Compressed Sparse Row Matrix Library (CSR) - C++

This library implements a Compressed Sparse Row (CSR) matrix in C++, optimizing storage and operations on sparse matrices. The library also implements conversion of matrices into row- reduced echelon form using gaussian elimination algorithms The library supports addition, subtraction, multiplication, and elementary row operations of matrices.

What is CSR?

The Compressed Sparse Row or Yale matrix format is useful for large matrices common in data analysis and machine learning. For matrices with sparsely distributed non-zero elements, the CSR format utilizes much less memory overhead than a standard matrix data structure. The CSR format stores the locations and values of non-zero elements within the matrix, therefore implying the location of all zero elements.

Features

• Efficient Storage: Stores only non-zero elements.
• Matrix Operations: Add, subtract, and multiply matrices.
• Elementary Row Operations: Swap, scale, and add rows.
• Row Reduction: Perform Gaussian elimination for solving linear systems.

How It Works

The CSR format uses:

1. values[]: Stores non-zero matrix values.
2. col_ind[]: Column indices corresponding to values[].
3. row_ptr[]: Pointers to the start of each row.

Matrix Operations

• Addition/Subtraction: Efficient operations across matching non-zero elements.
• Multiplication: Optimized for sparse data.
• Elementary Row Operations: Easily manipulate rows for the row reduction algorithm.

Benefits

• Memory Efficient: Ideal for sparse matrices.
• Fast Access: Efficient row-based modifications.
• Performance: Minimizes operations, improving performance.