# Story 4.1: Solver Trait Abstraction

Status: done

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## Story

As a numerical developer,
I want a generic Solver trait,
so that strategies are interchangeable.

## Acceptance Criteria

1. **Solver Trait Defined** (AC: #1)
   - Given a system of equations represented by `System`
   - When implementing a solver strategy
   - Then it must implement the common `Solver` trait
   - And the trait provides `solve()` and `with_timeout()` methods
   - And the trait is object-safe for dynamic dispatch

2. **Zero-Cost Abstraction via Enum Dispatch** (AC: #2)
   - Given multiple solver strategies (Newton-Raphson, Sequential Substitution)
   - When selecting a strategy at runtime
   - Then an enum `SolverStrategy` dispatches to the correct implementation
   - And there is no vtable overhead (monomorphization via enum)
   - And the pattern matches the architecture decision for static polymorphism

3. **Timeout Support** (AC: #3)
   - Given a solver with a configured timeout
   - When the solver exceeds the time budget
   - Then it stops immediately and returns `SolverError::Timeout`
   - And the timeout is configurable via `with_timeout(Duration)`

4. **Error Handling** (AC: #4)
   - Given a solver that fails to converge
   - When checking the result
   - Then it returns `SolverError::NonConvergence` with iteration count and final residual
   - And all error variants are documented and follow the `thiserror` pattern

## Tasks / Subtasks

- [x] Define `Solver` trait in `crates/solver/src/solver.rs` (AC: #1)
  - [x] Create new module `solver.rs` with `Solver` trait
  - [x] Define `solve(&mut self, system: &mut System) -> Result<ConvergedState, SolverError>`
  - [x] Define `with_timeout(self, timeout: Duration) -> Self` (builder pattern)
  - [x] Ensure trait is object-safe (no generic methods, no `Self` in return types)
  - [x] Add rustdoc with KaTeX equations for convergence criteria

- [x] Define `SolverError` enum (AC: #4)
  - [x] Add `NonConvergence { iterations: usize, final_residual: f64 }`
  - [x] Add `Timeout { timeout_ms: u64 }`
  - [x] Add `Divergence { reason: String }`
  - [x] Add `InvalidSystem { message: String }`
  - [x] Use `thiserror::Error` derive

- [x] Define `ConvergedState` struct (AC: #1)
  - [x] Store final state vector `Vec<f64>`
  - [x] Store iteration count `usize`
  - [x] Store final residual norm `f64`
  - [x] Store convergence status `ConvergenceStatus` enum

- [x] Define `SolverStrategy` enum (AC: #2)
  - [x] `NewtonRaphson(NewtonConfig)` variant
  - [x] `SequentialSubstitution(PicardConfig)` variant
  - [x] Implement `Solver` for `SolverStrategy` with match dispatch
  - [x] Add `Default` impl returning Newton-Raphson

- [x] Define configuration structs (AC: #2)
  - [x] `NewtonConfig` with max_iterations, tolerance, line_search flag
  - [x] `PicardConfig` with max_iterations, tolerance, relaxation_factor
  - [x] Both implement `Default` with sensible defaults (100 iterations, 1e-6 tolerance)

- [x] Add timeout infrastructure (AC: #3)
  - [x] Add `timeout: Option<Duration>` to config structs
  - [x] Add `with_timeout()` builder method
  - [x] Note: Actual timeout enforcement will be in Story 4.2/4.3; this story only defines the API

- [x] Update `crates/solver/src/lib.rs` (AC: #1)
  - [x] Add `pub mod solver;`
  - [x] Re-export `Solver`, `SolverError`, `SolverStrategy`, `ConvergedState`
  - [x] Re-export `NewtonConfig`, `PicardConfig`

- [x] Tests (AC: #1, #2, #3, #4)
  - [x] Test `Solver` trait object safety (`Box<dyn Solver>` compiles)
  - [x] Test `SolverStrategy::default()` returns Newton-Raphson
  - [x] Test `with_timeout()` returns modified config
  - [x] Test error variants have correct Display messages
  - [x] Test `ConvergedState` fields are accessible

## Dev Notes

### Epic Context

**Epic 4: Intelligent Solver Engine** — Solve any system with < 1s guarantee, Newton-Raphson ↔ Sequential Substitution fallback.

