sdpb-python

Python bindings for SDPB, the arbitrary precision semidefinite program solver used in the conformal bootstrap, built against a fork that exposes SDPB’s solver as a library.

With sdpb-python you describe a polynomial matrix program (or a plain linear matrix inequality) with Python objects, solve it in-process without writing SDPB’s input directories, and get the solution back as mpmath numbers. On Linux x86_64 it installs from the prebuilt wheels of a release:

pip install sdpb-python --find-links https://github.com/YPWang0818/sdpb-python/releases/expanded_assets/v0.4.0

import sdpb_python as sdpb

pmp = sdpb.PMP(
    objective=[0, -1], normalization=[1, 0],
    matrices=[sdpb.PolynomialMatrix([[[[1, 0, 0, 0, 1], [0, 0, 1, 0, "1/12"]]]])],
)
solution = pmp.solve(precision=768)
print(solution.status.value, solution.dual_objective)

Getting started

• Installation
  • Binary wheels (Linux x86_64)
  • Building from source
  • How the wheels are made
• Quickstart
  • 1. Fix the precision
  • 2. Describe the problem
  • 3. Solve
  • 4. Ask for more of the solution
  • 5. Linear matrix inequalities
  • 6. Keep the solver alive
  • 7. Files
  • A complete script
• Background: what SDPB solves
  • Polynomial matrix programs
  • Linear matrix inequalities
  • Precision

User guide

• Describing problems
  • Polynomials
  • Polynomial matrices
  • Polynomial matrix programs
  • Linear matrix inequalities
• Solving
  • solve()
  • Precision
  • Many solves in parallel
  • Results
  • Files SDPB writes
  • Errors
  • Unbounded and infeasible programs
• The solver handle
  • Repeated runs
  • Warm starts
  • Checkpoints
  • Interrupting
• Files and interoperability
  • pmp.json
  • Working with SDPB’s command line tools
  • Numbers in files
• Numbers and precision
  • Inputs
  • Outputs
  • One precision per process
• Development install
  • Prerequisites
  • Installing into your project’s environment
  • Picking up fixes
  • Working on the library
  • Without installing the dependencies: Docker
• Testing

Reference

• API reference
• Building the dependencies (Ubuntu 24.04)
• Design notes

Scope

• Single-process solving of PMPs and LMIs at arbitrary precision.

• Full access to SDPB’s solver options, termination reasons, and solution parts (x, y, z, X, Y, c - B·y).

• A solver handle for repeated runs, warm starts, checkpoints, and clean interruption with Ctrl-C.

• pmp.json reading and writing for interoperability with SDPB’s command line tools (pmp2sdp, sdpb, spectrum).

Not covered (yet): multi-rank MPI runs, the spectrum and approx_objective tools, and SDPB’s Mathematica and XML input formats.

License

MIT, like SDPB itself. See the LICENSE file and the README for the licenses of the linked libraries.