libcalculus 0.2.1

Real/Complex analysis library for Python 3.

libcalculus: A comprehensive real and complex analysis library for Python

libcalculus is fully written in C++ and Cython for bindings to Python; all numeric calculations take place in C++ and take full advantage of SIMD vectorization and OpenMP threading wherever available.

Features

• Functional programming approach to analysis in Python
• Numeric integration and differentiation of real and complex functions
• Full integration with NumPy: functions support array inputs
• LaTeX support: every function object has a .latex() that produces its LaTeX markup

Technology

libcalculus is written in C++20 and bound to Python via Cython; operations between functions are performed using C++ lambdas, and all calculations happen at the C++ level, with Python only interfacing methods and results.

Installation

libcalculus can be installed from pip:

pip install libcalculus

Examples

Here is a snippet demonstrating some of the library's features:

>>> import libcalculus, numpy as np
>>> z = libcalculus.ComplexFunction.Identity() # Shorten syntax
>>> f = z ** 2 * (libcalculus.ComplexFunction.Sin() @ (3 / z)) # represents z^2 + sin(3/z)
>>> f(1 + 2j)
(1.9161297498044316+7.826928799856612j)
>>> libcalculus.residue(f, 0, tol=1e-4) # residue of f around z=0, with an error tolerance of 1e-4
(-4.499999999971643+1.3805827092608378e-05j)
>>> print(f.latex())
{z}^{2}\sin\left( \frac{3}{z}\right)
>>> contour = libcalculus.Contour.Cosh() + libcalculus.ComplexFunction.Exp() @ (1j * libcalculus.Contour.Identity()) # represents the contour cosh(t) + e^(i*t)
>>> libcalculus.integrate(f, contour, 1, 2) # integrate along the contour between t=1 and t=2
(8.225229199586169+4.308468258475392j)
>>> libcalculus.threads(4) # Enable threading when working with arrays
>>> arr = np.array([[1, 2j, 3], [4 + 1j, 5 + 2j, 7 + 3j]])
>>> f(arr)
array([[1.41120008e-01+0.j        , 1.04304611e-15+8.51711782j,
        7.57323886e+00+0.j        ],
       [1.09624856e+01+3.24567376j, 1.42295657e+01+6.29864507j,
        2.04585023e+01+9.22847707j]])

License

Copyright (c) 2022, Ariel Terkeltoub All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above
   copyright notice, this list of conditions and the following
   disclaimer in the documentation and/or other materials provided
   with the distribution.

* Neither the name of the NumPy Developers nor the names of any
   contributors may be used to endorse or promote products derived
   from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE