qudit-tensor 0.3.4

use std::collections::BTreeMap;
use std::collections::BTreeSet;
use std::collections::HashMap;
use std::sync::Arc;
use std::sync::Mutex;

use crate::network::network::NetworkEdge;
use qudit_core::ComplexScalar;
use qudit_core::ParamInfo;
use qudit_core::Radices;
use qudit_core::UnitaryMatrix;
use qudit_expr::ExpressionCache;
use qudit_expr::ExpressionId;
use qudit_expr::TensorExpression;
use qudit_expr::UnitaryExpression;

use super::index::ContractionIndex;
use super::index::IndexDirection;
use super::index::IndexId;
use super::index::IndexSize;
use super::index::NetworkIndex;
use super::index::TensorIndex;
use super::network::QuditTensorNetwork;
use super::tensor::QuditTensor;

#[derive(Debug, Clone, Copy, Hash, PartialEq, Eq, PartialOrd, Ord)]
enum Wire {
    Empty,
    Closed,
    Connected(usize, usize), // node_id, local_index_id
}

impl Wire {
    pub fn is_empty(&self) -> bool {
        match self {
            Wire::Empty => true,
            Wire::Closed => false,
            Wire::Connected(_, _) => false,
        }
    }

    pub fn is_active(&self) -> bool {
        match self {
            Wire::Empty => true,
            Wire::Closed => false,
            Wire::Connected(_, _) => true,
        }
    }
}

#[derive(Debug, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
enum NetworkBuilderIndex {
    Front(usize),
    Rear(usize),
    Batch(String),
    Contraction(usize),
}

pub struct QuditCircuitTensorNetworkBuilder {
    tensors: Vec<QuditTensor>,
    local_to_network_index_map: Vec<Vec<NetworkBuilderIndex>>,
    radices: Radices,

    expressions: Arc<Mutex<ExpressionCache>>,

    /// Pointer to front (left in math/right in circuit diagram) of the network for each qudit.
    front: Vec<Wire>,

    /// Pointer to rear (right in math/left in circuit diagram) of the network for each qudit.
    rear: Vec<Wire>,
    batch_indices: HashMap<String, IndexSize>,
    contracted_indices: Vec<ContractionIndex>,
}

impl QuditCircuitTensorNetworkBuilder {
    pub fn new(radices: Radices, expressions: Option<Arc<Mutex<ExpressionCache>>>) -> Self {
        let expressions = match expressions {
            Some(cache) => cache,
            None => ExpressionCache::new_shared(),
        };

        QuditCircuitTensorNetworkBuilder {
            tensors: vec![],
            local_to_network_index_map: vec![],
            front: vec![Wire::Empty; radices.len()],
            rear: vec![Wire::Empty; radices.len()],
            batch_indices: HashMap::new(),
            radices,
            expressions,
            contracted_indices: vec![],
        }
    }

    /// Output indices stick out from the front of the Circuit Tensor Network.
    ///
    /// These correspond to wires exiting a circuit in a normal circuit diagram.
    pub fn open_output_indices(&self) -> Vec<usize> {
        self.front
            .iter()
            .enumerate()
            .filter(|(_, wire)| wire.is_active())
            .map(|(id, _)| id)
            .collect()
    }

    /// Input indices stick out from the rear of the Circuit Tensor Network.
    ///
    /// These correspond to wires entering a circuit in a normal circuit diagram.
    pub fn open_input_indices(&self) -> Vec<usize> {
        self.rear
            .iter()
            .enumerate()
            .filter(|(_, wire)| wire.is_active())
            .map(|(id, _)| id)
            .collect()
    }

    pub fn num_open_output_indices(&self) -> usize {
        self.front.iter().filter(|wire| wire.is_active()).count()
    }

    pub fn num_open_input_indices(&self) -> usize {
        self.rear.iter().filter(|wire| wire.is_active()).count()
    }

    pub fn expression_get(&mut self, expression: TensorExpression) -> ExpressionId {
        let result = { self.expressions.lock().unwrap().lookup(&expression) };
        match result {
            None => self.expressions.lock().unwrap().insert(expression),
            Some(id) => id,
        }
    }

    pub fn prepend_expression(
        mut self,
        expression: TensorExpression,
        param_info: ParamInfo,
        input_index_map: Vec<usize>,
        output_index_map: Vec<usize>,
        batch_index_map: Vec<String>,
    ) -> Self {
        let indices = expression.indices().to_owned();
        let id = self.expression_get(expression);
        let tensor = QuditTensor::new(indices, id, param_info);
        self.prepend(tensor, input_index_map, output_index_map, batch_index_map)
    }

