integral 0.4.0

//! Independent SIGNED cross-check of `c2s_matrix`.
//!
//! Unlike `tests/c2s_reference.rs` (which sign-fixes each row and therefore pins
//! coefficients only *up to an arbitrary per-row sign*), this reference carries a
//! DEFINITE sign per (l, m), derived through a genuinely different route: the
//! complex `mpmath.spherharm` combined via the standard Blanco-Florez-Bermejo
//! (1997) complex->real unitary transform (which removes the Condon-Shortley
//! phase), projected onto Cartesian monomials at 60 digits, then unit-normalized
//! against the raw Gaussian self-overlap WITHOUT any sign-fix.
//!
//! Asserting `c2s_matrix(l)` equals this table element-by-element INCLUDING SIGN
//! establishes that the implementation's coefficient signs are fixed by the
//! literature real-solid-harmonic convention — not "fitted" to a reference. (The
//! m-ordering used here is the implementation's claimed order; for l != 1 that is
//! the literature-standard ascending m, the l == 1 (px,py,pz) reorder being the
//! only convention-specific reordering.)

#![allow(clippy::unreadable_literal, clippy::excessive_precision)]

use integral::math::am::n_cart;
use integral::math::solid_harmonics::c2s_matrix;

#[test]
fn c2s_matches_independent_signed_reference() {
    let mut ref_rows = C2S_SIGNED_REF.iter();
    let mut worst = 0.0_f64;
    for l in 0..=6 {
        let mat = c2s_matrix(l);
        let nc = n_cart(l);
        for p in 0..(2 * l + 1) {
            let row = &mat[p * nc..(p + 1) * nc];
            let refr = ref_rows.next().expect("missing reference row");
            assert_eq!(refr.len(), nc, "l={l} row={p}: width mismatch");
            for (i, (&a, &b)) in row.iter().zip(refr.iter()).enumerate() {
                let d = (a - b).abs();
                worst = worst.max(d);
                assert!(
                    d < 1e-12,
                    "l={l} row={p} col={i}: rust={a} signed_ref={b} (Δ={d:e}) \
                     — SIGN OR VALUE MISMATCH"
                );
            }
        }
    }
    assert!(ref_rows.next().is_none(), "reference has extra rows");
    eprintln!("c2s vs independent signed reference: worst |Δ| = {worst:e}");
}

