Pull Request Description

Title: Add Memory Estimation Functionality to Ripser

Related Issue: #145 - Knowing required RAM to run ripser

Background:
This pull request addresses the concerns raised in issue #145, where users experience out-of-memory errors when running Ripser due to varying parameters such as the number of points, the number of features, and the maximum dimension value. To mitigate this issue, we introduce a new functionality to estimate the RAM requirements prior to executing Ripser.

Summary of Changes Implemented:

1. New Memory Estimation Function:

   • Implemented the function estimate_ripser_memory which allows users to estimate the RAM requirements based on key parameters:
     • Number of Points: The amount of data points in the dataset.
     • Maxdim: The maximum homology dimension the user intends to compute.
     • Distance Matrix Memory: Calculated as (O(n^2)).
     • Simplicial Complex Memory: Calculated as (O(n^{(d+1)})), where (d) is the dimension of the data.
     • Persistence Computation Memory: Calculated as (O(n^3)).

2. Testing:

   • Comprehensive test cases have been added in the file test/test_memory_estimation.py to ensure:
     • Memory usage correctly increases with the dimensionality.
     • Memory usage scales proportionately concerning the number of points.
     • The function operates correctly with both point clouds and distance matrices.

3. Documentation Updates:

   • Updated the __all__ list in the module to include the new memory estimation function.
   • Added an example usage section in README.md, showcasing how to utilize the estimate_ripser_memory function to assess memory requirements.

Usage Example:
Users can estimate the RAM needed for their runs of Ripser using the following code snippet:

import numpy as np
from ripser import estimate_ripser_memory

data = np.random.random((1000, 2))
estimated_gb = estimate_ripser_memory(data, maxdim=2)
print(f"Estimated RAM required: {estimated_gb:.2f} GB")

These enhancements will help users to preemptively gauge the memory needs for their computations, reducing the likelihood of experiencing out-of-memory errors during execution.

Conclusion:
This pull request aims to improve the user experience by providing a reliable method for estimating RAM usage, thus addressing the issue raised in #145 effectively.

Fixes #145.