r"""
Full Generic Workflow
=====================================

A complete ``unite`` fit on simulated data using a fully custom spectrograph.
No real data files required — we generate a synthetic spectrum in the first step.

We fit H\ :math:`\alpha` + [NII]\ :math:`\lambda\lambda`\ 6549,6585 with a
**narrow + broad** decomposition on a linear continuum.  The focus here is on
customisation: building a disperser from scratch, loading a spectrum from raw
arrays, and exercising the full inference and diagnostics pipeline.  The
emission-line and continuum configuration, inference, and result-extraction
steps are identical to the NIRSpec tutorial — refer back to those sections for
deeper discussion.
"""

# %%
# Step 0 — Imports and Setup
# --------------------------

import astropy.units as u
import jax
import jax.numpy as jnp
import numpy as np
from matplotlib import pyplot
from numpyro import infer

from unite import continuum, line, model, prior, results, spectrum

pyplot.style.use('unite.mplstyle')

# %%
# Step 1 — Configure the Disperser
# ---------------------------------
#
# :class:`~unite.instrument.generic.GenericDisperser` accepts arbitrary
# JAX-jittable callables for *R(λ)* and *dλ/dpix(λ)*, making it suitable for
# any instrument whose response cannot be expressed as a constant or simple grid.
# Here we model a low-resolution spectrograph whose resolving power rises linearly
# from *R* = 800 at 6200 Å to *R* = 1200 at 6900 Å — realistic for, e.g., a
# longslit spectrograph with a grism tilted off blaze.
#
# The pixel scale is uniform (constant *dλ/dpix*), so we hard-code it from the
# grid spacing.
#
# If your instrument has a constant *R* or a simple pixel-sampled grid, use
# :class:`~unite.instrument.generic.SimpleDisperser` instead — it only needs a
# wavelength array and one of ``R``, ``dlam``, or ``dvel``.  Built-in dispersers
# (e.g. :class:`~unite.instrument.nirspec.G395M`,
# :class:`~unite.instrument.sdss.SDSSDisperser`) are drop-in replacements — the
# rest of the workflow is identical.
#
# An optional :class:`~unite.instrument.RScale` calibration token is attached to
# leave the effective resolution as a free parameter in the model.  This is
# useful when the true LSF width is uncertain (slit filling, seeing, etc.).
#
# See :doc:`../usage/instrument` for the full disperser and calibration token
# reference.

from unite.instrument import RScale
from unite.instrument.generic import GenericDisperser
from unite.spectrum import Spectrum

WL_MIN, WL_MAX, N_PIX = 6200.0, 6900.0, 500
dlam_pix = (WL_MAX - WL_MIN) / (N_PIX - 1)  # Å/pixel (uniform grid)

disperser = GenericDisperser(
    R_func=lambda w: 800.0 + (w - WL_MIN) / (WL_MAX - WL_MIN) * 400.0,
    dlam_dpix_func=lambda w: jnp.full_like(w, dlam_pix),
    unit=u.AA,
    name='custom_grism',
    r_scale=RScale(prior=prior.TruncatedNormal(low=0.7, high=1.3, loc=1.0, scale=0.1)),
)

# For a constant-R instrument the simpler alternative is:
# disperser = SimpleDisperser(wavelength=wavelength_q, R=1000.0, name='custom_grism')

print(disperser)

# %%
# Step 2 — Simulate and Load the Spectrum
# ----------------------------------------
#
# We generate a 500-pixel synthetic spectrum with:
#
# * A narrow H\ :math:`\alpha` + [NII] triplet (FWHM ≈ 300 km/s intrinsic,
#   convolved with the LSF)
# * A broad H\ :math:`\alpha` component (FWHM ≈ 2000 km/s, mimicking a
#   broad-line region)
# * A gently sloping linear continuum
# * Gaussian noise at S/N ≈ 5 per pixel on the continuum
#
# :class:`~unite.spectrum.Spectrum` takes pixel *edges* (``low``,
# ``high``) rather than centers, which ``unite`` uses for exact pixel
# integration.  Flux and error must be :class:`~astropy.units.Quantity` with
# f-lambda units.
#
# See :doc:`../usage/instrument` (Generic Dispersers section) for the full
# ``Spectrum`` API.

rng = np.random.default_rng(0)

wavelength_q = np.linspace(WL_MIN, WL_MAX, N_PIX) * u.AA
wl = wavelength_q.value

# LSF FWHM at Ha for the disperser (R ~ 1030 at 6563 Å)
R_ha = 800.0 + (6563.0 - WL_MIN) / (WL_MAX - WL_MIN) * 400.0
lsf_fwhm_ha = 6563.0 / R_ha  # Å

