rexafs 0.2.6

//! Evaluate the FEFF scattering-path model on a requested k grid.
//!
//! [`path2chi`] returns the imaginary part of the complex path expression;
//! [`ff2chi`] sums enabled paths. Amplitudes include the file's reduction
//! factor, and total phase is `real_phc + pha_feff`. The energy correction uses
//! signed `q = sign(k² - e0·ETOK) sqrt(abs(k² - e0·ETOK))`; `e0` is a relative
//! shift in eV, not the absolute absorption-edge energy.
//!
//! # Implemented path equation
//!
//! To calculate the signal contributed by one path, the implementation uses
//! the following expression away from its numerical guards:
//!
//! ```text
//! q = sign(k² - α ΔE₀) sqrt(|k² - α ΔE₀|)
//! p = sqrt((p_re(q) + i/λ(q))² + i α E_i)
//! X = N S₀² F(q) / [q (R₀ + ΔR)²]
//!     · exp(-2 R₀ Im(p) - 2 p²(σ² - p² C₄/3)
//!           + i[2 q R₀ + φ(q) + 2 p(ΔR - 2 σ²/R₀ - 2 p² C₃/3)])
//! χ(k) = Im(X)
//! ```
//!
//! Here `α` is [`ETOK`] in Å⁻²/eV; `k`, shifted wave number `q`, and complex
//! momentum `p` use Å⁻¹. `p_re` and mean free path `λ` (Å) come from the file.
//! `R₀` is the reference half-path length in Å, `N` the dimensionless
//! degeneracy, and `S₀²` the dimensionless amplitude correction. `ΔE₀` and
//! `E_i` are real and imaginary energy corrections in eV. `ΔR` uses Å;
//! the distance cumulants `σ²`, `C₃`, and `C₄` use Ų, ų, and Å⁴.
//! `F = mag_feff · red_fact` is the reduced amplitude in Å, while
//! `φ = real_phc + pha_feff` is the total phase in radians; `i² = -1` and
//! the complex square root uses its principal branch. Consequently the
//! exponent and χ are dimensionless. The first exponential term describes
//! propagation loss, the cumulants describe disorder, and the phase controls
//! the oscillations. Larger positive σ² generally suppresses high-k signal.
//! `N` and `S₀²` enter only through their product and cannot be inferred
//! independently from that product alone.
//!
//! This is a truncated cumulant/reference-path model: large distance changes
//! or strongly non-Gaussian disorder need additional physical justification.
//! Varying these parameters does not rerun the underlying scattering calculation.
//! The equation is traced directly to `calc_path_chi`; the published
//! multiple-scattering theory is described by Rehr and Albers, cited below.
//!
//! FEFF columns are interpolated with a not-a-knot cubic spline (linear for
//! at most three samples). Outside tabulated k, the end polynomial pieces are
//! extrapolated; the historical helper name containing `clamped` does not mean
//! endpoint values are held. Prefer grids inside the available FEFF range.
//! Small-denominator guards regularize near-zero q, mean free path, and distance.
//! The first returned complex sample is replaced by `2·sample[1] - sample[2]`
//! for every input grid. This is an implementation convention, not an extra
//! physical scattering term. See [`super::types::FeffPathModel`] for parameter
//! units and [Rehr and Albers (2000)](https://doi.org/10.1103/RevModPhys.72.621)
//! for the multiple-scattering basis of EXAFS modeling.

use std::collections::BTreeMap;
use std::path::Path;

use nalgebra::DVector;
use num_complex::Complex64;

use crate::xafs::xafsutils::constants::ETOK;

use super::errors::FittingError;
use super::feffdat::parse_feff_path_file;
use super::types::{FeffFlavor, FeffPathModel, FitVariables};
use super::variables::resolve_path_param;

const SMALL_ENERGY: f64 = 1.0e-6;

#[derive(Debug, Clone)]
/// Owned total and individual path spectra, without k-weighting or windows.
pub struct FF2ChiOutput {
    /// Sum of enabled paths, dimensionless on the supplied k grid.
    pub chi: DVector<f64>,
    /// Path labels and dimensionless contributions, in enabled input order.
    pub path_chi: Vec<(String, DVector<f64>)>,
}

