Module integrate 

Numerical integration and ODE solvers for solvr.

This module provides Runtime-first numerical methods for:

• Quadrature: Numerical integration of functions (definite integrals)
• ODE Solvers: Initial value problem solvers for ordinary differential equations
• BVP Solvers: Boundary value problem solvers

Architecture

All algorithms implement the IntegrationAlgorithms trait and use Tensor<R> for data, enabling GPU acceleration and batch operations.

Quadrature Methods

• IntegrationAlgorithms::trapezoid - Trapezoidal rule with tensor support
• IntegrationAlgorithms::simpson - Simpson’s rule with tensor support
• IntegrationAlgorithms::fixed_quad - Gaussian quadrature with tensor functions
• IntegrationAlgorithms::quad - Adaptive Gauss-Kronrod quadrature
• IntegrationAlgorithms::romberg - Romberg integration via Richardson extrapolation
• IntegrationAlgorithms::tanh_sinh - Double-exponential for endpoint singularities
• IntegrationAlgorithms::monte_carlo - Monte Carlo integration
• IntegrationAlgorithms::qmc_quad - Quasi-Monte Carlo with Sobol/Halton
• IntegrationAlgorithms::dblquad - Double integrals
• IntegrationAlgorithms::nquad - N-dimensional adaptive quadrature

ODE Solvers

Explicit Methods (Non-Stiff)

• RK23: Bogacki-Shampine 2(3) - Low accuracy, fast
• RK45: Dormand-Prince 4(5) - General purpose (default)
• DOP853: Dormand-Prince 8(5,3) - High accuracy

Implicit Methods (Stiff)

• BDF: Backward Differentiation Formula (orders 1-5)
• Radau: Radau IIA order 5 for very stiff problems
• LSODA: Automatic stiff/non-stiff switching

Symplectic Methods (Hamiltonian Systems)

• Verlet: Störmer-Verlet for energy conservation
• Leapfrog: N-body simulations

BVP Solvers

• IntegrationAlgorithms::solve_bvp - Two-point BVP via collocation

Example

use solvr::integrate::IntegrationAlgorithms;
// Tensor-based integration
let result = client.trapezoid(&y, &x)?;

Re-exports

pub use error::IntegrateError;

pub use error::IntegrateResult;

pub use ode::BDFOptions;

pub use ode::BVPOptions;

pub use ode::DAEOptions;

pub use ode::DAEResultTensor;

pub use ode::DAEVariableType;

pub use ode::EventDirection;

pub use ode::EventOptions;

pub use ode::EventRecord;

pub use ode::EventSpec;

pub use ode::LSODAOptions;

pub use ode::ODEMethod;

pub use ode::ODEOptions;

pub use ode::ODEResultWithEvents;

pub use ode::RadauOptions;

pub use ode::SymplecticOptions;

pub use impl_generic::ode::ODEResultTensor;

pub use impl_generic::ode::rk45_with_events_impl;

pub use impl_generic::ode::solve_ivp_impl;

pub use sensitivity::AdjointSensitivityAlgorithms;

pub use sensitivity::Checkpoint;

pub use sensitivity::CheckpointManager;

pub use sensitivity::CheckpointStrategy;

pub use sensitivity::SensitivityOptions;

pub use sensitivity::SensitivityResult;

pub use sensitivity::adjoint_sensitivity_impl;

Modules

error

Error types for numerical integration operations.

impl_generic

Generic implementations of integration algorithms.

ode

Ordinary differential equation (ODE) solvers.

sensitivity

Adjoint sensitivity analysis for ODE solvers.

Structs

BVPResult

Result of boundary value problem (BVP) solver.

EventFn

Wrapper for closure-based event functions.

EventSet

Collection of event functions with their specifications.

MonteCarloOptions

Options for Monte Carlo integration.

MonteCarloResult

Result of Monte Carlo integration.

NQuadOptions

Options for n-dimensional adaptive quadrature (dblquad, tplquad, nquad).

QMCOptions

Options for Quasi-Monte Carlo integration.

QuadOptions

Options for adaptive quadrature.

QuadResult

Result of adaptive quadrature.

RombergOptions

Options for Romberg integration.

SymplecticResult

Result of symplectic integration.

TanhSinhOptions

Options for tanh-sinh (double exponential) quadrature.

Enums

MonteCarloMethod

Method for Monte Carlo integration.

QMCSequence

Low-discrepancy sequence type for QMC integration.

Traits

EventFunction

Trait for event functions used in ODE integration.

IntegrationAlgorithms

Trait for integration algorithms that work across all Runtime backends.