This library is a collection of functions and classes for doing math on small matrices with less than 2kb of instruction memory and 1kb of RAM.

It is available as:

• a library in the Arduino Library Manager and the PlatformIO registry
• a CMake library (TARGET_LINK_LIBRARIES (${EXECUTABLE_NAME} tinymatrixmath)) compatible with C++ 11+

It sacrifices some of the power of more feature-rich libraries like Basic Linear Algebra or Eigen to minimize memory footprint and standardize matrix storage across devices, possibly simplifying the process of passing matrices around across devices.

The Sheldrake library employs this library to send matrices between desktop environments and microcontrollers.

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Features

Despite this library being "tiny", it supports many common matrix operations including:

• matrix-scalar
  • addition
  • subtraction
  • multiplication
  • division
• matrix-matrix
  • addition
  • subtraction
  • multiplication
  • elementwise multiplication
• negation
• transpose
• cofactor
• determinant
• 🚧 inverse (implemented, not working)
• 🚧 eigenvalues and eigenvectors
• 🚧 characteristic polynomial

Elements with 🚧 are not yet stable or implemented.

Most common mistakes with matrix operations are checked for at compile-time, so there's no need to worry about deploying code with the following issues:

• matrices with invalid dimensions for matrix-matrix multiplication
• matrices with mismatching dimensions for elementwise operators
• taking the determinant, cofactor, and inverse of non-square matrices.

Matrices with less than 256 rows and 256 columns are supported by this library (if your device can store a matrix with a whopping 263kb RAM!). Larger matrices might be processed more efficiently with Eigen.

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Examples

Here are some examples of how to use the library:

Including the library

#include "TinyMatrixMath.hpp"

Creating a 3x3 identity matrix:

  tmm::Matrix<3,3> eye = tmm::Identity<3>();

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Creating a 3x3 matrix from a float array

  const tmm::Scalar A_raw[3][3] = {
  {1, 2, 3},
  {4, 5, 6},
  {9, 8, 9}
  };

  tmm::Matrix<3,3> A(A_raw);

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Getting the inverse of a square matrix

  tmm::Matrix<3,3> A_inv = A.inverse();

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Printing a matrix to Serial if the Arduio library is available

  A.printTo(Serial); // Arduino
  A.printTo(std::cout); // CMake

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Getting the determinant of a square matrix

  tmm::Scalar det_A = A.determinant();

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Use any sized matrix

  tmm::Matrix<4,5> B;         // 4 rows, 5 columns
  tmm::Matrix<5,2> C;         // 5 rows, 2 columns
  tmm::Matrix<5,2> D;         // 5 rows, 2 columns

  // Matrix-matrix multiplication
  tmm::Matrix<4,2> E = B * C; // 4 rows, 2 columns
  // Elementwise addition
  tmm::Matrix<5,2> F = C + D;
  // Elementwise multiplication
  F = C.elementwise_times(D);
  // Elementwise subtraction, and print the result to Serial
  (C - D).printTo(Serial);    // Arduino
  (C - D).printTo(std::cout); // CMake

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Invalid matrix multiplication is checked at compile-time.

  tmm::Matrix<4,2> G = C * B; // error: no match for 'operator*' (operand types are 'tmm::Matrix<5, 2, float>' and 'tmm::Matrix<4, 5, float>')

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Elementwise scalar operations are supported

  tmm::Matrix<2> H = 5;   // set all elements to 5
  H = H+1; // add 1 to every element
  H = H-2; // reduce every element by 2
  H = H*3; // multiply every element by 3
  H = H/4; // divide every element by 4

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1x1 matrices can be implicitly cast to Scalars

  tmm::Matrix<1,1> I = 5;
  tmm::Scalar s = I; // s = 5
  s = H; // error: cannot convert 'tmm::Matrix<2,2,float>' to 'float' in assignment

More examples

• Arduino examples can be found in the "examples" folder
• Examples for CMake project can be found in the "cmake_examples" folder

Using this Repo as a Template

The following projects were initially generated from this template:

• TinySerializer
• TinyControlPolicies

For making your own CMake/Arduino library from this template, complete the following steps:

• Hit the "Use this template" button on the GitHub repo to copy this project to your account.
• Delete the source code (under src) and add your own.
• In the root-level CMakeLists.txt
  • On the line containing project ("tinymatrixmath" C CXX), replace tinymatrixmath wtih the name of your project. We'll use this name later.
  • There is a list of files under the line containing add_library (${PROJECT_NAME}. Replace that list with a list of the files that belong to your new library.
• In .github/workflows/cmake_docs.yml, there is a line containing make tinymatrixmath_doxygen -j $(nproc). Replace tinymatrixmath with the name of your project.
• For automatically publishing documentation:
  • In the root folder of a clone of your new repo, Run the following code snippet to make a new, blank docs branch:

    git switch --orphan docs
    git commit --allow-empty -m "Initial commit on orphan branch"
    git push -u origin docs

  • On GitHub, in this repo,
    • under settings -> Pages -> Build and deployment -> Branch, select the docs branch.
    • under settings -> Actions -> General -> Workflow Permissions, select the Read and write permissions radio button to allow the docs workflow to push to the docs branch.
• Clear the examples folder and place all your Arduino example sketches there.
• Clear the cmake_examples folder and place all your CMake example executables there. Update cmake_examples/CmakeLists.txt accordingly.
• Clear the test folder and place all your unit tests there. Update test/CMakeLists.txt accordingly.
• After testing your new library thoroughly, add it to the Arduino Library Manager by following the official instructions

And you're finally done!

If you run into any issues along the way, file them here