^rho reused from _forward (issue #63)
            logab = rho_h.unsqueeze(0) * torch.log(ay.clamp_min(tiny))  # rho*ln|y|
            logab = torch.where(ayrho < _EPSDBLE, torch.zeros_like(logab), logab)
            drho_n.index_add_(1, idx, (u * (ayrho * logab)).sum(0).T)

            g = (beta_h * ufp).sum(-1)  # g_i = sum_j sbeta*ufp (:1493)
            dWtmp[:, :, h] = g.T @ b  # source-space sum g_t b_t^T (:1592)
            # Data-space bias accumulator: dc_numer[i,h] = sum_t v_h(t)*x(i,t)
            # (Fortran :1423-1429). The denominator is dgm[h] = sum_t v_h(t).
            # NOTE: this replaces the old gradient-style bias g.sum(0), which was
            # accumulated but never applied (c was frozen at 0); the Fortran
            # update is the data-space responsibility-weighted mean (issue #27).
            dc_numer[:, h] = X @ v_h

            if do_newton:
                # Newton curvature accumulators (Fortran amica17.f90:1419,
                # 1500-1514), in terms of the score fp (not dpdf).
                dsigma2_numer[:, h] = (v_h.unsqueeze(-1) * b.pow(2)).sum(0)  # (:1419)
                dkappa_numer[:, :, h] = (
                    (u * fp.pow(2)).sum(0) * beta_h.squeeze(0).pow(2)
                ).T  # (:1500)
                dlambda_numer[:, :, h] = (u * (fp * y - 1.0).pow(2)).sum(0).T  # (:1511)

        updates = {
            "dgm": dgm,
            "dalpha_n": dalpha_n,
            "dmu_n": dmu_n,
            "dmu_d": dmu_d,
            "dbeta_n": dbeta_n,
            "dbeta_d": dbeta_d,
            "drho_n": drho_n,
            "dWtmp": dWtmp,
            "dc_numer": dc_numer,
            "ll": block_ll,
        }
        if do_newton:
            updates["dsigma2_numer"] = dsigma2_numer
            updates["dkappa_numer"] = dkappa_numer
            updates["dlambda_numer"] = dlambda_numer
        return updates

    def _accumulate_blocks(self, X: torch.Tensor) -> Dict[str, torch.Tensor]:
        """Sum sufficient statistics over all blocks of ``X``.

        Peak memory scales with ``block_size`` (each block's intermediates
        are freed once accumulated), not with ``X.shape[1]``.
        """
        n_samples = X.shape[1]
        acc: Optional[Dict[str, torch.Tensor]] = None
        for start in range(0, n_samples, self.block_size):
            end = min(start + self.block_size, n_samples)
            block_acc = self._get_block_updates(X[:, start:end])
            if acc is None:
                acc = block_acc
            else:
                for key in acc:
                    acc[key] = acc[key] + block_acc[key]
        assert acc is not None
        return acc

    # ------------------------------------------------------------------
    # M-step parameter update
    # ------------------------------------------------------------------
    def _finalize_newton_stats(self, acc: Dict[str, torch.Tensor]):
        """Reduce the Newton block accumulators into ``(sigma2, lambda, kappa)``.

        Ports the Fortran finalization (amica17.f90:1762-1776). The Fortran
        ``baralpha``/``dkappa_denom``/``dlambda_denom`` responsibility masses
        all cancel algebraically against the per-mixture ``dalpha`` weighting,
        leaving simply (with ``dgm = sum_t v_h`` the raw model mass):

            sigma2[i,h] = dsigma2_numer[i,h] / dgm[h]
            kappa[i,h]  = sum_j dkappa_numer[j,i,h] / dgm[h]
            lambda[i,h] = sum_j (dlambda_numer[j,i,h]
                                 + dkappa_numer[j,i,h] * mu[j,comp(i,h)]^2) / dgm[h]

        Returns (sigma2, lambda_, kappa), each (n_channels, n_models).
        """
        assert self.mu is not None and self.comp_list is not None
        dgm = acc["dgm"].unsqueeze(0)  # (1, n_models)
        sigma2 = acc["dsigma2_numer"] / dgm
        kappa = acc["dkappa_numer"].sum(dim=0) / dgm
        # mu at each source's component: mu[j, comp_list[i,h]] -> (n_mix, n_ch, n_models)
        mu_at = self.mu[:, self.comp_list]
        lambda_ = (acc["dlambda_numer"] + acc["dkappa_numer"] * mu_at.pow(2)).sum(
            dim=0
        ) / dgm
        return sigma2, lambda_, kappa

    def _newton_direction(self, dA_h, sigma2_h, lambda_h, kappa_h):
        """Per-model Newton direction ``H`` from the natural gradient ``dA_h``.

        Vectorized port of the per-source-pair 2x2 solve (amica17.f90:1817-1832,
        pyAMICA.py:802-813):

            H[i,i] = dA_h[i,i] / lambda[i]
            sk1 = sigma2[i]*kappa[k];  sk2 = sigma2[k]*kappa[i]   (i != k)
            H[i,k] = (sk1*dA_h[i,k] - dA_h[k,i]) / (sk1*sk2 - 1)  if sk1*sk2 > 1

        Returns ``(H, posdef)``. ``posdef`` is False if any off-diagonal pair
        fails ``sk1*sk2 > 1`` (the positive-definiteness guard); the caller
        then falls back to the natural gradient for this model.
        """
        n = self.n_channels
        sk1 = sigma2_h.unsqueeze(1) * kappa_h.unsqueeze(0)  # [i,k] = sigma2[i]*kappa[k]
        sk2 = sigma2_h.unsqueeze(0) * kappa_h.unsqueeze(1)  # [i,k] = sigma2[k]*kappa[i]
        prod = sk1 * sk2
        valid = prod > 1.0
        denom = torch.where(valid, prod - 1.0, torch.ones_like(prod))
        h_off = (sk1 * dA_h - dA_h.T) / denom
        H = torch.where(valid, h_off, torch.zeros_like(h_off))
        # Diagonal overrides (uses lambda, not the off-diagonal formula).
        diag = torch.diagonal(dA_h) / lambda_h
        H = H - torch.diag(torch.diagonal(H)) + torch.diag(diag)
        # Positive-definite iff every off-diagonal pair passed the guard.
        offdiag = ~torch.eye(n, dtype=torch.bool, device=dA_h.device)
        posdef = bool(valid[offdiag].all().item())
        return H, posdef

    def _update_parameters(self, acc: Dict[str, torch.Tensor], n_samples: int):
        """Apply the M-step parameter update, matching
        ``pyAMICA.AMICA._update_parameters`` (natural-gradient and Newton).

        ``n_samples`` is the number of samples that fed the accumulators (the
        good-sample count when ``do_reject`` is active), so ``gm`` and the
        reported log-likelihood are normalized by the effective sample count.

        The mixture parameters use exact-EM fixed-point updates (no ``lrate``);
        only the ``A``/``W`` step is scaled by ``lrate`` (Fortran amica17.f90:
        1890-2035). The per-model data-space bias ``c`` uses Fortran's exact-EM
        ``update_c`` (amica17.f90:1423-1429/1899-1901): ``c[i,h] = sum_t v_h*x /
        sum_t v_h``, the responsibility-weighted data mean for model ``h``. For
        ``n_models=1`` on mean-removed data ``v == 1`` so ``c`` collapses to the
        (zero) data mean; the update is skipped there so single-model parity stays
        bit-exact (issue #24). For ``n_models>1`` the per-model ``v`` is
        non-uniform and ``c`` moves each iteration (issue #27).
        """
        assert (
            self.c is not None
            and self.alpha is not None
            and self.mu is not None
            and self.beta is not None
            and self.rho is not None
            and self.A is not None
            and self.comp_list is not None
        )
        self.gm = acc["dgm"] / n_samples

        # Per-model data-space bias (Fortran's `update_c` flag, amica17.f90:1423-
        # 1429 numerator / :1899-1901 division). Skipped for a single model to keep
        # the issue #24 parity bit-exact: with v==1 the update would add a ~1e-13
        # float-sum residual of the (mean-removed) data, perturbing the
        # otherwise-exact single-model trajectory. dgm[h] = sum_t v_h(t) is the
        # denominator (Fortran `dc_denom`). A fully-dead model (dgm[h]==0 => v_h==0
        # for all t, so dc_numer[:,h]==0 too) gives 0/0; keep its PRIOR c rather
        # than write a NaN. A NaN c would poison the NEXT iteration's cross-model
        # softmax for EVERY model (unlike log(gm[h])=-inf, which softmax tolerates,
        # so a dead model was previously inert) -- this containment mirrors the
        # mu/beta/rho non-finite guards below. `dgm>0` is also False for a NaN dgm
        # from upstream corruption, so that is contained too.
        if self.n_models > 1:
            dgm = acc["dgm"]
            live = dgm > 0.0
            new_c = acc["dc_numer"] / dgm.clamp_min(torch.finfo(self.dtype).tiny)
            self.c = torch.where(live.unsqueeze(0), new_c, self.c)
            if not bool(live.all()):
                logger.warning(
                    "Zero-responsibility model(s) at iter %d; kept their prior "
                    "bias c (dead-model guard).",
                    self.iteration,
                )

        # Component sharing (#60): a component that was merged away is no longer
        # referenced by comp_list, so no sufficient statistic accumulates into
        # its column (dalpha_n/dmu_d/dbeta_d == 0) and the divisions below would
        # be 0/0 = NaN. Update only USED columns and freeze the rest at their
        # last finite value (Fortran carries NaN there harmlessly behind its
        # comp_used mask; we keep them finite so save/the degenerate guard are
        # not tripped). With the default full comp_list every column is used, so
        # ``used`` is all-True and every update below is byte-for-byte unchanged.
        used = self.comp_used.unsqueeze(0)  # (1, n_comps)

        self.alpha = torch.where(
            used, acc["dalpha_n"] / acc["dalpha_n"].sum(dim=0, keepdim=True), self.alpha
        )

        # Finalize the Newton curvature with the PRE-update mu. Fortran folds the
        # mu^2 term into lambda during E-step accumulation, before the M-step
        # moves mu (amica17.f90:1762-1774), and the NumPy port bakes it in at
        # accumulation time. Do it here, before self.mu is reassigned below, so
        # lambda uses this iteration's mu rather than the updated one.
        newton_active = self.do_newton and self.iteration >= self.newt_start
        if newton_active:
            sigma2, lambda_, kappa = self._finalize_newton_stats(acc)

