pmcore/routines/

output.rs

use crate::prelude::*;
use crate::structs::psi::Psi;
use crate::structs::theta::Theta;
use anyhow::{bail, Context, Result};
use csv::WriterBuilder;
use faer::linalg::zip::IntoView;
use faer_ext::IntoNdarray;
use ndarray::{Array, Array1, Array2, Axis};
use pharmsol::prelude::data::*;
use pharmsol::prelude::simulator::Equation;
use serde::Serialize;
// use pharmsol::Cache;
use crate::routines::settings::Settings;
use faer::{Col, Mat};
use std::fs::{create_dir_all, File, OpenOptions};
use std::path::{Path, PathBuf};

/// Defines the result objects from an NPAG run
/// An [NPResult] contains the necessary information to generate predictions and summary statistics
#[derive(Debug)]
pub struct NPResult<E: Equation> {
    equation: E,
    data: Data,
    theta: Theta,
    psi: Psi,
    w: Col<f64>,
    objf: f64,
    cycles: usize,
    converged: bool,
    par_names: Vec<String>,
    settings: Settings,
    cyclelog: CycleLog,
}

#[allow(clippy::too_many_arguments)]
impl<E: Equation> NPResult<E> {
    /// Create a new NPResult object
    pub fn new(
        equation: E,
        data: Data,
        theta: Theta,
        psi: Psi,
        w: Col<f64>,
        objf: f64,
        cycles: usize,
        converged: bool,
        settings: Settings,
        cyclelog: CycleLog,
    ) -> Self {
        // TODO: Add support for fixed and constant parameters

        let par_names = settings.parameters().names();

        Self {
            equation,
            data,
            theta,
            psi,
            w,
            objf,
            cycles,
            converged,
            par_names,
            settings,
            cyclelog,
        }
    }

    pub fn cycles(&self) -> usize {
        self.cycles
    }

    pub fn objf(&self) -> f64 {
        self.objf
    }

    pub fn converged(&self) -> bool {
        self.converged
    }

    pub fn get_theta(&self) -> &Theta {
        &self.theta
    }

    pub fn get_psi(&self) -> &Psi {
        &self.psi
    }

    pub fn get_w(&self) -> &Col<f64> {
        &self.w
    }

    pub fn write_outputs(&self) -> Result<()> {
        if self.settings.output().write {
            self.settings.write()?;
            let idelta: f64 = self.settings.predictions().idelta;
            let tad = self.settings.predictions().tad;
            self.cyclelog.write(&self.settings)?;
            self.write_obs().context("Failed to write observations")?;
            self.write_theta().context("Failed to write theta")?;
            self.write_obspred()
                .context("Failed to write observed-predicted file")?;
            self.write_pred(idelta, tad)
                .context("Failed to write predictions")?;
            self.write_covs().context("Failed to write covariates")?;
            if !(self.w.nrows() == 0) {
                self.write_posterior()
                    .context("Failed to write posterior")?;
            }
        }
        Ok(())
    }

    /// Writes the observations and predictions to a single file
    pub fn write_obspred(&self) -> Result<()> {
        tracing::debug!("Writing observations and predictions...");

        #[derive(Debug, Clone, Serialize)]
        struct Row {
            id: String,
            time: f64,
            outeq: usize,
            block: usize,
            obs: f64,
            pop_mean: f64,
            pop_median: f64,
            post_mean: f64,
            post_median: f64,
        }

        let theta: Array2<f64> = self
            .theta
            .matrix()
            .clone()
            .as_mut()
            .into_ndarray()
            .to_owned();
        let w: Array1<f64> = self.w.clone().into_view().iter().cloned().collect();
        let psi: Array2<f64> = self.psi.matrix().as_ref().into_ndarray().to_owned();

        let (post_mean, post_median) = posterior_mean_median(&theta, &psi, &w)
            .context("Failed to calculate posterior mean and median")?;

        let (pop_mean, pop_median) = population_mean_median(&theta, &w)
            .context("Failed to calculate posterior mean and median")?;

