"""Official-style NeuralGCM trajectory losses.

The released NeuralGCM repository contains the public metric primitives, but
the Gin binding used by Google's training jobs is proprietary.  This module
assembles the deterministic five-term objective described in Supplementary
G.3/G.4 while exposing unpublished numerical tables explicitly in YAML.  Both
the deterministic loss and the public two-member CRPS objective are built from
the released implementations.
"""
from __future__ import annotations

from collections.abc import Mapping
import functools
from typing import Any

import jax
import jax.numpy as jnp
import numpy as np


def _leaf_items(tree: Any, prefix: tuple[str, ...] = ()):
    if isinstance(tree, Mapping):
        for key, value in tree.items():
            yield from _leaf_items(value, prefix + (str(key),))
    else:
        yield prefix, tree


def _lookup_scale(path: tuple[str, ...], scales: Mapping[str, float]) -> float:
    """Returns a physical-unit scale using the leaf name as the key."""
    leaf = path[-1] if path else "default"
    # A tracer's full path is checked first, then its leaf name, then default.
    full = ".".join(path)
    value = scales.get(full, scales.get(leaf, scales.get("default", 1.0)))
    return max(float(value), 1e-12)


def _canonical_variable(path: tuple[str, ...]) -> str:
    """Map pressure-level and model-state names to configured loss groups."""
    leaf = path[-1] if path else "default"
    aliases = {
        "geopotential": "z",
        "temperature": "t",
        "temperature_variation": "t",
        "u_component_of_wind": "u",
        "v_component_of_wind": "v",
    }
    return aliases.get(leaf, leaf)


def _lookup_named_value(
    path: tuple[str, ...], values: Mapping[str, Any], default: float
) -> Any:
    full = ".".join(path)
    leaf = path[-1] if path else "default"
    canonical = _canonical_variable(path)
    return values.get(
        full,
        values.get(leaf, values.get(canonical, values.get("default", default))),
    )


def _broadcast_level_value(value: Any, error, *, name: str):
    """Broadcast a scalar or pressure/sigma-level vector over a trajectory."""
    value = jnp.asarray(value, dtype=jnp.asarray(error).real.dtype)
    if value.ndim == 0:
        return value
    if value.ndim != 1 or getattr(error, "ndim", 0) < 2:
        raise ValueError(f"loss {name} must be scalar or a one-dimensional level vector")
    if value.shape[0] != error.shape[1]:
        raise ValueError(
            f"loss {name} has {value.shape[0]} levels, but the trajectory has "
            f"{error.shape[1]}"
        )
    return value.reshape((1, value.shape[0]) + (1,) * (error.ndim - 2))


def _map_named(tree: Any, fn, prefix: tuple[str, ...] = ()):
    if isinstance(tree, Mapping):
        return {
            key: _map_named(value, fn, prefix + (str(key),))
            for key, value in tree.items()
        }
    return fn(prefix, tree)


class _PaperVariableRescaling:
    """Paper G.3 scaling with YAML-overridable 24-hour difference scales."""

    def __init__(
        self,
        trajectory_spec,
        *,
        scales: Mapping[str, Any],
        factors: Mapping[str, Any],
        weights: Mapping[str, Any] | None = None,
    ):
        del trajectory_spec
        self.scales = scales
        self.factors = factors
        self.weights = weights

    def __call__(self, errors, targets):
        del targets

        def rescale(path, error):
            if self.weights is not None:
                weight = _broadcast_level_value(
                    _lookup_named_value(path, self.weights, 1.0),
                    error,
                    name=f"variable_weights.{'.'.join(path)}",
                )
                weight = jnp.maximum(weight, 0.0)
                return error * jnp.sqrt(weight)
            scale = _broadcast_level_value(
                _lookup_named_value(path, self.scales, 1.0),
                error,
                name=f"variable_scales.{'.'.join(path)}",
            )
            scale = jnp.maximum(scale, 1e-12)
            factor = _broadcast_level_value(
                _lookup_named_value(path, self.factors, 1.0),
                error,
                name=f"variable_factors.{'.'.join(path)}",
            )
            return error * (factor / scale)