        # Exact-EM mixture location/scale (Fortran :1978/:1993). No lrate.
        # ``used`` masks merged-away columns (no-op for the default comp_list).
        self.mu = torch.where(used, self.mu + acc["dmu_n"] / acc["dmu_d"], self.mu)
        self.beta = torch.where(
            used,
            torch.clamp(
                self.beta * torch.sqrt(acc["dbeta_n"] / acc["dbeta_d"]),
                self.invsigmin,
                self.invsigmax,
            ),
            self.beta,
        )
        # Fortran keeps a live "NaN in sbeta!" canary here (amica17.f90:1996-2000).
        # The exact-EM mu/beta divisions are unguarded (matching Fortran, whose own
        # mu/beta guard is commented out), so surface a non-finite value here
        # instead of letting it propagate to a later, unattributable nan-LL stop.
        if (
            not torch.isfinite(self.mu).all()
            or not torch.isfinite(self.beta).all()
            or not torch.isfinite(self.alpha).all()
        ):
            logger.warning(
                "Non-finite mu/beta/alpha at iter %d (a mixture component's mass "
                "likely collapsed).",
                self.iteration,
            )

        # GG shape update with the 1/psi(1+1/rho) digamma factor (Fortran
        # :2013-2014); the divisor is the per-component responsibility mass
        # dalpha_n (floored so a near-empty component cannot poison rho). A NaN
        # here (e.g. from upstream mu/beta corruption) is reset to rho0 -- but
        # logged first, so the reset does not silently erase the failure origin.
        # Skipped for every non-GG family: Fortran sets dorho=.false. when
        # pdftype/=0 (amica15.f90:3682), freezing rho at rho0.
        if (
            self.dorho
            and not torch.all(self.rho == 1.0)
            and not torch.all(self.rho == 2.0)
        ):
            drho = acc["drho_n"] / acc["dalpha_n"].clamp_min(1e-8)
            psi = torch.special.digamma(1.0 + 1.0 / self.rho)
            new_rho = self.rho + self.rholrate * (1.0 - (self.rho / psi) * drho)
            nan_mask = torch.isnan(new_rho)
            if nan_mask.any():
                logger.warning(
                    "NaN in rho update at iter %d for %d component(s); resetting "
                    "to rho0=%g.",
                    self.iteration,
                    int(nan_mask.sum()),
                    self.rho0,
                )
                new_rho = torch.where(
                    nan_mask, torch.full_like(new_rho, self.rho0), new_rho
                )
            self.rho = torch.where(
                used, torch.clamp(new_rho, self.minrho, self.maxrho), self.rho
            )

        # --- A / W update: natural gradient, optionally Newton-preconditioned.
        # A is stored as Fortran's A^T (the true unmixing is W^T = inv(A)^T), so
        # Fortran's A_fort -= lrate*A_fort @ dir becomes, transposed,
        # A -= lrate*dir^T @ A (LEFT-multiply by the TRANSPOSED direction). The
        # direction ``dir`` (natural gradient I - <g b^T>/dgm, or its Newton
        # precondition) is built in Fortran's untransposed convention. Getting
        # this wrong (right-multiply by the untransposed dir) is invisible at the
        # fixed point but sends the free-running fit downhill -- issue #24 root
        # cause (.context/issue-24/root_cause_Aupdate.py, machine-exact check).
        # (newton_active / sigma2 / lambda_ / kappa were finalized above.)
        # A-update. When sharing holds A this iteration (the post-merge settle
        # window, Fortran amica15.f90:1785), skip the whole block -- direction
        # computation, lrate ramp, and step -- so a discarded Newton direction
        # cannot pollute the fallback counter. _a_frozen is always False when
        # sharing is off, so the default path is unchanged.
        if not self._a_frozen():
            eye = torch.eye(self.n_channels, dtype=self.dtype, device=self.device)
            directions = []
            no_newt = False
            for h in range(self.n_models):
                dA_h = -acc["dWtmp"][:, :, h] / acc["dgm"][h] + eye  # I - <g b^T>/dgm
                if newton_active:
                    H, posdef = self._newton_direction(
                        dA_h, sigma2[:, h], lambda_[:, h], kappa[:, h]
                    )
                    if posdef:
                        directions.append(H)
                    else:
                        no_newt = True
                        directions.append(dA_h)  # fall back to natural gradient
                else:
                    directions.append(dA_h)

            if newton_active and no_newt:
                # Fortran prints "Hessian not positive definite, using natural
                # gradient" (amica15.f90:1791-1793). Surface the same signal so an
                # all-fallback run (issue #21) is visible without re-instrumenting.
                self.n_newton_fallbacks += 1
                logger.warning(
                    "Newton not positive definite at iter %d; using natural gradient.",
                    self.iteration,
                )

            # Learning-rate ramp: toward newtrate while Newton is active and
            # stable, otherwise toward lrate0 (Fortran amica15.f90:1786-1797).
            # Ramped after mu/beta/rho (exact-EM, lrate-free) and before A.
            if newton_active and not no_newt:
                self.lrate = min(
                    self.newtrate, self.lrate + min(1.0 / self.newt_ramp, self.lrate)
                )
            else:
                self.lrate = min(
                    self.lrate_cap, self.lrate + min(1.0 / self.newt_ramp, self.lrate)
                )

            # Accumulate each model's natural-gradient/Newton contribution per
            # mixing COLUMN as a gm-WEIGHTED AVERAGE (Fortran dAk/zeta,
            # amica15.f90:1730-1743): dAk = sum_h gm[h]*dir_h scattered by
            # comp_list, zeta = sum_h gm[h] per column, then dAk /= zeta. For the
            # default disjoint comp_list every column has exactly one contributor,
            # so gm cancels (dAk = dir) and single-model (gm=[1]) is byte-for-byte
            # unchanged; for a SHARED column (issue #60) the step is Fortran's
            # responsibility-weighted average, NOT a raw sum (a raw sum would
            # over-step by the contributor count and destabilize the fit).
            dAk = torch.zeros_like(self.A)
            zeta = torch.zeros(self.n_comps, dtype=self.dtype, device=self.device)
            for h in range(self.n_models):
                idx = self.comp_list[:, h]
                dAk.index_add_(1, idx, self.gm[h] * (directions[h].T @ self.A[:, idx]))
                zeta.index_add_(0, idx, self.gm[h].expand(idx.shape[0]))
            dAk = dAk / zeta.clamp_min(torch.finfo(self.dtype).tiny)
            self.A = self.A - self.lrate * dAk

        if self.doscaling and (self.iteration % self.scalestep == 0):
            assert self.A is not None and self.mu is not None and self.beta is not None
            scale = torch.sqrt((self.A**2).sum(dim=0))  # (n_comps,)
            nonzero = scale > 0
            self.A[:, nonzero] = self.A[:, nonzero] / scale[nonzero]
            self.mu[:, nonzero] = self.mu[:, nonzero] * scale[nonzero]
            self.beta[:, nonzero] = self.beta[:, nonzero] / scale[nonzero]

        self._update_unmixing_matrices()

    def _a_frozen(self) -> bool:
        """Whether the A-update (and its lrate ramp) is held this iteration.

        A is frozen for the first 6 iterations of every ``share_iter``-length
        window once ``iter >= share_start`` -- i.e. the merge iteration and the 5
        after it -- so the density parameters can settle onto any freshly merged
        component before the mixing matrix moves again (Fortran A-freeze,
        amica15.f90:1785). The window fires each cycle regardless of whether that
        cycle's ``_identify_shared_comps`` actually merged a pair.

        Anchored on ``(itf - share_start) % share_iter`` so it stays aligned with
        the merge schedule for any ``share_start``; the literal Fortran formula
        uses ``mod(iter, share_iter)`` (misaligned unless share_start is a
        multiple of share_iter, and a permanent freeze for ``share_iter <= 6``),
        but that path is dead in the reference (see :meth:`_identify_shared_comps`)
        so there is no parity constraint -- the constructor requires
        ``share_iter > 6`` so the window never consumes the whole cycle. Gated
        behind ``share_comps`` and ``n_models >= 2``, so with sharing off it is
        always False and the validated default trajectory is untouched.
        """
        if not self.share_comps or self.n_models < 2:
            return False
        itf = self.iteration + 1  # Fortran-style 1-indexed iteration
        if itf < self.share_start:
            return False
        return (itf - self.share_start) % self.share_iter <= 5

    def _identify_shared_comps(self) -> None:
        """Merge near-collinear mixing columns across models (Fortran
        ``identify_shared_comps``, amica15.f90:1898).

        Two components (model ``h`` source ``i`` and model ``hh`` source ``ii``,
        ``h < hh``) are identified when the angle between their mixing columns,
        measured in the original (de-sphered) data space, is below the
        ``comp_thresh`` cutoff::

            t0 = |a . b| / (||a|| ||b||),   a = Spinv A[:,ci], b = Spinv A[:,cj]

        where ``Spinv = sphere^-1`` de-spheres the columns back to sensor space
        (so the similarity compares scalp maps). On a match, ``cj`` is folded
        into ``ci``: every ``comp_list`` entry equal to ``cj`` is reassigned to
        ``ci``, so the two now share one mixing column and one density (the
        M-step already accumulates every sufficient statistic through
        ``comp_list`` via index_add, so shared components sum automatically).

        Greedy and order-dependent, matching the reference's quadruple loop.
        Skips a pair already merged, or one whose two columns coexist in some
        single model (a model cannot share a component with itself).

