sva-samples 0.7.17

// Concern: one hammer/unison-string-set call site's finite-difference state | Non-concern: argument evaluation, builtin dispatch | IO: (params, sr) -> a site; () -> a sample

//! Chaigne & Askenfelt 1994's coupled hammer/stiff-string model. A physics citation, not an
//! instrument: nothing here, or anywhere this is wired in, may name one.

use crate::error::SampleError;
use crate::physics::{Solver, Varies};

use crate::physics::ball::Ball;
use crate::physics::bound::Bound::*;
use crate::physics::bound::all;
use crate::physics::hammer::Hammer;
use crate::physics::stiff_string::{
    StringGrid, Wire, dispersive_grid, grid_tension, point_weights, read_at, spread, stencil_update,
};
use crate::physics::string_energy::{Felt, energy, press};
use crate::physics::unison_energy::{unison_energy, unison_stable};

#[derive(Clone, Debug, PartialEq)]
pub struct ChaigneAskenfeltParams {
    pub f0: f64,
    pub b: f64,
    pub strike_pos: f64,
    pub vel: f64,
    pub hammer_mass: f64,
    pub hammer_k: f64,
    pub hammer_p: f64,
    pub damp_dc: f64,
    pub damp_freq: f64,
    pub unison_count: f64,
    pub detune: f64,
    pub bridge_coupling: f64,
    /// kg; `0` is massless.
    pub bridge_mass: f64,
    /// Cents off `detune`'s placing.
    pub string_cents: [f64; MAX_UNISON],
    pub string_hammer_k_ratio: [f64; MAX_UNISON],
    pub damper_pos: f64,
    /// N s/m.
    pub damper_r: f64,
    /// N/m.
    pub damper_k: f64,
}

impl ChaigneAskenfeltParams {
    /// Chaigne & Askenfelt's own C4 reference set, at the fundamental asked for.
    pub fn at(f0: f64) -> ChaigneAskenfeltParams {
        ChaigneAskenfeltParams {
            f0,
            b: 0.00021,
            strike_pos: 0.125,
            vel: 3.2,
            hammer_mass: 2.9e-3,
            hammer_k: 2.6646e8,
            hammer_p: 2.5,
            damp_dc: 0.6,
            damp_freq: 1.6e-4,
            unison_count: 1.0,
            detune: 2f64.powf(3.0 / 1200.0),
            bridge_coupling: 1000.0,
            bridge_mass: 0.0,
            string_cents: [0.0; MAX_UNISON],
            string_hammer_k_ratio: [1.0; MAX_UNISON],
            damper_pos: DAMPER_POS,
            damper_r: 0.0,
            damper_k: 0.0,
        }
    }
}

impl ChaigneAskenfeltParams {
    pub fn valid(&self) -> bool {
        let [c1, c2, c3] = self.string_cents;
        let [k1, k2, k3] = self.string_hammer_k_ratio;
        all(&[
            (self.f0, Positive),
            (self.b, NonNegative),
            (self.strike_pos, OpenUnit),
            (self.vel, Positive),
            (self.hammer_mass, Positive),
            (self.hammer_k, Positive),
            (self.hammer_p, Positive),
            (self.damp_dc, NonNegative),
            (self.damp_freq, NonNegative),
            (self.unison_count, Within(1.0, MAX_UNISON as f64)),
            (self.detune, AtLeast(1.0)),
            (self.bridge_coupling, Positive),
            (self.bridge_mass, NonNegative),
            (c1, Finite),
            (c2, Finite),
            (c3, Finite),
            (k1, Positive),
            (k2, Positive),
            (k3, Positive),
            (self.damper_pos, OpenUnit),
            (self.damper_r, NonNegative),
            (self.damper_k, NonNegative),
        ])
    }
}

/// The dashpot moves every sample; the spring stores energy, so it only jumps.
pub const VARYING: &[(&str, Varies)] = &[
    ("damper_r", Varies::PerSample),
    ("damper_k", Varies::Piecewise),
];

