Merge pull request 'Updating the readme' (#7) from update-readme into main

Reviewed-on: #7

.gitea/workflows/Merge-Checker.yaml

@@ -3,8 +3,6 @@ name: Merge-Checker
 on:
   pull_request:
     branches: ["**"]
-    paths-ignore:
-        - 'unit-tests/timing-results/**'
 
 jobs:
   build_and_test:
@@ -38,46 +36,67 @@ jobs:
               echo "Warning: $test_exec not found or not executable"
             fi
           done
-
-      - name: Run matrix-timing-tests with per-test timing output and save results
+      - name: Run matrix-timing-tests
         run: |
           mkdir -p unit-tests/timing-results
           if [ -x build/unit-tests/matrix-timing-tests ]; then
             echo "Running matrix-timing-tests with timing"
             /usr/bin/time -v build/unit-tests/matrix-timing-tests -d yes &> unit-tests/timing-results/matrix-timing-tests.txt
+            cat unit-tests/timing-results/matrix-timing-tests.txt
           else
             echo "matrix-timing-tests executable not found or not executable"
             exit 1
           fi
-      - name: Commit and push timing results
-        if: github.event.pull_request.head.repo.full_name == github.repository
+
+      - name: Compare timing results
+        id: check_diff
         run: |
-          git config --global user.name "ci-bot"
-          git config --global user.email "ci-bot@local"
+          git show origin/${{ github.event.pull_request.head.ref }}:unit-tests/timing-results/matrix-timing-tests.txt > old.txt || echo "" > old.txt
+          cp unit-tests/timing-results/matrix-timing-tests.txt new.txt
 
-          BRANCH_NAME="${{ github.event.pull_request.head.ref }}"
+          echo "Comparing timing results for changes ≥ 0.1s (ignoring 'Timing Tests' lines)..."
 
-          echo "Checking if last commit was a timing update"
-          LAST_COMMIT_MSG=$(git log -1 --pretty=%B)
+          changed=0
 
-          if echo "$LAST_COMMIT_MSG" | grep -q "Update matrix-timing-tests timings"; then
-            echo "Last commit was a timing update, skipping commit."
-            exit 0
+          awk -v changed_ref=/tmp/timings_changed.flag '
+            BEGIN {
+              change_threshold = 0.1
+            }
+            FILENAME == "old.txt" && /^[0-9]+\.[0-9]+ s: / {
+              label = substr($0, index($0, ":") + 2)
+              if (label != "Timing Tests") {
+                label_times[label] = $1
+              }
+            }
+            FILENAME == "new.txt" && /^[0-9]+\.[0-9]+ s: / {
+              new_time = $1
+              label = substr($0, index($0, ":") + 2)
+              if (label == "Timing Tests") next
+
+              old_time = label_times[label]
+              delta = new_time - old_time
+              if (delta < 0) delta = -delta
+
+              if (old_time != "" && delta >= change_threshold) {
+                printf "⚠️  %.3f s → %.3f s: %s (Δ=%.3f s)\n", old_time, new_time, label, delta
+                system("touch " changed_ref)
+              } else if (old_time == "") {
+                printf "🆕 New timing entry: %.3f s: %s\n", new_time, label
+                system("touch " changed_ref)
+              }
+            }
+            END {
+              if (!system("test -f " changed_ref)) {
+                exit 0
+              } else {
+                print "✅ Timings haven’t changed significantly (Δ < 0.1s)."
+                exit 0
+              }
+            }
+          ' old.txt new.txt
+
+          if [ -f /tmp/timings_changed.flag ]; then
+            echo "timings_changed=true" >> $GITHUB_OUTPUT
           else
-            echo "Last commit name was: {$LAST_COMMIT_MSG}"
-          fi
-
-          echo "Checking out source branch $BRANCH_NAME"
-          git stash
-          git fetch origin "$BRANCH_NAME"
-          git checkout -B "$BRANCH_NAME" "origin/$BRANCH_NAME"
-          git stash pop
-
-          git add unit-tests/timing-results/matrix-timing-tests.txt
-
-          if git diff --quiet --cached; then
-            echo "No changes to commit"
-          else
-            git commit -m "Update matrix-timing-tests timings [skip ci]"
-            git push origin "$BRANCH_NAME"
-          fi
+            echo "timings_changed=false" >> $GITHUB_OUTPUT
+          fi

.vscode/settings.json

@@ -75,5 +75,9 @@
     },
     "clangd.enable": true,
     "C_Cpp.dimInactiveRegions": false,
-    "editor.defaultFormatter": "xaver.clang-format"
+    "editor.defaultFormatter": "xaver.clang-format",
+    "clangd.inactiveRegions.useBackgroundHighlight": false,
+    "clangd.arguments": [
+        "--compile-commands-dir=${workspaceFolder}/build"
+    ],
 }

CMakeLists.txt

@@ -6,7 +6,9 @@ add_subdirectory(unit-tests)
 
 set(CMAKE_CXX_STANDARD 11)
 
-add_compile_options(-fdiagnostics-color=always -Wall -Wextra -Wpedantic)
+add_compile_options(-Wall -Wextra -Wpedantic)
+add_compile_options (-fdiagnostics-color=always)
+set(CMAKE_COLOR_DIAGNOSTICS ON)
 
 include(FetchContent)
  