        No bit-exact oracle: ``Spinv2`` is *declared* in the reference headers
        but never *allocated* anywhere in ``amica15.f90``/``amica17.f90`` (unlike
        ``Spinv``, allocated at :551), so invoking ``identify_shared_comps`` with
        ``share_comps=.true.`` would read an unallocated array through ``DGEMV``
        -- undefined behavior, most likely a crash, not a benign no-op. The
        routine is effectively unrunnable in the reference (cf. the also-dead
        ``do_choose_pdfs`` switch, #26), so this implements the intended
        algorithm and validates it on real data, not against byte parity.
        """
        if self.n_models < 2:
            return
        assert self.A is not None and self.comp_list is not None
        if self._spinv is None:
            # The de-sphering metric needs a full-rank, invertible sphere.
            # Average-referenced EEG (covariance rank n_channels-1) or naturally
            # rank-deficient data makes the sphere singular; surface it loudly
            # rather than merging on garbage (the degenerate-fit philosophy,
            # amica.py). (pcakeep/pcadb reduction is already rejected in __init__.)
            assert self.sphere is not None
            try:
                spinv = torch.linalg.inv(self.sphere)
            except RuntimeError as exc:
                raise RuntimeError(
                    "Component sharing needs an invertible sphere, but it is "
                    "singular (common with average-referenced or rank-deficient "
                    "data). Disable share_comps or use full-rank data."
                ) from exc
            if not torch.isfinite(spinv).all():
                raise RuntimeError(
                    "Component sharing produced a non-finite de-sphering matrix "
                    "(the sphere is singular/ill-conditioned). Disable share_comps "
                    "or use full-rank data."
                )
            self._spinv = spinv
        # De-sphered mixing columns in sensor space, on CPU for the small greedy
        # scan (n_models^2 * n_channels^2 pairs; avoids per-element GPU syncs).
        atil = (self._spinv @ self.A).detach().cpu().numpy()
        norms = np.linalg.norm(atil, axis=0)
        cl = self.comp_list.detach().cpu().numpy().copy()  # (nw, n_models)
        nw, m = cl.shape
        tiny = np.finfo(atil.dtype).tiny
        merged = 0
        for h in range(m):
            for hh in range(h + 1, m):
                for i in range(nw):
                    for ii in range(nw):
                        ci, cj = int(cl[i, h]), int(cl[ii, hh])
                        if ci == cj:
                            continue
                        t0 = abs(atil[:, ci] @ atil[:, cj]) / (
                            norms[ci] * norms[cj] + tiny
                        )
                        # NaN t0 (e.g. a zero-norm column) must NOT merge:
                        # `NaN < thresh` is False, so guard finiteness explicitly.
                        if not np.isfinite(t0) or t0 < self.comp_thresh:
                            continue
                        # A model cannot share a component with itself: skip if
                        # any single model already uses both columns.
                        if any(
                            (cl[:, k] == ci).any() and (cl[:, k] == cj).any()
                            for k in range(m)
                        ):
                            continue
                        cl[cl == cj] = ci  # fold cj into ci everywhere
                        merged += 1
        if merged:
            self.comp_list = torch.from_numpy(cl).to(self.comp_list.device)
            logger.info(
                "Component sharing (iter %d): %d merge(s), %d unique components.",
                self.iteration,
                merged,
                int(np.unique(cl).size),
            )

    @property
    def comp_used(self) -> torch.Tensor:
        """Boolean mask (n_comps,) of components still referenced by comp_list.

        A component drops out of use when it is folded into another by
        :meth:`_identify_shared_comps`; unused columns receive no gradient and
        are never read by the E-step. Derived from ``comp_list`` (not stored).
        """
        assert self.comp_list is not None
        used = torch.zeros(self.n_comps, dtype=torch.bool, device=self.comp_list.device)
        used[self.comp_list.reshape(-1)] = True
        return used

    def _choose_pdfs(self, X: torch.Tensor) -> None:
        """Extended-Infomax adaptive PDF switch (Fortran ``do_choose_pdfs``).

        Re-estimates each source's kurtosis from the current model activations
        and sets its density family to the super-Gaussian (code 1) or
        sub-Gaussian (code 4) cosh density by kurtosis sign. This is the
        extended-Infomax rule that ``runamica15.m`` documents for the
        ``kurt_start``/``num_kurt``/``kurt_int`` schedule (the super/sub-Gaussian
        scores ``y +/- tanh(y)`` are exactly the two families 1/4). The
        reference binary declares this (``pdftype==1`` sets ``do_choose_pdfs``,
        amica15.f90:594) but never runs the switch (``m2sum``/``m4sum`` are
        never accumulated), so there is no bit-exact oracle; validated by
        real-data log-likelihood (must not decrease vs the fixed GG default).
        """
        n_ch, n_models = self.n_channels, self.n_models
        m2 = torch.zeros(n_ch, n_models, dtype=self.dtype, device=self.device)
        m4 = torch.zeros_like(m2)
        nsub = torch.zeros(n_models, dtype=self.dtype, device=self.device)
        n_samples = X.shape[1]
        for start in range(0, n_samples, self.block_size):
            block = X[:, start : start + self.block_size]
            logV, b_list, *_ = self._forward(block)
            v = torch.softmax(logV, dim=1)  # (batch, n_models)
            for h in range(n_models):
                b = b_list[h]  # (batch, n_ch)
                vh = v[:, h].unsqueeze(1)
                m2[:, h] += (vh * b.pow(2)).sum(0)
                m4[:, h] += (vh * b.pow(4)).sum(0)
                nsub[h] += v[:, h].sum()

        # Kurtosis = E[b^4]/E[b^2]^2 - 3 = nsub * m4 / m2^2 - 3, per (source, model).
        tiny = torch.finfo(self.dtype).tiny
        kurt = nsub.unsqueeze(0) * m4 / m2.pow(2).clamp_min(tiny) - 3.0
        self.pdtype = self._pdtype_from_kurtosis(kurt, nsub)

    def _pdtype_from_kurtosis(
        self, kurt: torch.Tensor, nsub: torch.Tensor
    ) -> torch.Tensor:
        """Map per-source excess kurtosis to a density-family code (pure).

        Super-Gaussian (positive kurtosis) -> code 1; sub-Gaussian -> code 4.
        Only sources with a meaningful signal switch: a dead model
        (``nsub[h]==0`` => ``kurt==-3.0``, finite) or a numerically blown-up
        source (``kurt`` NaN, and ``NaN>0`` is False) would otherwise be silently
        assigned code 4 with no diagnostic, so those keep their prior ``pdtype``
        and are logged -- mirroring the dead-model / non-finite guards in
        ``_update_parameters``. Split out from ``_choose_pdfs`` so the decision
        (including the sub-Gaussian branch, which real EEG rarely triggers) is
        unit-testable on a constructed ``kurt`` tensor.
        """
        assert self.pdtype is not None
        ones = torch.ones_like(self.pdtype)
        new_pdtype = torch.where(kurt > 0.0, ones, ones * 4)
        valid = torch.isfinite(kurt) & (nsub.unsqueeze(0) > 0.0)
        result = torch.where(valid, new_pdtype, self.pdtype)
        if not bool(valid.all()):
            logger.warning(
                "Non-finite or zero-mass kurtosis for %d source/model pair(s) at "
                "iter %d; kept their prior pdtype (adaptive-switch guard).",
                int((~valid).sum()),
                self.iteration,
            )
        return result

    def _snapshot_params(self) -> Dict[str, object]:
        """Snapshot the fitted state for the best-iterate safeguard (issue #51).

        Clones each ``_PARAM_TENSORS`` tensor (not an alias) so the live in-place
        M-step updates do not roll the snapshot forward; the constant
        preprocessing tensors (``mean``/``sphere``) are included so a restore is a
        total rollback. Also captures the scalar ``n_kurt_done`` (the adaptive-PDF
        switch counter that gates ``pdtype``) so a restored model's switch count
        stays consistent with its rolled-back ``pdtype`` -- otherwise a switch
        applied after the peak iterate would leave the two out of sync in a saved
        model (silent-failure review)."""
        snap: Dict[str, object] = {
            name: getattr(self, name).clone() for name in self._PARAM_TENSORS
        }
        snap["n_kurt_done"] = self.n_kurt_done
        return snap

    def _restore_params(self, snapshot: Dict[str, object]) -> None:
        """Restore the state captured by :meth:`_snapshot_params`."""
        for name, value in snapshot.items():
            setattr(self, name, value)

    # ------------------------------------------------------------------
    # Public API
    # ------------------------------------------------------------------
    def fit(
        self, X: np.ndarray, max_iter: int = 100, verbose: bool = True
    ) -> "AMICATorchNG":
        """Fit the model to data.

        Parameters
        ----------
        X : np.ndarray of shape (n_channels, n_samples)
            Input data.
        max_iter : int, default=100
            Number of natural-gradient EM iterations.
        verbose : bool, default=True
            Show a tqdm progress bar.

        Returns
        -------
        self : AMICATorchNG
        """
        if X.ndim != 2:
            raise ValueError(
                f"X must be a 2D array (n_channels, n_samples), got shape {X.shape}"
            )
        if X.shape[0] != self.n_channels:
            raise ValueError(
                f"X has {X.shape[0]} channels, model expects {self.n_channels}"
            )

        X_t = self._preprocess(X)
        n_total = X_t.shape[1]

        self._initialize_parameters()
        self.ll_history = []
        self.numrej = 0
        self.n_newton_fallbacks = 0
        self._spinv = None  # rebuild the de-sphering metric for this fit's sphere
        self.stop_reason = "max_iter"
        self.good_idx = (
            torch.arange(n_total, device=self.device) if self.do_reject else None
        )
        numdecs = 0

        # Best-iterate safeguard (issue #51): track the highest-LL iterate so a
        # late Newton-fallback overshoot cannot leave the returned model below a
        # peak it already reached. Inactive under do_reject (the good set, and so
        # the LL normalization, changes across iterations) and under share_comps
        # (a merge drops parameters, so pre- and post-merge LLs are not
        # comparable AND the snapshot's comp_list would revert the merge -- the
        # returned model would silently be unmerged; #60). In both cases fit()
        # returns the last iterate, matching Fortran.
        track_best = self.keep_best and not self.do_reject and not self.share_comps
        best_ll = -math.inf
        best_snapshot: Optional[Dict[str, object]] = None
        if self.keep_best and (self.do_reject or self.share_comps):
            # keep_best defaults on, so a user enabling rejection/sharing would
            # otherwise silently lose the safeguard; surface it once.
            reason = "do_reject" if self.do_reject else "share_comps"
            logger.warning(
                "keep_best is inactive under %s: best-iterate selection by LL is "
                "not well-defined (%s), so fit() returns the last iterate.",
                reason,
                "the good-sample set / LL normalization changes across iterations"
                if self.do_reject
                else "a merge changes the parameter count and reverting to an "
                "earlier snapshot would undo the merge",
            )

        iterator = tqdm(range(max_iter), desc="AMICA-NG", disable=not verbose)
        for it in iterator:
            self.iteration = it

