vector

An infinite-dimensional vector Python package.

>>> from vector import vecadd
>>> vecadd((1, 2), (4, 5, 6))
(5, 7, 6)
>>> 
>>> from vector import Vector
>>> v = Vector((1, 2))
>>> w = Vector((4, 5, 6))
>>> v + w
Vector(5, 7, 6, ...)
>>> 
>>> from vector import vecnpadd
>>> vecnpadd((1, 2), ((3, 4, 5),
...                   (6, 7, 8)))
array([[4, 6, 5],
       [7, 9, 8]])

Installation

pip install git+https://github.com/goessl/vector.git

Usage

This package includes

• general-purpose functions (prefixed vec...) in pure Python with perfect complexity,
• lazy generators (prefixed vecl...),
• in-place modifications (prefixed veci...),
• dicts as sparse vectors (prefixed vecs...),
• tensor functions (prefixed ten...) for multilinear operations,
• sparse tensor functions (prefixed tens...) for multilinear sparse operations &
• improved numpy-routines (prefixed vecnp...) for parallelised operations.

Functional, sparse and multilinear sparse additionally contain wrapper classes.

to handle type-independent, infinite-dimensional vectors. It operates on vectors of different lengths, treating them as infinite-dimensional by assuming that all components after the given ones are zero.

All vectors are zero-indexed.

Operation	Dense	Lazy	In-place	Sparse	Multilinear	Multilinear sparse	Parallelised
Creation
Zero constant	veczero	veclzero	vecizero	vecszero	tenzero	tenszero	vecnpzero
Basis	vecbasis	veclbasis	vecibasis	vecsbasis	tenbasis	tensbasis	vecnpbasis
Bases	vecbases	veclbases	vecibases	vecsbases
Random uniform	vecrand	veclrand	vecirand	vecsrand	tenrand	tensrand	vecnprand
Random normal	vecrandn	veclrandn	vecirandn	vecsrandn	tenrandn	tensrandn	vecnprandn
Conversion
to special type				vecdtos
from special type				vecstod
Utility
Dimensionality	veclen				tendim	tensdim	vecnpdim
Rank				vecslen	tenrank	tensrank
Comparison	veceq	vecleq		vecseq		tenseq	vecnpeq
Trimming	vectrim	vecltrim		vecstrim	tentrim	tenstrim	vecnptrim
in-place			vecitrim	vecsitrim		tensitrim
Right shift	vecrshift	veclrshift		vecsrshift	tenrshift	tensrshift
in-place			vecirshift	vecsirshift
Left shift	veclshift	vecllshift		vecslshift	tenlshift	tenslshift
in-place			vecilshift	vecsilshift
Hilbert space
Conjugation	vecconj	veclconj		vecsconj	tenconj	tensconj
in-place			veciconj	vecsiconj		tensiconj
Norm	vecabs			vecsabs			vecnpabs
Norm squared	vecabsq			vecsabsq			vecnpabsq
Inner product	vecdot			vecsdot			vecnpdot
Vector space
Positive	vecpos	veclpos		vecspos	tenpos	tenspos	vecnppos
in-place			vecipos	vecsipos		tensipos
Negative	vecneg	veclneg		vecsneg	tenneg	tensneg	vecnpneg
in-place			vecineg	vecsineg		tensineg
Addition	vecadd	vecladd		vecsadd	tenadd	tensadd	vecnpadd
in-place			veciadd	vecsiadd		tensiadd
Basis addition	vecaddc	vecladdc		vecsaddc	tenaddc	tensaddc
in-place			veciaddc	vecsiaddc		tensiaddc
Subtraction	vecsub	veclsub		vecssub	tensub	tenssub	vecnpsub
in-place			vecisub	vecsisub		tensisub
Basis subtraction	vecsubc	veclsubc		vecssubc	tensubc	tenssubc
in-place			vecisubc	vecsisubc		tensisubc
Multiplication	vecrmul	veclrmul		vecsrmul	tenrmul	tensrmul
from left	vecmul	veclmul		vecsmul	tenmul	tensmul	vecnpmul
in-place			vecimul	vecsimul		tensimul
True division	vectruediv	vecltruediv		vecstruediv	tentruediv	tenstruediv	vecnptruediv
in-place			vecitruediv	vecsitruediv		tensitruediv
Floor division	vecfloordiv	veclfloordiv		vecsfloordiv	tenfloordiv	tensfloordiv	vecnpfloordiv
in-place			vecifloordiv	vecsifloordiv		tensifloordiv
Mod	vecmod	veclmod		vecstruediv	tenmod	tensmod	vecnpmod
in-place			vecimod	vecsitruediv		tensimod
Divmod	vecdivmod	vecldivmod		vecsdivmod	tendivmod	tensdivmod
Elementwise
Multiplication	vechadamard	veclhadamard	vecihadamard	vecshadamard	tenhadamard	tenshadamard
True division	vechadamardtruediv	veclhadamardtruediv	vecihadamardtruediv	vecshadamardtruediv	tenhadamardtruediv	tenshadamardtruediv
Floor division	vechadamardfloordiv	veclhadamardfloordiv	vecihadamardfloordiv	vecshadamardfloordiv	tenhadamardfloordiv	tenshadamardfloordiv
Mod	vechadamardmod	veclhadamardmod	vecihadamardmod	vecshadamardmod	tenhadamardmod	tenshadamardmod
Divmod	vechadamarddivmod	veclhadamarddivmod		vecshadamarddivmod	tenhadamarddivmod	tenshadamarddivmod
Min	vechadamardmin	veclhadamardmin		vecshadamardmin	tenhadamardmin	tenshadamardmin
Max	vechadamardmax	veclhadamardmax		vecshadamardmax	tenhadamardmax	tenshadamardmax

Design choices

1. Integers are the best. As many functions as possible should work with pure integer arithmetic.
2. Floats are necessary. (Also let's don't forget about complex numbers.) When possible, extended precision intermediates are used (sum, sumprod, ...)
3. Python allows operator overloading. Exclusive type arithmetic should be possible (zero, one & inf arguments; ...)

Prefix Design

Could use no prefix to be more mathematically pure, like add instead of vecadd, but then you would always have to use from vec import add as vecadd if used with other libraries (like operator).

Also avoids keyword collisions (abs is reserved, vecabs isn't).

Do it like numpy.polynomial.polynomial. ....

Roadmap

• zip version between zip & zip_longest. Yields different sized tuples. Done: goessl/zipvar
• vecdivmod
• docstrings
• numpy routines
• multilinear vectors: tensors?
• Absolute type safety.
• Complexity analysis. Perfect complexity
• dimensionality signature (e.g. vecadd: \(\mathbb{K}^m\times\mathbb{K}^n\to\mathbb{K}^{\max{m, n}}\))
• sparse vectors (dicts)
• in-place
• veceq to veccmp?
• argument checks
• lp-norms & metrics
• vechadamardminmax
• never use numpy.int64, they don't detect overflows
• C++ & Java version
• Ballin
• Fields medal

License (MIT)

Copyright (c) 2022-2025 Sebastian Gössl

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.