causal_hub/models/graphs/

undirected.rs

use ndarray::prelude::*;
use serde::{
    Deserialize, Deserializer, Serialize, Serializer,
    de::{MapAccess, Visitor},
    ser::SerializeMap,
};

use crate::{
    impl_json_io,
    models::{Graph, HasLabels},
    types::{Error, Labels, Result, Set},
};

/// A struct representing an undirected graph using an adjacency matrix.
#[derive(Clone, Debug)]
pub struct UnGraph {
    labels: Labels,
    adjacency_matrix: Array2<bool>,
}

impl UnGraph {
    /// Check if a vertex is within bounds.
    #[inline]
    fn check_vertex(&self, x: usize) -> Result<()> {
        if x >= self.labels.len() {
            return Err(Error::IndexOutOfBounds(x));
        }
        Ok(())
    }

    /// Returns the neighbors of a set of vertices.
    ///
    /// # Arguments
    ///
    /// * `x` - The set of vertices for which to find the neighbors.
    ///
    /// # Errors
    ///
    /// * If any vertex is out of bounds.
    ///
    /// # Returns
    ///
    /// The neighbors of the vertex.
    ///
    pub fn neighbors(&self, x: &Set<usize>) -> Result<Set<usize>> {
        // Check if the vertices are within bounds.
        x.iter().try_for_each(|&v| self.check_vertex(v))?;

        // Iterate over all vertices and filter the ones that are neighbors.
        let mut neighbors: Set<_> = x
            .iter()
            .flat_map(|&v| {
                self.adjacency_matrix
                    .row(v)
                    .into_iter()
                    .enumerate()
                    .filter_map(|(y, &has_edge)| has_edge.then_some(y))
            })
            .collect();

        // Sort the neighbors.
        neighbors.sort();

        // Return the neighbors.
        Ok(neighbors)
    }
}

impl HasLabels for UnGraph {
    fn labels(&self) -> &Labels {
        &self.labels
    }
}

impl Graph for UnGraph {
    fn empty<I, V>(labels: I) -> Result<Self>
    where
        I: IntoIterator<Item = V>,
        V: AsRef<str>,
    {
        // Initialize labels counter.
        let mut n = 0;
        // Collect the labels.
        let mut labels: Labels = labels
            .into_iter()
            .inspect(|_| n += 1)
            .map(|x| x.as_ref().to_owned())
            .collect();

        // Check for duplicate labels.
        if labels.len() != n {
            return Err(Error::NonUniqueLabels());
        }

        // Sort the labels.
        labels.sort();

        // Initialize the adjacency matrix with `false` values.
        let adjacency_matrix: Array2<_> = Array::from_elem((n, n), false);

        Ok(Self {
            labels,
            adjacency_matrix,
        })
    }

    fn complete<I, V>(labels: I) -> Result<Self>
    where
        I: IntoIterator<Item = V>,
        V: AsRef<str>,
    {
        // Construct the empty graph.
        let mut graph = Self::empty(labels)?;
        // Fill the adjacency matrix with `true` values.
        graph.adjacency_matrix.fill(true);
        // Remove the self-loops.
        graph.adjacency_matrix.diag_mut().fill(false);

        Ok(graph)
    }

    fn vertices(&self) -> Set<usize> {
        (0..self.labels.len()).collect()
    }

    fn has_vertex(&self, x: usize) -> bool {
        // Check if the vertex is within bounds.
        x < self.labels.len()
    }

    fn add_vertex<V>(&mut self, x: V) -> usize
    where
        V: AsRef<str>,
    {
        // Cast the vertex label.
        let x = x.as_ref().to_owned();
        // Try to insert the vertex label.
        let (i, f) = self.labels.insert_full(x.clone());

        // If the vertex was already present ...
        if !f {
            // ... return early.
            return i;
        }

        // Sort the labels.
        self.labels.sort();

        // Assert the vertex has been added.
        debug_assert!(self.labels.contains(&x));
        // Assert the labels are still sorted.
        debug_assert!(self.labels.iter().is_sorted());