#[derive(Debug, Clone, Copy)]
pub(crate) struct PathParams {
    degen: f64,
    s02: f64,
    e0: f64,
    ei: f64,
    deltar: f64,
    sigma2: f64,
    third: f64,
    fourth: f64,
}

/// Read a path and initialize corrections to their documented defaults.
/// See [`super::feffpath`] for supported file flavors and failure conditions.
pub fn feffpath<P: AsRef<Path>>(
    path: P,
    flavor: FeffFlavor,
) -> Result<FeffPathModel, FittingError> {
    let parsed = parse_feff_path_file(path.as_ref(), flavor)?;
    let label = path
        .as_ref()
        .file_name()
        .map(|s| s.to_string_lossy().to_string())
        .unwrap_or_else(|| "path".to_string());
    Ok(FeffPathModel::from_feffdat(label, parsed))
}

/// Evaluate one path on a finite k grid in Å⁻¹, returning owned dimensionless χ.
/// Requires at least three samples; see the module documentation for conventions.
pub fn path2chi(
    path: &FeffPathModel,
    vars: &FitVariables,
    k: &DVector<f64>,
) -> Result<DVector<f64>, FittingError> {
    let globals = vars.resolve_values()?;
    let params = resolve_params(path, &globals)?;
    let (_cchi, chi) = calc_path_chi(path, &params, k)?;
    Ok(chi)
}

/// Sum enabled paths on the supplied k grid and retain each contribution.
/// Returns an error if no path is enabled or an expression/path cannot be evaluated.
pub fn ff2chi(
    paths: &[FeffPathModel],
    vars: &FitVariables,
    k: &DVector<f64>,
) -> Result<FF2ChiOutput, FittingError> {
    if paths.is_empty() {
        return Err(FittingError::EmptyPaths);
    }

    let globals = vars.resolve_values()?;
    let mut total = DVector::zeros(k.len());
    let mut path_chi = Vec::with_capacity(paths.len());

    for path in paths.iter().filter(|path| path.use_path) {
        let params = resolve_params(path, &globals)?;
        let (_cchi, chi) = calc_path_chi(path, &params, k)?;
        total += &chi;
        path_chi.push((path.label.clone(), chi));
    }

    if path_chi.is_empty() {
        return Err(FittingError::EmptyPaths);
    }

    Ok(FF2ChiOutput {
        chi: total,
        path_chi,
    })
}

pub(crate) fn calc_path_chi(
    path: &FeffPathModel,
    params: &PathParams,
    k: &DVector<f64>,
) -> Result<(Vec<Complex64>, DVector<f64>), FittingError> {
    if path.feff.reff < 0.05 {
        return Err(FittingError::InvalidFeffData {
            reason: format!("path '{}' has invalid reff {}", path.label, path.feff.reff),
        });
    }
    if k.len() < 3 {
        return Err(FittingError::InvalidDataset {
            reason: "k grid must contain at least 3 points".to_string(),
        });
    }
    if let Some(index) = k.iter().position(|kv| !kv.is_finite()) {
        return Err(FittingError::InvalidDataset {
            reason: format!("k grid contains non-finite value at index {index}"),
        });
    }

    let reff = path.feff.reff;
    let q = k.map(|kv| {
        let mut energy = kv * kv - params.e0 * ETOK;
        // Preserve sign when clamping near zero so q continuity matches FEFF/Larch behavior.
        let sign = if energy < 0.0 { -1.0 } else { 1.0 };
        if energy.abs() < 1.5 * SMALL_ENERGY {
            energy = sign * SMALL_ENERGY;
        }
        energy.signum() * energy.abs().sqrt()
    });

    let pha = interp_cubic_spline_clamped(&path.feff.k, &path.feff.pha, &q)?;
    let amp = interp_cubic_spline_clamped(&path.feff.k, &path.feff.amp, &q)?;
    let rep = interp_cubic_spline_clamped(&path.feff.k, &path.feff.rep, &q)?;
    let lam = interp_cubic_spline_clamped(&path.feff.k, &path.feff.lam, &q)?;