README.md

@@ -1,3 +1,12 @@
 # Introduction
 This matrix math library is focused on embedded development and avoids any heap memory allocation unless you explicitly ask for it.
-It uses templates to pre-allocate matrices on the stack.
+It uses templates to pre-allocate matrices on the stack.
+
+# Building
+1. Initialize the repositiory with the command:
+```bash
+cmake -S . -B build -G Ninja
+```
+
+2. Go into the build folder and run `ninja`
+3. That's it. You can test out the build by running `./unit-tests/matrix-tests`

src/Matrix.cpp

@@ -1,3 +1,10 @@
+// This #ifndef section makes clangd happy so that it can properly do type hints
+// in this file
+#ifndef MATRIX_H_
+#define MATRIX_H_
+#include "Matrix.hpp"
+#endif
+
 #ifdef MATRIX_H_ // since the .cpp file has to be included by the .hpp file this
                  // will evaluate to true
 #include "Matrix.hpp"
@@ -5,29 +12,28 @@
 #include <algorithm>
 #include <cmath>
 #include <cstdlib>
-#include <type_traits>
 #include <cstring>
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns>::Matrix(float value)
-{
-  this->Fill(value);
-}
-
-template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns>::Matrix(const std::array<float, rows * columns> &array)
-{
+Matrix<rows, columns>::Matrix(const std::array<float, rows * columns> &array) {
   this->setMatrixToArray(array);
 }
 
 template <uint8_t rows, uint8_t columns>
 template <typename... Args>
-Matrix<rows, columns>::Matrix(Args... args)
-{
+Matrix<rows, columns>::Matrix(Args... args) {
   constexpr uint16_t arraySize{static_cast<uint16_t>(rows) *
                                static_cast<uint16_t>(columns)};
 
   std::initializer_list<float> initList{static_cast<float>(args)...};
+  // if there is only one value, we actually want to do a fill
+  if (sizeof...(args) == 1) {
+    this->Fill(*initList.begin());
+  }
+  static_assert(sizeof...(args) == arraySize || sizeof...(args) == 1,
+                "You did not provide the right amount of initializers for this "
+                "matrix size");
+
   // choose whichever buffer size is smaller for the copy length
   uint32_t minSize =
       std::min(arraySize, static_cast<uint16_t>(initList.size()));
@@ -35,22 +41,19 @@ Matrix<rows, columns>::Matrix(Args... args)
 }
 
 template <uint8_t rows, uint8_t columns>
-void Matrix<rows, columns>::Identity()
-{
-  this->Fill(0);
-  for (uint8_t idx{0}; idx < rows; idx++)
-  {
-    this->matrix[idx * columns + idx] = 1;
+Matrix<rows, columns> Matrix<rows, columns>::Identity() {
+  Matrix<rows, columns> identityMatrix{0};
+  uint32_t minDimension = std::min(rows, columns);
+  for (uint8_t idx{0}; idx < minDimension; idx++) {
+    identityMatrix[idx][idx] = 1;
   }
+  return identityMatrix;
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns>::Matrix(const Matrix<rows, columns> &other)
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+Matrix<rows, columns>::Matrix(const Matrix<rows, columns> &other) {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       this->matrix[row_idx * columns + column_idx] =
           other.Get(row_idx, column_idx);
     }
@@ -59,21 +62,15 @@ Matrix<rows, columns>::Matrix(const Matrix<rows, columns> &other)
 
 template <uint8_t rows, uint8_t columns>
 void Matrix<rows, columns>::setMatrixToArray(
-    const std::array<float, rows * columns> &array)
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+    const std::array<float, rows * columns> &array) {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       uint16_t array_idx =
           static_cast<uint16_t>(row_idx) * static_cast<uint16_t>(columns) +
           static_cast<uint16_t>(column_idx);
-      if (array_idx < array.size())
-      {
+      if (array_idx < array.size()) {
         this->matrix[row_idx * columns + column_idx] = array[array_idx];
-      }
-      else
-      {
+      } else {
         this->matrix[row_idx * columns + column_idx] = 0;
       }
     }
@@ -83,12 +80,9 @@ void Matrix<rows, columns>::setMatrixToArray(
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, columns> &
 Matrix<rows, columns>::Add(const Matrix<rows, columns> &other,
-                           Matrix<rows, columns> &result) const
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+                           Matrix<rows, columns> &result) const {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       result[row_idx][column_idx] =
           this->Get(row_idx, column_idx) + other.Get(row_idx, column_idx);
     }
@@ -99,12 +93,9 @@ Matrix<rows, columns>::Add(const Matrix<rows, columns> &other,
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, columns> &
 Matrix<rows, columns>::Sub(const Matrix<rows, columns> &other,
-                           Matrix<rows, columns> &result) const
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+                           Matrix<rows, columns> &result) const {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       result[row_idx][column_idx] =
           this->Get(row_idx, column_idx) - other.Get(row_idx, column_idx);
     }
@@ -117,18 +108,15 @@ template <uint8_t rows, uint8_t columns>
 template <uint8_t other_columns>
 Matrix<rows, other_columns> &
 Matrix<rows, columns>::Mult(const Matrix<columns, other_columns> &other,
-                            Matrix<rows, other_columns> &result) const
-{
+                            Matrix<rows, other_columns> &result) const {
   // allocate some buffers for all of our dot products
   Matrix<1, columns> this_row;
   Matrix<columns, 1> other_column;
 