        // Compute the index of the new vertex:
        // since labels are unique and sorted, it is
        // the number of labels preceding the new one.
        let i = self
            .labels
            .iter()
            .filter(|&y| y.as_str() < x.as_str())
            .count();

        // Compute the size of the adjacency matrix.
        let n = self.adjacency_matrix.nrows();
        // Allocate the new adjacency matrix.
        let mut adjacency_matrix = Array2::from_elem((n + 1, n + 1), false);
        // Copy the top-left block.
        adjacency_matrix
            .slice_mut(s![0..i, 0..i])
            .assign(&self.adjacency_matrix.slice(s![0..i, 0..i]));
        // Copy the top-right block.
        adjacency_matrix
            .slice_mut(s![0..i, (i + 1)..(n + 1)])
            .assign(&self.adjacency_matrix.slice(s![0..i, i..n]));
        // Copy the bottom-left block.
        adjacency_matrix
            .slice_mut(s![(i + 1)..(n + 1), 0..i])
            .assign(&self.adjacency_matrix.slice(s![i..n, 0..i]));
        // Copy the bottom-right block.
        adjacency_matrix
            .slice_mut(s![(i + 1)..(n + 1), (i + 1)..(n + 1)])
            .assign(&self.adjacency_matrix.slice(s![i..n, i..n]));
        // Replace the old adjacency matrix.
        self.adjacency_matrix = adjacency_matrix;

        // Assert the label set is still consistent with the adjacency matrix shape.
        debug_assert_eq!(self.labels.len(), self.adjacency_matrix.nrows());
        // Assert the adjacency matrix is still square.
        debug_assert!(self.adjacency_matrix.is_square());

        // Return the new vertex index.
        i
    }

    fn del_vertex(&mut self, x: usize) -> bool {
        // Remove the vertex label, shifting the subsequent indices.
        let Some(label) = self.labels.shift_remove_index(x) else {
            // If the vertex was not present, return early.
            return false;
        };

        // Assert the vertex has been removed.
        debug_assert!(!self.labels.contains(&label));
        // Assert the labels are still sorted.
        debug_assert!(self.labels.iter().is_sorted());

        // Compute the size of the adjacency matrix.
        let n = self.adjacency_matrix.nrows();
        // Allocate the new adjacency matrix.
        let mut adjacency_matrix = Array2::from_elem((n - 1, n - 1), false);
        // Copy the top-left block.
        adjacency_matrix
            .slice_mut(s![0..x, 0..x])
            .assign(&self.adjacency_matrix.slice(s![0..x, 0..x]));
        // Copy the top-right block.
        adjacency_matrix
            .slice_mut(s![0..x, x..(n - 1)])
            .assign(&self.adjacency_matrix.slice(s![0..x, (x + 1)..n]));
        // Copy the bottom-left block.
        adjacency_matrix
            .slice_mut(s![x..(n - 1), 0..x])
            .assign(&self.adjacency_matrix.slice(s![(x + 1)..n, 0..x]));
        // Copy the bottom-right block.
        adjacency_matrix
            .slice_mut(s![x..(n - 1), x..(n - 1)])
            .assign(&self.adjacency_matrix.slice(s![(x + 1)..n, (x + 1)..n]));
        // Replace the old adjacency matrix.
        self.adjacency_matrix = adjacency_matrix;

        // Assert the label set is still consistent with the adjacency matrix shape.
        debug_assert_eq!(self.labels.len(), self.adjacency_matrix.nrows());
        // Assert the adjacency matrix is still square.
        debug_assert!(self.adjacency_matrix.is_square());

        true
    }

    fn edges(&self) -> Set<(usize, usize)> {
        // Iterate over the adjacency matrix and collect the edges.
        self.adjacency_matrix
            .indexed_iter()
            .filter_map(|((x, y), &has_edge)| {
                // Since the graph is undirected, we only need to check one direction.
                (has_edge && x <= y).then_some((x, y))
            })
            .collect()
    }

    fn has_edge(&self, x: usize, y: usize) -> Result<bool> {
        // Check if the vertices are within bounds.
        self.check_vertex(x)?;
        self.check_vertex(y)?;