        return _map_named(errors, rescale)


def _filter_group(path: tuple[str, ...]) -> str:
    variable = _canonical_variable(path)
    if variable in {
        "specific_humidity",
        "specific_cloud_ice_water_content",
        "specific_cloud_liquid_water_content",
    }:
        return "moisture"
    if variable in {"divergence", "vorticity", "log_surface_pressure"}:
        return "divergence"
    if variable in {"u", "v"}:
        return "wind"
    if variable == "t":
        return "temperature"
    return "default"


class _PaperPredictabilityFilter:
    """Order-12 lead-time filter reconstructed from Supplementary Fig. 8."""

    def __init__(
        self,
        trajectory_spec,
        *,
        schedules: Mapping[str, list[float]],
        lead_hours: list[float],
        order: int = 12,
        is_encoded: bool = False,
    ):
        from dinosaur import filtering

        self._filtering = filtering
        self.grid = (
            trajectory_spec.coords.horizontal
            if is_encoded
            else trajectory_spec.data_coords.horizontal
        )
        self.order = int(order)
        if self.order <= 0:
            raise ValueError("loss.predictability_filter.order must be positive")
        n = int(trajectory_spec.trajectory_length)
        source_hours = np.asarray(lead_hours, dtype=np.float64)
        if source_hours.ndim != 1 or source_hours.size == 0:
            raise ValueError("loss.predictability_filter.lead_hours must be non-empty")
        if np.any(np.diff(source_hours) <= 0):
            raise ValueError("loss.predictability_filter.lead_hours must increase")
        target_hours = np.arange(n, dtype=np.float64) * float(
            trajectory_spec.steps_per_save
        )
        self.cutoffs = {}
        for group, values in schedules.items():
            values = np.asarray(values, dtype=np.float64)
            if values.shape != source_hours.shape:
                raise ValueError(
                    f"loss.predictability_filter.cutoffs.{group} has "
                    f"{values.size} entries; expected {source_hours.size}"
                )
            self.cutoffs[str(group)] = np.interp(
                target_hours, source_hours, values
            )
        if "default" not in self.cutoffs:
            raise ValueError("loss.predictability_filter.cutoffs.default is required")

    def __call__(self, errors, targets):
        del targets
        max_wavenumber = float(np.max(np.asarray(self.grid.modal_axes[1])))

        def apply_filter(path, error):
            if getattr(error, "ndim", 0) < 2:
                return error
            group = _filter_group(path)
            cutoffs = self.cutoffs.get(group, self.cutoffs["default"])
            cutoffs = np.clip(cutoffs, 1.0, max_wavenumber)
            # dinosaur.exponential_filter uses normalized total wavenumber.
            # Choose attenuation so the response is 0.5 at each configured
            # absolute cutoff. This preserves the paper's order-12 profile.
            attenuation = np.log(2.0) * np.power(
                max_wavenumber / cutoffs, 2 * self.order
            )
            attenuation = attenuation.reshape((-1,) + (1,) * (error.ndim - 1))
            filter_fn = self._filtering.exponential_filter(
                self.grid,
                attenuation=jnp.asarray(attenuation, dtype=jnp.float32),
                order=self.order,
            )
            return filter_fn(error)

        return _map_named(errors, apply_filter)


class _PaperDeterministicLoss:
    """Five-term deterministic objective from Supplementary section G.4."""

    def __init__(self, terms, bias_metric, coefficients: Mapping[str, float]):
        self.terms = terms
        self.bias_metric = bias_metric
        self.coefficients = coefficients