            X_use = X_t[:, self.good_idx] if self.do_reject else X_t
            n_use = X_use.shape[1]
            acc = self._accumulate_blocks(X_use)

            # Log-likelihood of the CURRENT (pre-update) parameters: acc["ll"] is
            # this iteration's E-step total, computed before _update_parameters
            # moves the parameters. A singular W makes logdet -> -inf (not NaN),
            # so guard on isfinite, not isnan alone: a -inf LL would otherwise
            # sail past as a mere "decrease" and the run would "complete"
            # (stop_reason=max_iter) on a degenerate model. Checking here, before
            # the update, stops on the last finite parameters instead of
            # overwriting them with a garbage update first.
            ll = (acc["ll"] / (n_use * self.n_channels)).item()
            if not math.isfinite(ll):
                self.stop_reason = "nan_ll" if math.isnan(ll) else "singular_ll"
                logger.warning(
                    "Non-finite log-likelihood (%s) at iteration %d; stopping.",
                    ll,
                    it,
                )
                break

            # Best-iterate safeguard (issue #51): remember the parameters that
            # produced this LL when it is the best seen, so a later overshoot
            # does not leave the returned model below this peak.
            if track_best and ll > best_ll:
                best_ll = ll
                best_snapshot = self._snapshot_params()

            # Whether rejection fires this iteration (Fortran schedule,
            # amica17.f90:1141-1146). Fortran rejects using the per-sample
            # log-likelihood from THIS iteration's E-step, i.e. the PRE-update
            # parameters (loglik is stored in get_updates_and_likelihood before
            # update_params runs). Capture it here, before _update_parameters,
            # to match that ordering.
            will_reject = (
                self.do_reject
                and self.maxrej > 0
                and (
                    it == self.rejstart
                    or (
                        max(1, it - self.rejstart) % self.rejint == 0
                        and self.numrej < self.maxrej
                    )
                )
            )
            if will_reject:
                assert self.good_idx is not None
                reject_ll = self._sample_ll(self.good_idx, X_t)
            else:
                reject_ll = None

            self._update_parameters(acc, n_use)

            # Extended-Infomax adaptive PDF switch (Fortran do_choose_pdfs). Runs
            # on the kurt_start/num_kurt/kurt_int schedule using the just-updated
            # W; the new per-source families take effect from the next E-step.
            # itf is the Fortran-style 1-indexed iteration. num_kurt=0 disables
            # switching (the family stays at its pdftype=1 super-Gaussian init).
            if self.do_choose_pdfs and self.n_kurt_done < self.num_kurt:
                itf = it + 1
                if (
                    itf >= self.kurt_start
                    and (itf - self.kurt_start) % self.kurt_int == 0
                ):
                    self._choose_pdfs(X_use)
                    self.n_kurt_done += 1

            # Component sharing (Fortran identify_shared_comps schedule,
            # amica15.f90:1838): once per share_iter cycle from share_start,
            # merge near-collinear mixing columns across models using the
            # just-updated A. Fortran runs identify_shared_comps BEFORE
            # get_unmixing_matrices (amica15.f90:1840,1845), so rebuild W from the
            # merged comp_list -- otherwise the next E-step would read a stale W
            # (pre-merge comp_list) while indexing the densities by the merged
            # comp_list. No-op when share_comps is off or n_models == 1.
            if self.share_comps:
                itf = it + 1
                if (
                    itf >= self.share_start
                    and (itf - self.share_start) % self.share_iter == 0
                ):
                    self._identify_shared_comps()
                    self._update_unmixing_matrices()

            self.ll_history.append(ll)

            # Learning-rate control, ported from Fortran (amica17.f90:1062-1108).
            # Natural-gradient/Newton ascent is not monotonic at a fixed rate:
            # when the log-likelihood decreases, anneal the working rates
            # (lrate, rholrate). If decreases persist for maxdecs iterations,
            # ratchet the *ceilings* down (lrate_cap, and newtrate once Newton
            # is running) so the per-iteration ramp can no longer re-inflate
            # lrate back to the overshooting value -- without this the ramp and
            # a one-shot halving just oscillate and the LL drifts down.
            if len(self.ll_history) > 1 and ll < self.ll_history[-2]:
                if self.lrate <= self.minlrate:
                    logger.warning(
                        "lrate floor (%g) reached at iter %d; stopping.",
                        self.minlrate,
                        it,
                    )
                    self.stop_reason = "lrate_floor"
                    break
                self.lrate *= self.lratefact
                self.rholrate *= self.rholratefact
                numdecs += 1
                if numdecs >= self.maxdecs:
                    self.lrate_cap *= self.lratefact
                    if self.do_newton and it > self.newt_start:
                        self.newtrate *= self.lratefact
                    numdecs = 0
            if self.do_newton and it == self.newt_start:
                numdecs = 0

            # Outlier rejection, after the parameter update (Fortran order,
            # amica17.f90:1141-1146) but using the pre-update per-sample LL
            # captured above.
            if will_reject:
                assert reject_ll is not None
                self._reject_outliers(reject_ll)

            iterator.set_postfix({"LL": f"{ll:.4f}", "lrate": f"{self.lrate:.4g}"})

        # Log-likelihood of the parameters fit() returns. A degenerate stop
        # leaves the model on the diverged parameters, whose LL is NOT the last
        # finite ll_history value (the guard breaks before appending), so report
        # NaN there rather than a stale healthy-looking number (silent-failure
        # review). Otherwise it is the last trajectory value, overwritten with the
        # best iterate's LL below if the safeguard restores it.
        if self.stop_reason in self._DEGENERATE_STOP_REASONS:
            self.final_ll_ = float("nan")
        else:
            self.final_ll_ = self.ll_history[-1] if self.ll_history else float("nan")

        # Restore the best iterate if the run ended materially below it (issue
        # #51). Skipped for a degenerate stop -- not because the parameters are
        # necessarily non-finite (a singular_ll stop leaves A/W finite but
        # singular) but because salvaging a diverged run here would pre-empt issue
        # #50's degenerate-fit contract; state_dict() already refuses to persist
        # any model whose stop_reason is degenerate. Also skipped when the final
        # LL is within _KEEP_BEST_TOL of the best -- a monotone single-model run
        # has final == best, so no restore fires and issue #24 parity stays
        # bit-exact.
        if (
            track_best
            and best_snapshot is not None
            and self.stop_reason not in self._DEGENERATE_STOP_REASONS
            and self.ll_history
            and best_ll - self.ll_history[-1] > _KEEP_BEST_TOL
        ):
            logger.info(
                "Restoring best iterate (LL %.6f) over final LL %.6f "
                "(issue #51 best-iterate safeguard).",
                best_ll,
                self.ll_history[-1],
            )
            self._restore_params(best_snapshot)
            self.final_ll_ = best_ll

        return self

    def _sample_ll(self, good_idx: torch.Tensor, X_t: torch.Tensor) -> torch.Tensor:
        """Per-sample total log-likelihood over ``good_idx``, block by block, in
        ``good_idx`` order (so a keep-mask over the result maps back correctly)."""
        parts = [
            self._block_sample_ll(X_t[:, good_idx[start : start + self.block_size]])
            for start in range(0, int(good_idx.numel()), self.block_size)
        ]
        return torch.cat(parts)

    def _reject_outliers(self, ll_vec: torch.Tensor):
        """Permanently drop samples whose (pre-update) log-likelihood is a low
        outlier.

        Fortran ``reject_data`` (amica17.f90:2380-2464): reject any currently-good
        sample with ``loglik < mean - rejsig*std`` (population std). The rejection
        is one-directional; ``good_idx`` only ever shrinks, and the good-sample
        count drives the ``gm``/LL normalization thereafter. ``ll_vec`` is the
        per-sample log-likelihood over the current good set, in ``good_idx`` order.
        """
        assert self.good_idx is not None
        good = self.good_idx
        mean = ll_vec.mean()
        std = torch.sqrt((ll_vec.pow(2).mean() - mean.pow(2)).clamp_min(0.0))
        keep = ll_vec >= (mean - self.rejsig * std)

        if not bool(keep.any()):
            # For finite log-likelihoods the max sample is always >= mean >=
            # mean - rejsig*std (rejsig>0 is validated at construction), so it is
            # always kept; the only way every sample is dropped is a non-finite
            # per-sample LL (one NaN poisons mean/std, making every comparison
            # False). Report that accurately instead of blaming rejsig (issue
            # #127), which a user cannot fix by tuning rejsig. In a normal fit()
            # the earlier aggregate non-finite-LL guard (the sum is non-finite
            # iff a term is) stops the loop first, so this mainly serves direct
            # callers of _reject_outliers and is defense in depth.
            n_bad = int((~torch.isfinite(ll_vec)).sum())
            if n_bad:
                raise ValueError(
                    f"{n_bad} of {ll_vec.numel()} samples have a non-finite "
                    "log-likelihood; this indicates numerical instability "
                    "upstream (singular W / overflow), not a rejsig "
                    "miscalibration. Check for rank-deficient or "
                    "average-referenced data, or reduce the learning rate."
                )
            raise ValueError(  # defensive: unreachable for finite LL, rejsig>0
                f"Outlier rejection removed all {good.numel()} samples "
                f"(rejsig={self.rejsig} too aggressive for this data)."
            )

        self.good_idx = good[keep]
        self.numrej += 1
        n_rejected = int(good.numel() - self.good_idx.numel())
        logger.info(
            "Rejection %d at iter %d: dropped %d samples (%d good remaining).",
            self.numrej,
            self.iteration,
            n_rejected,
            int(self.good_idx.numel()),
        )

    def transform(self, X: np.ndarray, model_idx: int = 0) -> np.ndarray:
        """Apply the learned unmixing matrix to (new) data.