        Ok(self.adjacency_matrix[[x, y]])
    }

    fn add_edge(&mut self, x: usize, y: usize) -> Result<bool> {
        // Check if the vertices are within bounds.
        self.check_vertex(x)?;
        self.check_vertex(y)?;

        // Check if the edge already exists.
        if self.adjacency_matrix[[x, y]] {
            return Ok(false);
        }

        // Add the edge.
        self.adjacency_matrix[[x, y]] = true;
        self.adjacency_matrix[[y, x]] = true;

        Ok(true)
    }

    fn del_edge(&mut self, x: usize, y: usize) -> Result<bool> {
        // Check if the vertices are within bounds.
        self.check_vertex(x)?;
        self.check_vertex(y)?;

        // Check if the edge exists.
        if !self.adjacency_matrix[[x, y]] {
            return Ok(false);
        }

        // Delete the edge.
        self.adjacency_matrix[[x, y]] = false;
        self.adjacency_matrix[[y, x]] = false;

        Ok(true)
    }

    fn select(&self, x: &Set<usize>) -> Result<Self>
    where
        Self: Sized,
    {
        // Check if the vertices are within bounds.
        x.iter().try_for_each(|&v| self.check_vertex(v))?;

        // Clone and sort the vertices.
        let mut x = x.clone();
        x.sort();

        // Allocate the new labels.
        let labels: Labels = x.iter().map(|&v| self.labels[v].clone()).collect();
        // Allocate the new adjacency matrix.
        let mut adjacency_matrix: Array2<bool> = Array::from_elem((x.len(), x.len()), false);
        // Fill the new adjacency matrix.
        for (i, &v_i) in x.iter().enumerate() {
            for (j, &v_j) in x.iter().enumerate() {
                adjacency_matrix[[i, j]] = self.adjacency_matrix[[v_i, v_j]];
            }
        }

        Self::from_adjacency_matrix(labels, adjacency_matrix)
    }

    fn from_adjacency_matrix(
        mut labels: Labels,
        mut adjacency_matrix: Array2<bool>,
    ) -> Result<Self> {
        // Check labels and adjacency matrix dimensions match.
        if labels.len() != adjacency_matrix.nrows() {
            return Err(Error::IncompatibleShape(
                &labels.len().to_string(),
                &adjacency_matrix.nrows().to_string(),
            ));
        }
        // Check adjacency matrix must be square.
        if adjacency_matrix.nrows() != adjacency_matrix.ncols() {
            return Err(Error::IncompatibleShape(
                &adjacency_matrix.nrows().to_string(),
                &adjacency_matrix.ncols().to_string(),
            ));
        }
        // Check the adjacency matrix is symmetric.
        if adjacency_matrix != adjacency_matrix.t() {
            return Err(Error::InvalidParameter(
                "adjacency_matrix",
                "Adjacency matrix must be symmetric.",
            ));
        }

        // Check if the labels are sorted.
        if !labels.is_sorted() {
            // Allocate the sorted indices.
            let mut indices: Vec<usize> = (0..labels.len()).collect();
            // Sort the indices based on the labels.
            indices.sort_by_key(|&i| &labels[i]);
            // Sort the labels.
            labels.sort();
            // Allocate a new adjacency matrix.
            let mut new_adjacency_matrix = adjacency_matrix.clone();
            // Fill the rows.
            indices.iter().enumerate().for_each(|(i, &j)| {
                new_adjacency_matrix
                    .row_mut(i)
                    .assign(&adjacency_matrix.row(j));
            });
            // Update the adjacency matrix.
            adjacency_matrix = new_adjacency_matrix;
            // Allocate a new adjacency matrix.
            let mut new_adjacency_matrix = adjacency_matrix.clone();
            // Fill the columns.
            indices.iter().enumerate().for_each(|(i, &j)| {
                new_adjacency_matrix
                    .column_mut(i)
                    .assign(&adjacency_matrix.column(j));
            });
            // Update the adjacency matrix.
            adjacency_matrix = new_adjacency_matrix;
        }

        // Create a new graph instance.
        Ok(Self {
            labels,
            adjacency_matrix,
        })
    }