    @staticmethod
    def _global_bias_per_example(metric, prediction, target, axis_names):
        """Extend the released bias metric over local and device batch axes."""
        from model.reference_code import linear_transforms

        prediction = metric.get_representation(prediction)
        target = metric.get_representation(target)
        truncate = metric.transform.transforms[0]
        if not isinstance(truncate, linear_transforms.TruncateToTrajectoryLength):
            raise TypeError("BatchMeanSquaredBias must start with trajectory truncation")
        prediction = metric.getter(truncate(prediction, None))
        target = metric.getter(truncate(target, None))
        prediction = metric.metric_fn(prediction)
        target = metric.metric_fn(target)
        prediction = jax.tree_util.tree_map(
            lambda value: jax.lax.pmean(value, axis_name=axis_names), prediction
        )
        target = jax.tree_util.tree_map(
            lambda value: jax.lax.pmean(value, axis_name=axis_names), target
        )
        prediction = jax.tree_util.tree_map(
            lambda value: jnp.mean(value, axis=0, keepdims=True), prediction
        )
        target = jax.tree_util.tree_map(
            lambda value: jnp.mean(value, axis=0, keepdims=True), target
        )
        errors = jax.tree_util.tree_map(jnp.subtract, prediction, target)
        errors = metric.transform(errors, target)
        per_variable = jax.tree_util.tree_map(
            lambda value: jnp.mean(jnp.square(value)), errors
        )
        return sum(jax.tree_util.tree_leaves(per_variable))

    def evaluate_batch(self, prediction, target, *, device_axis_name=None):
        """Evaluate one global batch, including a true global spectral bias."""
        values = {}
        for name, metric in self.terms.items():
            per_example = jax.vmap(metric.evaluate, in_axes=(0, 0))(
                prediction, target
            )
            values[name] = jnp.mean(per_example)
        axis_names = (
            ("loss_batch",)
            if device_axis_name is None
            else ("loss_batch", device_axis_name)
        )
        bias = jax.vmap(
            functools.partial(
                self._global_bias_per_example,
                self.bias_metric,
                axis_names=axis_names,
            ),
            in_axes=(0, 0),
            axis_name="loss_batch",
        )(prediction, target)
        values["bias"] = jnp.mean(bias)
        return sum(
            self.coefficients[name] * value for name, value in values.items()
        )

    def __call__(self, prediction, target):
        prediction = jax.tree_util.tree_map(lambda value: value[None], prediction)
        target = jax.tree_util.tree_map(lambda value: value[None], target)
        return self.evaluate_batch(prediction, target)


def _time_factor(n_time: int, steps_per_save: int, mode: str) -> jnp.ndarray:
    """Public NeuralGCM time rescaling, returned as squared-error factors."""
    if n_time <= 0:
        return jnp.ones((0,), dtype=jnp.float32)
    if mode == "none":
        return jnp.ones((n_time,), dtype=jnp.float32)
    if mode == "legacy":
        # linear_transforms.LegacyTimeRescaling: errors /
        # sqrt((trajectory_length - 1) * steps_per_save).
        denominator = max((n_time - 1) * int(steps_per_save), 1)
        return jnp.full((n_time,), 1.0 / denominator, dtype=jnp.float32)
    if mode == "random_walk":
        # Same normalized inverse-variance weighting as the public
        # TimeRescaling transform with base_squared_error_in_hours=1.
        t = jnp.arange(n_time, dtype=jnp.float32) * float(steps_per_save)
        inv_variance = 1.0 / (1.0 + t)
        return inv_variance / jnp.sum(inv_variance)
    raise ValueError(f"Unknown loss.time_rescaling mode: {mode!r}")


def _surface_mean(square_error, coords):
    """Computes the public metrics_util.nodal_surface_mean for one leaf."""
    horizontal = coords.horizontal
    expected = tuple(horizontal.nodal_shape[-2:])
    if getattr(square_error, "ndim", 0) >= 2 and tuple(square_error.shape[-2:]) == expected:
        surface_area = 4 * jnp.pi * horizontal.radius**2
        return horizontal.integrate(square_error) / surface_area
    # Metadata or scalar diagnostics are not part of the official loss, but
    # retaining a finite scalar here makes custom profiles easier to inspect.
    return jnp.mean(square_error)


