LibSparseIR.jl

Julia wrapper for the libsparseir C++ library, providing high-performance sparse intermediate representation (IR) of correlation functions in many-body physics.

Warning

This Julia wrapper is still under development. For production use, please consider:

• SparseIR.jl - Pure Julia implementation (recommended)
• sparse-ir - Python implementation
• sparse-ir-fortran - Fortran implementation

Overview

LibSparseIR.jl provides Julia bindings to the C++ libsparseir library, offering optimized routines for:

• Basis construction: Finite temperature basis using singular value expansion (SVE)
• Sparse sampling: Efficient sampling in imaginary time and Matsubara frequencies
• DLR transformations: Discrete Lehmann Representation for compact representation
• Augmented basis: Extended basis for vertex functions and multi-point correlations

Features

Implemented Components

• ✅ Statistics: Fermionic and Bosonic
• ✅ Kernels: LogisticKernel, RegularizedBoseKernel
• ✅ Basis Functions: FiniteTempBasis with SVE
• ✅ Sampling: TauSampling, MatsubaraSampling
• ✅ DLR: DiscreteLehmannRepresentation
• ✅ Augmentation: TauConst, TauLinear, MatsubaraConst
• ✅ Basis Sets: FiniteTempBasisSet for multi-Λ calculations

API Example

using LibSparseIR

# Create basis for fermionic system
β = 10.0        # Inverse temperature
ωmax = 1.0      # Frequency cutoff
ε = 1e-10       # Accuracy parameter

basis = FiniteTempBasis(Fermionic(), β, ωmax, ε)

# Sparse sampling in imaginary time
tau_sampling = TauSampling(basis)
tau_points = tau_sampling.sampling_points

# Transform between representations
coeffs = fit(tau_sampling, gtau_values)
gtau_reconstructed = evaluate(tau_sampling, coeffs)

Installation

Prerequisites

1. Julia 1.10+
2. libsparseir C++ library built with C API support

Setup Instructions

1. Build libsparseir with C API:

   git clone https://github.com/SpM-lab/libsparseir.git
   cd libsparseir
   ./build_capi.sh

2. Clone and install LibSparseIR.jl:

   git clone https://github.com/SpM-lab/LibSparseIR.jl.git
   cd LibSparseIR.jl

3. Build the Julia package:

   julia --project -e 'using Pkg; Pkg.instantiate(); Pkg.build()'

   This generates src/C_API.jl by parsing the C headers using Clang.jl.

4. Run tests:

   julia --project -e 'using Pkg; Pkg.test()'

Testing

We use ReTestItems.jl for testing with tagged test groups:

• Run all tests: julia -e 'using Pkg; Pkg.test()'
• Run specific test groups:

  using Pkg
  Pkg.test(test_args=["--tags", "julia"])      # Pure Julia tests
  Pkg.test(test_args=["--tags", "wrapper"])    # C wrapper tests
  Pkg.test(test_args=["--tags", "cinterface"]) # C interface tests

Tutorials

Interactive tutorials are available in the tutorials/ directory:

• Pluto notebooks (tutorials/pluto/):

  • sparse_sampling.jl - Introduction to sparse sampling
  • transformation_IR.jl - IR basis transformations
  • dlr.jl - Discrete Lehmann Representation
  • dmft_ipt.jl - DMFT with IPT solver
  • flex.jl - FLEX approximation example
  • BgG.jl - Bethe-Goldstone calculations

• Jupyter notebooks (tutorials/jupyter/) - Similar content in Jupyter format

To run Pluto tutorials:

using Pluto
Pluto.run(notebook="tutorials/pluto/sparse_sampling.jl")

Project Structure

LibSparseIR.jl/
├── src/
│   ├── LibSparseIR.jl      # Main module
│   ├── C_API.jl            # Auto-generated C bindings
│   ├── abstract.jl         # Abstract interfaces
│   ├── lib/                # C library wrappers
│   │   ├── basis.jl        # Basis functions
│   │   ├── kernel.jl       # Kernel implementations
│   │   ├── sampling.jl     # Sampling routines
│   │   ├── dlr.jl          # DLR transformations
│   │   └── sve.jl          # SVE computations
│   └── spir/               # Pure Julia extensions
│       ├── augment.jl      # Augmented basis
│       └── basis_set.jl    # Multi-Λ basis sets
├── test/                   # Test suites
├── tutorials/              # Interactive tutorials
└── builder/                # BinaryBuilder scripts