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
     // get our row
     this->GetRow(row_idx, this_row);
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+    for (uint8_t column_idx{0}; column_idx < other_columns; column_idx++) {
       // get the other matrix'ss column
       other.GetColumn(column_idx, other_column);
 
@@ -143,12 +131,9 @@ Matrix<rows, columns>::Mult(const Matrix<columns, other_columns> &other,
 
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, columns> &
-Matrix<rows, columns>::Mult(float scalar, Matrix<rows, columns> &result) const
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+Matrix<rows, columns>::Mult(float scalar, Matrix<rows, columns> &result) const {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       result[row_idx][column_idx] = this->Get(row_idx, column_idx) * scalar;
     }
   }
@@ -157,9 +142,7 @@ Matrix<rows, columns>::Mult(float scalar, Matrix<rows, columns> &result) const
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns>
-Matrix<rows, columns>::Invert() const
-{
+Matrix<rows, columns> Matrix<rows, columns>::Invert() const {
   // since all matrix sizes have to be statically specified at compile time we
   // can do this
   static_assert(rows == columns,
@@ -169,8 +152,7 @@ Matrix<rows, columns>::Invert() const
   // unfortunately we can't calculate this at compile time so we'll just reurn
   // zeros
   float determinant{this->Det()};
-  if (determinant == 0)
-  {
+  if (determinant == 0) {
     // you can't invert a matrix with a negative determinant
     result.Fill(0);
     return result;
@@ -195,14 +177,10 @@ Matrix<rows, columns>::Invert() const
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<columns, rows>
-Matrix<rows, columns>::Transpose() const
-{
+Matrix<columns, rows> Matrix<rows, columns>::Transpose() const {
   Matrix<columns, rows> result{};
-  for (uint8_t column_idx{0}; column_idx < rows; column_idx++)
-  {
-    for (uint8_t row_idx{0}; row_idx < columns; row_idx++)
-    {
+  for (uint8_t column_idx{0}; column_idx < rows; column_idx++) {
+    for (uint8_t row_idx{0}; row_idx < columns; row_idx++) {
       result[row_idx][column_idx] = this->Get(column_idx, row_idx);
     }
   }
@@ -214,24 +192,19 @@ Matrix<rows, columns>::Transpose() const
 // the fastest way to calculate a 2x2 matrix determinant
 // template <>
 // inline float Matrix<0, 0>::Det() const { return 1e+6; }
-template <>
-inline float Matrix<1, 1>::Det() const { return this->matrix[0]; }
-template <>
-inline float Matrix<2, 2>::Det() const
-{
+template <> inline float Matrix<1, 1>::Det() const { return this->matrix[0]; }
+template <> inline float Matrix<2, 2>::Det() const {
   return this->matrix[0] * this->matrix[3] - this->matrix[1] * this->matrix[2];
 }
 
 template <uint8_t rows, uint8_t columns>
-float Matrix<rows, columns>::Det() const
-{
+float Matrix<rows, columns>::Det() const {
   static_assert(rows == columns,
                 "You can't take the determinant of a non-square matrix.");
 
   Matrix<rows - 1, columns - 1> MinorMatrix{};
   float determinant{0};
-  for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-  {
+  for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
     // for odd indices the sign is negative
     float sign = (column_idx % 2 == 0) ? 1 : -1;
     determinant += sign * this->matrix[column_idx] *
@@ -244,12 +217,9 @@ float Matrix<rows, columns>::Det() const
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, columns> &
 Matrix<rows, columns>::ElementMultiply(const Matrix<rows, columns> &other,
-                                       Matrix<rows, columns> &result) const
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+                                       Matrix<rows, columns> &result) const {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       result[row_idx][column_idx] =
           this->Get(row_idx, column_idx) * other.Get(row_idx, column_idx);
     }
@@ -261,12 +231,9 @@ Matrix<rows, columns>::ElementMultiply(const Matrix<rows, columns> &other,
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, columns> &
 Matrix<rows, columns>::ElementDivide(const Matrix<rows, columns> &other,
-                                     Matrix<rows, columns> &result) const
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+                                     Matrix<rows, columns> &result) const {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       result[row_idx][column_idx] =
           this->Get(row_idx, column_idx) / other.Get(row_idx, column_idx);
     }
@@ -277,10 +244,8 @@ Matrix<rows, columns>::ElementDivide(const Matrix<rows, columns> &other,
 
 template <uint8_t rows, uint8_t columns>
 float Matrix<rows, columns>::Get(uint8_t row_index,
-                                 uint8_t column_index) const
-{
-  if (row_index > rows - 1 || column_index > columns - 1)
-  {
+                                 uint8_t column_index) const {
+  if (row_index > rows - 1 || column_index > columns - 1) {
     return 1e+10; // TODO: We should throw something here instead of failing
                   // quietly
   }
@@ -290,8 +255,7 @@ float Matrix<rows, columns>::Get(uint8_t row_index,
 template <uint8_t rows, uint8_t columns>
 Matrix<1, columns> &
 Matrix<rows, columns>::GetRow(uint8_t row_index,
-                              Matrix<1, columns> &row) const
-{
+                              Matrix<1, columns> &row) const {
   memcpy(&(row[0]), this->matrix.begin() + row_index * columns,
          columns * sizeof(float));
 
