https://github.com/xzackli/wignerfamilies.jl

compute families of wigner symbols with recurrence relations
https://github.com/xzackli/wignerfamilies.jl

cosmology julia quantum wigner-3j wigner-symbols

Last synced: 3 months ago
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compute families of wigner symbols with recurrence relations

• Host: GitHub
• URL: https://github.com/xzackli/wignerfamilies.jl
• Owner: xzackli
• License: mit
• Created: 2020-04-30T16:18:25.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2023-07-07T14:26:56.000Z (over 1 year ago)
• Last Synced: 2024-10-12T23:22:46.367Z (3 months ago)
• Topics: cosmology, julia, quantum, wigner-3j, wigner-symbols
• Language: Julia
• Size: 479 KB
• Stars: 11
• Watchers: 3
• Forks: 1
• Open Issues: 3
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# WignerFamilies

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://xzackli.github.io/WignerFamilies.jl/dev)

[![Build Status](https://github.com/xzackli/WignerFamilies.jl/workflows/CI/badge.svg)](https://github.com/xzackli/WignerFamilies.jl/actions)

[![Coverage](https://codecov.io/gh/xzackli/WignerFamilies.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/xzackli/WignerFamilies.jl)

This package implements methods described in [Luscombe and Luban 1998](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.57.7274), based on the work of [Schulten and Gordon 1961](https://aip.scitation.org/doi/10.1063/1.522426), for generating families of Wigner 3j and 6j symbols by recurrence relation. These exact methods are orders of magnitude more efficient than strategies like [prime factorization](https://github.com/Jutho/WignerSymbols.jl) for problems which require every non-trivial symbol in a family, and really shine for large quantum numbers. WignerFamilies.jl is thread-safe and **very fast**, beating the standard Fortran routine DRC3JJ from SLATEC by a factor of 2-4 (see [notebook](https://nbviewer.jupyter.org/github/xzackli/WignerFamilies.jl/blob/master/test/benchmarks.ipynb)).

## Installation

```julia

using Pkg

Pkg.add("WignerFamilies")

```

## Usage

WignerFamilies.jl currently computes the nontrivial 3j symbols over `j` with the other 

quantum numbers fixed, in the family of symbols,







It exposes `wigner3j_f(j₂, j₃, m₂, m₃)` which returns a simple wrapper around a vector of 

the type`WignerSymbolVector`. This vector contains the computed symbols, indexed by the 

quantum number `j`. The type supports 

[half-integer](https://github.com/sostock/HalfIntegers.jl) quantum numbers as indices.

```julia

using WignerFamilies

# wigner3j for all j fixing j₂=100, j₃=60, m₂=70, m₃=-55, m₁=-m₂-m₃

w3j = wigner3j_f(100, 60, 70, -55) 

js = collect(eachindex(w3j))  # indices are the quantum numbers

plot(js, w3j.symbols)   # you can get the underlying array with w3j.symbols

```

This generates the symbols in Figure 1 of Luscombe and Luban 1998.







## Advanced Use

One can compute symbols in a fully non-allocating way by using the mutating `wigner3j_f!`. This requires 

one to initialize a `WignerF` struct describing the problem, put a wrapper around the piece of memory

you want to deposit the symbols using WignerSymbolVector, and then calling the mutating method.

```julia

j₂, j₃, m₂, m₃ = 100, 100, -2, 2

w = WignerF(Float64, j₂, j₃, m₂, m₃)

buffer = zeros(Float64, length(w.nₘᵢₙ:w.nₘₐₓ))

w3j = WignerSymbolVector(buffer, w.nₘᵢₙ:w.nₘₐₓ)

WignerFamilies.wigner3j_f!(w, w3j)

```

This is the best way to get symbols if you're using them in a tight loop, since allocations really hurt in those cases. Typically you would preallocate a buffer and then give this package a `view` into it.

```julia

using BenchmarkTools

@btime WignerFamilies.wigner3j_f!(w, w3j)

```

```

1.660 μs (0 allocations: 0 bytes)

```