    let mut cchi: Vec<Complex64> = Vec::with_capacity(k.len());
    for i in 0..k.len() {
        // Avoid blow-ups when spline interpolation makes lambda very small.
        let denom_lam = if lam[i].abs() < SMALL_ENERGY {
            SMALL_ENERGY.copysign(lam[i])
        } else {
            lam[i]
        };
        let pp =
            Complex64::new(rep[i], 1.0 / denom_lam).powi(2) + Complex64::new(0.0, params.ei * ETOK);
        let p = pp.sqrt();

        let sigma_term = params.sigma2 - pp * (params.fourth / 3.0);
        let delta_term = params.deltar - 2.0 * params.sigma2 / reff - 2.0 * pp * params.third / 3.0;
        let phase_inner = Complex64::new(2.0 * q[i] * reff + pha[i], 0.0) + 2.0 * p * delta_term;

        let exponent = Complex64::new(-2.0 * reff * p.im, 0.0) - 2.0 * pp * sigma_term
            + Complex64::new(0.0, 1.0) * phase_inner;

        let denom_q = if q[i].abs() < SMALL_ENERGY {
            SMALL_ENERGY.copysign(q[i])
        } else {
            q[i]
        };
        let denom_r = (reff + params.deltar).powi(2).max(SMALL_ENERGY);

        let scale = params.degen * params.s02 * amp[i] / (denom_q * denom_r);
        cchi.push(scale * exponent.exp());
    }

    if cchi.len() >= 3 {
        cchi[0] = 2.0 * cchi[1] - cchi[2];
    }

    let chi = DVector::from_iterator(cchi.len(), cchi.iter().map(|value| value.im));
    Ok((cchi, chi))
}

pub(crate) fn resolve_params(
    path: &FeffPathModel,
    globals: &BTreeMap<String, f64>,
) -> Result<PathParams, FittingError> {
    let mut locals = BTreeMap::new();
    locals.insert("reff".to_string(), path.feff.reff);
    locals.insert("degen".to_string(), path.feff.degen);

    Ok(PathParams {
        degen: resolve_path_param(&path.degen, path.feff.degen, globals, &locals)?,
        s02: resolve_path_param(&path.s02, 1.0, globals, &locals)?,
        e0: resolve_path_param(&path.e0, 0.0, globals, &locals)?,
        ei: resolve_path_param(&path.ei, 0.0, globals, &locals)?,
        deltar: resolve_path_param(&path.deltar, 0.0, globals, &locals)?,
        sigma2: resolve_path_param(&path.sigma2, 0.0, globals, &locals)?,
        third: resolve_path_param(&path.third, 0.0, globals, &locals)?,
        fourth: resolve_path_param(&path.fourth, 0.0, globals, &locals)?,
    })
}

fn interp_cubic_spline_clamped(
    xin: &DVector<f64>,
    yin: &DVector<f64>,
    xout: &DVector<f64>,
) -> Result<DVector<f64>, FittingError> {
    if xin.len() != yin.len() || xin.len() < 2 {
        return Err(FittingError::InvalidFeffData {
            reason: "interpolation requires at least 2 FEFF grid points".to_string(),
        });
    }
    if let Some(index) = xin.iter().position(|value| !value.is_finite()) {
        return Err(FittingError::InvalidFeffData {
            reason: format!("FEFF k grid contains non-finite value at index {index}"),
        });
    }
    if let Some(index) = yin.iter().position(|value| !value.is_finite()) {
        return Err(FittingError::InvalidFeffData {
            reason: format!("FEFF data contains non-finite value at index {index}"),
        });
    }
    if let Some(index) = xout.iter().position(|value| !value.is_finite()) {
        return Err(FittingError::InvalidDataset {
            reason: format!("interpolation target grid contains non-finite value at index {index}"),
        });
    }

    for i in 1..xin.len() {
        if xin[i] < xin[i - 1] {
            return Err(FittingError::InvalidFeffData {
                reason: "FEFF k grid must be monotonic for interpolation".to_string(),
            });
        }
    }

    let order = if xin.len() > 3 { 3 } else { 1 };
    let (knots, coefs) = crate::xafs::spline::interpolate(xin.as_slice(), yin.as_slice(), order)
        .map_err(|reason| FittingError::InvalidFeffData { reason })?;
    let values = crate::xafs::spline::evaluate(&knots, &coefs, order, xout.as_slice(), false);
    Ok(DVector::from_vec(values))
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::xafs::fitting::types::{FeffFlavor, PathParamSpec};
    use crate::xafs::tests::{PARAM_LOADTXT, TOP_DIR};
    use approx::assert_abs_diff_eq;
    use data_reader::reader::load_txt_f64;