**Story Dependencies:**
- Epic 1 (Component trait) — done; `Component` trait provides `compute_residuals`, `jacobian_entries`
- Epic 2 (Fluid properties) — done; fluid backends available
- Epic 3 (System topology) — done; `System` struct with graph, state vector, residual/Jacobian assembly
- Story 4.2 (Newton-Raphson) — will implement `NewtonRaphson` solver
- Story 4.3 (Sequential Substitution) — will implement `SequentialSubstitution` solver
- Story 4.4 (Intelligent Fallback) — will use `SolverStrategy` enum for auto-switching

**FRs covered:** FR14 (Newton-Raphson), FR15 (Sequential Substitution), FR17 (timeout), FR18 (best state on timeout)

### Architecture Context

**Technical Stack:**
- Rust, `thiserror` for error handling, `tracing` for observability
- No new external crates; use `std::time::Duration` for timeout
- `nalgebra` will be used in Story 4.2 for linear algebra (not this story)

**Code Structure:**
- `crates/solver/src/solver.rs` — new file for `Solver` trait, `SolverError`, `SolverStrategy`, configs
- `crates/solver/src/lib.rs` — re-exports
- `crates/solver/src/system.rs` — existing `System` struct (no changes needed)

**Relevant Architecture Decisions:**
- **Solver Architecture:** Trait-based static polymorphism with enum dispatch [Source: architecture.md]
- **Zero-cost abstraction:** Enum dispatch avoids vtable overhead while allowing runtime selection
- **Error Handling:** Centralized error enum with `thiserror` [Source: architecture.md]
- **No panic policy:** All errors return `Result<T, SolverError>`

### Developer Context

**Existing Implementation:**
- **System struct** (`crates/solver/src/system.rs`):
  - `compute_residuals(&self, state: &StateSlice, residuals: &mut ResidualVector)`
  - `assemble_jacobian(&self, state: &StateSlice, jacobian: &mut JacobianBuilder)`
  - `state_vector_len()`, `edge_count()`, `node_count()`
  - `finalize()` must be called before solving
- **Component trait** (`crates/components/src/lib.rs`):
  - `compute_residuals`, `jacobian_entries`, `n_equations`, `get_ports`
  - Object-safe, used via `Box<dyn Component>`
- **JacobianBuilder** (`crates/components/src/lib.rs`):
  - `add_entry(row, col, value)`, `entries()`, `clear()`
- **TopologyError** (`crates/solver/src/error.rs`):
  - Pattern for error enum with `thiserror`

**Design Decisions:**
1. **Trait vs Enum:** The architecture specifies enum dispatch for zero-cost abstraction. The `Solver` trait defines the interface, and `SolverStrategy` enum provides the dispatch mechanism. Both are needed.
2. **Object Safety:** The `Solver` trait must be object-safe to allow `Box<dyn Solver>` for advanced use cases (e.g., user-provided custom solvers). This means:
   - No generic methods
   - No `Self` in return types
   - No methods that take `self` by value (use `&self` or `&mut self`)
3. **Timeout API:** This story defines the `with_timeout()` API. Actual enforcement requires `std::time::Instant` checks in the solve loop (Story 4.2/4.3).
4. **ConvergedState vs SystemState:** `ConvergedState` is the result type returned by solvers, containing metadata. `SystemState` (alias for `Vec<f64>`) is the state vector used during solving.

### Technical Requirements

**Solver Trait:**
```rust
pub trait Solver {
    /// Solve the system of equations.
    ///
    /// # Errors
    ///
    /// Returns `SolverError::NonConvergence` if max iterations exceeded.
    /// Returns `SolverError::Timeout` if time budget exceeded.
    fn solve(&mut self, system: &mut System) -> Result<ConvergedState, SolverError>;

    /// Set a timeout for the solver.
    ///
    /// If the solver exceeds this duration, it returns `SolverError::Timeout`.
    fn with_timeout(self, timeout: Duration) -> Self;
}
```

**SolverStrategy Enum:**
```rust
pub enum SolverStrategy {
    NewtonRaphson(NewtonConfig),
    SequentialSubstitution(PicardConfig),
}

impl Solver for SolverStrategy {
    fn solve(&mut self, system: &mut System) -> Result<ConvergedState, SolverError> {
        match self {
            Self::NewtonRaphson(cfg) => cfg.solve(system), // Story 4.2
            Self::SequentialSubstitution(cfg) => cfg.solve(system), // Story 4.3
        }
    }
    // ...
}
```

**Error Handling:**
- All errors use `thiserror::Error` derive
- Error messages are clear and actionable
- No panics in solver code paths

### Architecture Compliance

- **NewType pattern:** Use `Pressure`, `Temperature` from core where applicable (not directly in Solver trait, but in convergence criteria)
- **No bare f64** in public API where physical meaning exists
- **tracing:** Add `tracing::info!` for solver start/end, `tracing::debug!` for iterations
- **Result<T, E>:** All fallible operations return `Result`
- **approx:** Use for convergence checks in implementations (Story 4.2/4.3)

### Library/Framework Requirements

- **std::time::Duration** — timeout configuration
- **thiserror** — error enum derive (already in solver Cargo.toml)
- **tracing** — structured logging (already used in solver)

