Theoretical Principles & Computational Physics Guide
Matrix using List Comprehension: Pythonic Data Generation & Grid Creation
Dr. Alorika Chatterjee & Dr. Anirban Shaw
Science & Physics Learners
Python 3 / NumPy / SciPy
1. Core Principles & Theoretical Framework
Declarative Construction: Generates complex numerical arrays and spatial grids in clean, readable, single-line expressions.
Discretized Meshes: Ideal for building 2D spatial coordinate lattices $(x_i, y_j)$ for PDE solving and potential grids.
Avoiding Pointer Bugs: Prevents shallow copy bugs associated with multiplying lists (
[[0]*n]*m creates linked row pointers!).2. Mathematical Formulation & Algorithmic Pipeline
Discrete 2D mesh grid generation via Cartesian product:
$$ \mathbf{G}_{ij} = (x_0 + i\Delta x, \; y_0 + j\Delta y) \quad \forall i \in \{0,\dots,N_x-1\}, \; j \in \{0,\dots,N_y-1\} $$
3. Numerical Mechanics & Implementation Logic
- Independent Row Instantiation: Use
[[0 for j in range(cols)] for i in range(rows)]to ensure each row is an independent object. - Conditional Filtering: Embed boolean conditions to construct sparse or upper triangular matrices:
[val if i <= j else 0 ...]. - Functional Evaluation: Direct potential evaluation:
[[potential(x[i], y[j]) for j in range(M)] for i in range(N)].
4. Relevant Computational Practice Exercises
Exercise 1
Construct a $5 \times 5$ Kronecker delta matrix $\delta_{ij}$ using a single nested list comprehension with an <code>if/else</code> condition.
Exercise 2
Generate a $10 \times 10$ 2D spatial grid representing gravitational potential $V(x, y) = -G / \sqrt{x^2 + y^2 + \epsilon^2}$.
Exercise 3
Demonstrate the shallow-copy pitfall of <code>[[0]*3]*3</code> when mutating a single element versus independent list comprehension.
- Hans Petter Langtangen, "A Primer on Scientific Programming with Python", Springer (2016).