ELDA

ELDA is a small C++17 linear algebra library built with CMake. It provides a dense linalg::matrix type, common matrix operations, decomposition helpers, homogeneous transformation builders, and column-vector utilities.

The public headers live under include/elda/. The library target is elda, and the repository also includes a small demo executable named main.

For the primary documentation set, open docs/index.html in a browser. The site is fully static and now organizes the public API by header, with declaration blocks and usage examples for each exported entry, along with behavioral notes and visual 3x3 examples.

Open Source Contributions

ELDA is open for contributions through GSSoC 2026. Contributors can start by reviewing issues.md for tasks grouped by difficulty, then follow the guidelines in CONTRIBUTING.md and the community standards in CODE_OF_CONDUCT.md.

For contribution-related questions, contact ayushmaankumarverma@gmail.com.

Features

• Dense matrix storage backed by std::vector<std::vector<double>>
• Matrix addition, subtraction, multiplication, assignment, and scalar multiplication
• Elementary row and column operations
• Echelon, Gaussian, Gauss-Jordan, and canonical-style reduction helpers
• Determinant, inverse, transpose, adjoint, rank, norm, trace, characteristic polynomial, and linear-system solving helpers
• Gram-Schmidt orthogonalization and orthonormalization
• QR decomposition, LU decomposition, and eigenvalue estimation helpers
• 2D and 3D homogeneous translation, scaling, and rotation matrix builders
• vec1 through vec5 helpers for constructing zero or value-filled column vectors
• check_lin_comb overloads for span-membership checks on small column-vector sets
• Near-zero floating-point cleanup through fpg()

Repository Layout

lin_alg_lib/
├── CMakeLists.txt
├── main.cpp
├── LICENSE
├── CONTRIBUTING.md
├── CODE_OF_CONDUCT.md
├── issues.md
├── include/
│   └── elda/
│       ├── linalg.hpp
│       ├── matrix.hpp
│       ├── transforms.hpp
│       └── vector_utils.hpp
├── src/
│   ├── matrix.cpp
│   ├── transforms.cpp
│   └── vector_utils.cpp
├── docs/
│   ├── index.html
│   ├── styles.css
│   └── app.js
├── DOCUMENTATION.MD
└── FUNCTIONS.MD

Requirements

• CMake 3.14 or newer
• A C++17-compatible compiler such as g++ or clang++
• A native build tool supported by CMake

Build

Configure and compile the library and demo:

cmake -S . -B build
cmake --build build

This produces:

• build/libelda.a
• build/main

Run the Demo

The demo reads a 3 x 3 matrix from standard input and prints the eigenvalue estimates returned by matrix::eigenvalues().

printf "3 4 5\n6 7 8\n8 2 3\n" | ./build/main

Use the Library

Include the full public API:

#include <elda/linalg.hpp>

Or include only the pieces you need:

#include <elda/matrix.hpp>
#include <elda/transforms.hpp>
#include <elda/vector_utils.hpp>

If you consume this repository from another CMake project, link against the elda target after adding the source tree:

add_subdirectory(path/to/lin_alg_lib)
target_link_libraries(your_target PRIVATE elda)

API Modules

• matrix.hpp: the linalg::matrix type plus arithmetic, reductions, decompositions, spectral helpers, and matrix utility functions
• transforms.hpp: 2D and 3D homogeneous translation, scaling, and rotation matrices
• vector_utils.hpp: vec1-vec5 column-vector constructors and check_lin_comb helpers
• linalg.hpp: umbrella header that includes all public headers

Behavior Notes

• The library namespace is linalg.
• Matrix entries are stored in matrix::arr as std::vector<std::vector<double>>.
• Many transformation helpers return a new matrix, while reduction helpers such as echelon(), gaussian(), gauss_jordan(), and canonical() modify the matrix in place.
• Most dimension mismatches are reported with std::runtime_error.
• Angles are interpreted in radians.
• trace(), det(), inverse(), char_poly(), and eigenvalues() are defined only for square matrices.
• solve() expects an augmented matrix with shape N x (N + 1).
• EPS is 1e-6, and fpg() zeros values whose absolute value is at most that threshold.
• Several low-level helpers assume valid indices and do not perform bounds checking.
• QR and eigenvalue routines use unshifted Gram-Schmidt/QR logic and are intended for simple real-valued workflows.

Further Reference

• docs/index.html: primary static documentation site
• DOCUMENTATION.MD: markdown summary aligned with the web docs
• FUNCTIONS.MD: compact public function index
• issues.md: contributor issue backlog grouped by difficulty
• CONTRIBUTING.md: contribution workflow and development guidelines
• CODE_OF_CONDUCT.md: community standards and reporting guidance
• LICENSE: MIT License terms