def _per_leaf_loss(error, path, coords, scales, level_weights, time_factors):
    error = jnp.asarray(error)
    if error.dtype.kind in ("O", "U", "S"):
        return jnp.asarray(0.0, dtype=jnp.float32)
    # Trajectory representations conventionally use [time, level, lon, lat].
    # A few surface fields omit the level axis; both are handled by broadcasting
    # the time factor along all remaining dimensions.
    if error.ndim == 0:
        return jnp.mean(jnp.square(error / _lookup_scale(path, scales)))
    factor = time_factors
    if error.shape[0] != factor.shape[0]:
        # The prediction may omit the initialization frame.  The caller aligns
        # target and prediction; this defensive slice handles custom adapters.
        factor = factor[-error.shape[0]:]
    reshape = (factor.shape[0],) + (1,) * (error.ndim - 1)
    transformed = error / _lookup_scale(path, scales)
    transformed = transformed * jnp.sqrt(factor.reshape(reshape))
    squared = jnp.square(transformed)
    if level_weights and squared.ndim >= 4:
        weights = jnp.asarray(level_weights, dtype=squared.dtype)
        weights = weights[: squared.shape[1]]
        squared = squared * weights.reshape((1, weights.shape[0]) + (1,) * (squared.ndim - 2))
    return jnp.mean(_surface_mean(squared, coords))


def make_loss_fn(
    model,
    *,
    steps_per_save: int,
    trajectory_length: int | None = None,
    config: Mapping[str, Any] | None = None,
    mode: str | None = None,
):
    """Build a JAX-compatible trajectory loss.

    ``backend=official`` uses the paper's five-term deterministic objective,
    assembled from the released metric primitives. ``backend=legacy_official``
    retains the earlier public WeightedL2CumulativeLoss baseline.
    ``backend=crps`` builds the released two-member nodal + spectral CRPS
    objective described in supplementary section G.6.  ``backend=scaled``
    keeps the historical deterministic approximation.
    """
    cfg = dict(config or {})
    backend = str(cfg.get("backend", "official")).lower()
    if backend in {"official", "paper", "legacy_official", "crps"}:
        if trajectory_length is None:
            raise ValueError(f"trajectory_length is required for the {backend} loss backend")
        from model.reference_code import metrics_util

        trajectory_spec = metrics_util.TrajectorySpec(
            trajectory_length=int(trajectory_length),
            max_trajectory_length=int(trajectory_length),
            steps_per_save=int(steps_per_save),
            coords=model.coords,
            data_coords=model.data_coords,
        )
        if backend == "crps":
            from model.reference_code import linear_transforms
            from model.reference_code import stochastic_losses

            weights = cfg.get("variable_weights")
            variable_scale = float(cfg.get("variable_scale", 1.0))
            nodal_hours = float(cfg.get("nodal_time_scale_hours", 24.0))
            spectral_hours = float(cfg.get("spectral_time_scale_hours", 40.0))
            max_wavenumber = int(cfg.get("spectral_max_wavenumber", 80))
            if nodal_hours <= 0 or spectral_hours <= 0:
                raise ValueError("CRPS time scale hours must be positive")
            if max_wavenumber <= 0:
                raise ValueError("loss.spectral_max_wavenumber must be positive")

            variable_rescaling = functools.partial(
                linear_transforms.PerVariableRescaling,
                weights=weights,
                scale=variable_scale,
            )
            nodal_time_rescaling = functools.partial(
                linear_transforms.DelayedTimeRescaling,
                base_squared_error_in_hours=nodal_hours,
                delay_power=1.0,
                decay_power=1.0,
            )
            spectral_time_rescaling = functools.partial(
                linear_transforms.DelayedTimeRescaling,
                base_squared_error_in_hours=spectral_hours,
                delay_power=4.0,
                decay_power=1.0,
            )
            wavenumber_mask = functools.partial(
                linear_transforms.TotalWavenumberMasking,
                max_wavenumber=max_wavenumber,
                is_encoded=False,
            )
            nodal_crps = stochastic_losses.CRPSLoss(
                trajectory_spec,
                components=(variable_rescaling, nodal_time_rescaling),
                beta=1.0,
                ensemble_term_weight=0.5,
                is_nodal=True,
                is_encoded=False,
            )
            spectral_crps = stochastic_losses.CRPSLoss(
                trajectory_spec,
                components=(
                    variable_rescaling,
                    spectral_time_rescaling,
                    wavenumber_mask,
                ),
                beta=1.0,
                ensemble_term_weight=0.5,
                is_nodal=False,
                is_encoded=False,
            )

