matext

C++ Extension for Python implementing Vector and Matrix classes The library implements Vector and Matrix classes with the following features:

• Matrix and Vector classes with underlying float32 arrays.
• Elementwise addition and subtraction.
• Elementwise multiplication and division by scalar number.
• Regular matrix and vector multiplications (M*V and M*M).
• Matrix inverse calculation based on LU decomposition with partial pivoting.
• Fast Computation of Moore-Penrose Inverse Matrices

Prerequisites

These prerequisites are automatically installed when installing library from pip wheel.

• Python (tested with Python 3.6.8 x64)
• pip
• wheel
• [automatically installed] pybind11
• [automatically installed] numpy (required to initiate Matrices and Vectors)

Install from pip wheel

[Windows 10 only]
Clone the repository and cd into the matext/distfolder.
The matext library can be installed from wheel file with following command executed from the dist directory:

pip install matext-0.1-cp36-cp36m-win_amd64.whl

Build from source

Build .pyddynamic library with the following command executed from the project root directory:

python setup.py build_ext --inplace

For the build process msvc is foced to used hence Visual Studio and MSBuild is assumed to be installated and MSBuild is assumed to be in the PATH).

The build process was tested with MSVC++ 14.25. Though other versions may be used too, be aware that overload_cast syntax in the binding code in src/main.cpp is a C++14-only feature so trying older version than MSVC++14.00 will result in problem.

Produce new wheel distribution file with the following command executed from the project root directory

python setup.py bdist_wheel

How to use

import matext as mx
import numpy as np

# Create numpy arrays
# float32 recommended to reduce conversion and copy overhead
npmat = np.array([[1,3,6],[3,9,4]],dtype=np.float32)
npvec = np.array([7,8,9],dtype=np.float32)

# Create matrix and vector objects
mat = mx.Matrix(npmat)
vec = mx.Vector(npvec)

# Multiply them and print results
vec_result = mat * vec
print(vec_result.toNumpy())

Some design considerations...

• Pybind11 is used to create extension module becaus of its simplicity.
• Because both Marix and Vector objects should be created with numpy arrays py::array_t<float> type is used instead of raw buffer type. (see further notes in Pybind11 doc
• py::array::c_style ensures that arrays are stored in a dense manner and c-stlye (row major) ordering is used.
• <py::array::forcecast> ensures that non-conforming arguments are converted into an array satisfying the specified requirements.
• This way, numpy arrays storing float32 data will not be copied but will be directly referenced by the Matrix and Vector objects. Other types will induce conversion, first.
• C160-C170 guidelines from ISOC++ Core Guidelines were taken into considerations except C163 beause of how Pybind11 works.

Performance

Run tests/benchmark.py to benchmark speed and accurary by comparing results with numpy.

The following runtimes were measured when executing operations with 400x400 matrices.

Operation	matext	Numpy
Addition	0.000 sec	0.001 sec
Multiplication	0.181 sec	0.000 sec
Transpose	0.001 sec	0.000 sec
Inverse	0.217 sec	0.013 sec
Pseudoinverse (400x600)	1.486 sec	0.098 sec

CPU	OS	Compiler
[Intel® Core™ i7-7700HQ @ 2.8 GHz]	Windows 10 x64 (18363)	MSVC++ 14.25