        let subjects = self.data.get_subjects();
        if subjects.len() != post_mean.nrows() {
            bail!(
                "Number of subjects: {} and number of posterior means: {} do not match",
                subjects.len(),
                post_mean.nrows()
            );
        }

        let outputfile = OutputFile::new(&self.settings.output().path, "op.csv")?;
        let mut writer = WriterBuilder::new()
            .has_headers(true)
            .from_writer(&outputfile.file);

        for (i, subject) in subjects.iter().enumerate() {
            for occasion in subject.occasions() {
                let id = subject.id();
                let occ = occasion.index();

                let subject = Subject::from_occasions(id.clone(), vec![occasion.clone()]);

                // Population predictions
                let pop_mean_pred = self
                    .equation
                    .simulate_subject(&subject, &pop_mean.to_vec(), None)
                    .0
                    .get_predictions()
                    .clone();

                let pop_median_pred = self
                    .equation
                    .simulate_subject(&subject, &pop_median.to_vec(), None)
                    .0
                    .get_predictions()
                    .clone();

                // Posterior predictions
                let post_mean_spp: Vec<f64> = post_mean.row(i).to_vec();
                let post_mean_pred = self
                    .equation
                    .simulate_subject(&subject, &post_mean_spp, None)
                    .0
                    .get_predictions()
                    .clone();
                let post_median_spp: Vec<f64> = post_median.row(i).to_vec();
                let post_median_pred = self
                    .equation
                    .simulate_subject(&subject, &post_median_spp, None)
                    .0
                    .get_predictions()
                    .clone();
                assert_eq!(
                    pop_mean_pred.len(),
                    pop_median_pred.len(),
                    "The number of predictions do not match (pop_mean vs pop_median)"
                );

                assert_eq!(
                    post_mean_pred.len(),
                    post_median_pred.len(),
                    "The number of predictions do not match (post_mean vs post_median)"
                );

                assert_eq!(
                    pop_mean_pred.len(),
                    post_mean_pred.len(),
                    "The number of predictions do not match (pop_mean vs post_mean)"
                );

                for (((pop_mean_pred, pop_median_pred), post_mean_pred), post_median_pred) in
                    pop_mean_pred
                        .iter()
                        .zip(pop_median_pred.iter())
                        .zip(post_mean_pred.iter())
                        .zip(post_median_pred.iter())
                {
                    let row = Row {
                        id: id.clone(),
                        time: pop_mean_pred.time(),
                        outeq: pop_mean_pred.outeq(),
                        block: occ,
                        obs: pop_mean_pred.observation(),
                        pop_mean: pop_mean_pred.prediction(),
                        pop_median: pop_median_pred.prediction(),
                        post_mean: post_mean_pred.prediction(),
                        post_median: post_median_pred.prediction(),
                    };
                    writer.serialize(row)?;
                }
            }
        }
        writer.flush()?;
        tracing::info!(
            "Observations with predictions written to {:?}",
            &outputfile.get_relative_path()
        );
        Ok(())
    }

    /// Writes theta, which contains the population support points and their associated probabilities
    /// Each row is one support point, the last column being probability
    pub fn write_theta(&self) -> Result<()> {
        tracing::debug!("Writing population parameter distribution...");

        let theta = &self.theta;
        let w: Vec<f64> = self.w.clone().into_view().iter().cloned().collect();
        /* let w = if self.w.len() != theta.matrix().nrows() {
                   tracing::warn!("Number of weights and number of support points do not match. Setting all weights to 0.");
                   Array1::zeros(theta.matrix().nrows())
               } else {
                   self.w.clone()
               };
        */
        let outputfile = OutputFile::new(&self.settings.output().path, "theta.csv")
            .context("Failed to create output file for theta")?;

        let mut writer = WriterBuilder::new()
            .has_headers(true)
            .from_writer(&outputfile.file);