        The internal ``W = inv(A)`` is stored transposed relative to the true
        unmixing (the E-step forms activations as ``(X-c)^T @ W``, see
        ``_forward``), so the unmixing applied here is ``W^T`` (issue #24
        transpose convention) with the per-model data-space center ``c``
        subtracted first (issue #27).
        """
        if self.sphere is None or self.mean is None or self.W is None or self.c is None:
            raise RuntimeError(
                "AMICATorchNG.transform() requires a fitted model; call fit() first."
            )
        X_t = torch.from_numpy(np.ascontiguousarray(X)).to(self.device, self.dtype)
        X_t = self.sphere @ (X_t - self.mean)
        # c is the per-model data-space center: unmix as W(x - c) (issue #27).
        S = self.W[:, :, model_idx].T @ (X_t - self.c[:, model_idx : model_idx + 1])
        return S.cpu().numpy()

    def get_mixing_matrix(self, model_idx: int = 0) -> np.ndarray:
        """True mixing matrix ``A_fort`` = (stored A)^T (issue #24 convention)."""
        if self.A is None or self.comp_list is None:
            raise RuntimeError(
                "AMICATorchNG.get_mixing_matrix() requires a fitted model; call "
                "fit() first."
            )
        return self.A[:, self.comp_list[:, model_idx]].T.cpu().numpy()

    def get_unmixing_matrix(self, model_idx: int = 0) -> np.ndarray:
        """True unmixing matrix ``W_fort`` = (stored W)^T (issue #24 convention)."""
        if self.W is None:
            raise RuntimeError(
                "AMICATorchNG.get_unmixing_matrix() requires a fitted model; call "
                "fit() first."
            )
        return self.W[:, :, model_idx].T.cpu().numpy()

    # ------------------------------------------------------------------
    # EEGLAB drop-in output (issue #92)
    # ------------------------------------------------------------------
    def variance_order(
        self, model_idx: int = 0, return_svar: bool = False
    ) -> Union[np.ndarray, tuple]:
        """EEGLAB back-projected-variance component order (IC1 = highest variance).

        Returns the source indices sorted by descending back-projected variance,
        the ordering EEGLAB's ``loadmodout15.m`` applies on load (so ``order[0]``
        is IC1). The de-sphered sensor-space mixing column ``a_i = pinv(W S)[:, i]``
        contributes ``||a_i||^2 * sum_k alpha_ki (mu_ki^2 + r_ki / sbeta_ki^2)``
        with ``r_ki = gamma(3/rho_ki)/gamma(1/rho_ki)`` (the source's mixture
        variance), matching ``loadmodout15`` exactly. Non-mutating: the stored
        parameters keep their fit order; this only reports the display order.

        Parameters
        ----------
        model_idx : int, default=0
            Which model's components to order.
        return_svar : bool, default=False
            If True, also return the per-source variance sorted to ``order``.

        Returns
        -------
        order : np.ndarray of int, shape (n_sources,)
            Source indices, highest back-projected variance first.
        svar : np.ndarray, optional
            Present only when ``return_svar``; the sorted variances.
        """
        from scipy.special import gamma

        if (
            self.comp_list is None
            or self.alpha is None
            or self.mu is None
            or self.beta is None
            or self.rho is None
            or self.W is None
            or self.sphere is None
        ):
            raise RuntimeError(
                "AMICATorchNG.variance_order() requires a fitted model; call "
                "fit() first."
            )
        cl = self.comp_list[:, model_idx].cpu().numpy()
        alpha = self.alpha[:, cl].cpu().numpy()
        mu = self.mu[:, cl].cpu().numpy()
        sbeta = self.beta[:, cl].cpu().numpy()
        rho = self.rho[:, cl].cpu().numpy()
        # source mixture variance (sum over the mixture components); unused
        # mixtures carry alpha == 0 and drop out, matching loadmodout15.
        ratio = gamma(3.0 / rho) / gamma(1.0 / rho)
        mix_var = (alpha * (mu**2 + ratio / sbeta**2)).sum(axis=0)
        # de-sphered sensor-space mixing: A = pinv(W_fort @ S), columns = maps.
        w_fort = self.W[:, :, model_idx].T.cpu().numpy()
        sphere = self.sphere.cpu().numpy()
        a_sensor = np.linalg.pinv(w_fort @ sphere)
        svar = mix_var * (a_sensor**2).sum(axis=0)
        order = np.argsort(-svar)
        if return_svar:
            return order, svar[order]
        return order

    def write_amica_output(self, outdir) -> None:
        """Write this fitted model as the Fortran/EEGLAB AMICA output directory.

        Produces the raw binary files that EEGLAB's ``loadmodout15.m`` (and the
        Python port :func:`pyAMICA.numpy_impl.load.loadmodout`) read, so a
        PyTorch NG fit drops directly into an EEGLAB workflow (issue #92).
        ``loadmodout15`` performs the variance-ordering and unit-norm
        normalization on load, so the on-disk parameters are written in fit
        order. Single-model output is byte-compatible with the Fortran reference.

        Parameters
        ----------
        outdir : str or path-like
            Destination directory (created if absent).
        """
        if self.A is None:
            raise RuntimeError(
                "write_amica_output requires a fitted model; call fit() first."
            )

        from ..numpy_impl.load import write_amicaout

        def _np(t):
            return t.detach().cpu().numpy()

        # The exported parameters are the fit()-kept iterate (LL == final_ll_).
        # Under the keep_best safeguard (#51) that can be an earlier iterate than
        # the last, so end the written LL trajectory at that iterate rather than
        # at a later, discarded overshoot -- otherwise LL[-1] would not match the
        # model just written. Monotone runs keep the full trajectory unchanged.
        ll = np.asarray(self.ll_history, dtype=np.float64)
        if (
            self.final_ll_ is not None
            and np.isfinite(self.final_ll_)
            and ll.size
            and not np.isclose(ll[-1], self.final_ll_)
        ):
            ll = ll[: int(np.argmax(ll)) + 1]

        write_amicaout(
            outdir,
            gm=_np(self.gm),
            W=_np(self.W),
            sphere=_np(self.sphere),
            mean=_np(self.mean),
            c=_np(self.c),
            alpha=_np(self.alpha),
            mu=_np(self.mu),
            sbeta=_np(self.beta),  # Fortran's 'sbeta' is pyAMICA's beta (scale)
            rho=_np(self.rho),
            comp_list=_np(self.comp_list),
            ll=ll,
            A=_np(self.A),
        )

    # ------------------------------------------------------------------
    # Persistence (issue #36)
    # ------------------------------------------------------------------
    # Full fitted-parameter snapshot. A/W/c/comp_list/mean/sphere are what
    # transform()/get_*matrix() read back; mu/alpha/beta/rho/gm are the
    # mixture-PDF EM state, included for a complete snapshot (and for parity/
    # continued-analysis) even though no public method currently reads them.
    # pdtype is the per-source density-family code (issue #26): a non-default
    # pdftype model, or the adaptive switcher's chosen 1/4 assignments, would
    # otherwise silently revert to GG on reload. comp_list and pdtype are integer
    # tensors (dtype preserved on load); the rest follow self.dtype.
    _PARAM_TENSORS = (
        "A", "W", "c", "mu", "alpha", "beta", "rho", "gm",
        "comp_list", "mean", "sphere", "pdtype",
    )  # fmt: skip
    # Integer tensors in _PARAM_TENSORS: keep their dtype on load, only move device.
    _INT_PARAM_TENSORS = ("comp_list", "pdtype")

    # Stop reasons that mark a fit as degenerate (non-finite log-likelihood).
    # Such a model yields NaN sources, so state_dict() refuses to persist it
    # rather than let it round-trip silently (silent-failure review, PR #44).
    _DEGENERATE_STOP_REASONS = ("nan_ll", "singular_ll")

    def state_dict(self) -> dict:
        """Serialize the fitted model to a plain, device-agnostic dict.

        The returned dict has three parts: ``config`` (the constructor
        arguments needed to rebuild the object), ``params`` (the fitted
        tensors, moved to CPU), and ``extra`` (scalar/schedule state, plus the
        optional ``good_idx`` index tensor). Every value is a tensor or a plain
        Python primitive, so the dict round-trips through
        ``torch.save``/``torch.load`` with ``weights_only=True`` (no custom
        classes or ``torch.dtype`` objects: dtype is stored by name). Rebuild
        with :meth:`from_state_dict`.

        Raises if the model is unfitted or degenerate (a fit that ended on a
        non-finite log-likelihood): a NaN model must not be persisted silently.
        """
        if self.A is None:
            raise RuntimeError(
                "AMICATorchNG.state_dict() requires a fitted model; call fit() first."
            )
        if self.stop_reason in self._DEGENERATE_STOP_REASONS:
            raise RuntimeError(
                f"Refusing to serialize a degenerate model (stop_reason="
                f"{self.stop_reason!r}): fit() hit a non-finite log-likelihood at "
                f"iteration {self.iteration}. Fix the instability (lower lrate, "
                f"disable Newton, or check data conditioning) before saving."
            )
        # Defense-in-depth: catch a non-finite parameter even if stop_reason
        # bookkeeping ever misses it (the codebase has known NaN-suppression
        # risks). isfinite on the integer comp_list is trivially all-True.
        nonfinite = [
            name
            for name in self._PARAM_TENSORS
            if not torch.isfinite(getattr(self, name)).all()
        ]
        if nonfinite:
            raise RuntimeError(
                f"Refusing to serialize a model with non-finite parameters "
                f"{nonfinite} (stop_reason={self.stop_reason!r})."
            )
        config = {
            "n_channels": self.n_channels,
            "n_models": self.n_models,
            "n_mix": self.n_mix,
            "block_size": self.block_size,
            # lrate/newtrate/rholrate are annealed during fit; persist the
            # original constructor values (lrate0/newtrate0/rholrate0) and
            # restore the mutated ones from ``extra`` below.
            "lrate": self.lrate0,
            "minlrate": self.minlrate,
            "lratefact": self.lratefact,
            "maxdecs": self.maxdecs,
            "newt_ramp": self.newt_ramp,
            "do_newton": self.do_newton,
            "newt_start": self.newt_start,
            "newtrate": self.newtrate0,
            "do_reject": self.do_reject,
            "rejsig": self.rejsig,
            "rejstart": self.rejstart,
            "rejint": self.rejint,
            "maxrej": self.maxrej,
            "rho0": self.rho0,
            "minrho": self.minrho,
            "maxrho": self.maxrho,
            "rholrate": self.rholrate0,
            "rholratefact": self.rholratefact,
            # Best-iterate safeguard flag (issue #51); only affects a re-fit, but
            # persisted so a reloaded model reconstructs its exact configuration.
            "keep_best": self.keep_best,
            # Density-family selection (issue #26): needed so a reloaded model
            # rebuilds with the right pdftype/dorho/do_choose_pdfs and switch
            # schedule instead of the GG default.
            "pdftype": self.pdftype,
            "kurt_start": self.kurt_start,
            "num_kurt": self.num_kurt,
            "kurt_int": self.kurt_int,
            "invsigmin": self.invsigmin,
            "invsigmax": self.invsigmax,
            "doscaling": self.doscaling,
            "scalestep": self.scalestep,
            # Component sharing (issue #60): persisted so a reloaded multi-model
            # run keeps its schedule; the merged comp_list itself is in params.
            "share_comps": self.share_comps,
            "share_start": self.share_start,
            "share_iter": self.share_iter,
            "comp_thresh": self.comp_thresh,
            "do_mean": self.do_mean,
            "do_sphere": self.do_sphere,
            "do_approx_sphere": self.do_approx_sphere,
            "pcakeep": self.pcakeep,
            "pcadb": self.pcadb,
            "seed": self.seed,
            # Store dtype by name (e.g. "float64") to keep the payload
            # weights_only-safe; rebuilt via getattr(torch, ...) on load.
            "dtype": str(self.dtype).split(".")[-1],
        }
        # .clone() forces an independent copy even when self.device is already
        # CPU (where .cpu() would alias): fit() mutates A/mu/beta in place each
        # iteration, so an aliased snapshot would silently roll forward if
        # state_dict() were ever called mid-fit (e.g. best-so-far checkpointing).
        params = {
            name: getattr(self, name).detach().cpu().clone()
            for name in self._PARAM_TENSORS
        }
        extra = {
            "sldet": float(self.sldet),
            "iteration": int(self.iteration),
            "ll_history": [float(v) for v in self.ll_history],
            "final_ll": None if self.final_ll_ is None else float(self.final_ll_),
            "stop_reason": self.stop_reason,
            "n_newton_fallbacks": int(self.n_newton_fallbacks),
            "n_kurt_done": int(self.n_kurt_done),
            "numrej": int(self.numrej),
            "good_idx": None
            if self.good_idx is None
            else self.good_idx.detach().cpu().clone(),
            "lrate": float(self.lrate),
            "lrate_cap": float(self.lrate_cap),
            "newtrate": float(self.newtrate),
            "rholrate": float(self.rholrate),
        }
        return {
            "format_version": 3,
            "config": config,
            "params": params,
            "extra": extra,
        }