@@ -301,10 +265,8 @@ Matrix<rows, columns>::GetRow(uint8_t row_index,
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, 1> &
 Matrix<rows, columns>::GetColumn(uint8_t column_index,
-                                 Matrix<rows, 1> &column) const
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
+                                 Matrix<rows, 1> &column) const {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
     column[row_idx][0] = this->Get(row_idx, column_index);
   }
 
@@ -312,17 +274,13 @@ Matrix<rows, columns>::GetColumn(uint8_t column_index,
 }
 
 template <uint8_t rows, uint8_t columns>
-void Matrix<rows, columns>::ToString(std::string &stringBuffer) const
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
+void Matrix<rows, columns>::ToString(std::string &stringBuffer) const {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
     stringBuffer += "|";
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       stringBuffer +=
           std::to_string(this->matrix[row_idx * columns + column_idx]);
-      if (column_idx != columns - 1)
-      {
+      if (column_idx != columns - 1) {
         stringBuffer += "\t";
       }
     }
@@ -331,11 +289,14 @@ void Matrix<rows, columns>::ToString(std::string &stringBuffer) const
 }
 
 template <uint8_t rows, uint8_t columns>
-std::array<float, columns> &Matrix<rows, columns>::
-operator[](uint8_t row_index)
-{
-  if (row_index > rows - 1)
-  {
+const float *Matrix<rows, columns>::ToArray() const {
+  return this->matrix.data();
+}
+
+template <uint8_t rows, uint8_t columns>
+std::array<float, columns> &
+Matrix<rows, columns>::operator[](uint8_t row_index) {
+  if (row_index > rows - 1) {
     // TODO: We should throw something here instead of failing quietly.
     row_index = 0;
   }
@@ -346,9 +307,8 @@ operator[](uint8_t row_index)
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns> &Matrix<rows, columns>::
-operator=(const Matrix<rows, columns> &other)
-{
+Matrix<rows, columns> &
+Matrix<rows, columns>::operator=(const Matrix<rows, columns> &other) {
   memcpy(this->matrix.begin(), other.matrix.begin(),
          rows * columns * sizeof(float));
 
@@ -357,18 +317,16 @@ operator=(const Matrix<rows, columns> &other)
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns> Matrix<rows, columns>::
-operator+(const Matrix<rows, columns> &other) const
-{
+Matrix<rows, columns>
+Matrix<rows, columns>::operator+(const Matrix<rows, columns> &other) const {
   Matrix<rows, columns> buffer{};
   this->Add(other, buffer);
   return buffer;
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns> Matrix<rows, columns>::
-operator-(const Matrix<rows, columns> &other) const
-{
+Matrix<rows, columns>
+Matrix<rows, columns>::operator-(const Matrix<rows, columns> &other) const {
   Matrix<rows, columns> buffer{};
   this->Sub(other, buffer);
   return buffer;
@@ -376,30 +334,42 @@ operator-(const Matrix<rows, columns> &other) const
 
 template <uint8_t rows, uint8_t columns>
 template <uint8_t other_columns>
-Matrix<rows, other_columns> Matrix<rows, columns>::
-operator*(const Matrix<columns, other_columns> &other) const
-{
+Matrix<rows, other_columns> Matrix<rows, columns>::operator*(
+    const Matrix<columns, other_columns> &other) const {
   Matrix<rows, other_columns> buffer{};
   this->Mult(other, buffer);
   return buffer;
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns> Matrix<rows, columns>::operator*(float scalar) const
-{
+Matrix<rows, columns> Matrix<rows, columns>::operator*(float scalar) const {
   Matrix<rows, columns> buffer{};
   this->Mult(scalar, buffer);
   return buffer;
 }
 
+template <uint8_t rows, uint8_t columns>
+Matrix<rows, columns> Matrix<rows, columns>::operator/(float scalar) const {
+  Matrix<rows, columns> buffer = *this;
+  if (scalar == 0) {
+    buffer.Fill(1e+10);
+    return buffer;
+  }
+
+  for (uint8_t row = 0; row < rows; row++) {
+    for (uint8_t column = 0; column < columns; column++) {
+      buffer[row][column] /= scalar;
+    }
+  }
+  return buffer;
+}
+
 template <uint8_t rows, uint8_t columns>
 template <uint8_t vector_size>
 float Matrix<rows, columns>::DotProduct(const Matrix<1, vector_size> &vec1,
-                                        const Matrix<1, vector_size> &vec2)
-{
+                                        const Matrix<1, vector_size> &vec2) {
   float sum{0};
-  for (uint8_t i{0}; i < vector_size; i++)
-  {
+  for (uint8_t i{0}; i < vector_size; i++) {
     sum += vec1.Get(0, i) * vec2.Get(0, i);
   }
 