/// Fitted to MAPS ENSTDkCl forte key-off slopes (Emiya, Badeau & David 2010) beside a caller's
/// `damper_r = 0.1 (262/f0)^2` ramped in over 0.03 s; unpressed, the felt is lifted.
const DAMPER_POS: f64 = 0.15;
const FELT_LENGTH_M: f64 = 0.04;

const WIRE_DENSITY_KG_M3: f64 = 7850.0;
/// A generic wire radius, tuned against this module's bridge-force and contact-time tests.
const WIRE_RADIUS_M: f64 = 0.6e-3;
/// A generic string tension, tuned alongside [`WIRE_RADIUS_M`].
const STRING_TENSION_N: f64 = 1500.0;
/// `L = c/(2 f0)` on a generic wire.
fn build_grid(params: &ChaigneAskenfeltParams, f0: f64, sr: f64) -> Option<StringGrid> {
    let rho = std::f64::consts::PI * WIRE_RADIUS_M * WIRE_RADIUS_M * WIRE_DENSITY_KG_M3;
    let c = (STRING_TENSION_N / rho).sqrt();
    let length = c / (2.0 * f0);
    dispersive_grid(
        Wire { rho, c, length },
        f0,
        params.b,
        params.damp_dc,
        params.damp_freq,
        sr,
    )
}

/// Strings placed symmetrically in log frequency around `f0` at `+-sqrt(detune)`, then each
/// moved by its own `cents`.
fn unison_frequencies(f0: f64, detune: f64, unison_count: usize, cents: &[f64]) -> Vec<f64> {
    let spread = detune.sqrt();
    let placed = match unison_count {
        1 => vec![f0],
        2 => vec![f0 / spread, f0 * spread],
        _ => vec![f0 / spread, f0, f0 * spread],
    };
    placed
        .iter()
        .zip(cents)
        .map(|(&f, &c)| f * 2f64.powf(c / 1200.0))
        .collect()
}

/// Bounds `valid()`: the force buffer is a stack array.
const MAX_UNISON: usize = 3;

#[derive(Clone)]
pub struct ChaigneAskenfeltSite {
    pub(crate) strings: Vec<StringGrid>,
    /// Per string, `rho (lambda dx/dt)^2`.
    pub(crate) tensions: Vec<f64>,
    strike: Vec<Vec<f64>>,
    hammer: Hammer,
    detached: Vec<bool>,
    pub(crate) bridge_now: f64,
    pub(crate) bridge_prev: f64,
    bridge_coupling: f64,
    pub(crate) bridge_mass: f64,
    pub(crate) dt: f64,
    pub(crate) felt: Vec<Vec<Felt>>,
    /// Per string, nodes under the felt, each share, `dt/(rho dx)`.
    under_felt: Vec<(Vec<usize>, f64, f64)>,
    /// `(damper_r, damper_k)` as opened, and as the felt is designed for.
    own: (f64, f64),
    designed_for: (f64, f64),
    pub(crate) steps: u64,
}

/// Every node under the felt, or the nearest, sharing it evenly.
fn under_felt(
    grid: &StringGrid,
    params: &ChaigneAskenfeltParams,
    dt: f64,
) -> (Vec<usize>, f64, f64) {
    let n = grid.n;
    let at = params.damper_pos * n as f64;
    let half = FELT_LENGTH_M / 2.0 / grid.dx;
    let mut nodes: Vec<usize> = (1..n).filter(|&j| (j as f64 - at).abs() <= half).collect();
    if nodes.is_empty() {
        nodes.push((at.round() as usize).clamp(1, n - 1));
    }
    let psi = 1.0 / nodes.len() as f64;
    (nodes, psi, dt / (grid.rho * grid.dx))
}

fn designed(under: &[(Vec<usize>, f64, f64)], dt: f64, (r, k): (f64, f64)) -> Vec<Vec<Felt>> {
    under
        .iter()
        .map(|(nodes, psi, unit)| {
            nodes
                .iter()
                .map(|&j| (j, k * psi * dt * unit, r * psi * unit / 2.0))
                .collect()
        })
        .collect()
}