    /// Prepend a tensor onto the circuit network.
    ///
    /// # Arguments
    ///
    /// * `tensor` - The tensor to prepend
    ///
    /// * `input_qudit_map` - An array of qudit ids. It maps the tensors input indices to the
    ///   qudits at the front of the network that will be connected. `input_qudit_map[i] ==
    ///   qudit_id` implies that `tensor.input_indices()[i]` will be connected to the
    ///   `front[qudit_id]` edge.
    ///
    /// * `output_qudit_map` - An array of qudit ids. It maps the tensors output indices to
    ///   the qudits at the front of the network which will become the new open edges for
    ///   the network front. `output_qudit_map[i] == qudit_id` implies that
    ///   `tensor.output_tensor_indices()[i]` will be the open edge on qudit_id after the
    ///   operation.
    ///
    /// * `batch_index_map` - An array of strings. It provides names for the tensors batch
    ///   indices. All batch indices in the network with the same name identify the same
    ///   network indices. These indices can appear on both sides of a pairwise contraction
    ///   without being contracted over.
    ///
    /// # Panics
    ///
    /// - If the length of an index map doesn't match the number of indices the tensor has in that
    ///   direction.
    ///
    /// - If any of the `qudit_ids` referenced by the index maps are invalid or out of bounds.
    ///
    /// - If the size of a tensor's index doesn't match the radix of the qudit it's mapped to.
    ///
    /// - If a batch index with the same name exists in the network, they must have the same
    ///   dimension.
    pub fn prepend(
        mut self,
        tensor: QuditTensor,
        input_index_map: Vec<usize>,
        output_index_map: Vec<usize>,
        batch_index_map: Vec<String>,
    ) -> Self {
        // Check error conditions
        let batch_tensor_indices = tensor.batch_indices();
        let output_tensor_indices = tensor.output_indices();
        let input_tensor_indices = tensor.input_indices();
        let batch_tensor_index_sizes = tensor.batch_sizes();
        let output_tensor_index_sizes = tensor.output_sizes();
        let input_tensor_index_sizes = tensor.input_sizes();

        if batch_tensor_indices.len() != batch_index_map.len() {
            panic!("Batch tensor indices and batch qudit map lengths do not match");
        }

        if output_tensor_indices.len() != output_index_map.len() {
            panic!("Output tensor indices and output qudit map lengths do not match");
        }

        if input_tensor_indices.len() != input_index_map.len() {
            panic!("Input tensor indices and input qudit map lengths do not match");
        }

        for (i, qudit_id) in output_index_map.iter().enumerate() {
            if *qudit_id >= self.radices.len() {
                panic!("Qudit id {qudit_id} is out of bounds from tensor's output map");
            }
            assert_eq!(
                self.radices[*qudit_id], output_tensor_index_sizes[i],
                "Tensor index size doesn't match mapped qudit radix.",
            );
        }

        for (i, qudit_id) in input_index_map.iter().enumerate() {
            if *qudit_id >= self.radices.len() {
                panic!("Qudit id {qudit_id} is out of bounds from tensor's input map");
            }
            assert_eq!(
                self.radices[*qudit_id], input_tensor_index_sizes[i],
                "Tensor index size doesn't match mapped qudit radix.",
            );
        }

        let num_qudits_involved = input_index_map
            .iter()
            .chain(output_index_map.iter())
            .copied()
            .collect::<BTreeSet<_>>()
            .len();
        if num_qudits_involved > input_index_map.len()
            && num_qudits_involved > output_index_map.len()
        {
            // Every wire involved needs to do one of three things:
            //  1. Pass through the tensor
            //  2. Start at this tensor
            //  3. End at this tensor
            // This check among others enforces these constraints
            panic!("Invalid input and output index map for QuditCircuitTensorNetworkBuilder.");
        }

        // Permute tensor and index maps so that indices are sequential
        // For example, a CNOT applied to (1, 0) will be permuted,
        // so that a permuted cnot is applied to (0, 1). This makes further processing easier.

