A Million Particles in a Box

A Monte Carlo diffusion model moves a very large number of particles around a rectangular box, so every particle object should be as small as possible, and a typo such as p.vY = 0 must fail loudly rather than quietly create a new attribute.

Write a class Particle with exactly the four fields x, y, vx and vy, declared with __slots__, so that its objects have no __dict__ and assigning any other attribute raises AttributeError:

• Particle(x, y, vx, vy) stores the position and velocity.
• step(dt, width, height) moves the particle by vx * dt and vy * dt inside the box 0 <= x <= width, 0 <= y <= height. A particle that ends up beyond a wall is reflected: past the left wall, x becomes -x; past the right wall, x becomes 2 * width - x; and the matching velocity changes sign. The same holds for y with the bottom and top walls. (A step never crosses more than one wall per direction.)
• energy() returns the kinetic energy (vx ** 2 + vy ** 2) / 2.

Setup helpers you can use with Run: cloud(n, seed) makes particles, simulate(n, steps, seed, dt=0.05) runs a cloud and returns the mean position, the total energy and how many particles are in the left half, fixed_fields() checks the slots, and one_bounce() steps particles next to each wall.

Examples

Input:  fixed_fields()
Output: (["vx", "vy", "x", "y"], False, "AttributeError", None, 0.0)

Input:  one_bounce()[:2]
Output: [(0.3, 5.0, 4.0, 0.0), (9.7, 5.1, -4.0, 1.0)]

Constraints

• Up to 20,000 particles and 200,000 particle steps per test.
• Floats are compared with a tolerance of 1e-6.

Goals

• Declare a class's fields with `__slots__` so its objects have no `__dict__`
• See how slots turn a misspelt attribute into an error instead of a silent new attribute
• Write the small methods of a simulation class that will have very many instances