impl ChaigneAskenfeltSite {
    pub fn new(params: &ChaigneAskenfeltParams, sr: f64) -> Result<Self, SampleError> {
        let unison_count = params.unison_count.round().clamp(1.0, MAX_UNISON as f64) as usize;
        let freqs =
            unison_frequencies(params.f0, params.detune, unison_count, &params.string_cents);
        let strings = freqs
            .iter()
            .map(|&f0| build_grid(params, f0, sr))
            .collect::<Option<Vec<StringGrid>>>()
            .ok_or(SampleError::StringPastRate {
                model: "chaigne_askenfelt",
            })?;
        let dt = 1.0 / sr;
        let tensions = strings.iter().map(|g| grid_tension(g, dt)).collect();
        let strike = strings
            .iter()
            .map(|g| point_weights(g.n, params.strike_pos))
            .collect();
        let under: Vec<_> = strings.iter().map(|g| under_felt(g, params, dt)).collect();
        let own = (params.damper_r, params.damper_k);
        let site = ChaigneAskenfeltSite {
            felt: designed(&under, dt, own),
            under_felt: under,
            own,
            designed_for: own,
            steps: 0,
            detached: vec![false; strings.len()],
            strings,
            tensions,
            strike,
            hammer: Hammer::new(
                params.hammer_mass,
                params.hammer_k,
                params.hammer_p,
                params.vel,
                dt,
            )
            .with_anvil_ratios(&params.string_hammer_k_ratio[..unison_count]),
            bridge_now: 0.0,
            bridge_prev: 0.0,
            bridge_coupling: params.bridge_coupling,
            bridge_mass: params.bridge_mass,
            dt,
        };
        match site.strings.len() == 1 || unison_stable(&site) {
            true => Ok(site),
            false => Err(SampleError::BridgeUnstable {
                model: "chaigne_askenfelt",
            }),
        }
    }
}

impl ChaigneAskenfeltSite {
    pub(crate) fn advance(&mut self) -> f64 {
        // One string ends on a rigid pin; a unison ends on its shared bridge.
        let sample = match self.strings.len() {
            1 => self.step_single(),
            _ => self.step_unison(),
        };
        self.steps += 1;
        sample
    }
}

impl ChaigneAskenfeltSite {
    /// No later step is driven.
    pub fn let_go(&self) -> bool {
        self.detached.iter().all(|d| *d)
    }

    /// The discrete energy in joules: the strings', and a unison's bridge's.
    pub fn energy(&self) -> f64 {
        match self.strings.as_slice() {
            [grid] => energy(grid, self.dt, self.springs(0)).0,
            _ => unison_energy(self).0,
        }
    }

    /// The bridge's dashpot `R_B`, `bridge_coupling sqrt(T rho)` of the first string.
    pub(crate) fn bridge_r(&self) -> f64 {
        self.bridge_coupling * (self.tensions[0] * self.strings[0].rho).sqrt()
    }

    /// [`Self::bridge_r`] as the exact real its stored operands make.
    pub(crate) fn bridge_r_enclosed(&self) -> Ball {
        let z = Ball::exact(self.tensions[0])
            .scale(self.strings[0].rho)
            .sqrt();
        z.expect("a positive tension").scale(self.bridge_coupling)
    }

    pub(crate) fn springs(&self, i: usize) -> &[Felt] {
        &self.felt[i]
    }

    /// With neither dashpot nor spring the felt leaves the string, to the bit.
    pub(crate) fn pressing(&self) -> bool {
        self.designed_for.0.to_bits() != 0 || self.designed_for.1.to_bits() != 0
    }
}

impl Solver for ChaigneAskenfeltSite {
    fn step(&mut self, args: &[f64]) -> Result<f64, SampleError> {
        let now = (
            args.first().copied().unwrap_or(self.own.0),
            args.get(1).copied().unwrap_or(self.own.1),
        );
        for ((name, _), value) in VARYING.iter().zip([now.0, now.1]) {
            if !(value >= 0.0 && value.is_finite()) {
                return Err(SampleError::ArgumentOutOfRange {
                    model: "chaigne_askenfelt",
                    name,
                    bits: value.to_bits(),
                    sample: self.steps,
                });
            }
        }
        let bits = |(r, k): (f64, f64)| (r.to_bits(), k.to_bits());
        if bits(now) != bits(self.designed_for) {
            self.felt = designed(&self.under_felt, self.dt, now);
            self.designed_for = now;
        }
        Ok(self.advance())
    }