        let argsorted_output_index_map = {
            let mut argsorted_indices = (0..output_index_map.len()).collect::<Vec<_>>();
            argsorted_indices.sort_by_key(|&i| output_index_map[i]);
            argsorted_indices
        };
        let argsorted_input_index_map = {
            let mut argsorted_indices = (0..input_index_map.len()).collect::<Vec<_>>();
            argsorted_indices.sort_by_key(|&i| input_index_map[i]);
            argsorted_indices
        };
        let perm = (0..batch_index_map.len())
            .chain(
                argsorted_output_index_map
                    .iter()
                    .cloned()
                    .map(|idx| idx + batch_index_map.len()),
            )
            .chain(
                argsorted_input_index_map
                    .iter()
                    .cloned()
                    .map(|idx| idx + output_index_map.len() + batch_index_map.len()),
            )
            .collect::<Vec<_>>();
        let sequential_expr_id = self.expressions.lock().unwrap().permute_reshape(
            tensor.expression,
            perm,
            tensor.shape(),
        );
        let sequential_indices = self.expressions.lock().unwrap().indices(sequential_expr_id);

        let tensor = QuditTensor::new(sequential_indices, sequential_expr_id, tensor.param_info);
        let output_index_map = argsorted_output_index_map
            .into_iter()
            .map(|i| output_index_map[i])
            .collect::<Vec<_>>();
        let input_index_map = argsorted_input_index_map
            .into_iter()
            .map(|i| input_index_map[i])
            .collect::<Vec<_>>();

        // Add Tensor to network
        let tensor_id = self.tensors.len();
        let mut tensor_local_to_network_map = vec![None; tensor.num_indices()];
        self.tensors.push(tensor);

        // Handle Input Indices
        let mut new_contraction_ids: BTreeMap<usize, usize> = BTreeMap::new();
        for (tensor_input_idx_id, qudit_id) in input_index_map.iter().enumerate() {
            let local_index_id = input_tensor_indices[tensor_input_idx_id];
            match self.front[*qudit_id] {
                Wire::Empty => {
                    self.rear[*qudit_id] = Wire::Connected(tensor_id, local_index_id);
                    tensor_local_to_network_map[local_index_id] =
                        Some(NetworkBuilderIndex::Rear(*qudit_id));
                }
                Wire::Closed => {
                    panic!("Cannot contract tensor index with a closed qudit.");
                }
                Wire::Connected(existing_tensor_id, existing_local_index_id) => {
                    // Record a new or update existing contraction between existing_tensor_id and
                    // tensor_id.

                    let contraction_id = *new_contraction_ids
                        .entry(existing_tensor_id)
                        .or_insert_with(|| {
                            let id = self.contracted_indices.len();
                            self.contracted_indices.push(ContractionIndex {
                                left_id: tensor_id,
                                right_id: existing_tensor_id,
                                total_dimension: 1,
                            });
                            id
                        });

                    self.contracted_indices[contraction_id].total_dimension *=
                        usize::from(self.radices[*qudit_id]);
                    self.local_to_network_index_map[existing_tensor_id][existing_local_index_id] =
                        NetworkBuilderIndex::Contraction(contraction_id);
                    tensor_local_to_network_map[local_index_id] =
                        Some(NetworkBuilderIndex::Contraction(contraction_id));
                }
            }

            if !output_index_map.contains(qudit_id) {
                // The network wire becomes inactive/closed if this tensor is the first one on it
                // without a corresponding open (output) edge leaving it.
                self.front[*qudit_id] = Wire::Closed;
            }
        }

        // Handle Output Indices
        for (tensor_output_idx_id, qudit_id) in output_index_map.iter().enumerate() {
            let local_index_id = output_tensor_indices[tensor_output_idx_id];
            // Either needs to start here or pass through
            if !input_index_map.contains(qudit_id) {
                match self.front[*qudit_id] {
                    Wire::Empty => {
                        // Make the start of this wire this tensor by closing rear
                        self.rear[*qudit_id] = Wire::Closed;
                    }
                    Wire::Closed => {}
                    Wire::Connected(_, _) => {
                        panic!(
                            "Cannot map a tensor output qudit over an active edge without connecting on the input side."
                        );
                    }
                }
            }
            tensor_local_to_network_map[local_index_id] =
                Some(NetworkBuilderIndex::Front(*qudit_id));
            self.front[*qudit_id] = Wire::Connected(tensor_id, local_index_id);
        }