    #[test]
    fn test_path2chi_returns_finite_values() {
        let pathfile = format!("{TOP_DIR}/tests/testfiles/feffcu01.dat");
        let mut path = feffpath(pathfile, FeffFlavor::Feff85L).unwrap();
        path.s02 = PathParamSpec::Expression("amp".to_string());
        path.e0 = PathParamSpec::Expression("de0".to_string());
        path.sigma2 = PathParamSpec::Expression("sig2".to_string());

        let mut vars = FitVariables::new();
        vars.insert("amp", super::super::types::FitVariable::new(0.95, true));
        vars.insert("de0", super::super::types::FitVariable::new(1.5, true));
        vars.insert("sig2", super::super::types::FitVariable::new(0.003, true));

        let k = DVector::from_iterator(240, (0..240).map(|i| 0.05 * (i as f64 + 1.0)));
        let chi = path2chi(&path, &vars, &k).unwrap();

        assert_eq!(chi.len(), k.len());
        assert!(chi.iter().all(|value| value.is_finite()));
    }

    #[test]
    fn degen_defaults_to_feff_and_is_a_path_local_in_expressions() {
        let pathfile = format!("{TOP_DIR}/tests/testfiles/feffcu01.dat");
        let path = feffpath(pathfile, FeffFlavor::Feff85L).unwrap();
        let feff_degen = path.feff.degen;
        assert!(feff_degen > 0.0);
        let globals = BTreeMap::new();
        let params = resolve_params(&path, &globals).unwrap();
        assert_abs_diff_eq!(params.degen, feff_degen, epsilon = 1e-12);

        let halved = path
            .clone()
            .set_degen(PathParamSpec::Expression("degen / 2".into()));
        let params = resolve_params(&halved, &globals).unwrap();
        assert_abs_diff_eq!(params.degen, feff_degen / 2.0, epsilon = 1e-12);

        let fixed = path.set_degen(PathParamSpec::Value(1.0));
        let params = resolve_params(&fixed, &globals).unwrap();
        assert_abs_diff_eq!(params.degen, 1.0, epsilon = 1e-12);
    }

    #[test]
    fn test_path2chi_rejects_non_finite_k_grid() {
        let pathfile = format!("{TOP_DIR}/tests/testfiles/feffcu01.dat");
        let path = feffpath(pathfile, FeffFlavor::Feff85L).unwrap();
        let vars = FitVariables::new();

        let mut k = DVector::from_iterator(240, (0..240).map(|i| 0.05 * (i as f64 + 1.0)));
        k[10] = f64::NAN;

        let err = path2chi(&path, &vars, &k).unwrap_err();
        assert!(matches!(err, FittingError::InvalidDataset { .. }));
    }

    #[test]
    fn test_ff2chi_combines_multiple_paths() {
        let pathfile1 = format!("{TOP_DIR}/tests/testfiles/feffcu01.dat");
        let pathfile2 = format!("{TOP_DIR}/tests/testfiles/feff0002.dat");

        let path1 = feffpath(pathfile1, FeffFlavor::Feff85L).unwrap();
        let path2 = feffpath(pathfile2, FeffFlavor::Feff85L).unwrap();

        let vars = FitVariables::new();
        let k = DVector::from_iterator(200, (0..200).map(|i| 0.05 * (i as f64 + 1.0)));

        let out = ff2chi(&[path1, path2], &vars, &k).unwrap();
        assert_eq!(out.chi.len(), k.len());
        assert_eq!(out.path_chi.len(), 2);
    }