    fn bytes(&self) -> usize {
        let grids: usize = self.strings.iter().map(StringGrid::bytes).sum();
        let strike: usize = self.strike.iter().map(|w| super::floats(w)).sum();
        let felt: usize = self.felt.iter().map(std::mem::size_of_val).sum::<usize>()
            + self
                .under_felt
                .iter()
                .map(|(nodes, ..)| std::mem::size_of_val(nodes.as_slice()))
                .sum::<usize>();
        size_of::<Self>() + grids + strike + felt + super::floats(&self.tensions)
    }
}

impl ChaigneAskenfeltSite {
    /// A released anvil is not read.
    fn hammer_forces(&mut self, forces: &mut [f64]) {
        let mut y_h = [0.0f64; MAX_UNISON];
        for (i, grid) in self.strings.iter().enumerate() {
            if !self.detached[i] {
                y_h[i] = read_at(&self.strike[i], &grid.y_now);
            }
        }
        self.hammer.substeps(
            self.dt,
            &y_h[..self.strings.len()],
            &mut self.detached,
            forces,
        );
    }

    fn step_single(&mut self) -> f64 {
        let mut forces = [0.0f64; 1];
        self.hammer_forces(&mut forces);
        let pressing = self.pressing();
        let grid = &mut self.strings[0];
        let n = grid.n;
        for i in 1..n {
            grid.y_next[i] = stencil_update(grid, i, 0.0, 0.0);
        }
        spread(grid, &self.strike[0], forces[0], self.dt);
        if pressing {
            press(grid, &self.felt[0]);
        }
        grid.y_next[0] = 0.0;
        grid.y_next[n] = 0.0;

        let sample = self.tensions[0] * (grid.y_now[n] - grid.y_now[n - 1]) / grid.dx;

        std::mem::swap(&mut grid.y_prev, &mut grid.y_now);
        std::mem::swap(&mut grid.y_now, &mut grid.y_next);

        sample
    }

    /// The hammer's reaction is summed over the strings, not divided.
    fn step_unison(&mut self) -> f64 {
        let mut forces = [0.0f64; MAX_UNISON];
        let forces = &mut forces[..self.strings.len()];
        self.hammer_forces(forces);
        let pressing = self.pressing();

        let (bridge_now, bridge_prev) = (self.bridge_now, self.bridge_prev);
        let dt2 = self.dt * self.dt;
        // `M a + R_B v = net string force`: tension implicit in p+, bending and b-loss at p^n.
        let mut k_eff = 0.0;
        let mut rhs_sum = 0.0;
        let mut sample = 0.0;
        for (i, &force) in forces.iter().enumerate() {
            let grid = &mut self.strings[i];
            let tension = self.tensions[i];
            let n = grid.n;
            for j in 1..n {
                grid.y_next[j] = stencil_update(grid, j, bridge_now, bridge_prev);
            }
            spread(grid, &self.strike[i], force, self.dt);
            if pressing {
                press(grid, &self.felt[i]);
            }
            grid.y_next[0] = 0.0;
            let w = grid.rho * grid.dx / dt2;
            let (y, yp) = (&grid.y_now, &grid.y_prev);
            k_eff += tension / grid.dx;
            rhs_sum += tension * y[n - 1] / grid.dx
                + w * grid.stiff_sq * (2.0 * y[n - 1] - y[n - 2] - bridge_now)
                + w * grid.damp_b * ((y[n - 1] - yp[n - 1]) - (bridge_now - bridge_prev));
            sample += tension * (grid.y_now[n] - grid.y_now[n - 1]) / grid.dx;
        }

        let r_over_dt = self.bridge_r() / self.dt;
        let m_over_dt2 = self.bridge_mass / (self.dt * self.dt);
        let bridge_next =
            (rhs_sum + r_over_dt * bridge_now + m_over_dt2 * (2.0 * bridge_now - bridge_prev))
                / (k_eff + r_over_dt + m_over_dt2);
        for grid in &mut self.strings {
            let n = grid.n;
            grid.y_next[n] = bridge_next;
        }

        self.bridge_prev = bridge_now;
        self.bridge_now = bridge_next;

        for grid in &mut self.strings {
            std::mem::swap(&mut grid.y_prev, &mut grid.y_now);
            std::mem::swap(&mut grid.y_now, &mut grid.y_next);
        }

        sample
    }
}