// Generated by an mpmath script (60 dps, Blanco real harmonics, definite signs,
// no sign-fix). This remains an independent reference for the signed c2s tables.
pub const C2S_SIGNED_REF: &[&[f64]] = &[
    // l = 0  m_order = [0]
    &[1.0000000000000000],
    // l = 1  m_order = [1, -1, 0]
    &[1.0000000000000000, 0.0, 0.0],
    &[0.0, 1.0000000000000000, 0.0],
    &[0.0, 0.0, 1.0000000000000000],
    // l = 2  m_order = [-2, -1, 0, 1, 2]
    &[0.0, 1.0925484305920791, 0.0, 0.0, 0.0, 0.0],
    &[0.0, 0.0, 0.0, 0.0, 1.0925484305920791, 0.0],
    &[
        -0.31539156525252001,
        0.0,
        0.0,
        -0.31539156525252001,
        0.0,
        0.63078313050504001,
    ],
    &[0.0, 0.0, 1.0925484305920791, 0.0, 0.0, 0.0],
    &[
        0.54627421529603954,
        0.0,
        0.0,
        -0.54627421529603954,
        0.0,
        0.0,
    ],
    // l = 3  m_order = [-3, -2, -1, 0, 1, 2, 3]
    &[
        0.0,
        1.7701307697799305,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.59004358992664351,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        2.8906114426405541,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        -0.45704579946446574,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.45704579946446574,
        0.0,
        1.8281831978578629,
        0.0,
    ],
    &[
        0.0,
        0.0,
        -1.1195289977703462,
        0.0,
        0.0,
        0.0,
        0.0,
        -1.1195289977703462,
        0.0,
        0.74635266518023078,
    ],
    &[
        -0.45704579946446574,
        0.0,
        0.0,
        -0.45704579946446574,
        0.0,
        1.8281831978578629,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        1.4453057213202770,
        0.0,
        0.0,
        0.0,
        0.0,
        -1.4453057213202770,
        0.0,
        0.0,
    ],
    &[
        0.59004358992664351,
        0.0,
        0.0,
        -1.7701307697799305,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    // l = 4  m_order = [-4, -3, -2, -1, 0, 1, 2, 3, 4]
    &[
        0.0,
        2.5033429417967045,
        0.0,
        0.0,
        0.0,
        0.0,
        -2.5033429417967045,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        5.3103923093397916,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -1.7701307697799305,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        -0.94617469575756002,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.94617469575756002,
        0.0,
        5.6770481745453601,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        -2.0071396306718675,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -2.0071396306718675,
        0.0,
        2.6761861742291567,
        0.0,
    ],
    &[
        0.31735664074561291,
        0.0,
        0.0,
        0.63471328149122582,
        0.0,
        -2.5388531259649033,
        0.0,
        0.0,
        0.0,
        0.0,
        0.31735664074561291,
        0.0,
        -2.5388531259649033,
        0.0,
        0.84628437532163443,
    ],
    &[
        0.0,
        0.0,
        -2.0071396306718675,
        0.0,
        0.0,
        0.0,
        0.0,
        -2.0071396306718675,
        0.0,
        2.6761861742291567,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        -0.47308734787878001,
        0.0,
        0.0,
        0.0,
        0.0,
        2.8385240872726801,
        0.0,
        0.0,
        0.0,
        0.0,
        0.47308734787878001,
        0.0,
        -2.8385240872726801,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        1.7701307697799305,
        0.0,
        0.0,
        0.0,
        0.0,
        -5.3103923093397916,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.62583573544917613,
        0.0,
        0.0,
        -3.7550144126950568,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.62583573544917613,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    // l = 5  m_order = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]
    &[
        0.0,
        3.2819102842008505,
        0.0,
        0.0,
        0.0,
        0.0,
        -6.5638205684017010,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.65638205684017010,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        8.3026492595241651,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -8.3026492595241651,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        -1.4677148983057512,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.97847659887050078,
        0.0,
        11.741719186446009,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.48923829943525039,
        0.0,
        -3.9139063954820031,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        -4.7935367849733238,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -4.7935367849733238,
        0.0,
        9.5870735699466475,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.45294665119569692,
        0.0,
        0.0,
        0.0,
        0.0,
        0.90589330239139384,
        0.0,
        -5.4353598143483631,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.45294665119569692,
        0.0,
        -5.4353598143483631,
        0.0,
        3.6235732095655754,
        0.0,
    ],
    &[
        0.0,
        0.0,
        1.7542548368013539,
        0.0,
        0.0,
        0.0,
        0.0,
        3.5085096736027079,
        0.0,
        -4.6780128981369439,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        1.7542548368013539,
        0.0,
        -4.6780128981369439,
        0.0,
        0.93560257962738877,
    ],
    &[
        0.45294665119569692,
        0.0,
        0.0,
        0.90589330239139384,
        0.0,
        -5.4353598143483631,
        0.0,
        0.0,
        0.0,
        0.0,
        0.45294665119569692,
        0.0,
        -5.4353598143483631,
        0.0,
        3.6235732095655754,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        -2.3967683924866619,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        4.7935367849733238,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        2.3967683924866619,
        0.0,
        -4.7935367849733238,
        0.0,
        0.0,
    ],
    &[
        -0.48923829943525039,
        0.0,
        0.0,
        0.97847659887050078,
        0.0,
        3.9139063954820031,
        0.0,
        0.0,
        0.0,
        0.0,
        1.4677148983057512,
        0.0,
        -11.741719186446009,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        2.0756623148810413,
        0.0,
        0.0,
        0.0,
        0.0,
        -12.453973889286248,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        2.0756623148810413,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.65638205684017010,
        0.0,
        0.0,
        -6.5638205684017010,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        3.2819102842008505,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    // l = 6  m_order = [-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
    &[
        0.0,
        4.0991046311514859,
        0.0,
        0.0,
        0.0,
        0.0,
        -13.663682103838286,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        4.0991046311514859,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        11.833095811158760,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -23.666191622317520,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        2.3666191622317520,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        -2.0182596029148966,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        20.182596029148966,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        2.0182596029148966,
        0.0,
        -20.182596029148966,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        -8.2908473356343115,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -5.5272315570895410,
        0.0,
        22.108926228358164,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        2.7636157785447705,
        0.0,
        -7.3696420761193880,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.92120525951492350,
        0.0,
        0.0,
        0.0,
        0.0,
        1.8424105190298470,
        0.0,
        -14.739284152238776,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.92120525951492350,
        0.0,
        -14.739284152238776,
        0.0,
        14.739284152238776,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        0.0,
        0.0,
        2.9131068125936569,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        5.8262136251873139,
        0.0,
        -11.652427250374628,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        2.9131068125936569,
        0.0,
        -11.652427250374628,
        0.0,
        4.6609709001498511,
        0.0,
    ],
    &[
        -0.31784601133814213,
        0.0,
        0.0,
        -0.95353803401442639,
        0.0,
        5.7212282040865583,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.95353803401442639,
        0.0,
        11.442456408173117,
        0.0,
        -7.6283042721154111,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.31784601133814213,
        0.0,
        5.7212282040865583,
        0.0,
        -7.6283042721154111,
        0.0,
        1.0171072362820548,
    ],
    &[
        0.0,
        0.0,
        2.9131068125936569,
        0.0,
        0.0,
        0.0,
        0.0,
        5.8262136251873139,
        0.0,
        -11.652427250374628,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        2.9131068125936569,
        0.0,
        -11.652427250374628,
        0.0,
        4.6609709001498511,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        0.46060262975746175,
        0.0,
        0.0,
        0.46060262975746175,
        0.0,
        -7.3696420761193880,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.46060262975746175,
        0.0,
        0.0,
        0.0,
        7.3696420761193880,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        -0.46060262975746175,
        0.0,
        7.3696420761193880,
        0.0,
        -7.3696420761193880,
        0.0,
        0.0,
    ],
    &[
        0.0,
        0.0,
        -2.7636157785447705,
        0.0,
        0.0,
        0.0,
        0.0,
        5.5272315570895410,
        0.0,
        7.3696420761193880,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        8.2908473356343115,
        0.0,
        -22.108926228358164,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
        0.0,
    ],
    &[
        -0.50456490072872416,
        0.0,
        0.0,
        2.5228245036436208,
        0.0,
        5.0456490072872416,
        0.0,
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        2.5228245036436208,
        0.0,
        -30.273894043723450,
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        -0.50456490072872416,
        0.0,
        5.0456490072872416,
        0.0,
        0.0,
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    ],
    &[
        0.0,
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        2.3666191622317520,
        0.0,
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        0.0,
        0.0,
        -23.666191622317520,
        0.0,
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        0.0,
        0.0,
        11.833095811158760,
        0.0,
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    ],
    &[
        0.68318410519191432,
        0.0,
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        -10.247761577878715,
        0.0,
        0.0,
        0.0,
        0.0,
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        0.0,
        10.247761577878715,
        0.0,
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        0.0,
        0.0,
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