An infinite dimensional vector package.
>>> from vector import Vector
>>> v = Vector((1, 2))
>>> w = Vector((4, 5, 6))
>>> v+w
Vector(5, 7, 6, 0, ...)pip install git+https://github.com/goessl/vector.gitThis package provides a single class, Vector, to handle infinite dimensional vectors.
A vector can be initialized in two ways:
- With the constructor
Vector(coef), that takes a non-negative integer to create a basis vector with the given index, or an iterable of coefficients to create a vector with the given coefficients as the first elements. - With the random factory
Vector.random(n, normed=True)for a random vector of a given dimensionality. A static helper methodVector.basis_tuple(i)is also provided, that generates a basis vector in form of a tuple. The objects are immutable (coefficients are internally stored in a tuple) and zero-indexed.
>>> from vector import Vector
>>> v = Vector((1, 2, 3))
>>> w = Vector.random(3)
>>> v
Vector(1, 2, 3, 0, ...)
>>> w
Vector(-0.5613820142699765, -0.028308921297709365, 0.8270724508948077, 0, ...)
>>> Vector.basis_tuple(3)
(0, 0, 0, 1)Container and sequence interfaces are implemented so the coefficients can be
- accessed by indexing:
v[2](coefficients not set return to 0), - iterated over:
for c in v(stops at last set coefficient), - counted:
len(v)(number of set coefficients), - compared:
v == w(tuple of coefficients get compared), - shifted:
v >> 1, w << 2& - trimmed:
v.trim()(trailing non-zero coefficients get removed).
Hilbert space operations are provided:
- Vector addition & subtraction
v + w, v - w, - scalar multiplication & division
2 * v, w / 2, - inner product & norm
v @ w, abs(v)(real inner product; complex conjugation of an argument has to be handled by the user; to comply with numpy.matmul).
The multiplicative operations are overloaded to perform scalar multiplication/division if the other argument is a scalar, or elementwise multiplication/division if both operands are Vectors, v*w.
A static zero-vector Vector.ZERO is provided.
For most methods a runtime comparison between different approaches has been made. The results can be found in profiling.ipynb or profiling.ipynb.
Copyright (c) 2023 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.
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