# Narrow component: 300 km/s intrinsic, convolved with LSF
c_kms = 299792.458
fwhm_narrow_aa = 6563.0 * 200.0 / c_kms
sigma_narrow = np.sqrt(fwhm_narrow_aa**2 + lsf_fwhm_ha**2) / (
    2 * np.sqrt(2 * np.log(2))
)

# Broad component: 2000 km/s (much wider than LSF, so LSF convolution is negligible)
sigma_broad = 6563.0 * 2000.0 / c_kms / (2 * np.sqrt(2 * np.log(2)))

true_flux = (
    # Narrow Ha + [NII] doublet (1:3 ratio for NII 6549:6585 is approximate)
    60.0 * np.exp(-0.5 * ((wl - 6563.0) / sigma_narrow) ** 2)
    + 15.0 * np.exp(-0.5 * ((wl - 6549.0) / sigma_narrow) ** 2)
    + 45.0 * np.exp(-0.5 * ((wl - 6585.0) / sigma_narrow) ** 2)
    # Broad Ha
    + 20.0 * np.exp(-0.5 * ((wl - 6563.0) / sigma_broad) ** 2)
)
true_continuum = 20.0 + 0.008 * (wl - 6550.0)
noise_sigma = 3.0

flux_arr = (true_flux + true_continuum + rng.normal(0, noise_sigma, N_PIX)) * 1e-17
error_arr = np.full(N_PIX, noise_sigma * 1e-17)

flux_q = flux_arr * u.erg / u.s / u.cm**2 / u.AA
error_q = error_arr * u.erg / u.s / u.cm**2 / u.AA

# Pixel edges from the uniform grid
half = 0.5 * dlam_pix
low_q = (wl - half) * u.AA
high_q = (wl + half) * u.AA

spec = Spectrum(
    low=low_q,
    high=high_q,
    flux=flux_q,
    error=error_q,
    disperser=disperser,
    name='custom',
)
print(spec)

# %%
# Plot the raw spectrum to guide model design.

fig, ax = pyplot.subplots(figsize=(10, 8))
ax.step(wl, flux_q.value * 1e17, where='mid', color='k', lw=0.8, label='Simulated data')
ax.fill_between(
    wl,
    (flux_q - error_q).value * 1e17,
    (flux_q + error_q).value * 1e17,
    alpha=0.3,
    color='k',
)
ax.set(
    xlabel=r'$\lambda$ [\AA]',
    ylabel=r'$f_\lambda$ [$10^{-17}$ erg s$^{-1}$ cm$^{-2}$ \AA$^{-1}$]',
    title=r'Synthetic H$\alpha$ + [NII] — narrow + broad',
)
pyplot.tight_layout()
# pyplot.show()

# %%
# Step 3 — Configure the Emission Lines
# ----------------------------------------
#
# We build the same narrow + broad decomposition as the NIRSpec tutorial:
#
# * **Narrow**: shared redshift and FWHM across H\ :math:`\alpha` and the
#   [NII] doublet
# * **[NII] doublet**: approximate 1:3 strength ratio via ``strength``
# * **Broad**: FWHM prior that must exceed ``narrow + 300`` km/s, keeping the
#   two components identifiable
#
# See :doc:`../usage/line_configuration` for the full line and profile reference
# and :doc:`../usage/priors` for dependent priors and all supported prior types.

line_configuration = line.LineConfiguration()

z_common = line.Redshift('common', prior=prior.Uniform(-0.001, 0.001))
fwhm_narrow = line.FWHM('narrow', prior=prior.Uniform(50, 300))
fwhm_broad = line.FWHM('broad', prior=prior.Uniform(fwhm_narrow + 150, 3000))

# Narrow Ha
line_configuration.add_line(
    'Ha',
    6563.0 * u.AA,
    profile='Gaussian',
    redshift=z_common,
    fwhm_gauss=fwhm_narrow,
    flux=line.Flux(prior=prior.Uniform(0, 3)),
)

# [NII] doublet — fixed 1:3 flux ratio
line_configuration.add_lines(
    'NII',
    np.array([6549.0, 6585.0]) * u.AA,
    profile='Gaussian',
    redshift=z_common,
    fwhm_gauss=fwhm_narrow,
    strength=[1.0, 3.0],
    flux=line.Flux(prior=prior.Uniform(0, 3)),
)