        // Handle Batch Indices
        for (tensor_batch_idx_id, batch_idx_name) in batch_index_map.into_iter().enumerate() {
            let local_index_id = batch_tensor_indices[tensor_batch_idx_id];
            let batch_tensor_index_size = batch_tensor_index_sizes[tensor_batch_idx_id];

            match self.batch_indices.get(&batch_idx_name) {
                Some(index_size) => {
                    assert_eq!(batch_tensor_index_size, *index_size);
                }
                None => {
                    self.batch_indices
                        .insert(batch_idx_name.clone(), batch_tensor_index_size);
                }
            }

            tensor_local_to_network_map[local_index_id] =
                Some(NetworkBuilderIndex::Batch(batch_idx_name));
        }

        // Finalize tensor addition
        self.local_to_network_index_map.push(
            tensor_local_to_network_map
                .into_iter()
                .map(|idx| match idx {
                    Some(idx) => idx,
                    None => panic!("Failed to map local tensor index to network index."),
                })
                .collect(),
        );

        self
    }

    // pub fn append(
    //     self,
    //     tensor: QuditTensor,
    //     left_qudit_map: Vec<usize>,
    //     right_qudit_map: Vec<usize>,
    //     batch_index_map: Vec<String>,
    // ) -> Self {
    //     todo!()
    // }

    pub fn prepend_unitary<C: ComplexScalar>(
        mut self,
        utry: UnitaryMatrix<C>,
        qudits: Vec<usize>,
    ) -> Self {
        let expr: TensorExpression = UnitaryExpression::from(utry).into();
        let indices = expr.indices().to_owned();
        let id = self.expression_get(expr);
        self.prepend(
            QuditTensor::new(indices, id, ParamInfo::empty()),
            qudits.clone(),
            qudits,
            vec![],
        )
    }

    pub fn trace_wire(mut self, front_qudit: usize, rear_qudit: usize) -> Self {
        assert_eq!(self.radices[front_qudit], self.radices[rear_qudit]);
        assert!(self.front[front_qudit].is_active() && self.rear[rear_qudit].is_active());

        if self.front[front_qudit].is_empty() {
            let identity =
                UnitaryExpression::identity("Identity", [self.radices[front_qudit]]).into();
            self = self.prepend_expression(
                identity,
                ParamInfo::empty(),
                [front_qudit].into(),
                [front_qudit].into(),
                vec![],
            );
        }

        if self.rear[rear_qudit].is_empty() {
            let identity =
                UnitaryExpression::identity("Identity", [self.radices[rear_qudit]]).into();
            self = self.prepend_expression(
                identity,
                ParamInfo::empty(),
                [rear_qudit].into(),
                [rear_qudit].into(),
                vec![],
            );
        }

        match (&self.front[front_qudit], &self.rear[rear_qudit]) {
            (Wire::Connected(tid_f, local_id_f), Wire::Connected(tid_r, local_id_r)) => {
                debug_assert_eq!(
                    self.local_to_network_index_map[*tid_f][*local_id_f],
                    NetworkBuilderIndex::Front(front_qudit)
                );
                debug_assert_eq!(
                    self.local_to_network_index_map[*tid_r][*local_id_r],
                    NetworkBuilderIndex::Rear(rear_qudit)
                );

                // Find an existing contraction between tid_f and tid_r or create new one
                let contraction_id = {
                    let mut contraction_id = None;
                    for net_index in &self.local_to_network_index_map[*tid_f] {
                        if let NetworkBuilderIndex::Contraction(cid) = net_index {
                            let contraction = &self.contracted_indices[*cid];
                            if contraction.left_id == *tid_r || contraction.right_id == *tid_r {
                                contraction_id = Some(*cid);
                                break;
                            }
                        }
                    }
                    contraction_id.unwrap_or_else(|| {
                        let cid = self.contracted_indices.len();
                        self.contracted_indices.push(ContractionIndex {
                            left_id: *tid_f,
                            right_id: *tid_r,
                            total_dimension: self.radices[front_qudit].into(),
                        });
                        cid
                    })
                };