        // Create the headers
        let mut theta_header = self.par_names.clone();
        theta_header.push("prob".to_string());
        writer.write_record(&theta_header)?;

        // Write contents
        for (theta_row, &w_val) in theta.matrix().row_iter().zip(w.iter()) {
            let mut row: Vec<String> = theta_row.iter().map(|&val| val.to_string()).collect();
            row.push(w_val.to_string());
            writer.write_record(&row)?;
        }
        writer.flush()?;
        tracing::info!(
            "Population parameter distribution written to {:?}",
            &outputfile.get_relative_path()
        );
        Ok(())
    }

    /// Writes the posterior support points for each individual
    pub fn write_posterior(&self) -> Result<()> {
        tracing::debug!("Writing posterior parameter probabilities...");
        let theta = &self.theta;
        let w = &self.w;
        let psi = &self.psi;

        // Calculate the posterior probabilities
        let posterior = posterior(psi, w)?;

        // Create the output folder if it doesn't exist
        let outputfile = match OutputFile::new(&self.settings.output().path, "posterior.csv") {
            Ok(of) => of,
            Err(e) => {
                tracing::error!("Failed to create output file: {}", e);
                return Err(e.context("Failed to create output file"));
            }
        };

        // Create a new writer
        let mut writer = WriterBuilder::new()
            .has_headers(true)
            .from_writer(&outputfile.file);

        // Create the headers
        writer.write_field("id")?;
        writer.write_field("point")?;
        theta.param_names().iter().for_each(|name| {
            writer.write_field(name).unwrap();
        });
        writer.write_field("prob")?;
        writer.write_record(None::<&[u8]>)?;

        // Write contents
        let subjects = self.data.get_subjects();
        posterior.row_iter().enumerate().for_each(|(i, row)| {
            let subject = subjects.get(i).unwrap();
            let id = subject.id();

            row.iter().enumerate().for_each(|(spp, prob)| {
                writer.write_field(id.clone()).unwrap();
                writer.write_field(i.to_string()).unwrap();

                theta
                    .matrix()
                    .row(spp)
                    .iter()
                    .enumerate()
                    .for_each(|(_, val)| {
                        writer.write_field(val.to_string()).unwrap();
                    });

                writer.write_field(prob.to_string()).unwrap();
                writer.write_record(None::<&[u8]>).unwrap();
            });
        });

        writer.flush()?;
        tracing::info!(
            "Posterior parameters written to {:?}",
            &outputfile.get_relative_path()
        );

        Ok(())
    }

    /// Write the observations, which is the reformatted input data
    pub fn write_obs(&self) -> Result<()> {
        tracing::debug!("Writing observations...");
        let outputfile = OutputFile::new(&self.settings.output().path, "obs.csv")?;
        write_pmetrics_observations(&self.data, &outputfile.file)?;
        tracing::info!(
            "Observations written to {:?}",
            &outputfile.get_relative_path()
        );
        Ok(())
    }

    /// Writes the predictions
    pub fn write_pred(&self, idelta: f64, tad: f64) -> Result<()> {
        tracing::debug!("Writing predictions...");
        let data = self.data.expand(idelta, tad);

        let theta: Array2<f64> = self
            .theta
            .matrix()
            .clone()
            .as_mut()
            .into_ndarray()
            .to_owned();
        let w: Array1<f64> = self.w.clone().into_view().iter().cloned().collect();
        let psi: Array2<f64> = self.psi.matrix().as_ref().into_ndarray().to_owned();

        let (post_mean, post_median) = posterior_mean_median(&theta, &psi, &w)
            .context("Failed to calculate posterior mean and median")?;

        let (pop_mean, pop_median) = population_mean_median(&theta, &w)
            .context("Failed to calculate population mean and median")?;

        let subjects = data.get_subjects();
        if subjects.len() != post_mean.nrows() {
            bail!("Number of subjects and number of posterior means do not match");
        }

        let outputfile = OutputFile::new(&self.settings.output().path, "pred.csv")?;
        let mut writer = WriterBuilder::new()
            .has_headers(true)
            .from_writer(&outputfile.file);