    @classmethod
    def from_state_dict(
        cls, state: dict, device: Optional[Union[str, torch.device]] = None
    ) -> "AMICATorchNG":
        """Rebuild a fitted :class:`AMICATorchNG` from :meth:`state_dict` output.

        ``device`` overrides where the restored tensors live (the constructor
        picks a default when ``None``); ``dtype`` always comes from the saved
        ``config``.
        """
        version = state.get("format_version")
        if version != 3:
            raise ValueError(
                f"unsupported AMICATorchNG state format_version: {version!r} "
                "(expected 3)"
            )
        for section in ("config", "params", "extra"):
            if section not in state:
                raise ValueError(
                    f"malformed AMICATorchNG state: missing {section!r} section "
                    f"(format_version={version}); the payload may be truncated."
                )
        config = dict(state["config"])
        config["dtype"] = getattr(torch, config["dtype"])
        obj = cls(device=device, **config)
        obj._load_params(state)
        return obj

    def _load_params(self, state: dict) -> None:
        """Restore fitted tensors/scalars from :meth:`state_dict` output onto
        this instance's device/dtype."""
        params = state["params"]
        missing = [name for name in self._PARAM_TENSORS if name not in params]
        if missing:
            raise ValueError(f"malformed AMICATorchNG state: missing params {missing}")
        # Guard against config/params drift: A and comp_list must match the
        # dimensions the constructor just derived, or transform()/the E-step
        # would fail later with a confusing matmul error far from load().
        if tuple(params["A"].shape) != (self.n_channels, self.n_comps):
            raise ValueError(
                f"restored A has shape {tuple(params['A'].shape)}, expected "
                f"{(self.n_channels, self.n_comps)} for n_channels="
                f"{self.n_channels}, n_models={self.n_models}"
            )
        if tuple(params["comp_list"].shape) != (self.n_channels, self.n_models):
            raise ValueError(
                f"restored comp_list has shape {tuple(params['comp_list'].shape)}, "
                f"expected {(self.n_channels, self.n_models)}"
            )
        for name in self._PARAM_TENSORS:
            tensor = params[name]
            # comp_list/pdtype hold integer indices/codes; preserve their dtype
            # and only move devices. The float parameters follow self.dtype.
            if name in self._INT_PARAM_TENSORS:
                setattr(self, name, tensor.to(self.device))
            else:
                setattr(self, name, tensor.to(self.device, self.dtype))

        extra = state["extra"]
        self.sldet = extra["sldet"]
        self.iteration = extra["iteration"]
        self.ll_history = list(extra["ll_history"])
        self.final_ll_ = extra["final_ll"]
        self.stop_reason = extra["stop_reason"]
        self.n_newton_fallbacks = extra["n_newton_fallbacks"]
        self.n_kurt_done = extra["n_kurt_done"]
        self.numrej = extra["numrej"]
        good_idx = extra["good_idx"]
        self.good_idx = None if good_idx is None else good_idx.to(self.device)
        self.lrate = extra["lrate"]
        self.lrate_cap = extra["lrate_cap"]
        self.newtrate = extra["newtrate"]
        self.rholrate = extra["rholrate"]

comp_used property

Boolean mask (n_comps,) of components still referenced by comp_list.

A component drops out of use when it is folded into another by :meth:_identify_shared_comps; unused columns receive no gradient and are never read by the E-step. Derived from comp_list (not stored).

fit(X, max_iter=100, verbose=True)

Fit the model to data.

Parameters:

Name Type Description Default
X np.ndarray of shape (n_channels, n_samples)

Input data.

required
max_iter int

Number of natural-gradient EM iterations.

100
verbose bool

Show a tqdm progress bar.

True

Returns:

Name Type Description
self AMICATorchNG
Source code in pyAMICA/torch_impl/core.py
def fit(
    self, X: np.ndarray, max_iter: int = 100, verbose: bool = True
) -> "AMICATorchNG":
    """Fit the model to data.

    Parameters
    ----------
    X : np.ndarray of shape (n_channels, n_samples)
        Input data.
    max_iter : int, default=100
        Number of natural-gradient EM iterations.
    verbose : bool, default=True
        Show a tqdm progress bar.

    Returns
    -------
    self : AMICATorchNG
    """
    if X.ndim != 2:
        raise ValueError(
            f"X must be a 2D array (n_channels, n_samples), got shape {X.shape}"
        )
    if X.shape[0] != self.n_channels:
        raise ValueError(
            f"X has {X.shape[0]} channels, model expects {self.n_channels}"
        )

    X_t = self._preprocess(X)
    n_total = X_t.shape[1]

    self._initialize_parameters()
    self.ll_history = []
    self.numrej = 0
    self.n_newton_fallbacks = 0
    self._spinv = None  # rebuild the de-sphering metric for this fit's sphere
    self.stop_reason = "max_iter"
    self.good_idx = (
        torch.arange(n_total, device=self.device) if self.do_reject else None
    )
    numdecs = 0

    # Best-iterate safeguard (issue #51): track the highest-LL iterate so a
    # late Newton-fallback overshoot cannot leave the returned model below a
    # peak it already reached. Inactive under do_reject (the good set, and so
    # the LL normalization, changes across iterations) and under share_comps
    # (a merge drops parameters, so pre- and post-merge LLs are not
    # comparable AND the snapshot's comp_list would revert the merge -- the
    # returned model would silently be unmerged; #60). In both cases fit()
    # returns the last iterate, matching Fortran.
    track_best = self.keep_best and not self.do_reject and not self.share_comps
    best_ll = -math.inf
    best_snapshot: Optional[Dict[str, object]] = None
    if self.keep_best and (self.do_reject or self.share_comps):
        # keep_best defaults on, so a user enabling rejection/sharing would
        # otherwise silently lose the safeguard; surface it once.
        reason = "do_reject" if self.do_reject else "share_comps"
        logger.warning(
            "keep_best is inactive under %s: best-iterate selection by LL is "
            "not well-defined (%s), so fit() returns the last iterate.",
            reason,
            "the good-sample set / LL normalization changes across iterations"
            if self.do_reject
            else "a merge changes the parameter count and reverting to an "
            "earlier snapshot would undo the merge",
        )

    iterator = tqdm(range(max_iter), desc="AMICA-NG", disable=not verbose)
    for it in iterator:
        self.iteration = it

        X_use = X_t[:, self.good_idx] if self.do_reject else X_t
        n_use = X_use.shape[1]
        acc = self._accumulate_blocks(X_use)

        # Log-likelihood of the CURRENT (pre-update) parameters: acc["ll"] is
        # this iteration's E-step total, computed before _update_parameters
        # moves the parameters. A singular W makes logdet -> -inf (not NaN),
        # so guard on isfinite, not isnan alone: a -inf LL would otherwise
        # sail past as a mere "decrease" and the run would "complete"
        # (stop_reason=max_iter) on a degenerate model. Checking here, before
        # the update, stops on the last finite parameters instead of
        # overwriting them with a garbage update first.
        ll = (acc["ll"] / (n_use * self.n_channels)).item()
        if not math.isfinite(ll):
            self.stop_reason = "nan_ll" if math.isnan(ll) else "singular_ll"
            logger.warning(
                "Non-finite log-likelihood (%s) at iteration %d; stopping.",
                ll,
                it,
            )
            break

        # Best-iterate safeguard (issue #51): remember the parameters that
        # produced this LL when it is the best seen, so a later overshoot
        # does not leave the returned model below this peak.
        if track_best and ll > best_ll:
            best_ll = ll
            best_snapshot = self._snapshot_params()

        # Whether rejection fires this iteration (Fortran schedule,
        # amica17.f90:1141-1146). Fortran rejects using the per-sample
        # log-likelihood from THIS iteration's E-step, i.e. the PRE-update
        # parameters (loglik is stored in get_updates_and_likelihood before
        # update_params runs). Capture it here, before _update_parameters,
        # to match that ordering.
        will_reject = (
            self.do_reject
            and self.maxrej > 0
            and (
                it == self.rejstart
                or (
                    max(1, it - self.rejstart) % self.rejint == 0
                    and self.numrej < self.maxrej
                )
            )
        )
        if will_reject:
            assert self.good_idx is not None
            reject_ll = self._sample_ll(self.good_idx, X_t)
        else:
            reject_ll = None

        self._update_parameters(acc, n_use)