@@ -409,11 +379,9 @@ float Matrix<rows, columns>::DotProduct(const Matrix<1, vector_size> &vec1,
 template <uint8_t rows, uint8_t columns>
 template <uint8_t vector_size>
 float Matrix<rows, columns>::DotProduct(const Matrix<vector_size, 1> &vec1,
-                                        const Matrix<vector_size, 1> &vec2)
-{
+                                        const Matrix<vector_size, 1> &vec2) {
   float sum{0};
-  for (uint8_t i{0}; i < vector_size; i++)
-  {
+  for (uint8_t i{0}; i < vector_size; i++) {
     sum += vec1.Get(i, 0) * vec2.Get(i, 0);
   }
 
@@ -421,12 +389,9 @@ float Matrix<rows, columns>::DotProduct(const Matrix<vector_size, 1> &vec1,
 }
 
 template <uint8_t rows, uint8_t columns>
-void Matrix<rows, columns>::Fill(float value)
-{
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+void Matrix<rows, columns>::Fill(float value) {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       this->matrix[row_idx * columns + column_idx] = value;
     }
   }
@@ -434,14 +399,11 @@ void Matrix<rows, columns>::Fill(float value)
 
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, columns> &
-Matrix<rows, columns>::MatrixOfMinors(Matrix<rows, columns> &result) const
-{
+Matrix<rows, columns>::MatrixOfMinors(Matrix<rows, columns> &result) const {
   Matrix<rows - 1, columns - 1> MinorMatrix{};
 
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       this->MinorMatrix(MinorMatrix, row_idx, column_idx);
       result[row_idx][column_idx] = MinorMatrix.Det();
     }
@@ -453,20 +415,15 @@ Matrix<rows, columns>::MatrixOfMinors(Matrix<rows, columns> &result) const
 template <uint8_t rows, uint8_t columns>
 Matrix<rows - 1, columns - 1> &
 Matrix<rows, columns>::MinorMatrix(Matrix<rows - 1, columns - 1> &result,
-                                   uint8_t row_idx, uint8_t column_idx) const
-{
+                                   uint8_t row_idx, uint8_t column_idx) const {
   std::array<float, (rows - 1) * (columns - 1)> subArray{};
   uint16_t array_idx{0};
-  for (uint8_t row_iter{0}; row_iter < rows; row_iter++)
-  {
-    if (row_iter == row_idx)
-    {
+  for (uint8_t row_iter{0}; row_iter < rows; row_iter++) {
+    if (row_iter == row_idx) {
       continue;
     }
-    for (uint8_t column_iter{0}; column_iter < columns; column_iter++)
-    {
-      if (column_iter == column_idx)
-      {
+    for (uint8_t column_iter{0}; column_iter < columns; column_iter++) {
+      if (column_iter == column_idx) {
         continue;
       }
       subArray[array_idx] = this->Get(row_iter, column_iter);
@@ -480,12 +437,9 @@ Matrix<rows, columns>::MinorMatrix(Matrix<rows - 1, columns - 1> &result,
 
 template <uint8_t rows, uint8_t columns>
 Matrix<rows, columns> &
-Matrix<rows, columns>::adjugate(Matrix<rows, columns> &result) const
-{
-  for (uint8_t row_iter{0}; row_iter < rows; row_iter++)
-  {
-    for (uint8_t column_iter{0}; column_iter < columns; column_iter++)
-    {
+Matrix<rows, columns>::adjugate(Matrix<rows, columns> &result) const {
+  for (uint8_t row_iter{0}; row_iter < rows; row_iter++) {
+    for (uint8_t column_iter{0}; column_iter < columns; column_iter++) {
       float sign = ((row_iter + 1) % 2) == 0 ? -1 : 1;
       sign *= ((column_iter + 1) % 2) == 0 ? -1 : 1;
       result[column_iter][row_iter] = this->Get(row_iter, column_iter) * sign;
@@ -496,55 +450,34 @@ Matrix<rows, columns>::adjugate(Matrix<rows, columns> &result) const
 }
 
 template <uint8_t rows, uint8_t columns>
-Matrix<rows, columns> &
-Matrix<rows, columns>::Normalize(Matrix<rows, columns> &result) const
-{
+float Matrix<rows, columns>::EuclideanNorm() const {
+
   float sum{0};
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
+  for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
       float val{this->Get(row_idx, column_idx)};
       sum += val * val;
     }
   }
 
-  if (sum == 0)
-  {
-    // this wouldn't do anything anyways
-    result.Fill(1e+6);
-    return result;
-  }
-
-  sum = sqrt(sum);
-
-  for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
-    {
-      result[row_idx][column_idx] = this->Get(row_idx, column_idx) / sum;
-    }
-  }
-
-  return result;
+  return sqrt(sum);
 }
 
 template <uint8_t rows, uint8_t columns>
-template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset, uint8_t column_offset>
-Matrix<sub_rows, sub_columns> Matrix<rows, columns>::SubMatrix() const
-{
+template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset,
+          uint8_t column_offset>
+Matrix<sub_rows, sub_columns> Matrix<rows, columns>::SubMatrix() const {
   // static assert that sub_rows + row_offset <= rows
   // static assert that sub_columns + column_offset <= columns
   static_assert(sub_rows + row_offset <= rows,
                 "The submatrix you're trying to get is out of bounds (rows)");
-  static_assert(sub_columns + column_offset <= columns,
-                "The submatrix you're trying to get is out of bounds (columns)");
+  static_assert(
+      sub_columns + column_offset <= columns,
+      "The submatrix you're trying to get is out of bounds (columns)");
 