        #[derive(Debug, Clone, Serialize)]
        struct Row {
            id: String,
            time: f64,
            outeq: usize,
            block: usize,
            pop_mean: f64,
            pop_median: f64,
            post_mean: f64,
            post_median: f64,
        }

        for (i, subject) in subjects.iter().enumerate() {
            for occasion in subject.occasions() {
                let id = subject.id();
                let block = occasion.index();

                // Create a new subject with only the current occasion
                let subject = Subject::from_occasions(id.clone(), vec![occasion.clone()]);

                // Population predictions
                let pop_mean_pred = self
                    .equation
                    .simulate_subject(&subject, &pop_mean.to_vec(), None)
                    .0
                    .get_predictions()
                    .clone();
                let pop_median_pred = self
                    .equation
                    .simulate_subject(&subject, &pop_median.to_vec(), None)
                    .0
                    .get_predictions()
                    .clone();

                // Posterior predictions
                let post_mean_spp: Vec<f64> = post_mean.row(i).to_vec();
                let post_mean_pred = self
                    .equation
                    .simulate_subject(&subject, &post_mean_spp, None)
                    .0
                    .get_predictions()
                    .clone();
                let post_median_spp: Vec<f64> = post_median.row(i).to_vec();
                let post_median_pred = self
                    .equation
                    .simulate_subject(&subject, &post_median_spp, None)
                    .0
                    .get_predictions()
                    .clone();

                // Write predictions for each time point
                for (((pop_mean, pop_median), post_mean), post_median) in pop_mean_pred
                    .iter()
                    .zip(pop_median_pred.iter())
                    .zip(post_mean_pred.iter())
                    .zip(post_median_pred.iter())
                {
                    let row = Row {
                        id: id.clone(),
                        time: pop_mean.time(),
                        outeq: pop_mean.outeq(),
                        block,
                        pop_mean: pop_mean.prediction(),
                        pop_median: pop_median.prediction(),
                        post_mean: post_mean.prediction(),
                        post_median: post_median.prediction(),
                    };
                    writer.serialize(row)?;
                }
            }
        }
        writer.flush()?;
        tracing::info!(
            "Predictions written to {:?}",
            &outputfile.get_relative_path()
        );
        Ok(())
    }

    /// Writes the covariates
    pub fn write_covs(&self) -> Result<()> {
        tracing::debug!("Writing covariates...");
        let outputfile = OutputFile::new(&self.settings.output().path, "covs.csv")?;
        let mut writer = WriterBuilder::new()
            .has_headers(true)
            .from_writer(&outputfile.file);

        // Collect all unique covariate names
        let mut covariate_names = std::collections::HashSet::new();
        for subject in self.data.get_subjects() {
            for occasion in subject.occasions() {
                if let Some(cov) = occasion.get_covariates() {
                    let covmap = cov.covariates();
                    for cov_name in covmap.keys() {
                        covariate_names.insert(cov_name.clone());
                    }
                }
            }
        }
        let mut covariate_names: Vec<String> = covariate_names.into_iter().collect();
        covariate_names.sort(); // Ensure consistent order

        // Write the header row: id, time, block, covariate names
        let mut headers = vec!["id", "time", "block"];
        headers.extend(covariate_names.iter().map(|s| s.as_str()));
        writer.write_record(&headers)?;

        // Write the data rows
        for subject in self.data.get_subjects() {
            for occasion in subject.occasions() {
                if let Some(cov) = occasion.get_covariates() {
                    let covmap = cov.covariates();

                    for event in occasion.get_events(&None, &None, false) {
                        let time = match event {
                            Event::Bolus(bolus) => bolus.time(),
                            Event::Infusion(infusion) => infusion.time(),
                            Event::Observation(observation) => observation.time(),
                        };

                        let mut row: Vec<String> = Vec::new();
                        row.push(subject.id().clone());
                        row.push(time.to_string());
                        row.push(occasion.index().to_string());

