# sparse-ir for Rust

> Rust library for compact representations of imaginary-time Green's functions: the IR basis with sparse sampling, the discrete Lehmann representation (DLR), and ESPRIT/MiniPole.

## Guide

- [Introduction](https://spm-lab.github.io/sparse-ir-rs/introduction.html): The three representations (IR, DLR, MiniPole) and how the book is organised.
- [Installation](https://spm-lab.github.io/sparse-ir-rs/getting-started/installation.html): Rust version, crates.io dependency, crate layout, and backend setup.
- [Conventions](https://spm-lab.github.io/sparse-ir-rs/getting-started/conventions.html): Notation, accuracy parameter per representation, the reduced Matsubara index n (iν = inπ/β), imaginary-time sampling, and SVE reuse.

## Representations

- [Sparse sampling](https://spm-lab.github.io/sparse-ir-rs/tutorials/sparse_sampling.html): Construct and use sparse sampling points.
- [Transformation](https://spm-lab.github.io/sparse-ir-rs/tutorials/transformation.html): Transform between imaginary time and Matsubara frequency.
- [Discrete Lehmann representation](https://spm-lab.github.io/sparse-ir-rs/tutorials/dlr.html): Build a DLR independently or from an IR basis, sample at its nodes, and fit.
- [MiniPole](https://spm-lab.github.io/sparse-ir-rs/tutorials/minipole.html): Extract a few complex poles from Matsubara data with ESPRIT; entry points and contour choice.

## Analytic continuation

- [Analytic continuation](https://spm-lab.github.io/sparse-ir-rs/tutorials/analytic_continuation.html): Reconstruct real-frequency behavior.
- [Sparse modeling](https://spm-lab.github.io/sparse-ir-rs/tutorials/spm.html): Use sparse modeling for coefficient recovery.

## Applied examples

- [Second-order perturbation](https://spm-lab.github.io/sparse-ir-rs/tutorials/second_order_perturbation.html): Apply the basis in a perturbation calculation.
- [GW](https://spm-lab.github.io/sparse-ir-rs/tutorials/gw.html): Green-function workflow for GW calculations.
- [Exchange interactions](https://spm-lab.github.io/sparse-ir-rs/tutorials/liechtenstein.html): Evaluate exchange interactions.
- [Orbital magnetic susceptibility](https://spm-lab.github.io/sparse-ir-rs/tutorials/orbital_magnetic_susceptibility.html): Compute an orbital response.
- [DMFT with IPT](https://spm-lab.github.io/sparse-ir-rs/tutorials/dmft_ipt.html): Use sparse sampling in an IPT solver.
- [Two-particle self-consistency](https://spm-lab.github.io/sparse-ir-rs/tutorials/tpsc.html): Apply the representation in TPSC.
- [Fluctuation exchange](https://spm-lab.github.io/sparse-ir-rs/tutorials/flex.html): Use the representation in FLEX.
- [Eliashberg-Holstein](https://spm-lab.github.io/sparse-ir-rs/tutorials/eliashberg_holstein.html): Solve an Eliashberg-Holstein example.

## API reference

- [Facade crate](https://spm-lab.github.io/sparse-ir-rs/api/sparse_ir/index.html): Main Rust API and re-exports.
- [Core crate](https://spm-lab.github.io/sparse-ir-rs/api/sparse_ir_core/index.html): Statistics, tensors, sampling, fitters, and errors.
- [DLR crate](https://spm-lab.github.io/sparse-ir-rs/api/sparse_ir_dlr/index.html): Discrete Lehmann representation.
- [MiniPole crate](https://spm-lab.github.io/sparse-ir-rs/api/sparse_ir_minipole/index.html): ESPRIT and minimal-pole routines.
- [Basis crate](https://spm-lab.github.io/sparse-ir-rs/api/sparse_ir_basis/index.html): Kernels, SVE, and IR basis.
- [C API crate](https://docs.rs/sparse-ir-capi/): C ABI and Rust wrapper API.

## Agent usage

- [Rust usage skill](https://github.com/SpM-lab/sparse-ir-rs/blob/main/agent-skills/sparse-ir-rust-usage/SKILL.md): Choosing crates, imports, numerical conventions, and common first-use errors.