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Compressed Continuous Computation (C3)

Computing with functions

The Compressed Continuous Computation (C3) package is intended to make it easy to perform continuous linear and multilinear algebra with multidimensional functions. It works by representing multidimensional functions in a low-rank format. Common tasks include taking "matrix" decompositions of vector- or matrix-valued functions, adding or multiplying functions together, integrating multidimensional functions, and much much more. The following is a sampling of capabilities

  • Adaptive approximation of a black-box model (specified as a function pointer)
  • Regression of a model from data
  • Both linear and nonlinear approximation
  • Approximation in polynomial, piecewise polynomial, linear element, and radial basis function spaces
  • General adaptive integration schemes
  • Differentiation
  • Multiplication
  • Addition
  • Rounding
  • Computing Jacobians and Hessians
  • UQ
    1. Expectation and variance
    2. Sobol sensitivities

In addition to the above capabilities, which are unique to the C3 package, I also have general optimization routines including

  • BFGS
  • Gradient descent
  • Stochastic Gradient with ADAM

Documentation of most functions is provided by Doxygen here.

Installation / Getting started

The dependencies for this code are

  1. BLAS
  3. SWIG (if building non-C interfaces)
  4. CMake

Usually, these dependencies can be installed via the package manager of your system (apt or brew or port)

From Source

git clone c3
cd c3
mkdir build
cd build
cmake ..

This will install all shared libraries into c3/build/src. The main shared library is libc3, the rest are all submodules. To install to a particular location use

cmake .. -DCMAKE_INSTALL_PREFIX=/your/choice
make install

Python interface

You can install the python interface using the pip utility through

pip install pathlib
pip install c3py

One can obtain some examples in the pyexamples subdirectory

python pywrappers/

An alternative way to install it is to download the git repository and then run

python build
python install

One workflow that works well is to install this package in a new virtual environment. For instance using conda one can run the following (from the c3 directory)

conda create -n c3pyenv python=3.7
conda activate c3pyenv
pip install numpy
python build
python install

If you have an old version installed and would like to upgrade the following command is effective at removing all old code and reinstalling

pip install --upgrade --force-reinstall c3py

Configuration Options

The following configuration options take boolean (true/false) values


Default: `OFF'

Using this option can toggle whether or not static or shared libraries should be built.

Note: This option cannot be set to ON if building the python wrapper


Default: `OFF'

Using this option can toggle whether or not to build each sub-library into its own library


Default: `OFF'

Using this option can toggle whether or not to build unit tests


Default: `OFF'

Using this option can toggle whether or not to compile exampels


Default: `OFF'

Using this option can toggle whether or not to compile the profiling executables


Default: `OFF'

Using this option can toggle whether or not to compile the benchmarks tests


Default: `OFF'

Using this option can toggle whether or not to compile the utilities


Default: `OFF'

Using this option addes the flag -fvisibility=hidden to compilation. Useful when embedding this library in a C++ library to hide its symbols.

Systems I have tested on

  1. Mac OS X with clang version 8.0
  2. Ubuntu with gcc version 5.0

Solutions to some possible problems

Error: Unable to find 'python.swg'

On Mac OS X, if SWIG is installed with macports using

sudo port install swig

then the above error might occur. To remedy this error install the swig-python package

sudo port install swig-python

(On Mac OS X) Error: stdio.h not found

This happens on some updated versions of Mac OS X. To solve this, the following StackOverflow thread seems to work

Numpy errors

Sometimes you may see the following errors

_frozen_importlib:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 216, got 192


RuntimeError: The current Numpy installation ('/Users/alex/anaconda3/envs/pytorch/lib/python3.6/site-packages/numpy/') fails to pass simple sanity checks. This can be caused for example by incorrect BLAS library being linked in, or by mixing package managers (pip, conda, apt, ...). Search closed numpy issues for similar problems.

One way that I have found ( that seems to solve this is to upgrade numpy by running the following command. I am really not sure why this works ...

sudo pip install numpy --upgrade --ignore-installed

Coding practices

I aim to document (with Doxygen) every function available to the user and provide a unit test. Furthermore, I won't push code to the master branch that has memory leaks. I am constantly looking for more suggestions for improving the robustness of the code if any issues are encountered.


Please open a Github issue to ask a question, report a bug, or to request features. To contribute, fork the repository and setup a branch.

Author: Alex A. Gorodetsky
Copyright (c) 2014-2016, Massachusetts Institute of Technology
Copyright (c) 2016-2017, Sandia National Laboratories
Copyright (c) 2018-2021, University of Michigan
License: BSD


Library for computing with multidimensional functions







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