                        // Add covariate values to the row
                        for cov_name in &covariate_names {
                            if let Some(cov) = covmap.get(cov_name) {
                                if let Some(value) = cov.interpolate(time) {
                                    row.push(value.to_string());
                                } else {
                                    row.push(String::new());
                                }
                            } else {
                                row.push(String::new());
                            }
                        }

                        writer.write_record(&row)?;
                    }
                }
            }
        }

        writer.flush()?;
        tracing::info!(
            "Covariates written to {:?}",
            &outputfile.get_relative_path()
        );
        Ok(())
    }
}

/// An [NPCycle] object contains the summary of a cycle
/// It holds the following information:
/// - `cycle`: The cycle number
/// - `objf`: The objective function value
/// - `gamlam`: The assay noise parameter, either gamma or lambda
/// - `theta`: The support points and their associated probabilities
/// - `nspp`: The number of support points
/// - `delta_objf`: The change in objective function value from last cycle
/// - `converged`: Whether the algorithm has reached convergence
#[derive(Debug, Clone)]
pub struct NPCycle {
    pub cycle: usize,
    pub objf: f64,
    pub gamlam: f64,
    pub theta: Theta,
    pub nspp: usize,
    pub delta_objf: f64,
    pub converged: bool,
}

impl NPCycle {
    pub fn new(
        cycle: usize,
        objf: f64,
        gamlam: f64,
        theta: Theta,
        nspp: usize,
        delta_objf: f64,
        converged: bool,
    ) -> Self {
        Self {
            cycle,
            objf,
            gamlam,
            theta,
            nspp,
            delta_objf,
            converged,
        }
    }

    pub fn placeholder() -> Self {
        Self {
            cycle: 0,
            objf: 0.0,
            gamlam: 0.0,
            theta: Theta::new(),
            nspp: 0,
            delta_objf: 0.0,
            converged: false,
        }
    }
}

/// This holdes a vector of [NPCycle] objects to provide a more detailed log
#[derive(Debug, Clone)]
pub struct CycleLog {
    pub cycles: Vec<NPCycle>,
}

impl CycleLog {
    pub fn new() -> Self {
        Self { cycles: Vec::new() }
    }

    pub fn push(&mut self, cycle: NPCycle) {
        self.cycles.push(cycle);
    }

    pub fn write(&self, settings: &Settings) -> Result<()> {
        tracing::debug!("Writing cycles...");
        let outputfile = OutputFile::new(&settings.output().path, "cycles.csv")?;
        let mut writer = WriterBuilder::new()
            .has_headers(false)
            .from_writer(&outputfile.file);

        // Write headers
        writer.write_field("cycle")?;
        writer.write_field("converged")?;
        writer.write_field("neg2ll")?;
        writer.write_field("gamlam")?;
        writer.write_field("nspp")?;

        let parameter_names = settings.parameters().names();
        for param_name in &parameter_names {
            writer.write_field(format!("{}.mean", param_name))?;
            writer.write_field(format!("{}.median", param_name))?;
            writer.write_field(format!("{}.sd", param_name))?;
        }

        writer.write_record(None::<&[u8]>)?;

        for cycle in &self.cycles {
            writer.write_field(format!("{}", cycle.cycle))?;
            writer.write_field(format!("{}", cycle.converged))?;
            writer.write_field(format!("{}", cycle.objf))?;
            writer.write_field(format!("{}", cycle.gamlam))?;
            writer
                .write_field(format!("{}", cycle.theta.matrix().nrows()))
                .unwrap();

            for param in cycle.theta.matrix().col_iter() {
                let param_values: Vec<f64> = param.iter().cloned().collect();

                let mean: f64 = param_values.iter().sum::<f64>() / param_values.len() as f64;
                let median = median(param_values.clone());
                let std = param_values.iter().map(|x| (x - mean).powi(2)).sum::<f64>()
                    / (param_values.len() as f64 - 1.0);

