neumann 0.0.2

A Python Library for Applied Mathematics in Physical Sciences.

Neumann - A Python Library for Applied Mathematics in Physical Sciences

Neumann is a rapid prototyping platform focused on numerical calculations mainly corcerned with simulations of natural phenomena. It provides a set of common functionalities and interfaces with a number of state-of-the-art open source packages to combine their power seamlessly under a single development environment.

The most important features:

• Numba-jitted classes and an extendible factory to define and manipulate vectors and tensors.

• Classes to define and solve linear and nonlinear optimization problems.

• A set of array routines for fast prorotyping, including random data creation to assure well posedness, or other properties of test problems.

Documentation

Click here to read the documentation.

Installation

This is optional, but we suggest you to create a dedicated virtual enviroment at all times to avoid conflicts with your other projects. Create a folder, open a command shell in that folder and use the following command

>>> python -m venv venv_name

Once the enviroment is created, activate it via typing

>>> .\venv_name\Scripts\activate

Neumann can be installed (either in a virtual enviroment or globally) from PyPI using pip on Python >= 3.6:

>>> pip install neumann

A Quick Tour

Linear Algebra

Define a reference frame (B) relative to the ambient frame (A):

>>> from neumann.linalg import ReferenceFrame
>>> A = ReferenceFrame(name='A', axes=np.eye(3))
>>> B = A.orient_new('Body', [0, 0, 90*np.pi/180], 'XYZ', name='B')

Get the DCM matrix of the transformation between two frames:

>>> B.dcm(target=A)

Define a vector in frame A and view the components of it in frame B:

>>> v = Vector([0.0, 1.0, 0.0], frame=A)
>>> v.view(B)

Define the same vector in frame B:

>>> v = Vector(v.show(B), frame=B)
>>> v.show(A)

Linear Programming

Solve a following Linear Programming Problem (LPP) with one unique solution:

>>> from neumann.optimize import LinearProgrammingProblem as LPP
>>> import sympy as sy
>>> variables = ['x1', 'x2', 'x3', 'x4']
>>> x1, x2, x3, x4 = syms = sy.symbols(variables, positive=True)
>>> obj1 = Function(3*x1 + 9*x3 + x2 + x4, variables=syms)
>>> eq11 = Equality(x1 + 2*x3 + x4 - 4, variables=syms)
>>> eq12 = Equality(x2 + x3 - x4 - 2, variables=syms)
>>> problem = LPP(cost=obj1, constraints=[eq11, eq12], variables=syms)
>>> problem.solve()['x']
array([0., 6., 0., 4.])

NonLinear Programming

Find the minimizer of the Rosenbrock function:

>>> from neumann.optimize import BinaryGeneticAlgorithm
>>> def Rosenbrock(x, y):
>>>     a = 1, b = 100
>>>     return (a-x)**2 + b*(y-x**2)**2
>>> ranges = [[-10, 10],[-10, 10]]
>>> BGA = BinaryGeneticAlgorithm(Rosenbrock, ranges, length=12, nPop=200)
>>> BGA.solve()
array([0.99389553, 0.98901176]) 

Testing

To run all tests, open up a console in the root directory of the project and type the following

>>> python -m unittest

Dependencies

must have

• Numba, NumPy, SciPy, SymPy, awkward

optional

• networkx

License

This package is licensed under the MIT license.