                self.local_to_network_index_map[*tid_f][*local_id_f] =
                    NetworkBuilderIndex::Contraction(contraction_id);
                self.local_to_network_index_map[*tid_r][*local_id_r] =
                    NetworkBuilderIndex::Contraction(contraction_id);
            }
            _ => panic!("Cannot connect a closed wire to another wire."),
        }

        self.front[front_qudit] = Wire::Closed;
        self.rear[rear_qudit] = Wire::Closed;
        self
    }

    pub fn trace_all_open_wires(mut self) -> Self {
        assert_eq!(
            self.num_open_input_indices(),
            self.num_open_output_indices()
        );
        for (f, r) in self
            .open_output_indices()
            .into_iter()
            .zip(self.open_input_indices())
        {
            self = self.trace_wire(f, r);
        }
        self
    }

    pub fn build(self) -> QuditTensorNetwork {
        let QuditCircuitTensorNetworkBuilder {
            mut tensors,
            mut local_to_network_index_map,
            expressions,
            front,
            rear,
            batch_indices,
            contracted_indices,
            ..
        } = self;

        // Build network indices, while building map from builder to network
        let mut indices = Vec::new();
        let mut builder_to_network_map = HashMap::new();

        let sorted_batch_indices = {
            let mut as_vec: Vec<(String, IndexSize)> = batch_indices.into_iter().collect();
            as_vec.sort();
            as_vec
        };

        for (batch_idx_name, batch_idx_size) in sorted_batch_indices.into_iter() {
            let index_id = indices.len();
            indices.push(NetworkIndex::Output(TensorIndex::new(
                IndexDirection::Batch,
                index_id,
                batch_idx_size,
            )));
            builder_to_network_map.insert(NetworkBuilderIndex::Batch(batch_idx_name), index_id);
        }

        for (qudit_id, wire) in front.into_iter().enumerate() {
            if wire.is_empty() {
                // Cannot have empty indices in network, so we need to explicitly add identity.
                let identity_expression: TensorExpression =
                    UnitaryExpression::identity("Identity", [self.radices[qudit_id]]).into();
                let identity_indices = identity_expression.indices().to_owned();
                let lookup_temp = expressions.lock().unwrap().lookup(&identity_expression);
                let identity_expr_id = match lookup_temp {
                    None => expressions.lock().unwrap().insert(identity_expression),
                    Some(id) => id,
                };
                let identity_tensor =
                    QuditTensor::new(identity_indices, identity_expr_id, ParamInfo::empty());
                tensors.push(identity_tensor);
                local_to_network_index_map.push(vec![
                    NetworkBuilderIndex::Front(qudit_id),
                    NetworkBuilderIndex::Rear(qudit_id),
                ]);
            }

            if wire.is_active() {
                let index_id = indices.len();
                indices.push(NetworkIndex::Output(TensorIndex::new(
                    IndexDirection::Output,
                    index_id,
                    self.radices[qudit_id].into(),
                )));
                builder_to_network_map.insert(NetworkBuilderIndex::Front(qudit_id), index_id);
            }
        }

        for (qudit_id, wire) in rear.into_iter().enumerate() {
            if wire.is_active() {
                let index_id = indices.len();
                indices.push(NetworkIndex::Output(TensorIndex::new(
                    IndexDirection::Input,
                    index_id,
                    self.radices[qudit_id].into(),
                )));
                builder_to_network_map.insert(NetworkBuilderIndex::Rear(qudit_id), index_id);
            }
        }

        for (cidx_id, contraction_index) in contracted_indices.into_iter().enumerate() {
            let index_id = indices.len();
            indices.push(NetworkIndex::Contracted(contraction_index));
            builder_to_network_map.insert(NetworkBuilderIndex::Contraction(cidx_id), index_id);
        }

        let mut index_edges: Vec<NetworkEdge> =
            indices.into_iter().map(|x| (x, BTreeSet::new())).collect();

        let new_index_map = local_to_network_index_map
            .into_iter()
            .enumerate()
            .map(|(tid, tidx_map)| {
                tidx_map
                    .into_iter()
                    .map(|index| {
                        let network_index = builder_to_network_map[&index];
                        index_edges[network_index].1.insert(tid);
                        network_index
                    })
                    .collect::<Vec<IndexId>>()
            })
            .collect::<Vec<Vec<IndexId>>>();

        QuditTensorNetwork::new(tensors, expressions, new_index_map, index_edges)
    }
}