                writer.write_field(format!("{}", mean))?;
                writer.write_field(format!("{}", median))?;
                writer.write_field(format!("{}", std))?;
            }
            writer.write_record(None::<&[u8]>)?;
        }
        writer.flush()?;
        tracing::info!("Cycles written to {:?}", &outputfile.get_relative_path());
        Ok(())
    }
}

impl Default for CycleLog {
    fn default() -> Self {
        Self::new()
    }
}

pub fn posterior(psi: &Psi, w: &Col<f64>) -> Result<Mat<f64>> {
    if psi.matrix().ncols() != w.nrows() {
        bail!(
            "Number of rows in psi ({}) and number of weights ({}) do not match.",
            psi.matrix().nrows(),
            w.nrows()
        );
    }

    let psi_matrix = psi.matrix();
    let py = psi_matrix * w;

    let posterior = Mat::from_fn(psi_matrix.nrows(), psi_matrix.ncols(), |i, j| {
        psi_matrix.get(i, j) * w.get(j) / py.get(i)
    });

    Ok(posterior)
}

pub fn median(data: Vec<f64>) -> f64 {
    let mut data = data.clone();
    data.sort_by(|a, b| a.partial_cmp(b).unwrap());

    let size = data.len();
    match size {
        even if even % 2 == 0 => {
            let fst = data.get(even / 2 - 1).unwrap();
            let snd = data.get(even / 2).unwrap();
            (fst + snd) / 2.0
        }
        odd => *data.get(odd / 2_usize).unwrap(),
    }
}

fn weighted_median(data: &Array1<f64>, weights: &Array1<f64>) -> f64 {
    // Ensure the data and weights arrays have the same length
    assert_eq!(
        data.len(),
        weights.len(),
        "The length of data and weights must be the same"
    );
    assert!(
        weights.iter().all(|&x| x >= 0.0),
        "Weights must be non-negative, weights: {:?}",
        weights
    );

    // Create a vector of tuples (data, weight)
    let mut weighted_data: Vec<(f64, f64)> = data
        .iter()
        .zip(weights.iter())
        .map(|(&d, &w)| (d, w))
        .collect();

    // Sort the vector by the data values
    weighted_data.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap());

    // Calculate the cumulative sum of weights
    let total_weight: f64 = weights.sum();
    let mut cumulative_sum = 0.0;

    for (i, &(_, weight)) in weighted_data.iter().enumerate() {
        cumulative_sum += weight;

        if cumulative_sum == total_weight / 2.0 {
            // If the cumulative sum equals half the total weight, average this value with the next
            if i + 1 < weighted_data.len() {
                return (weighted_data[i].0 + weighted_data[i + 1].0) / 2.0;
            } else {
                return weighted_data[i].0;
            }
        } else if cumulative_sum > total_weight / 2.0 {
            return weighted_data[i].0;
        }
    }

    unreachable!("The function should have returned a value before reaching this point.");
}

pub fn population_mean_median(
    theta: &Array2<f64>,
    w: &Array1<f64>,
) -> Result<(Array1<f64>, Array1<f64>)> {
    let w = if w.is_empty() {
        tracing::warn!("w.len() == 0, setting all weights to 1/n");
        Array1::from_elem(theta.nrows(), 1.0 / theta.nrows() as f64)
    } else {
        w.clone()
    };
    // Check for compatible sizes
    if theta.nrows() != w.len() {
        bail!(
            "Number of parameters and number of weights do not match. Theta: {}, w: {}",
            theta.nrows(),
            w.len()
        );
    }

    let mut mean = Array1::zeros(theta.ncols());
    let mut median = Array1::zeros(theta.ncols());

    for (i, (mn, mdn)) in mean.iter_mut().zip(&mut median).enumerate() {
        // Calculate the weighted mean
        let col = theta.column(i).to_owned() * w.to_owned();
        *mn = col.sum();