### File Structure Requirements

**New files:**
- `crates/solver/src/solver.rs` — Solver trait, SolverError, SolverStrategy, configs, ConvergedState

**Modified files:**
- `crates/solver/src/lib.rs` — add `pub mod solver;` and re-exports

**Tests:**
- Unit tests in `solver.rs` module (trait object safety, enum dispatch, error messages)
- Integration tests will be in Story 4.2/4.3 when actual solvers are implemented

### Testing Requirements

- **Trait object safety:** `let solver: Box<dyn Solver> = Box::new(NewtonConfig::default());` compiles
- **Enum dispatch:** `SolverStrategy::default().solve(&mut system)` dispatches correctly
- **Error Display:** All error variants have meaningful messages
- **Timeout builder:** `config.with_timeout(Duration::from_millis(100))` returns modified config
- **Default configs:** `NewtonConfig::default()` and `PicardConfig::default()` provide sensible values

### Previous Story Intelligence (3.5)

- Zero-flow regularization uses `MIN_MASS_FLOW_REGULARIZATION_KG_S` from core
- Components handle `OperationalState::Off` with zero mass flow
- Solver must handle systems with Off components (residuals/Jacobian already finite)
- Test pattern: `assert!(residuals.iter().all(|r| r.is_finite()))`

### Git Intelligence

Recent commits show:
- Epic 3 completion (multi-circuit, thermal coupling, zero-flow)
- Component framework mature (Compressor, HeatExchanger, Pipe, etc.)
- Fluid backends ready (CoolProp, Tabular, Cache)
- Ready for solver implementation

### Project Context Reference

- **FR14:** [Source: epics.md — System can solve equations using Newton-Raphson method]
- **FR15:** [Source: epics.md — System can solve equations using Sequential Substitution (Picard) method]
- **FR17:** [Source: epics.md — Solver respects configurable time budget (timeout)]
- **FR18:** [Source: epics.md — On timeout, solver returns best known state with NonConverged status]
- **Solver Architecture:** [Source: architecture.md — Trait-based static polymorphism with enum dispatch]
- **Error Handling:** [Source: architecture.md — Centralized error enum with thiserror]
- **Component Trait:** [Source: crates/components/src/lib.rs — Object-safe trait pattern]

### Story Completion Status

- **Status:** review
- **Completion note:** Story context created. Solver trait, SolverError, SolverStrategy enum, and config structs implemented. Actual solver algorithms in Stories 4.2 and 4.3.

## Change Log

- 2026-02-18: Story 4.1 created from create-story workflow. Epic 4 kickoff. Ready for dev.
- 2026-02-18: Story 4.1 implemented. All tasks complete. 74 tests pass (63 unit + 4 integration + 7 doc-tests). Status → review.
- 2026-02-18: Code review completed. Fixed: (1) doc-test `rust,ignore` → `rust,no_run` (now compiles), (2) added 3 dispatch tests for `SolverStrategy::solve()`, (3) fixed broken doc link in error.rs. 78 tests pass (66 unit + 4 integration + 8 doc-tests). Status → done.

## Dev Agent Record

### Agent Model Used

claude-sonnet-4-5 (via Cline)

### Debug Log References

- Doc-test failures on first run: `with_timeout` not in scope in doc examples. Fixed by adding `use entropyk_solver::solver::Solver;` to both doc examples.

### Completion Notes List

- ✅ Created `crates/solver/src/solver.rs` with `Solver` trait, `SolverError` (4 variants), `ConvergedState`, `ConvergenceStatus`, `SolverStrategy` enum, `NewtonConfig`, `PicardConfig`
- ✅ `Solver` trait is object-safe: `solve(&mut self, system: &mut System)` uses `&mut self`; `with_timeout` is `where Self: Sized` so it is excluded from the vtable
- ✅ `SolverStrategy` enum provides zero-cost static dispatch via `match` (no vtable)
- ✅ `SolverStrategy::default()` returns `NewtonRaphson(NewtonConfig::default())`
- ✅ `with_timeout()` builder pattern implemented on all three types (`NewtonConfig`, `PicardConfig`, `SolverStrategy`)
- ✅ `SolverError` uses `thiserror::Error` derive with 4 variants: `NonConvergence`, `Timeout`, `Divergence`, `InvalidSystem`
- ✅ `NewtonConfig` and `PicardConfig` stubs return `SolverError::InvalidSystem` (full implementation in Stories 4.2/4.3)
- ✅ `tracing::info!` added to solver dispatch and stub implementations
- ✅ Updated `crates/solver/src/lib.rs` with `pub mod solver;` and all re-exports
- ✅ 19 unit tests covering all ACs; 74 total tests pass with 0 regressions
- ✅ Code review: 3 issues fixed (doc-test, dispatch tests, doc link); 78 tests now pass

### File List

- `crates/solver/src/solver.rs` (new)
- `crates/solver/src/lib.rs` (modified)
- `crates/solver/src/error.rs` (modified — doc link fix)