   Matrix<sub_rows, sub_columns> buffer{};
-  for (uint8_t row_idx{0}; row_idx < sub_rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < sub_columns; column_idx++)
-    {
+  for (uint8_t row_idx{0}; row_idx < sub_rows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < sub_columns; column_idx++) {
       buffer[row_idx][column_idx] =
           this->Get(row_idx + row_offset, column_idx + column_offset);
     }
@@ -553,21 +486,121 @@ Matrix<sub_rows, sub_columns> Matrix<rows, columns>::SubMatrix() const
 }
 
 template <uint8_t rows, uint8_t columns>
-template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset, uint8_t column_offset>
-void Matrix<rows, columns>::SetSubMatrix(const Matrix<sub_rows, sub_columns> &sub_matrix)
-{
-  static_assert(sub_rows + row_offset <= rows,
-                "The submatrix you're trying to set is out of bounds (rows)");
-  static_assert(sub_columns + column_offset <= columns,
-                "The submatrix you're trying to set is out of bounds (columns)");
+template <uint8_t sub_rows, uint8_t sub_columns>
+void Matrix<rows, columns>::SetSubMatrix(
+    uint8_t rowOffset, uint8_t columnOffset,
+    const Matrix<sub_rows, sub_columns> &sub_matrix) {
+  int16_t adjustedSubRows = sub_rows;
+  int16_t adjustedSubColumns = sub_columns;
+  int16_t adjustedRowOffset = rowOffset;
+  int16_t adjustedColumnOffset = columnOffset;
 
-  for (uint8_t row_idx{0}; row_idx < sub_rows; row_idx++)
-  {
-    for (uint8_t column_idx{0}; column_idx < sub_columns; column_idx++)
-    {
-      this->matrix[(row_idx + row_offset) * columns + column_idx + column_offset] = sub_matrix.Get(row_idx, column_idx);
+  // a bunch of safety checks to make sure we don't overflow the matrix
+  if (sub_rows > rows) {
+    adjustedSubRows = rows;
+  }
+  if (sub_columns > columns) {
+    adjustedSubColumns = columns;
+  }
+
+  if (adjustedSubRows + adjustedRowOffset >= rows) {
+    adjustedRowOffset =
+        std::max(0, static_cast<int16_t>(rows) - adjustedSubRows);
+  }
+
+  if (adjustedSubColumns + adjustedColumnOffset >= columns) {
+    adjustedColumnOffset =
+        std::max(0, static_cast<int16_t>(columns) - adjustedSubColumns);
+  }
+
+  for (uint8_t row_idx{0}; row_idx < adjustedSubRows; row_idx++) {
+    for (uint8_t column_idx{0}; column_idx < adjustedSubColumns; column_idx++) {
+      this->matrix[(row_idx + adjustedRowOffset) * columns + column_idx +
+                   adjustedColumnOffset] = sub_matrix.Get(row_idx, column_idx);
     }
   }
 }
 
+// QR decomposition: decomposes this matrix A into Q and R
+// Assumes square matrix
+template <uint8_t rows, uint8_t columns>
+void Matrix<rows, columns>::QRDecomposition(Matrix<rows, columns> &Q,
+                                            Matrix<columns, columns> &R) const {
+  static_assert(columns <= rows, "QR decomposition requires columns <= rows");
+
+  Q.Fill(0);
+  R.Fill(0);
+  Matrix<rows, 1> a_col, e, u, Q_column_k{};
+  Matrix<1, rows> a_T, e_T{};
+
+  for (uint8_t column = 0; column < columns; column++) {
+    this->GetColumn(column, a_col);
+    u = a_col;
+    // -----------------------
+    // ----- CALCULATE Q -----
+    // -----------------------
+    for (uint8_t k = 0; k <= column; k++) {
+      Q.GetColumn(k, Q_column_k);
+      Matrix<1, rows> Q_column_k_T = Q_column_k.Transpose();
+      u = u - Q_column_k * (Q_column_k_T * a_col);
+    }
+    float norm = u.EuclideanNorm();
+    if (norm > 1e-4) {
+      u = u / norm;
+    } else {
+      u.Fill(0);
+    }
+    Q.SetSubMatrix(0, column, u);
+
+    // -----------------------
+    // ----- CALCULATE R -----
+    // -----------------------
+    for (uint8_t k = 0; k <= column; k++) {
+      Q.GetColumn(k, e);
+      R[k][column] = (a_col.Transpose() * e).Get(0, 0);
+    }
+  }
+}
+
+template <uint8_t rows, uint8_t columns>
+void Matrix<rows, columns>::EigenQR(Matrix<rows, rows> &eigenVectors,
+                                    Matrix<rows, 1> &eigenValues,
+                                    uint32_t maxIterations,
+                                    float tolerance) const {
+  static_assert(rows > 1, "Matrix size must be > 1 for QR iteration");
+  static_assert(rows == columns, "Matrix size must be square for QR iteration");
+
+  Matrix<rows, rows> Ak = *this; // Copy original matrix
+  Matrix<rows, rows> QQ{Matrix<rows, rows>::Identity()};
+  Matrix<rows, rows> shift{0};
+
+  for (uint32_t iter = 0; iter < maxIterations; ++iter) {
+    Matrix<rows, rows> Q, R;
+
+    // // QR shift lets us "attack" the first diagonal to speed up the algorithm
+    // shift = Matrix<rows, rows>::Identity() * Ak[rows - 1][rows - 1];
+    (Ak - shift).QRDecomposition(Q, R);
+    Ak = R * Q + shift;
+    QQ = QQ * Q;
+
+    // Check convergence: off-diagonal norm
+    float offDiagSum = 0.0f;
+    for (uint32_t row = 1; row < rows; row++) {
+      for (uint32_t column = 0; column < row; column++) {
+        offDiagSum += fabs(Ak[row][column]);
+      }
+    }
+
+    if (offDiagSum < tolerance) {
+      break;
+    }
+  }
+
+  // Diagonal elements are the eigenvalues
+  for (uint8_t i = 0; i < rows; i++) {
+    eigenValues[i][0] = Ak[i][i];
+  }
+  eigenVectors = QQ;
+}
+
 #endif // MATRIX_H_