        // Calculate the median
        let ct = theta.column(i);
        let mut params = vec![];
        let mut weights = vec![];
        for (ti, wi) in ct.iter().zip(w.clone()) {
            params.push(*ti);
            weights.push(wi);
        }

        *mdn = weighted_median(&Array::from(params), &Array::from(weights));
    }

    Ok((mean, median))
}

pub fn posterior_mean_median(
    theta: &Array2<f64>,
    psi: &Array2<f64>,
    w: &Array1<f64>,
) -> Result<(Array2<f64>, Array2<f64>)> {
    let mut mean = Array2::zeros((0, theta.ncols()));
    let mut median = Array2::zeros((0, theta.ncols()));

    let w = if w.is_empty() {
        tracing::warn!("w is empty, setting all weights to 1/n");
        Array1::from_elem(theta.nrows(), 1.0 / theta.nrows() as f64)
    } else {
        w.clone()
    };

    // Check for compatible sizes
    if theta.nrows() != w.len() || theta.nrows() != psi.ncols() || psi.ncols() != w.len() {
        bail!("Number of parameters and number of weights do not match, theta.nrows(): {}, w.len(): {}, psi.ncols(): {}", theta.nrows(), w.len(), psi.ncols());
    }

    // Normalize psi to get probabilities of each spp for each id
    let mut psi_norm: Array2<f64> = Array2::zeros((0, psi.ncols()));
    for (i, row) in psi.axis_iter(Axis(0)).enumerate() {
        let row_w = row.to_owned() * w.to_owned();
        let row_sum = row_w.sum();
        let row_norm = if row_sum == 0.0 {
            tracing::warn!("Sum of row {} of psi is 0.0, setting that row to 1/n", i);
            Array1::from_elem(psi.ncols(), 1.0 / psi.ncols() as f64)
        } else {
            &row_w / row_sum
        };
        psi_norm.push_row(row_norm.view())?;
    }
    if psi_norm.iter().any(|&x| x.is_nan()) {
        dbg!(&psi);
        bail!("NaN values found in psi_norm");
    };

    // Transpose normalized psi to get ID (col) by prob (row)
    // let psi_norm_transposed = psi_norm.t();

    // For each subject..
    for probs in psi_norm.axis_iter(Axis(0)) {
        let mut post_mean: Vec<f64> = Vec::new();
        let mut post_median: Vec<f64> = Vec::new();

        // For each parameter
        for pars in theta.axis_iter(Axis(1)) {
            // Calculate the mean
            let weighted_par = &probs * &pars;
            let the_mean = weighted_par.sum();
            post_mean.push(the_mean);

            // Calculate the median
            let median = weighted_median(&pars.to_owned(), &probs.to_owned());
            post_median.push(median);
        }

        mean.push_row(Array::from(post_mean.clone()).view())?;
        median.push_row(Array::from(post_median.clone()).view())?;
    }

    Ok((mean, median))
}

/// Contains all the necessary information of an output file
#[derive(Debug)]
pub struct OutputFile {
    pub file: File,
    pub relative_path: PathBuf,
}

impl OutputFile {
    pub fn new(folder: &str, file_name: &str) -> Result<Self> {
        let relative_path = Path::new(&folder).join(file_name);

        if let Some(parent) = relative_path.parent() {
            create_dir_all(parent)
                .with_context(|| format!("Failed to create directories for {:?}", parent))?;
        }

        let file = OpenOptions::new()
            .write(true)
            .create(true)
            .truncate(true)
            .open(&relative_path)
            .with_context(|| format!("Failed to open file: {:?}", relative_path))?;

        Ok(OutputFile {
            file,
            relative_path,
        })
    }

    pub fn get_relative_path(&self) -> &Path {
        &self.relative_path
    }
}

pub fn write_pmetrics_observations(data: &Data, file: &std::fs::File) -> Result<()> {
    let mut writer = WriterBuilder::new().has_headers(true).from_writer(file);

    writer.write_record(["id", "block", "time", "out", "outeq"])?;
    for subject in data.get_subjects() {
        for occasion in subject.occasions() {
            for event in occasion.get_events(&None, &None, false) {
                if let Event::Observation(event) = event {
                    writer.write_record([
                        subject.id(),
                        &occasion.index().to_string(),
                        &event.time().to_string(),
                        &event.value().to_string(),
                        &event.outeq().to_string(),
                    ])?;
                }
            }
        }
    }
    Ok(())
}