        # Extended-Infomax adaptive PDF switch (Fortran do_choose_pdfs). Runs
        # on the kurt_start/num_kurt/kurt_int schedule using the just-updated
        # W; the new per-source families take effect from the next E-step.
        # itf is the Fortran-style 1-indexed iteration. num_kurt=0 disables
        # switching (the family stays at its pdftype=1 super-Gaussian init).
        if self.do_choose_pdfs and self.n_kurt_done < self.num_kurt:
            itf = it + 1
            if (
                itf >= self.kurt_start
                and (itf - self.kurt_start) % self.kurt_int == 0
            ):
                self._choose_pdfs(X_use)
                self.n_kurt_done += 1

        # Component sharing (Fortran identify_shared_comps schedule,
        # amica15.f90:1838): once per share_iter cycle from share_start,
        # merge near-collinear mixing columns across models using the
        # just-updated A. Fortran runs identify_shared_comps BEFORE
        # get_unmixing_matrices (amica15.f90:1840,1845), so rebuild W from the
        # merged comp_list -- otherwise the next E-step would read a stale W
        # (pre-merge comp_list) while indexing the densities by the merged
        # comp_list. No-op when share_comps is off or n_models == 1.
        if self.share_comps:
            itf = it + 1
            if (
                itf >= self.share_start
                and (itf - self.share_start) % self.share_iter == 0
            ):
                self._identify_shared_comps()
                self._update_unmixing_matrices()

        self.ll_history.append(ll)

        # Learning-rate control, ported from Fortran (amica17.f90:1062-1108).
        # Natural-gradient/Newton ascent is not monotonic at a fixed rate:
        # when the log-likelihood decreases, anneal the working rates
        # (lrate, rholrate). If decreases persist for maxdecs iterations,
        # ratchet the *ceilings* down (lrate_cap, and newtrate once Newton
        # is running) so the per-iteration ramp can no longer re-inflate
        # lrate back to the overshooting value -- without this the ramp and
        # a one-shot halving just oscillate and the LL drifts down.
        if len(self.ll_history) > 1 and ll < self.ll_history[-2]:
            if self.lrate <= self.minlrate:
                logger.warning(
                    "lrate floor (%g) reached at iter %d; stopping.",
                    self.minlrate,
                    it,
                )
                self.stop_reason = "lrate_floor"
                break
            self.lrate *= self.lratefact
            self.rholrate *= self.rholratefact
            numdecs += 1
            if numdecs >= self.maxdecs:
                self.lrate_cap *= self.lratefact
                if self.do_newton and it > self.newt_start:
                    self.newtrate *= self.lratefact
                numdecs = 0
        if self.do_newton and it == self.newt_start:
            numdecs = 0

        # Outlier rejection, after the parameter update (Fortran order,
        # amica17.f90:1141-1146) but using the pre-update per-sample LL
        # captured above.
        if will_reject:
            assert reject_ll is not None
            self._reject_outliers(reject_ll)

        iterator.set_postfix({"LL": f"{ll:.4f}", "lrate": f"{self.lrate:.4g}"})

    # Log-likelihood of the parameters fit() returns. A degenerate stop
    # leaves the model on the diverged parameters, whose LL is NOT the last
    # finite ll_history value (the guard breaks before appending), so report
    # NaN there rather than a stale healthy-looking number (silent-failure
    # review). Otherwise it is the last trajectory value, overwritten with the
    # best iterate's LL below if the safeguard restores it.
    if self.stop_reason in self._DEGENERATE_STOP_REASONS:
        self.final_ll_ = float("nan")
    else:
        self.final_ll_ = self.ll_history[-1] if self.ll_history else float("nan")

    # Restore the best iterate if the run ended materially below it (issue
    # #51). Skipped for a degenerate stop -- not because the parameters are
    # necessarily non-finite (a singular_ll stop leaves A/W finite but
    # singular) but because salvaging a diverged run here would pre-empt issue
    # #50's degenerate-fit contract; state_dict() already refuses to persist
    # any model whose stop_reason is degenerate. Also skipped when the final
    # LL is within _KEEP_BEST_TOL of the best -- a monotone single-model run
    # has final == best, so no restore fires and issue #24 parity stays
    # bit-exact.
    if (
        track_best
        and best_snapshot is not None
        and self.stop_reason not in self._DEGENERATE_STOP_REASONS
        and self.ll_history
        and best_ll - self.ll_history[-1] > _KEEP_BEST_TOL
    ):
        logger.info(
            "Restoring best iterate (LL %.6f) over final LL %.6f "
            "(issue #51 best-iterate safeguard).",
            best_ll,
            self.ll_history[-1],
        )
        self._restore_params(best_snapshot)
        self.final_ll_ = best_ll

    return self

transform(X, model_idx=0)

Apply the learned unmixing matrix to (new) data.

The internal W = inv(A) is stored transposed relative to the true unmixing (the E-step forms activations as (X-c)^T @ W, see _forward), so the unmixing applied here is W^T (issue #24 transpose convention) with the per-model data-space center c subtracted first (issue #27).

Source code in pyAMICA/torch_impl/core.py
def transform(self, X: np.ndarray, model_idx: int = 0) -> np.ndarray:
    """Apply the learned unmixing matrix to (new) data.

    The internal ``W = inv(A)`` is stored transposed relative to the true
    unmixing (the E-step forms activations as ``(X-c)^T @ W``, see
    ``_forward``), so the unmixing applied here is ``W^T`` (issue #24
    transpose convention) with the per-model data-space center ``c``
    subtracted first (issue #27).
    """
    if self.sphere is None or self.mean is None or self.W is None or self.c is None:
        raise RuntimeError(
            "AMICATorchNG.transform() requires a fitted model; call fit() first."
        )
    X_t = torch.from_numpy(np.ascontiguousarray(X)).to(self.device, self.dtype)
    X_t = self.sphere @ (X_t - self.mean)
    # c is the per-model data-space center: unmix as W(x - c) (issue #27).
    S = self.W[:, :, model_idx].T @ (X_t - self.c[:, model_idx : model_idx + 1])
    return S.cpu().numpy()

get_mixing_matrix(model_idx=0)

True mixing matrix A_fort = (stored A)^T (issue #24 convention).

Source code in pyAMICA/torch_impl/core.py
def get_mixing_matrix(self, model_idx: int = 0) -> np.ndarray:
    """True mixing matrix ``A_fort`` = (stored A)^T (issue #24 convention)."""
    if self.A is None or self.comp_list is None:
        raise RuntimeError(
            "AMICATorchNG.get_mixing_matrix() requires a fitted model; call "
            "fit() first."
        )
    return self.A[:, self.comp_list[:, model_idx]].T.cpu().numpy()

get_unmixing_matrix(model_idx=0)

True unmixing matrix W_fort = (stored W)^T (issue #24 convention).

Source code in pyAMICA/torch_impl/core.py
def get_unmixing_matrix(self, model_idx: int = 0) -> np.ndarray:
    """True unmixing matrix ``W_fort`` = (stored W)^T (issue #24 convention)."""
    if self.W is None:
        raise RuntimeError(
            "AMICATorchNG.get_unmixing_matrix() requires a fitted model; call "
            "fit() first."
        )
    return self.W[:, :, model_idx].T.cpu().numpy()

variance_order(model_idx=0, return_svar=False)

EEGLAB back-projected-variance component order (IC1 = highest variance).

Returns the source indices sorted by descending back-projected variance, the ordering EEGLAB's loadmodout15.m applies on load (so order[0] is IC1). The de-sphered sensor-space mixing column a_i = pinv(W S)[:, i] contributes ||a_i||^2 * sum_k alpha_ki (mu_ki^2 + r_ki / sbeta_ki^2) with r_ki = gamma(3/rho_ki)/gamma(1/rho_ki) (the source's mixture variance), matching loadmodout15 exactly. Non-mutating: the stored parameters keep their fit order; this only reports the display order.

Parameters:

Name Type Description Default
model_idx int

Which model's components to order.

0
return_svar bool

If True, also return the per-source variance sorted to order.

False

Returns:

Name Type Description
order np.ndarray of int, shape (n_sources,)

Source indices, highest back-projected variance first.

svar (ndarray, optional)

Present only when return_svar; the sorted variances.

Source code in pyAMICA/torch_impl/core.py
def variance_order(
    self, model_idx: int = 0, return_svar: bool = False
) -> Union[np.ndarray, tuple]:
    """EEGLAB back-projected-variance component order (IC1 = highest variance).

    Returns the source indices sorted by descending back-projected variance,
    the ordering EEGLAB's ``loadmodout15.m`` applies on load (so ``order[0]``
    is IC1). The de-sphered sensor-space mixing column ``a_i = pinv(W S)[:, i]``
    contributes ``||a_i||^2 * sum_k alpha_ki (mu_ki^2 + r_ki / sbeta_ki^2)``
    with ``r_ki = gamma(3/rho_ki)/gamma(1/rho_ki)`` (the source's mixture
    variance), matching ``loadmodout15`` exactly. Non-mutating: the stored
    parameters keep their fit order; this only reports the display order.

    Parameters
    ----------
    model_idx : int, default=0
        Which model's components to order.
    return_svar : bool, default=False
        If True, also return the per-source variance sorted to ``order``.

    Returns
    -------
    order : np.ndarray of int, shape (n_sources,)
        Source indices, highest back-projected variance first.
    svar : np.ndarray, optional
        Present only when ``return_svar``; the sorted variances.
    """
    from scipy.special import gamma

    if (
        self.comp_list is None
        or self.alpha is None
        or self.mu is None
        or self.beta is None
        or self.rho is None
        or self.W is None
        or self.sphere is None
    ):
        raise RuntimeError(
            "AMICATorchNG.variance_order() requires a fitted model; call "
            "fit() first."
        )
    cl = self.comp_list[:, model_idx].cpu().numpy()
    alpha = self.alpha[:, cl].cpu().numpy()
    mu = self.mu[:, cl].cpu().numpy()
    sbeta = self.beta[:, cl].cpu().numpy()
    rho = self.rho[:, cl].cpu().numpy()
    # source mixture variance (sum over the mixture components); unused
    # mixtures carry alpha == 0 and drop out, matching loadmodout15.
    ratio = gamma(3.0 / rho) / gamma(1.0 / rho)
    mix_var = (alpha * (mu**2 + ratio / sbeta**2)).sum(axis=0)
    # de-sphered sensor-space mixing: A = pinv(W_fort @ S), columns = maps.
    w_fort = self.W[:, :, model_idx].T.cpu().numpy()
    sphere = self.sphere.cpu().numpy()
    a_sensor = np.linalg.pinv(w_fort @ sphere)
    svar = mix_var * (a_sensor**2).sum(axis=0)
    order = np.argsort(-svar)
    if return_svar:
        return order, svar[order]
    return order

write_amica_output(outdir)

Write this fitted model as the Fortran/EEGLAB AMICA output directory.