    #[test]
    fn test_path2chi_matches_larch_reference_within_tolerance() {
        let pathfile = format!("{TOP_DIR}/tests/testfiles/feffcu01.dat");
        let reference_path = format!("{TOP_DIR}/tests/testfiles/feff_path_chi_larch_ref.txt");

        let mut path = feffpath(pathfile, FeffFlavor::Feff85L).unwrap();
        path.s02 = PathParamSpec::Expression("amp".to_string());
        path.e0 = PathParamSpec::Expression("de0".to_string());
        path.sigma2 = PathParamSpec::Expression("sig2".to_string());
        path.deltar = PathParamSpec::Expression("dr".to_string());

        let mut vars = FitVariables::new();
        vars.insert("amp", super::super::types::FitVariable::new(0.92, false));
        vars.insert("de0", super::super::types::FitVariable::new(1.4, false));
        vars.insert("sig2", super::super::types::FitVariable::new(0.0031, false));
        vars.insert("dr", super::super::types::FitVariable::new(0.011, false));

        let reference = load_txt_f64(&reference_path, &PARAM_LOADTXT).unwrap();
        let k = DVector::from_vec(reference.get_col(0));
        let chi_expected = reference.get_col(1);
        let chi = path2chi(&path, &vars, &k).unwrap();

        for ((kv, actual), expected) in k.iter().zip(chi.iter()).zip(chi_expected.iter()) {
            if *kv < 2.0 {
                continue;
            }
            assert_abs_diff_eq!(actual, expected, epsilon = 3.0e-3);
        }
    }

    #[test]
    fn test_ff2chi_matches_larch_reference_within_tolerance() {
        let pathfile1 = format!("{TOP_DIR}/tests/testfiles/feffcu01.dat");
        let pathfile2 = format!("{TOP_DIR}/tests/testfiles/feff0002.dat");
        let reference_path = format!("{TOP_DIR}/tests/testfiles/feff_ff2chi_larch_ref.txt");

        let mut path1 = feffpath(pathfile1, FeffFlavor::Feff85L).unwrap();
        path1.s02 = PathParamSpec::Expression("amp".to_string());
        path1.e0 = PathParamSpec::Expression("de0".to_string());
        path1.sigma2 = PathParamSpec::Expression("sig2".to_string());
        path1.deltar = PathParamSpec::Expression("dr".to_string());

        let mut path2 = feffpath(pathfile2, FeffFlavor::Feff85L).unwrap();
        path2.s02 = PathParamSpec::Expression("amp2".to_string());
        path2.e0 = PathParamSpec::Expression("de0".to_string());
        path2.sigma2 = PathParamSpec::Expression("sig2".to_string());
        path2.deltar = PathParamSpec::Expression("dr2".to_string());

        let mut vars = FitVariables::new();
        vars.insert("amp", super::super::types::FitVariable::new(0.92, false));
        vars.insert("de0", super::super::types::FitVariable::new(1.4, false));
        vars.insert("sig2", super::super::types::FitVariable::new(0.0031, false));
        vars.insert("dr", super::super::types::FitVariable::new(0.011, false));
        vars.insert("amp2", super::super::types::FitVariable::new(0.35, false));
        vars.insert("dr2", super::super::types::FitVariable::new(0.0025, false));

        let reference = load_txt_f64(&reference_path, &PARAM_LOADTXT).unwrap();
        let k = DVector::from_vec(reference.get_col(0));
        let chi_expected = reference.get_col(1);

        let out = ff2chi(&[path1, path2], &vars, &k).unwrap();
        for ((kv, actual), expected) in k.iter().zip(out.chi.iter()).zip(chi_expected.iter()) {
            if *kv < 2.0 {
                continue;
            }
            assert_abs_diff_eq!(actual, expected, epsilon = 4.0e-3);
        }
    }

    #[test]
    fn test_interp_cubic_spline_clamped_rejects_non_finite_target_grid() {
        let xin = DVector::from_vec(vec![1.0, 2.0, 3.0]);
        let yin = DVector::from_vec(vec![10.0, 20.0, 30.0]);
        let xout = DVector::from_vec(vec![1.5, f64::NAN]);

        let err = interp_cubic_spline_clamped(&xin, &yin, &xout).unwrap_err();
        assert!(matches!(err, FittingError::InvalidDataset { .. }));
    }