#[cfg(test)]
mod tests {
    use super::median;

    #[test]
    fn test_median_odd() {
        let data = vec![1.0, 3.0, 2.0];
        assert_eq!(median(data), 2.0);
    }

    #[test]
    fn test_median_even() {
        let data = vec![1.0, 2.0, 3.0, 4.0];
        assert_eq!(median(data), 2.5);
    }

    #[test]
    fn test_median_single() {
        let data = vec![42.0];
        assert_eq!(median(data), 42.0);
    }

    #[test]
    fn test_median_sorted() {
        let data = vec![5.0, 10.0, 15.0, 20.0, 25.0];
        assert_eq!(median(data), 15.0);
    }

    #[test]
    fn test_median_unsorted() {
        let data = vec![10.0, 30.0, 20.0, 50.0, 40.0];
        assert_eq!(median(data), 30.0);
    }

    #[test]
    fn test_median_with_duplicates() {
        let data = vec![1.0, 2.0, 2.0, 3.0, 4.0];
        assert_eq!(median(data), 2.0);
    }

    use super::weighted_median;
    use ndarray::Array1;

    #[test]
    fn test_weighted_median_simple() {
        let data = Array1::from(vec![1.0, 2.0, 3.0]);
        let weights = Array1::from(vec![0.2, 0.5, 0.3]);
        assert_eq!(weighted_median(&data, &weights), 2.0);
    }

    #[test]
    fn test_weighted_median_even_weights() {
        let data = Array1::from(vec![1.0, 2.0, 3.0, 4.0]);
        let weights = Array1::from(vec![0.25, 0.25, 0.25, 0.25]);
        assert_eq!(weighted_median(&data, &weights), 2.5);
    }

    #[test]
    fn test_weighted_median_single_element() {
        let data = Array1::from(vec![42.0]);
        let weights = Array1::from(vec![1.0]);
        assert_eq!(weighted_median(&data, &weights), 42.0);
    }

    #[test]
    #[should_panic(expected = "The length of data and weights must be the same")]
    fn test_weighted_median_mismatched_lengths() {
        let data = Array1::from(vec![1.0, 2.0, 3.0]);
        let weights = Array1::from(vec![0.1, 0.2]);
        weighted_median(&data, &weights);
    }

    #[test]
    fn test_weighted_median_all_same_elements() {
        let data = Array1::from(vec![5.0, 5.0, 5.0, 5.0]);
        let weights = Array1::from(vec![0.1, 0.2, 0.3, 0.4]);
        assert_eq!(weighted_median(&data, &weights), 5.0);
    }

    #[test]
    #[should_panic(expected = "Weights must be non-negative")]
    fn test_weighted_median_negative_weights() {
        let data = Array1::from(vec![1.0, 2.0, 3.0, 4.0]);
        let weights = Array1::from(vec![0.2, -0.5, 0.5, 0.8]);
        assert_eq!(weighted_median(&data, &weights), 4.0);
    }

    #[test]
    fn test_weighted_median_unsorted_data() {
        let data = Array1::from(vec![3.0, 1.0, 4.0, 2.0]);
        let weights = Array1::from(vec![0.1, 0.3, 0.4, 0.2]);
        assert_eq!(weighted_median(&data, &weights), 2.5);
    }

    #[test]
    fn test_weighted_median_with_zero_weights() {
        let data = Array1::from(vec![1.0, 2.0, 3.0, 4.0]);
        let weights = Array1::from(vec![0.0, 0.0, 1.0, 0.0]);
        assert_eq!(weighted_median(&data, &weights), 3.0);
    }
}