py3nj

A small python library to calcluate wigner's 3j-, 6j- and 9j- symbols. py3nj is designed to be compatible with numpy's np.ndarray and its calculation is vectorized automatically.

Basic Usage

The basic interfaces are py3nj.wigner3j, py3nj.wigner6j, py3nj.wigner9j, and py3nj.clebsch_gordan.

>>> # Calculate (0/2, 1/2, 1/2,
... #           (0/2, 1/2,-1/2)
... # Note that all the arguments should be doubled
... py3nj.wigner3j(0, 1, 1,
...                0, 1,-1)
0.7071067811865476

>>> # vectorization is supported
... py3nj.wigner3j([0, 2], [1, 0], [ 1, 0],
...                [0, 0], [1, 0], [-1, 0])
array([0.70710678, 0.        ])

>>> # 6J symbol
>>> py3nj.wigner6j([2, 1], [1, 2], [1, 1],
...                [1, 2], [2, 1], [0, 0])
array([0.40824829, 0.40824829])

>>> # 9J symbol
>>> py3nj.wigner9j([2, 2], [4, 4], [2, 2],
...                [2, 4], [2, 6], [2, 2],
...                [2, 2], [2, 4], [2, 2])
array([0.05555556, 0.03651484])

>>> Clebsch Gordanh coefficient
>>> py3nj.clebsch_gordan(2, 2, 4,
...                      2, 0, 2)
0.7071067811865475

>>> # Vectorized calcluation of C.G. coef
... py3nj.clebsch_gordan([2, 1], [2, 1], [4, 0],
...                      [2,-1], [0, 1], [2, 0])
array([ 0.70710678, -0.70710678])

Install

py3nj can be installed through either pip or github repository. You'll likely need to have ninja installed.

Also, any fortran compiler must be installed in the system. An example setup for Windows systems will be found below.

Install by pip

pip install py3nj

Install through github

git clone https://github.com/fujiisoup/py3nj
cd py3nj
pip install .

Installing Fortran to Windows

There are several ways to install Fortran. Common ways are

• Install cygwin, or MinGW
• Install WSL (windows subsystem for linux)

Sometimes people have problems with installing Fortran, not only because of the lack of experience, but also due to the security rules from the owners institutes. In my case, I am not able to install WSL.

The following is one of the example installation configuration, which might not be affected by the security rules.

Install quickstart-fortran

quickstart-fortran is an easy Windows installer and launcher for GFortran and the Fortran Package Manager. This does not require the administrative privilege, and thus it might not be affected many of the security rules.

Go to their Release page, download the latest version of the installer, and run it after it is downloaded.

You may need to restart your terminal, such as Anaconda Prompt. Then, do either

pip install py3nj

or

git clone https://github.com/fujiisoup/py3nj
cd py3nj
pip install .

Acknowledgement

py3nj wraps slatec fortran implementation. See http://www.netlib.org/slatec/ for the details.

License

Copyright 2018, py3nj Developers

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.