multicomplex

multicomplex is a Python-based multi complex algebra library. This library is used to carry out numerical derivatives of (semi-)arbitrary numerical functions with nearly machine precision.

At its core is a minimal header-only C++11 library that does the heavy lifting, and pybind11 is used to make a 1-to-1 interface between the C++ code and the Python interface

Examples:

Try it in your browser:

Here is how to calculate the first 10 derivatives of sin(x) to numerical precision:

import multicomplex as mcx
import numpy as np
derivs = mcx.diff_mcx1(lambda x: np.sin(x), 0.1234, 10)

WARNING: Not all functions are implemented, due to the complications of multicomplex algebra. The following functions are implemented:

• Element-wise operations: *,+,/,-
• Trig functions: cos, sin, cosh, sinh
• Transcendental functions: ln, exp

More Reading Material

Info from around the interwebs:

• http://doi.acm.org/10.1145/2168773.2168774
• http://adl.stanford.edu/hyperdual/Fike_AD2012_slides.pdf
• http://folk.ntnu.no/preisig/HAP_Specials/AdvancedSimulation_files/2014/AdvSim-2014__Verheule_Adrian_Complex_differenetiation.pdf

License

*MIT licensed (see LICENSE for specifics), not subject to copyright in the USA. Foreign Rights Reserved, Secretary of Commerce.

Contacts

The C++ and Python code was written by Ian Bell (of NIST), with special thanks to Ulrich Deiters (University of Cologne) and Bradley Alpert (of NIST)

Dependencies

• Unmodified pybind11 for C++ <-> Python interfacing

Contributing/Getting Help

If you would like to contribute to multicomplex or report a problem, please open a pull request or submit an issue. Especially welcome would be additional tests.

If you want to discuss or request assistance, please open an issue.

To get started, you should check out the Jupyter notebook Tutorial in the notebooks folder; they demonstrate some of the capabilities of the Python interface.

Installation

Prerequisites

You will need:

• git
• cmake (on windows, install from cmake, on linux sudo apt install cmake should do it, on OSX, brew install cmake)
• Python (the anaconda distribution is used by the authors)
• a compiler (on windows, Visual Studio 2017+, g++ on linux/OSX)

If on linux you use Anaconda and end up with an error something like

ImportError: /home/theuser/anaconda3/bin/../lib/libstdc++.so.6: version `GLIBCXX_3.4.20' not found (required by /home/theuser/anaconda3/lib/python3.6/site-packages/pymcx.cpython-35m-x86_64-linux-gnu.so)

it can be sometimes fixed by installing libgcc with conda: conda install libgcc. This is due to an issue in Anaconda

To install in one line from github (easiest)

This will download the sources into a temporary directory and build and install the python extension so long as you have the necessary prerequisites:

pip install git+git://github.com/ianhbell/multicomplex.git

From a cloned repository

Alternatively, you can clone (recursively!) and run the setup.py script

git clone --recursive https://github.com/ianhbell/multicomplex
cd multicomplex
pip -vvv install .

to install, or

pip -v -e install .

to use a locally-compiled version for testing. If you want to build a debug version, you can do so with

python setup.py build -g develop

With a debug build, you can step into the debugger to debug the C++ code, for instance.

Cmake build for C++

Starting in the root of the repo (a debug build with the default compiler, here on linux):

git clone --recursive https://github.com/ianhbell/multicomplex
cd multicomplex/multicomplex
mkdir build
cd build
cmake ..
cmake --build .

For those using Anaconda on Linux, please use the following for cmake:

mkdir build
cd build
cmake .. -DPYTHON_EXECUTABLE=`which python`
cmake --build .

For Visual Studio 2015 (64-bit) in release mode, you would do:

git clone --recursive https://github.com/ianhbell/multicomplex
cd multicomplex/multicomplex
mkdir build
cd build
cmake .. -G "Visual Studio 14 2015 Win64"
cmake --build . --config Release

If you need to update your submodules (pybind11 and friends)

git submodule update --init

For other options, see the cmake docs