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Functions to create n-dimensional vector classes

This is a Python library with functions that create vector classes with 2, 3 or an arbitrary number of dimensions.

The name of the classes to be created, and the names of their vector components are set when calling the functions. The brackets for the vectors and the seperators for their components can also be given as arguments to these functions.

There are 11 functions that create vector classes. Each of them creates vector classes with a certain functionality. 8 of the functions create vector classes with a cartesian coordinate system and 4 of the functions create vector classes with tolerances for comparing vectors.

Created vector classes can be extended with extra functionality for processing their vector instances and ther component values.

Some of the vector classes are suitable for using e.g. NumPy's ndarrays, Pandas Series or SymPy's algebraic expressions as component values.

Project homepage

https://github.com/t-o-k/scikit-vectors

Project wiki

https://github.com/t-o-k/scikit-vectors/wiki

The wiki has links to documents that shows how created vector classes can be used.

Installation

scikit-vectors requires Python version 3.5 or higher.

pip install scikit-vectors

Examples

In addition to the short examples below, there are some more elaborate ones here:

https://github.com/t-o-k/scikit-vectors_examples

Simple examples

>>> from math import pi
>>> from skvectors import create_class_Cartesian_3D_Vector
>>> CV3D = create_class_Cartesian_3D_Vector('CV3D', 'xyz', brackets=[ '<< ', ' >>' ])
>>> u = CV3D(3, 0, -4)
>>> print(u)
<< 3, 0, -4 >>
>>> v = CV3D(1, -2, 3) * 2
>>> repr(v)
'CV3D(x=2, y=-4, z=6)'
>>> u.normalize()
CV3D(x=0.6, y=0.0, z=-0.8)
>>> u.dot(v)
-18
>>> u.cross(v)
CV3D(x=-16, y=-26, z=-12)
>>> u = CV3D(4.5, -3.0, -1.5)
>>> v = CV3D(-3, -3, -3)
>>> u.angle(v) / pi
0.49999999999999994
>>> u = CV3D(5, -4, -3)
>>> v = CV3D(-2, 0, 2)
>>> u.project(v)
CV3D(x=4.0, y=-0.0, z=-4.0)
>>> u = CV3D(-5, 0, 0)
>>> v = CV3D(0, 12, 0)
>>> (u - v).length()
13.0
>>> u = CV3D(-3, 4, -5)
>>> u.rotate_x(pi)
CV3D(x=-3, y=-3.9999999999999996, z=5.000000000000001)
>>> u = CV3D(-3, 4, -5)
>>> v = CV3D(0, -10, -8)
>>> u.axis_rotate(v, -pi)
CV3D(x=2.999999999999999, y=-4.0, z=5.0)
>>> u = CV3D(-3, 4, -5)
>>> v = CV3D(-6, 0, 0)
>>> w = CV3D(0, 0, 7)
>>> u.reorient(v, w)
CV3D(x=-5.0, y=4.0, z=3.0)
>>> u = CV3D(0, -1, 2)
>>> v = CV3D(-3, 4, -5)
>>> w = CV3D(3, 1, 2)
>>> u.stp(v, w)
-21
>>> 
>>> from skvectors import create_class_Simple_Vector
>>> SV = create_class_Simple_Vector('SV', [ 'first', 'second', 'third', 'fourth', 'fifth', 'sixth' ])
>>> u = SV(3, 1, -2, -3, 4, 2)
>>> u
SV(first=3, second=1, third=-2, fourth=-3, fifth=4, sixth=2)
>>> v = SV(2, -2, 1, 3, 1, 4)
>>> u * v + 10
SV(first=16, second=8, third=8, fourth=1, fifth=14, sixth=18)
>>> 2 * (u - v)
SV(first=2, second=6, third=-6, fourth=-12, fifth=6, sixth=-4)
>>> u**v / 2
SV(first=4.5, second=0.5, third=-1.0, fourth=-13.5, fifth=2.0, sixth=8.0)
>>> u *= 2 / v
>>> u
SV(first=3.0, second=-1.0, third=-4.0, fourth=-2.0, fifth=8.0, sixth=1.0)
>>> u.first
3.0
>>> (u + v).sixth
5.0
>>> u.fifth += 20
>>> u
SV(first=3.0, second=-1.0, third=-4.0, fourth=-2.0, fifth=28.0, sixth=1.0)
>>> u.c_add_third(24)
SV(first=3.0, second=-1.0, third=20.0, fourth=-2.0, fifth=28.0, sixth=1.0)
>>> u.c_imul_bar_second(1000)
>>> u
SV(first=3000.0, second=-1.0, third=-4000.0, fourth=-2000.0, fifth=28000.0, sixth=1000.0)
>>> v = SV(0, 1, 2, 3, 4, 5) / 6
>>> round(v, 3)
SV(first=0.0, second=0.167, third=0.333, fourth=0.5, fifth=0.667, sixth=0.833)
>>> 