            def crps_loss(prediction, target):
                return nodal_crps.evaluate(prediction, target) + spectral_crps.evaluate(
                    prediction, target
                )

            return crps_loss

        from model.reference_code import linear_transforms
        from model.reference_code import metrics

        if backend == "legacy_official":
            public_loss = metrics.WeightedL2CumulativeLoss(
                trajectory_spec, weights=None, scale=float(cfg.get("scale", 1.0))
            )
            return public_loss.evaluate

        if mode is None:
            raise ValueError("mode is required for the paper deterministic loss")
        cutoffs_by_mode = dict(
            cfg.get(
                "spectral_cutoff_by_mode",
                {
                    "weather_forecast": 120,
                    "climate_scale": 80,
                    "forecast_2_8_deg": 42,
                },
            )
        )
        if mode not in cutoffs_by_mode:
            raise ValueError(
                f"No deterministic spectral cutoff configured for {mode!r}"
            )
        spectral_cutoff = int(cutoffs_by_mode[mode])
        scales = dict(cfg.get("variable_scales", {}))
        factors = dict(cfg.get("variable_factors", {}))
        explicit_weights = cfg.get("variable_weights")
        variable_rescaling = functools.partial(
            _PaperVariableRescaling,
            scales=scales,
            factors=factors,
            weights=None if explicit_weights is None else dict(explicit_weights),
        )
        accuracy_time = functools.partial(
            linear_transforms.DelayedTimeRescaling,
            base_squared_error_in_hours=float(
                cfg.get("accuracy_time_scale_hours", 24.0)
            ),
            delay_power=1.0,
            decay_power=1.0,
        )
        spectral_time = functools.partial(
            linear_transforms.DelayedTimeRescaling,
            base_squared_error_in_hours=float(
                cfg.get("spectral_time_scale_hours", 40.0)
            ),
            delay_power=4.0,
            decay_power=1.0,
        )
        filter_cfg = dict(cfg.get("predictability_filter", {}))
        filter_enabled = bool(filter_cfg.get("enabled", True))

        def accuracy_components(is_encoded: bool):
            components = [variable_rescaling, accuracy_time]
            if filter_enabled:
                components.append(
                    functools.partial(
                        _PaperPredictabilityFilter,
                        schedules=dict(filter_cfg.get("cutoffs", {})),
                        lead_hours=list(filter_cfg.get("lead_hours", [])),
                        order=int(filter_cfg.get("order", 12)),
                        is_encoded=is_encoded,
                    )
                )
            return tuple(components)

        def spectrum_components(is_encoded: bool):
            return (
                variable_rescaling,
                spectral_time,
                functools.partial(
                    linear_transforms.TotalWavenumberMasking,
                    max_wavenumber=spectral_cutoff,
                    is_encoded=is_encoded,
                ),
            )

        terms = {
            "data": metrics.TransformedL2Loss(
                trajectory_spec,
                components=accuracy_components(False),
                is_nodal=False,
                is_encoded=False,
            ),
            "data_spectrum": metrics.TransformedL2SpectrumLoss(
                trajectory_spec,
                components=spectrum_components(False),
                is_nodal=False,
                is_encoded=False,
            ),
            "model": metrics.TransformedL2Loss(
                trajectory_spec,
                components=accuracy_components(True),
                is_nodal=False,
                is_encoded=True,
            ),
            "model_spectrum": metrics.TransformedL2SpectrumLoss(
                trajectory_spec,
                components=spectrum_components(True),
                is_nodal=False,
                is_encoded=True,
            ),
        }
        bias_metric = metrics.BatchMeanSquaredBias(
            trajectory_spec,
            components=(variable_rescaling,),
            is_nodal=False,
            is_encoded=False,
        )
        coefficients = {
            "data": float(cfg.get("data_weight", 20.0)),
            "data_spectrum": float(cfg.get("data_spectrum_weight", 0.1)),
            "model": float(cfg.get("model_weight", 1.0)),
            "model_spectrum": float(cfg.get("model_spectrum_weight", 0.1)),
            "bias": float(cfg.get("bias_weight", 2.0)),
        }
        return _PaperDeterministicLoss(terms, bias_metric, coefficients)

