Neumann
is a Python library that provides tools to formulate and solve problems related to all kinds of scientific disciplines. It is a part of the DewLoosh ecosystem which is designed mainly to solve problems related to computational solid mechanics, but if something is general enough, it ends up here. A good example is the included vector and tensor algebra modules, or the various optimizers, which are applicable in a much broader context than they were originally designed for.
The most important features:
-
Linear Algebra
- A mechanism that guarantees to maintain the property of objectivity of tensorial quantities.
- A
ReferenceFrame
class for all kinds of frames, and dedicatedRectangularFrame
andCartesianFrame
classes as special cases, all NumPy compliant. - NumPy compliant classes like
Tensor
andVector
to handle various kinds of tensorial quantities efficiently. - A
JaggedArray
and a Numba-jittablecsr_matrix
to handle sparse data.
-
Operations Research
- Classes to define and solve linear and nonlinear optimization problems.
- A
LinearProgrammingProblem
class to define and solve any kind of linear optimization problem. - A
BinaryGeneticAlgorithm
class to tackle more complicated optimization problems.
- A
- Classes to define and solve linear and nonlinear optimization problems.
-
Graph Theory
- Algorithms to calculate rooted level structures and pseudo peripheral nodes of a
networkx
graph, which are useful if you want to minimize the bandwidth of sparse symmetrix matrices.
- Algorithms to calculate rooted level structures and pseudo peripheral nodes of a
Note Be aware, that the library uses JIT-compilation through Numba, and as a result, first calls to these functions may take longer, but pay off in the long run.
The documentation is hosted on ReadTheDocs.
Neumann
can be installed (either in a virtual enviroment or globally) from PyPI using pip
on Python >= 3.7:
>>> pip install neumann
or chechkout with the following command using GitHub CLI
gh repo clone dewloosh/Neumann
and install from source by typing
>>> python install setup.py
Define a reference frame
>>> from neumann.linalg import ReferenceFrame, Vector, Tensor
>>> 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
>>> v = Vector([0.0, 1.0, 0.0], frame=A)
>>> v.show(B)
Define the same vector in frame
>>> v = Vector(v.show(B), frame=B)
>>> v.show(A)
Solve the following Linear Programming Problem (LPP) with one unique solution:
>>> from neumann.optimize import LinearProgrammingProblem as LPP
>>> from neumann.function import Function, Equality
>>> 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.])
Find the minimizer of the Rosenbrock function:
>>> from neumann.optimize import BinaryGeneticAlgorithm
>>> def Rosenbrock(x):
... a, b = 1, 100
... return (a-x[0])**2 + b*(x[1]-x[0]**2)**2
>>> ranges = [[-10, 10], [-10, 10]]
>>> BGA = BinaryGeneticAlgorithm(Rosenbrock, ranges, length=12, nPop=200)
>>> BGA.solve()
...
This package is licensed under the MIT license.