Produces the raw binary files that EEGLAB's loadmodout15.m (and the Python port :func:pyAMICA.numpy_impl.load.loadmodout) read, so a PyTorch NG fit drops directly into an EEGLAB workflow (issue #92). loadmodout15 performs the variance-ordering and unit-norm normalization on load, so the on-disk parameters are written in fit order. Single-model output is byte-compatible with the Fortran reference.

Parameters:

Name Type Description Default
outdir str or path - like

Destination directory (created if absent).

required
Source code in pyAMICA/torch_impl/core.py
def write_amica_output(self, outdir) -> None:
    """Write this fitted model as the Fortran/EEGLAB AMICA output directory.

    Produces the raw binary files that EEGLAB's ``loadmodout15.m`` (and the
    Python port :func:`pyAMICA.numpy_impl.load.loadmodout`) read, so a
    PyTorch NG fit drops directly into an EEGLAB workflow (issue #92).
    ``loadmodout15`` performs the variance-ordering and unit-norm
    normalization on load, so the on-disk parameters are written in fit
    order. Single-model output is byte-compatible with the Fortran reference.

    Parameters
    ----------
    outdir : str or path-like
        Destination directory (created if absent).
    """
    if self.A is None:
        raise RuntimeError(
            "write_amica_output requires a fitted model; call fit() first."
        )

    from ..numpy_impl.load import write_amicaout

    def _np(t):
        return t.detach().cpu().numpy()

    # The exported parameters are the fit()-kept iterate (LL == final_ll_).
    # Under the keep_best safeguard (#51) that can be an earlier iterate than
    # the last, so end the written LL trajectory at that iterate rather than
    # at a later, discarded overshoot -- otherwise LL[-1] would not match the
    # model just written. Monotone runs keep the full trajectory unchanged.
    ll = np.asarray(self.ll_history, dtype=np.float64)
    if (
        self.final_ll_ is not None
        and np.isfinite(self.final_ll_)
        and ll.size
        and not np.isclose(ll[-1], self.final_ll_)
    ):
        ll = ll[: int(np.argmax(ll)) + 1]

    write_amicaout(
        outdir,
        gm=_np(self.gm),
        W=_np(self.W),
        sphere=_np(self.sphere),
        mean=_np(self.mean),
        c=_np(self.c),
        alpha=_np(self.alpha),
        mu=_np(self.mu),
        sbeta=_np(self.beta),  # Fortran's 'sbeta' is pyAMICA's beta (scale)
        rho=_np(self.rho),
        comp_list=_np(self.comp_list),
        ll=ll,
        A=_np(self.A),
    )

state_dict()

Serialize the fitted model to a plain, device-agnostic dict.

The returned dict has three parts: config (the constructor arguments needed to rebuild the object), params (the fitted tensors, moved to CPU), and extra (scalar/schedule state, plus the optional good_idx index tensor). Every value is a tensor or a plain Python primitive, so the dict round-trips through torch.save/torch.load with weights_only=True (no custom classes or torch.dtype objects: dtype is stored by name). Rebuild with :meth:from_state_dict.

Raises if the model is unfitted or degenerate (a fit that ended on a non-finite log-likelihood): a NaN model must not be persisted silently.

Source code in pyAMICA/torch_impl/core.py
def state_dict(self) -> dict:
    """Serialize the fitted model to a plain, device-agnostic dict.

    The returned dict has three parts: ``config`` (the constructor
    arguments needed to rebuild the object), ``params`` (the fitted
    tensors, moved to CPU), and ``extra`` (scalar/schedule state, plus the
    optional ``good_idx`` index tensor). Every value is a tensor or a plain
    Python primitive, so the dict round-trips through
    ``torch.save``/``torch.load`` with ``weights_only=True`` (no custom
    classes or ``torch.dtype`` objects: dtype is stored by name). Rebuild
    with :meth:`from_state_dict`.

    Raises if the model is unfitted or degenerate (a fit that ended on a
    non-finite log-likelihood): a NaN model must not be persisted silently.
    """
    if self.A is None:
        raise RuntimeError(
            "AMICATorchNG.state_dict() requires a fitted model; call fit() first."
        )
    if self.stop_reason in self._DEGENERATE_STOP_REASONS:
        raise RuntimeError(
            f"Refusing to serialize a degenerate model (stop_reason="
            f"{self.stop_reason!r}): fit() hit a non-finite log-likelihood at "
            f"iteration {self.iteration}. Fix the instability (lower lrate, "
            f"disable Newton, or check data conditioning) before saving."
        )
    # Defense-in-depth: catch a non-finite parameter even if stop_reason
    # bookkeeping ever misses it (the codebase has known NaN-suppression
    # risks). isfinite on the integer comp_list is trivially all-True.
    nonfinite = [
        name
        for name in self._PARAM_TENSORS
        if not torch.isfinite(getattr(self, name)).all()
    ]
    if nonfinite:
        raise RuntimeError(
            f"Refusing to serialize a model with non-finite parameters "
            f"{nonfinite} (stop_reason={self.stop_reason!r})."
        )
    config = {
        "n_channels": self.n_channels,
        "n_models": self.n_models,
        "n_mix": self.n_mix,
        "block_size": self.block_size,
        # lrate/newtrate/rholrate are annealed during fit; persist the
        # original constructor values (lrate0/newtrate0/rholrate0) and
        # restore the mutated ones from ``extra`` below.
        "lrate": self.lrate0,
        "minlrate": self.minlrate,
        "lratefact": self.lratefact,
        "maxdecs": self.maxdecs,
        "newt_ramp": self.newt_ramp,
        "do_newton": self.do_newton,
        "newt_start": self.newt_start,
        "newtrate": self.newtrate0,
        "do_reject": self.do_reject,
        "rejsig": self.rejsig,
        "rejstart": self.rejstart,
        "rejint": self.rejint,
        "maxrej": self.maxrej,
        "rho0": self.rho0,
        "minrho": self.minrho,
        "maxrho": self.maxrho,
        "rholrate": self.rholrate0,
        "rholratefact": self.rholratefact,
        # Best-iterate safeguard flag (issue #51); only affects a re-fit, but
        # persisted so a reloaded model reconstructs its exact configuration.
        "keep_best": self.keep_best,
        # Density-family selection (issue #26): needed so a reloaded model
        # rebuilds with the right pdftype/dorho/do_choose_pdfs and switch
        # schedule instead of the GG default.
        "pdftype": self.pdftype,
        "kurt_start": self.kurt_start,
        "num_kurt": self.num_kurt,
        "kurt_int": self.kurt_int,
        "invsigmin": self.invsigmin,
        "invsigmax": self.invsigmax,
        "doscaling": self.doscaling,
        "scalestep": self.scalestep,
        # Component sharing (issue #60): persisted so a reloaded multi-model
        # run keeps its schedule; the merged comp_list itself is in params.
        "share_comps": self.share_comps,
        "share_start": self.share_start,
        "share_iter": self.share_iter,
        "comp_thresh": self.comp_thresh,
        "do_mean": self.do_mean,
        "do_sphere": self.do_sphere,
        "do_approx_sphere": self.do_approx_sphere,
        "pcakeep": self.pcakeep,
        "pcadb": self.pcadb,
        "seed": self.seed,
        # Store dtype by name (e.g. "float64") to keep the payload
        # weights_only-safe; rebuilt via getattr(torch, ...) on load.
        "dtype": str(self.dtype).split(".")[-1],
    }
    # .clone() forces an independent copy even when self.device is already
    # CPU (where .cpu() would alias): fit() mutates A/mu/beta in place each
    # iteration, so an aliased snapshot would silently roll forward if
    # state_dict() were ever called mid-fit (e.g. best-so-far checkpointing).
    params = {
        name: getattr(self, name).detach().cpu().clone()
        for name in self._PARAM_TENSORS
    }
    extra = {
        "sldet": float(self.sldet),
        "iteration": int(self.iteration),
        "ll_history": [float(v) for v in self.ll_history],
        "final_ll": None if self.final_ll_ is None else float(self.final_ll_),
        "stop_reason": self.stop_reason,
        "n_newton_fallbacks": int(self.n_newton_fallbacks),
        "n_kurt_done": int(self.n_kurt_done),
        "numrej": int(self.numrej),
        "good_idx": None
        if self.good_idx is None
        else self.good_idx.detach().cpu().clone(),
        "lrate": float(self.lrate),
        "lrate_cap": float(self.lrate_cap),
        "newtrate": float(self.newtrate),
        "rholrate": float(self.rholrate),
    }
    return {
        "format_version": 3,
        "config": config,
        "params": params,
        "extra": extra,
    }

from_state_dict(state, device=None) classmethod

Rebuild a fitted :class:AMICATorchNG from :meth:state_dict output.

device overrides where the restored tensors live (the constructor picks a default when None); dtype always comes from the saved config.

Source code in pyAMICA/torch_impl/core.py
@classmethod
def from_state_dict(
    cls, state: dict, device: Optional[Union[str, torch.device]] = None
) -> "AMICATorchNG":
    """Rebuild a fitted :class:`AMICATorchNG` from :meth:`state_dict` output.

    ``device`` overrides where the restored tensors live (the constructor
    picks a default when ``None``); ``dtype`` always comes from the saved
    ``config``.
    """
    version = state.get("format_version")
    if version != 3:
        raise ValueError(
            f"unsupported AMICATorchNG state format_version: {version!r} "
            "(expected 3)"
        )
    for section in ("config", "params", "extra"):
        if section not in state:
            raise ValueError(
                f"malformed AMICATorchNG state: missing {section!r} section "
                f"(format_version={version}); the payload may be truncated."
            )
    config = dict(state["config"])
    config["dtype"] = getattr(torch, config["dtype"])
    obj = cls(device=device, **config)
    obj._load_params(state)
    return obj