    if backend not in {"scaled", "legacy"}:
        raise ValueError(f"Unknown loss.backend {backend!r}")
    scales = dict(cfg.get("variable_scales", {}))
    scales.setdefault("z", 1.0e4)       # geopotential (m² s⁻²)
    scales.setdefault("t", 30.0)        # temperature (K)
    scales.setdefault("u", 30.0)        # zonal wind (m s⁻¹)
    scales.setdefault("v", 30.0)        # meridional wind (m s⁻¹)
    scales.setdefault("specific_humidity", 1.0e-2)
    scales.setdefault("default", 1.0)
    level_weights = cfg.get("level_weights", [])
    time_mode = str(cfg.get("time_rescaling", "legacy"))
    spectral_weight = float(cfg.get("spectral_weight", 0.0))
    bias_weight = float(cfg.get("bias_weight", 0.0))
    coords = model.data_coords

    def loss_fn(prediction, target):
        pred = dict(prediction.data_nodal_trajectory)
        truth = dict(target.data_nodal_trajectory)
        pred.pop("sim_time", None)
        truth.pop("sim_time", None)

        def align(a, b):
            if getattr(a, "ndim", 0) and getattr(b, "ndim", 0):
                if a.shape[0] != b.shape[0] and a.shape[1:] == b.shape[1:]:
                    return b[-a.shape[0]:]
            return b

        truth = __import__("jax").tree_util.tree_map(align, pred, truth)
        leaves = []
        first_array = next(
            (value for _, value in _leaf_items(pred) if getattr(value, "ndim", 0)),
            None,
        )
        if first_array is None:
            return jnp.asarray(0.0, dtype=jnp.float32)
        factors = _time_factor(int(first_array.shape[0]), steps_per_save, time_mode)
        for path, p in _leaf_items(pred):
            # Resolve the corresponding target leaf without assuming a flat tree.
            node = truth
            for key in path:
                node = node[key]
            if getattr(p, "dtype", None) is None or p.dtype.kind in ("O", "U", "S"):
                continue
            leaves.append(_per_leaf_loss(p - node, path, coords, scales, level_weights, factors))
        accuracy = jnp.sum(jnp.stack(leaves)) if leaves else jnp.asarray(0.0)

        # Optional public spectral-norm term.  It is disabled by default because
        # the private Gin files do not expose its coefficient.
        spectral = jnp.asarray(0.0)
        if spectral_weight:
            pmodal = dict(prediction.data_modal_trajectory)
            tmodal = dict(target.data_modal_trajectory)
            pmodal.pop("sim_time", None)
            tmodal.pop("sim_time", None)
            tmodal = __import__("jax").tree_util.tree_map(align, pmodal, tmodal)
            terms = []
            for path, p in _leaf_items(pmodal):
                node = tmodal
                for key in path:
                    node = node[key]
                if getattr(p, "ndim", 0) >= 4:
                    # Public _compute_spectral_norm: norm over longitude
                    # wavenumber, followed by MSE and variable scaling.
                    ps = jnp.sqrt(jnp.sum(jnp.real(p * jnp.conj(p)), axis=-2, keepdims=True) + 1e-12)
                    ts = jnp.sqrt(jnp.sum(jnp.real(node * jnp.conj(node)), axis=-2, keepdims=True) + 1e-12)
                    terms.append(jnp.mean(jnp.square((ps - ts) / _lookup_scale(path, scales))))
            if terms:
                spectral = jnp.sum(jnp.stack(terms))

        bias = jnp.asarray(0.0)
        if bias_weight:
            for path, p in _leaf_items(pred):
                node = truth
                for key in path:
                    node = node[key]
                pmean = jnp.mean(p, axis=0)
                tmean = jnp.mean(node, axis=0)
                bias = bias + jnp.mean(jnp.square((pmean - tmean) / _lookup_scale(path, scales)))
        return accuracy + spectral_weight * spectral + bias_weight * bias

    return loss_fn