    #[test]
    fn test_interp_cubic_spline_clamped_rejects_non_finite_source_grid() {
        let xin = DVector::from_vec(vec![1.0, f64::INFINITY, 3.0]);
        let yin = DVector::from_vec(vec![10.0, 20.0, 30.0]);
        let xout = DVector::from_vec(vec![1.5, 2.5]);

        let err = interp_cubic_spline_clamped(&xin, &yin, &xout).unwrap_err();
        assert!(matches!(err, FittingError::InvalidFeffData { .. }));
    }

    /// Larch `_calc_chi` evaluated directly (no spline) from pre-interpolated FEFF arrays.
    #[allow(clippy::too_many_arguments)]
    fn larch_cchi(
        reff: f64,
        degen: f64,
        s02: f64,
        e0: f64,
        ei: f64,
        deltar: f64,
        sigma2: f64,
        third: f64,
        fourth: f64,
        k: f64,
        pha: f64,
        amp: f64,
        rep: f64,
        lam: f64,
    ) -> Complex64 {
        let en = k * k - e0 * ETOK;
        let q = en.signum() * en.abs().sqrt();
        let pp = Complex64::new(rep, 1.0 / lam).powi(2) + Complex64::new(0.0, ei * ETOK);
        let p = pp.sqrt();
        let exponent = Complex64::new(-2.0 * reff * p.im, 0.0)
            - 2.0 * pp * (sigma2 - pp * fourth / 3.0)
            + Complex64::new(0.0, 1.0)
                * (Complex64::new(2.0 * q * reff + pha, 0.0)
                    + 2.0 * p * (deltar - 2.0 * sigma2 / reff - 2.0 * pp * third / 3.0));
        degen * s02 * amp * exponent.exp() / (q * (reff + deltar).powi(2))
    }

    #[test]
    fn test_cumulants_and_ei_follow_larch_formula() {
        let pathfile = format!("{TOP_DIR}/tests/testfiles/feffcu01.dat");
        let path = feffpath(pathfile, FeffFlavor::Feff85L).unwrap();
        // Evaluate on the FEFF k grid so the spline interpolation is the identity and the
        // Larch formula can be evaluated point-wise from the tabulated arrays.
        let k = path.feff.k.clone();
        let base = PathParams {
            degen: 12.0,
            s02: 0.9,
            e0: 0.0,
            ei: 0.0,
            deltar: 0.01,
            sigma2: 0.004,
            third: 0.0,
            fourth: 0.0,
        };
        let (_, chi_base) = calc_path_chi(&path, &base, &k).unwrap();

        for (label, params) in [
            (
                "third",
                PathParams {
                    third: 2.0e-4,
                    ..base
                },
            ),
            (
                "fourth",
                PathParams {
                    fourth: 5.0e-5,
                    ..base
                },
            ),
            ("ei", PathParams { ei: 1.5, ..base }),
        ] {
            let (_, chi) = calc_path_chi(&path, &params, &k).unwrap();
            let mut max_change = 0.0_f64;
            let mut max_err = 0.0_f64;
            for i in 1..k.len() {
                if k[i] < 3.0 {
                    continue;
                }
                let expected = larch_cchi(
                    path.feff.reff,
                    params.degen,
                    params.s02,
                    params.e0,
                    params.ei,
                    params.deltar,
                    params.sigma2,
                    params.third,
                    params.fourth,
                    k[i],
                    path.feff.pha[i],
                    path.feff.amp[i],
                    path.feff.rep[i],
                    path.feff.lam[i],
                )
                .im;
                max_err = max_err.max((chi[i] - expected).abs());
                max_change = max_change.max((chi[i] - chi_base[i]).abs());
            }
            assert!(
                max_err < 1.0e-6,
                "{label}: max deviation from Larch formula {max_err}"
            );
            assert!(
                max_change > 1.0e-3,
                "{label}: parameter had no effect on chi(k)"
            );
        }
    }
}