src/Matrix.hpp

@@ -1,5 +1,4 @@
-#ifndef MATRIX_H_
-#define MATRIX_H_
+#pragma once
 
 #include <array>
 #include <cstdint>
@@ -19,11 +18,6 @@ public:
    */
   Matrix() = default;
 
-  /**
-   * @brief Create a matrix but fill all of its entries with one value
-   */
-  Matrix(float value);
-
   /**
    * @brief Initialize a matrix with an array
    */
@@ -40,9 +34,9 @@ public:
   template <typename... Args> Matrix(Args... args);
 
   /**
-   * @brief set the matrix diagonals to 1 and all other values to 0
+   * @brief Create an identity matrix
    */
-  void Identity();
+  static Matrix<rows, columns> Identity();
 
   /**
    * @brief Set all elements in this to value
@@ -129,10 +123,11 @@ public:
   Matrix<columns, rows> Transpose() const;
 
   /**
-   * @brief reduce the matrix so the sum of its elements equal 1
+   * @brief Returns the euclidean magnitude of the matrix. Also known as the L2
+   * norm
    * @param result a buffer to store the result into
    */
-  Matrix<rows, columns> &Normalize(Matrix<rows, columns> &result) const;
+  float EuclideanNorm() const;
 
   /**
    * @brief Get a row from the matrix
@@ -159,8 +154,16 @@ public:
    */
   constexpr uint8_t GetColumnSize() { return columns; }
 
+  /**
+   * @brief Write a string representation of the matrix into the buffer
+   */
   void ToString(std::string &stringBuffer) const;
 
+  /**
+   * @brief Returns the internal representation of the matrix as an array
+   */
+  const float *ToArray() const;
+
   /**
    * @brief Get an element from the matrix
    * @param row the row index of the element
@@ -193,13 +196,15 @@ public:
 
   Matrix<rows, columns> operator*(float scalar) const;
 
+  Matrix<rows, columns> operator/(float scalar) const;
+
   template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset,
             uint8_t column_offset>
   Matrix<sub_rows, sub_columns> SubMatrix() const;
 
-  template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset,
-            uint8_t column_offset>
-  void SetSubMatrix(const Matrix<sub_rows, sub_columns> &sub_matrix);
+  template <uint8_t sub_rows, uint8_t sub_columns>
+  void SetSubMatrix(uint8_t rowOffset, uint8_t columnOffset,
+                    const Matrix<sub_rows, sub_columns> &sub_matrix);
 
   /**
    * @brief take the dot product of the two vectors
@@ -216,6 +221,28 @@ public:
     return vec1.Get(0, 0) * vec2.Get(0, 0);
   }
 
+  /**
+   * @brief Performs QR decomposition on this matrix
+   * @param Q a buffer that will contain Q after the function completes
+   * @param R a buffer that will contain R after the function completes
+   */
+  void QRDecomposition(Matrix<rows, columns> &Q,
+                       Matrix<columns, columns> &R) const;
+
+  /**
+   * @brief Uses QR decomposition to efficiently calculate the eigenvectors
+   * and values of this matrix
+   * @param eigenVectors a buffer that will contain the eigenvectors fo this
+   * matrix
+   * @param eigenValues a buffer that will contain the eigenValues fo this
+   * matrix
+   * @param maxIterations the number of iterations to perform before giving
+   * up on reaching the given tolerance
+   * @param tolerance the level of accuracy to obtain before stopping.
+   */
+  void EigenQR(Matrix<rows, rows> &eigenVectors, Matrix<rows, 1> &eigenValues,
+               uint32_t maxIterations = 1000, float tolerance = 1e-6f) const;
+
 protected:
   std::array<float, rows * columns> matrix;
 
@@ -225,6 +252,6 @@ private:
   void setMatrixToArray(const std::array<float, rows * columns> &array);
 };
 