# Broad Ha — independent flux, Gaussian profile
line_configuration.add_line(
    'Ha_broad',
    6563.0 * u.AA,
    profile='Gaussian',
    redshift=z_common,
    fwhm_gauss=fwhm_broad,
    flux=line.Flux(prior=prior.Uniform(0, 3)),
)

print(line_configuration)

# %%
# Step 4 — Configure the Continuum
# ----------------------------------
#
# Auto-generate a single linear continuum window around all line centers.
#
# See :doc:`../usage/continuum_configuration` for manual regions, other continuum
# forms (power law, Chebyshev, blackbody, …), and parameter sharing across regions.


cc = continuum.ContinuumConfiguration.from_lines(
    line_configuration.centers, width=15_000 * u.km / u.s, form=continuum.Linear()
)
print(cc)

# %%
# Step 5 — Prepare the Spectra
# ----------------------------
#
# :meth:`~unite.spectrum.Spectra.prepare` filters lines and continuum
# regions to those observable in the spectrum.
# :meth:`~unite.spectrum.Spectra.compute_scales` estimates the flux
# normalization and, with ``error_scale=True``, per-region error rescaling.
#
# See :doc:`../usage/build_model` for details on coverage filtering, flux scales,
# and the continuum diagnostic plots.

spectra = spectrum.Spectra([spec], redshift=0.0)

filtered_lines, filtered_cont = spectra.prepare(line_configuration, cc)

spectra.compute_scales(
    filtered_lines,
    filtered_cont,
    line_mask_width=3_000 * u.km / u.s,
    box_width=2_000 * u.km / u.s,
    error_scale=True,
)

print(f'Line scale:      {spectra.line_scale:.4g}')
print(f'Continuum scale: {spectra.continuum_scale:.4g}')

# %%
# Inspect the continuum fit before committing to inference.
# The broad component is not masked here — only the narrow-line region is excluded.
# A good fit (χ²ν ≈ 1) confirms the scale estimation is reliable.

fig, axes = pyplot.subplots(
    len(list(spectra)),
    len(filtered_cont),
    figsize=(10, 4 * len(list(spectra))),
    sharey='row',
    sharex='col',
)
axes = np.atleast_2d(axes)
fig.subplots_adjust(hspace=0.1, wspace=0)

for row, s in enumerate(spectra):
    diag = s.scale_diagnostic
    wl_s = s.wavelength
    mask = diag.line_mask

    for col, reg in enumerate(diag.regions):
        ax = axes[row, col]
        ax.step(wl_s, s.flux, where='mid', color='k', lw=0.6)
        ax.errorbar(
            wl_s,
            s.flux,
            yerr=s.error,
            fmt='none',
            ecolor='k',
            elinewidth=0.6,
            capsize=0,
        )
        masked = np.where(mask)[0]
        for group in np.split(masked, np.where(np.diff(masked) != 1)[0] + 1):
            if len(group):
                ax.axvspan(
                    s.low[group[0]], s.high[group[-1]], color='C0', alpha=0.3, lw=0
                )
        ax.plot(wl_s[reg.in_region], reg.model_on_region, lw=2, color='C3')
        ax.text(
            0.5,
            0.25,
            rf'$\chi^2_\nu = {reg.chi2_red:.2f}$',
            ha='center',
            va='center',
            transform=ax.transAxes,
        )
        if col == 0:
            ax.set(ylabel=s.name)
        if row == len(list(spectra)) - 1:
            ax.set(xlabel=r'$\lambda$ [\AA]')

# pyplot.show()

# %%
# Step 6 — Sample with MCMC
# -------------------------
#
# :class:`~unite.model.ModelBuilder` assembles the NumPyro model.
# We now will sample the posterior with MCMC.
#
# See :doc:`../usage/inference` for more information on NUTS, SVI, nested sampling, GPU acceleration,
# and using SVI to warm-start NUTS.  See :doc:`../usage/build_model` for the
# full ``ModelBuilder`` API. Notice the warning about not enough devices.

builder = model.ModelBuilder(filtered_lines, filtered_cont, spectra)
model_fn, model_args = builder.build()

kernel = infer.NUTS(
    model_fn, dense_mass=True
)  # dense_mass=True helps with correlated parameters
mcmc = infer.MCMC(
    kernel, num_warmup=500, num_samples=1000, num_chains=2, progress_bar=False
)
mcmc.run(jax.random.PRNGKey(0), model_args)
samples = mcmc.get_samples()