    #[inline]
    fn to_adjacency_matrix(&self) -> Array2<bool> {
        self.adjacency_matrix.clone()
    }
}

impl Serialize for UnGraph {
    fn serialize<S>(&self, serializer: S) -> std::result::Result<S::Ok, S::Error>
    where
        S: Serializer,
    {
        // Convert adjacency matrix to a flat format.
        let edges = self
            .edges()
            .into_iter()
            .map(|(x, y)| {
                let x = self.index_to_label(x).map_err(serde::ser::Error::custom)?;
                let y = self.index_to_label(y).map_err(serde::ser::Error::custom)?;
                Ok((x.to_owned(), y.to_owned()))
            })
            .collect::<std::result::Result<Vec<_>, S::Error>>()?;

        // Allocate the map.
        let mut map = serializer.serialize_map(Some(3))?;

        // Serialize labels.
        map.serialize_entry("labels", &self.labels)?;
        // Serialize edges.
        map.serialize_entry("edges", &edges)?;
        // Serialize type.
        map.serialize_entry("type", "ungraph")?;

        // Finalize the map serialization.
        map.end()
    }
}

impl<'de> Deserialize<'de> for UnGraph {
    fn deserialize<D>(deserializer: D) -> std::result::Result<Self, D::Error>
    where
        D: Deserializer<'de>,
    {
        #[derive(Deserialize)]
        #[serde(field_identifier, rename_all = "snake_case")]
        enum Field {
            Labels,
            Edges,
            Type,
        }

        struct UnGraphVisitor;

        impl<'de> Visitor<'de> for UnGraphVisitor {
            type Value = UnGraph;

            fn expecting(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result {
                formatter.write_str("struct UnGraph")
            }

            fn visit_map<V>(self, mut map: V) -> std::result::Result<UnGraph, V::Error>
            where
                V: MapAccess<'de>,
            {
                use serde::de::Error as E;

                // Allocate fields
                let mut labels = None;
                let mut edges = None;
                let mut type_ = None;

                // Parse the map.
                while let Some(key) = map.next_key()? {
                    match key {
                        Field::Labels => {
                            if labels.is_some() {
                                return Err(E::duplicate_field("labels"));
                            }
                            labels = Some(map.next_value()?);
                        }
                        Field::Edges => {
                            if edges.is_some() {
                                return Err(E::duplicate_field("edges"));
                            }
                            edges = Some(map.next_value()?);
                        }
                        Field::Type => {
                            if type_.is_some() {
                                return Err(E::duplicate_field("type"));
                            }
                            type_ = Some(map.next_value()?);
                        }
                    }
                }

                // Check required fields.
                let labels = labels.ok_or_else(|| E::missing_field("labels"))?;
                let edges = edges.ok_or_else(|| E::missing_field("edges"))?;

                // Check type is correct.
                let type_: String = type_.ok_or_else(|| E::missing_field("type"))?;
                if type_ != "ungraph" {
                    return Err(E::custom(format!(
                        "Invalid type for UnGraph: expected 'ungraph', found '{type_}'"
                    )));
                }

                // Convert edges to an adjacency matrix.
                let labels: Labels = labels;
                let edges: Vec<(String, String)> = edges;
                let shape = (labels.len(), labels.len());
                let mut adjacency_matrix = Array2::from_elem(shape, false);
                edges.into_iter().try_for_each(|(x, y)| {
                    let x = labels
                        .get_index_of(&x)
                        .ok_or_else(|| E::custom(format!("Vertex `{x}` label does not exist")))?;
                    let y = labels
                        .get_index_of(&y)
                        .ok_or_else(|| E::custom(format!("Vertex `{y}` label does not exist")))?;
                    adjacency_matrix[(x, y)] = true;
                    Ok(())
                })?;

                UnGraph::from_adjacency_matrix(labels, adjacency_matrix)
                    .map_err(|evidence| E::custom(evidence.to_string()))
            }
        }

        const FIELDS: &[&str] = &["labels", "edges", "type"];

        deserializer.deserialize_struct("UnGraph", FIELDS, UnGraphVisitor)
    }
}

// Implement `JsonIO` for `UnGraph`.
impl_json_io!(UnGraph);