pycauset 0.1.0

High-performance Causal Set matrix operations using memory-mapped files

PyCauset

PyCauset is a high-performance Python module designed for numerical work with Causal Sets. It is built to handle massive matrices (up to $N=10^6$) that exceed available RAM by leveraging memory-mapped files and efficient C++ backends.

Why PyCauset?

For a causal set of size $N$, the relevant mathematical objects are typically of order $\mathcal O(N^2)$ and operations are $\mathcal O(N^3)$. For even moderate sizes like $N=10,000$, standard in-memory libraries like NumPy can struggle with memory limits.

PyCauset solves this by:

• Memory Mapping: Storing matrices on disk and loading only necessary chunks into RAM.
• Bit Packing: Storing boolean matrices (causal relations) as individual bits, reducing storage requirements by 8x-64x compared to standard types.
• C++ Efficiency: Core operations are implemented in optimized C++.

Installation

Prerequisites

PyCauset requires a C++ compiler to build the native extension.

• Windows: Install Visual Studio Build Tools with the "Desktop development with C++" workload.
• Linux/macOS: Install gcc or clang.

Build & Install

Clone the repository and run the build script:

# Build the C++ extension and Python module
./build.ps1 -Python

# To run tests as well
./build.ps1 -All

Quick Start

1. Creating Matrices

The primary structure for causal sets is the TriangularBitMatrix (aliased as CausalMatrix).

import pycauset

# Create a random 1000x1000 causal matrix (Bernoulli p=0.5)
C = pycauset.CausalMatrix.random(1000, density=0.5)

# Create an empty matrix (initialized to zeros)
C_empty = pycauset.CausalMatrix(1000)

# Create from a NumPy array
import numpy as np
arr = np.triu(np.random.randint(0, 2, (10, 10)), k=1).astype(bool)
C_from_np = pycauset.CausalMatrix(arr)

2. Matrix Operations

PyCauset supports standard arithmetic and specialized causal set operations.

# Matrix Multiplication (Counting paths of length 2)
# Returns an IntegerMatrix
M = pycauset.matmul(C, C)

# Elementwise Multiplication
E = C * C

# Bitwise Inversion (NOT)
C_inv = ~C

# Linear Algebra Inversion (for dense float matrices)
# Returns a FloatMatrix
F = pycauset.FloatMatrix(100)
F_inv = pycauset.invert(F)

3. Computing the K-Matrix

A common operation in causal set theory is computing $K = C(aI + C)^{-1}$.

# Compute K with scalar a=1.0
# Returns a TriangularFloatMatrix
K = pycauset.compute_k(C, a=1.0)

Matrix Types

PyCauset uses a template-based architecture to support efficient storage for different data types:

Class	Description	Storage
TriangularBitMatrix	Strictly upper-triangular boolean matrix.	1 bit / element
IntegerMatrix	Dense matrix of 32-bit integers.	4 bytes / element
FloatMatrix	Dense matrix of 64-bit floats.	8 bytes / element
TriangularFloatMatrix	Strictly upper-triangular float matrix.	8 bytes / element

Storage Management

PyCauset manages disk storage automatically to keep your workspace clean.

• Temporary Files: All matrices are created as temporary files in a .pycauset/ directory. These files are automatically deleted when your Python script exits (even if it crashes or is interrupted).
• Permanent Storage: To keep a matrix, you must use the save() function.

# This matrix is temporary and will be deleted at exit
temp = pycauset.CausalMatrix(500)

# Save it permanently to a specific path
pycauset.save(temp, "my_causet.pycauset")