# **Neumann** - A Python Library for Applied Mathematics in Physical Sciences
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`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 dedicated `RectangularFrame` and `CartesianFrame` classes as special cases, all NumPy compliant.
* NumPy compliant classes like `Tensor` and `Vector` to handle various kinds of tensorial quantities efficiently.
* A `JaggedArray` and a Numba-jittable `csr_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.
* 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.
> **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.
## **Documentation**
The documentation is hosted on [ReadTheDocs](https://Neumann.readthedocs.io/en/latest/).
## **Installation**
`Neumann` can be installed (either in a virtual enviroment or globally) from PyPI using `pip` on Python >= 3.7:
```console
>>> pip install neumann
```
or chechkout with the following command using GitHub CLI
```console
gh repo clone dewloosh/Neumann
```
and install from source by typing
```console
>>> python install setup.py
```
## **Motivating Examples**
### Linear Algebra
Define a reference frame $\mathbf{B}$ relative to the frame $\mathbf{A}$:
```python
>>> 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:
```python
>>> B.dcm(target=A)
```
Define a vector $\mathbf{v}$ in frame $\mathbf{A}$ and show the components of it in frame $\mathbf{B}$:
```python
>>> v = Vector([0.0, 1.0, 0.0], frame=A)
>>> v.show(B)
```
Define the same vector in frame $\mathbf{B}$:
```python
>>> v = Vector(v.show(B), frame=B)
>>> v.show(A)
```
### Linear Programming
Solve the following Linear Programming Problem (LPP) with one unique solution:
```python
>>> 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.])
```
### NonLinear Programming
Find the minimizer of the Rosenbrock function:
```python
>>> 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()
...
```
## **License**
This package is licensed under the MIT license.
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"description": "# **Neumann** - A Python Library for Applied Mathematics in Physical Sciences\n\n[](https://circleci.com/gh/dewloosh/Neumann)\n[](https://neumann.readthedocs.io/en/latest/?badge=latest)\n[](https://opensource.org/licenses/MIT)\n[](https://pypi.org/project/Neumann)\n[](https://codecov.io/gh/dewloosh/Neumann)\n[](https://www.python.org)\n[](https://github.com/psf/black)\n\n`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.\n\nThe most important features:\n\n* Linear Algebra\n * A mechanism that guarantees to maintain the property of objectivity of tensorial quantities.\n * A `ReferenceFrame` class for all kinds of frames, and dedicated `RectangularFrame` and `CartesianFrame` classes as special cases, all NumPy compliant.\n * NumPy compliant classes like `Tensor` and `Vector` to handle various kinds of tensorial quantities efficiently.\n * A `JaggedArray` and a Numba-jittable `csr_matrix` to handle sparse data.\n\n* Operations Research\n * Classes to define and solve linear and nonlinear optimization problems.\n * A `LinearProgrammingProblem` class to define and solve any kind of linear optimization problem.\n * A `BinaryGeneticAlgorithm` class to tackle more complicated optimization problems.\n\n* Graph Theory\n * 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.\n\n> **Note**\n> Be aware, that the library uses JIT-compilation through Numba, and as a result,\n> first calls to these functions may take longer, but pay off in the long run.\n\n## **Documentation**\n\nThe documentation is hosted on [ReadTheDocs](https://Neumann.readthedocs.io/en/latest/).\n\n## **Installation**\n\n`Neumann` can be installed (either in a virtual enviroment or globally) from PyPI using `pip` on Python >= 3.7:\n\n```console\n>>> pip install neumann\n```\n\nor chechkout with the following command using GitHub CLI\n\n```console\ngh repo clone dewloosh/Neumann\n```\n\nand install from source by typing\n\n```console\n>>> python install setup.py\n```\n\n## **Motivating Examples**\n\n### Linear Algebra\n\nDefine a reference frame $\\mathbf{B}$ relative to the frame $\\mathbf{A}$:\n\n```python\n>>> from neumann.linalg import ReferenceFrame, Vector, Tensor\n>>> A = ReferenceFrame(name='A', axes=np.eye(3))\n>>> B = A.orient_new('Body', [0, 0, 90*np.pi/180], 'XYZ', name='B')\n```\n\nGet the *DCM matrix* of the transformation between two frames:\n\n```python\n>>> B.dcm(target=A)\n```\n\nDefine a vector $\\mathbf{v}$ in frame $\\mathbf{A}$ and show the components of it in frame $\\mathbf{B}$:\n\n```python\n>>> v = Vector([0.0, 1.0, 0.0], frame=A)\n>>> v.show(B)\n```\n\nDefine the same vector in frame $\\mathbf{B}$:\n\n```python\n>>> v = Vector(v.show(B), frame=B)\n>>> v.show(A)\n```\n\n### Linear Programming\n\nSolve the following Linear Programming Problem (LPP) with one unique solution:\n\n```python\n>>> from neumann.optimize import LinearProgrammingProblem as LPP\n>>> from neumann.function import Function, Equality\n>>> import sympy as sy\n>>> variables = ['x1', 'x2', 'x3', 'x4']\n>>> x1, x2, x3, x4 = syms = sy.symbols(variables, positive=True)\n>>> obj1 = Function(3*x1 + 9*x3 + x2 + x4, variables=syms)\n>>> eq11 = Equality(x1 + 2*x3 + x4 - 4, variables=syms)\n>>> eq12 = Equality(x2 + x3 - x4 - 2, variables=syms)\n>>> problem = LPP(cost=obj1, constraints=[eq11, eq12], variables=syms)\n>>> problem.solve()['x']\narray([0., 6., 0., 4.])\n```\n\n### NonLinear Programming\n\nFind the minimizer of the Rosenbrock function:\n\n```python\n>>> from neumann.optimize import BinaryGeneticAlgorithm\n>>> def Rosenbrock(x):\n... a, b = 1, 100\n... return (a-x[0])**2 + b*(x[1]-x[0]**2)**2\n>>> ranges = [[-10, 10], [-10, 10]]\n>>> BGA = BinaryGeneticAlgorithm(Rosenbrock, ranges, length=12, nPop=200)\n>>> BGA.solve()\n...\n```\n\n## **License**\n\nThis package is licensed under the MIT license.\n",
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