# %%
# Step 7 — Extract Results and Plot
# ---------------------------------
#
# :func:`~unite.results.make_parameter_table` returns physical-unit posteriors.
# :func:`~unite.results.make_spectra_tables` decomposes the model into per-line
# and continuum contributions.
#
# See :doc:`../usage/results` for FITS output, rest equivalent widths,
# and evaluating the model at arbitrary samples.

percentiles = np.array([0.16, 0.5, 0.84])
param_table = results.make_parameter_table(samples, model_args, percentiles=percentiles)
spectra_tables = results.make_spectra_tables(
    samples, model_args, insert_nan=True, percentiles=percentiles
)

print(param_table)

# %%
# Plot data, total model, and the broad component individually.

fig, ax = pyplot.subplots(figsize=(10, 5))

tab = spectra_tables[0]
median_model = tab['model_total'][:, 1]
broad = tab['Ha_broad'][:, 1]

ax.step(
    spec.wavelength,
    spec.flux * 1e17,
    where='mid',
    color='k',
    lw=0.6,
    alpha=0.7,
    label='Data',
)
ax.step(
    tab['wavelength'],
    median_model.value * 1e17,
    where='mid',
    color='C0',
    lw=1.5,
    label='Model (median)',
)
ax.step(
    tab['wavelength'],
    broad.value * 1e17 - 2,
    where='mid',
    color='C1',
    lw=1,
    label='Broad Ha (offset -2)',
)

ax.set(
    xlabel=r'$\lambda$ [\AA]',
    ylabel=r'$f_\lambda$ [$10^{-17}$ erg s$^{-1}$ cm$^{-2}$ \AA$^{-1}$]',
)
ax.legend()
pyplot.tight_layout()
# pyplot.show()


from numpyro.infer.util import log_density, log_likelihood

# %%
# **Degrees of freedom** — count the free scalar parameters in the compiled model.
# This traces the model once (no sampling) and is useful as a quick sanity check
# before comparing models.

from unite.results import count_parameters

n_params = count_parameters(model_fn, model_args)
print(f'Free parameters: {n_params}')

# %%
# **Reduced chi-square** — uses the median model from ``spectra_tables`` (Step 7)
# against the scaled errors.  NaN rows inserted by ``insert_nan=True`` are
# automatically excluded by the finite mask.

chi2_total = 0.0
n_pixels_total = 0
for t in spectra_tables:
    obs = t['observed_flux']
    err = t['scaled_error']
    med = t['model_total'][:, 1]  # median (50th percentile, could do it from max logL
    valid = jnp.isfinite(med)
    resid = (obs[valid] - med[valid]) / err[valid]
    chi2_total += (resid**2).sum()
    n_pixels_total += valid.sum()

dof = n_pixels_total - n_params
chi2_red = chi2_total / dof
print(
    f'χ²_nu = {chi2_red:.3f}  ({n_pixels_total} pixels - {n_params} params = {dof} DoF)'
)

# %%
# **Log-likelihood** — :func:`~numpyro.infer.util.log_likelihood` returns a dict
# mapping each observed site (one per spectrum) to an array of shape
# ``(n_samples, n_pixels)``.  Summing over pixels gives the total per-sample
# log-likelihood.

log_liks = log_likelihood(model_fn, samples, model_args)

ll_obs = jnp.hstack(list(log_liks.values()))
total_ll = ll_obs.sum(-1)
print(f'Mean log-likelihood: {total_ll.mean():.2f}')

# %%
# **Log-posterior** (unnormalized log-joint density: log p(θ, data)).
# :func:`~numpyro.infer.util.log_density` traces the full model including
# priors, so this includes both the likelihood and the prior log-probabilities.
# ``jax.jit(jax.vmap(...))`` compiles once and evaluates all samples in parallel.


def _log_joint(sample):
    ld, _ = log_density(model_fn, (model_args,), {}, sample)
    return ld


# log_density only accepts one sample, so we vectorize with JAX
log_joint = jax.jit(jax.vmap(_log_joint))(samples)
print(f'Mean log-posterior: {log_joint.mean():.2f}')

# %%
# **WAIC** (Widely Applicable Information Criterion).
# Computed per-pixel from the log-likelihood array — lower is better.
# ``lppd`` is the log pointwise predictive density.  Lower WAIC is better.

lppd = jnp.sum(jax.nn.logsumexp(ll_obs, axis=0) - jnp.log(ll_obs.shape[0]))
p_waic = jnp.sum(jnp.var(ll_obs, axis=0))
waic = -2.0 * (lppd - p_waic)
print(f'WAIC: {waic:.2f}')