Not so simple example with NumPy

>>> from skvectors import create_class_Cartesian_3D_Vector
>>> import numpy as np
>>> NP3 = \
...     create_class_Cartesian_3D_Vector(
...         name = 'NP3',
...         component_names = [ chr(0x03b1)*2, chr(0x03b2)*2, chr(0x03b3)*2 ],
...         brackets = [ chr(0x2770)*2 + ' ', ' ' + chr(0x2771)*2 ],
...         sep = ', ',
...         cnull = np.array([ 0., 0., 0., 0. ]),
...         cunit = np.array([ 1., 1., 1., 1. ]),
...         functions = \
...             {
...                 'eq': np.equal,
...                 'ne': np.not_equal,
...                 'not': np.logical_not,
...                 'and': np.logical_and,
...                 'or': np.logical_or,
...                 'all': np.all,
...                 'any': np.any,
...                 'min': np.minimum,
...                 'max': np.maximum,
...                 'abs': np.absolute,
...                 'int': np.rint,
...                 'ceil': np.ceil,
...                 'copysign': np.copysign,
...                 'log10': np.log10,
...                 'cos': np.cos,
...                 'sin': np.sin,
...                 'atan2': np.arctan2,
...                 'pi': np.pi
...             }
...     )
>>> NP3.component_names()
['αα', 'ββ', 'γγ']
>>> u = \
...     NP3(
...         np.random.randint(-10, 10, size=4),
...         np.random.randint(-10, 10, size=4),
...         np.random.randint(-10, 10, size=4)
...     )
>>> u
NP3(αα=array([ 7., -8.,  5.,  7.]), ββ=array([-1., -4.,  7., -4.]), γγ=array([ 1.,  6., -2.,  8.]))
>>> u /= 10
>>> u
NP3(αα=array([ 0.7, -0.8,  0.5,  0.7]), ββ=array([-0.1, -0.4,  0.7, -0.4]), γγ=array([ 0.1,  0.6, -0.2,  0.8]))
>>> v = \
...     NP3(
...         np.array([ -3,  5, -1,  2 ]),
...         np.array([  0, 12,  0, -1 ]),
...         np.array([  4,  0,  0,  2 ])
...     )
>>> str(v)
'❰❰ [-3.  5. -1.  2.], [  0.  12.   0.  -1.], [ 4.  0.  0.  2.] ❱❱'
>>> v.length()
array([  5.,  13.,   1.,   3.])
>>> v.contains(np.array([ 4.0, 2.0, -1.0, 3.0 ]))
array([ True, False,  True, False], dtype=bool)
>>> (u - v) * 10
NP3(αα=array([ 37., -58.,  15., -13.]), ββ=array([  -1., -124.,    7.,    6.]), γγ=array([-39.,   6.,  -2., -12.]))
>>> w = NP3(1, -1, 0)
>>> w
NP3(αα=array([ 1.,  1.,  1.,  1.]), ββ=array([-1., -1., -1., -1.]), γγ=array([ 0.,  0.,  0.,  0.]))
>>> u.reorient(v, w)
NP3(αα=array([ 0.1771821 , -0.0652714 , -0.84852814,  0.76479998]), ββ=array([ 0.65801471,  0.8920424 , -0.14142136, -0.83797539]), γγ=array([-0.21359575,  0.6       , -0.2       ,  0.05364919]))
>>> u.axis_rotate(NP3(1, -2, 1), np.pi/4)
NP3(αα=array([ 0.51492277, -0.76733621,  0.21325376,  0.26084032]), ββ=array([ 0.00486333, -0.74556654,  0.80444152, -0.53626169]), γγ=array([ 0.49480389, -0.12379688,  0.29562928,  0.96663629]))
>>> 

Running the tests

git clone https://github.com/t-o-k/scikit-vectors
cd scikit-vectors
python3 -m unittest discover

Here's more information: https://travis-ci.org/t-o-k/scikit-vectors

License information

See the file LICENSE for information on terms & conditions for usage, and a DISCLAIMER OF ALL WARRANTIES.

Author

Tor Olav Kristensen

http://subcube.com