rscopulas 0.2.1

Core Rust library for fitting, evaluating, and sampling copula models and vine copulas
Documentation 
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use crate::errors::CopulaError;

use super::common::KhoudrajiParams;

#[derive(Debug)]
struct KhoudrajiParts {
    cdf_first: f64,
    cdf_second: f64,
    h12_first: f64,
    h21_first: f64,
    h12_second: f64,
    h21_second: f64,
    log_pdf_first: f64,
    log_pdf_second: f64,
    du_first: f64,
    dv_first: f64,
    du_second: f64,
    dv_second: f64,
}

pub fn log_pdf(
    u1: f64,
    u2: f64,
    params: &KhoudrajiParams,
    clip_eps: f64,
) -> Result<f64, CopulaError> {
    let parts = evaluate_parts(u1, u2, params, clip_eps)?;
    let term_logs = [
        ln_if_positive(parts.du_first)
            + ln_if_positive(parts.dv_first)
            + parts.log_pdf_first
            + ln_if_positive(parts.cdf_second),
        ln_if_positive(parts.du_first)
            + ln_if_positive(parts.dv_second)
            + ln_if_positive(parts.h21_first)
            + ln_if_positive(parts.h12_second),
        ln_if_positive(parts.du_second)
            + ln_if_positive(parts.dv_first)
            + ln_if_positive(parts.h21_second)
            + ln_if_positive(parts.h12_first),
        ln_if_positive(parts.du_second)
            + ln_if_positive(parts.dv_second)
            + ln_if_positive(parts.cdf_first)
            + parts.log_pdf_second,
    ];
    Ok(logsumexp(&term_logs))
}

pub fn cond_first_given_second(
    u1: f64,
    u2: f64,
    params: &KhoudrajiParams,
    clip_eps: f64,
) -> Result<f64, CopulaError> {
    let parts = evaluate_parts(u1, u2, params, clip_eps)?;
    Ok((parts.dv_first * parts.h12_first * parts.cdf_second
        + parts.cdf_first * parts.dv_second * parts.h12_second)
        .clamp(clip_eps, 1.0 - clip_eps))
}

pub fn cond_second_given_first(
    u1: f64,
    u2: f64,
    params: &KhoudrajiParams,
    clip_eps: f64,
) -> Result<f64, CopulaError> {
    let parts = evaluate_parts(u1, u2, params, clip_eps)?;
    Ok((parts.du_first * parts.h21_first * parts.cdf_second
        + parts.cdf_first * parts.du_second * parts.h21_second)
        .clamp(clip_eps, 1.0 - clip_eps))
}

pub fn inv_first_given_second(
    p: f64,
    u2: f64,
    params: &KhoudrajiParams,
    clip_eps: f64,
) -> Result<f64, CopulaError> {
    invert_monotone(
        |u1| cond_first_given_second(u1, u2, params, clip_eps),
        p,
        clip_eps,
    )
}

pub fn inv_second_given_first(
    u1: f64,
    p: f64,
    params: &KhoudrajiParams,
    clip_eps: f64,
) -> Result<f64, CopulaError> {
    invert_monotone(
        |u2| cond_second_given_first(u1, u2, params, clip_eps),
        p,
        clip_eps,
    )
}

fn evaluate_parts(
    u1: f64,
    u2: f64,
    params: &KhoudrajiParams,
    clip_eps: f64,
) -> Result<KhoudrajiParts, CopulaError> {
    let u1 = u1.clamp(clip_eps, 1.0 - clip_eps);
    let u2 = u2.clamp(clip_eps, 1.0 - clip_eps);
    let alpha = 1.0 - params.shape_first;
    let beta = 1.0 - params.shape_second;
    let a = params.shape_first;
    let b = params.shape_second;

    let x1 = power_margin(u1, alpha, clip_eps);
    let y1 = power_margin(u2, beta, clip_eps);
    let x2 = power_margin(u1, a, clip_eps);
    let y2 = power_margin(u2, b, clip_eps);

    Ok(KhoudrajiParts {
        cdf_first: params.first.cdf(x1, y1, clip_eps)?,
        cdf_second: params.second.cdf(x2, y2, clip_eps)?,
        h12_first: params.first.cond_first_given_second(x1, y1, clip_eps)?,
        h21_first: params.first.cond_second_given_first(x1, y1, clip_eps)?,
        h12_second: params.second.cond_first_given_second(x2, y2, clip_eps)?,
        h21_second: params.second.cond_second_given_first(x2, y2, clip_eps)?,
        log_pdf_first: params.first.log_pdf(x1, y1, clip_eps)?,
        log_pdf_second: params.second.log_pdf(x2, y2, clip_eps)?,
        du_first: power_derivative(u1, alpha),
        dv_first: power_derivative(u2, beta),
        du_second: power_derivative(u1, a),
        dv_second: power_derivative(u2, b),
    })
}

fn power_margin(u: f64, exponent: f64, clip_eps: f64) -> f64 {
    u.powf(exponent).clamp(clip_eps, 1.0 - clip_eps)
}

fn power_derivative(u: f64, exponent: f64) -> f64 {
    if exponent <= 0.0 {
        0.0
    } else {
        exponent * u.powf(exponent - 1.0)
    }
}

fn invert_monotone<F>(f: F, target: f64, clip_eps: f64) -> Result<f64, CopulaError>
where
    F: Fn(f64) -> Result<f64, CopulaError>,
{
    let target = target.clamp(clip_eps, 1.0 - clip_eps);
    let mut low = clip_eps;
    let mut high = 1.0 - clip_eps;
    let low_value = f(low)?;
    if low_value >= target {
        return Ok(low);
    }
    let high_value = f(high)?;
    if high_value <= target {
        return Ok(high);
    }
    for _ in 0..64 {
        let mid = 0.5 * (low + high);
        let value = f(mid)?;
        if value < target {
            low = mid;
        } else {
            high = mid;
        }
    }
    Ok(0.5 * (low + high))
}

fn ln_if_positive(value: f64) -> f64 {
    if value > 0.0 {
        value.ln()
    } else {
        f64::NEG_INFINITY
    }
}

fn logsumexp(values: &[f64]) -> f64 {
    let max = values
        .iter()
        .copied()
        .fold(f64::NEG_INFINITY, |left, right| left.max(right));
    if !max.is_finite() {
        return f64::NEG_INFINITY;
    }
    let sum = values.iter().map(|value| (*value - max).exp()).sum::<f64>();
    max + sum.ln()
}