+#ifndef MATRIX_H_
 #include "Matrix.cpp"
-
 #endif // MATRIX_H_

src/Quaternion.cpp

@@ -6,115 +6,115 @@
  * @param angle The angle to rotate by
  * @param axis The axis to rotate around
  */
-Quaternion Quaternion::FromAngleAndAxis(float angle, const Matrix<1, 3> &axis)
-{
-    const float halfAngle = angle / 2;
-    const float sinHalfAngle = sin(halfAngle);
-    Matrix<1, 3> normalizedAxis{};
-    axis.Normalize(normalizedAxis);
-    return Quaternion{
-        static_cast<float>(cos(halfAngle)),
-        normalizedAxis.Get(0, 0) * sinHalfAngle,
-        normalizedAxis.Get(0, 1) * sinHalfAngle,
-        normalizedAxis.Get(0, 2) * sinHalfAngle};
+Quaternion Quaternion::FromAngleAndAxis(float angle, const Matrix<1, 3> &axis) {
+  const float halfAngle = angle / 2;
+  const float sinHalfAngle = sin(halfAngle);
+  Matrix<1, 3> normalizedAxis = axis / axis.EuclideanNorm();
+  return Quaternion{static_cast<float>(cos(halfAngle)),
+                    normalizedAxis.Get(0, 0) * sinHalfAngle,
+                    normalizedAxis.Get(0, 1) * sinHalfAngle,
+                    normalizedAxis.Get(0, 2) * sinHalfAngle};
 }
 
-float Quaternion::operator[](uint8_t index) const
-{
-    if (index < 4)
-    {
-        return this->matrix[index];
-    }
+float Quaternion::operator[](uint8_t index) const {
+  if (index < 4) {
+    return this->matrix[index];
+  }
 
-    // index out of bounds
-    return 1e+6;
+  // index out of bounds
+  return 1e+6;
 }
 
-void Quaternion::operator=(const Quaternion &other)
-{
-    memcpy(&(this->matrix), &(other.matrix), 4 * sizeof(float));
+void Quaternion::operator=(const Quaternion &other) {
+  memcpy(&(this->matrix), &(other.matrix), 4 * sizeof(float));
 }
 
-Quaternion Quaternion::operator*(const Quaternion &other) const
-{
-    Quaternion result{};
-    this->Q_Mult(other, result);
-    return result;
+Quaternion Quaternion::operator*(const Quaternion &other) const {
+  Quaternion result{};
+  this->Q_Mult(other, result);
+  return result;
 }
 
-Quaternion Quaternion::operator*(float scalar) const
-{
-    return Quaternion{this->w * scalar, this->v1 * scalar, this->v2 * scalar, this->v3 * scalar};
+Quaternion Quaternion::operator*(float scalar) const {
+  return Quaternion{this->w * scalar, this->v1 * scalar, this->v2 * scalar,
+                    this->v3 * scalar};
 }
 
-Quaternion Quaternion::operator+(const Quaternion &other) const
-{
-    return Quaternion{this->w + other.w, this->v1 + other.v1, this->v2 + other.v2, this->v3 + other.v3};
+Quaternion Quaternion::operator+(const Quaternion &other) const {
+  return Quaternion{this->w + other.w, this->v1 + other.v1, this->v2 + other.v2,
+                    this->v3 + other.v3};
 }
 
-Quaternion &
-Quaternion::Q_Mult(const Quaternion &other, Quaternion &buffer) const
-{
+Quaternion &Quaternion::Q_Mult(const Quaternion &other,
+                               Quaternion &buffer) const {
 
-    // eq. 6
-    buffer.w = (other.w * this->w - other.v1 * this->v1 - other.v2 * this->v2 - other.v3 * this->v3);
-    buffer.v1 = (other.w * this->v1 + other.v1 * this->w - other.v2 * this->v3 + other.v3 * this->v2);
-    buffer.v2 = (other.w * this->v2 + other.v1 * this->v3 + other.v2 * this->w - other.v3 * this->v1);
-    buffer.v3 = (other.w * this->v3 - other.v1 * this->v2 + other.v2 * this->v1 + other.v3 * this->w);
-    return buffer;
+  // eq. 6
+  buffer.w = (other.w * this->w - other.v1 * this->v1 - other.v2 * this->v2 -
+              other.v3 * this->v3);
+  buffer.v1 = (other.w * this->v1 + other.v1 * this->w - other.v2 * this->v3 +
+               other.v3 * this->v2);
+  buffer.v2 = (other.w * this->v2 + other.v1 * this->v3 + other.v2 * this->w -
+               other.v3 * this->v1);
+  buffer.v3 = (other.w * this->v3 - other.v1 * this->v2 + other.v2 * this->v1 +
+               other.v3 * this->w);
+  return buffer;
 }
 
-Quaternion &Quaternion::Rotate(Quaternion &other, Quaternion &buffer) const
-{
-    Quaternion prime{this->w, -this->v1, -this->v2, -this->v3};
-    buffer.v1 = other.v1;
-    buffer.v2 = other.v2;
-    buffer.v3 = other.v3;
-    buffer.w = 0;
+Quaternion &Quaternion::Rotate(Quaternion &other, Quaternion &buffer) const {
+  Quaternion prime{this->w, -this->v1, -this->v2, -this->v3};
+  buffer.v1 = other.v1;
+  buffer.v2 = other.v2;
+  buffer.v3 = other.v3;
+  buffer.w = 0;
 
-    Quaternion temp{};
-    this->Q_Mult(buffer, temp);
-    temp.Q_Mult(prime, buffer);
-    return buffer;
+  Quaternion temp{};
+  this->Q_Mult(buffer, temp);
+  temp.Q_Mult(prime, buffer);
+  return buffer;
 }
 
-void Quaternion::Normalize()
-{
-    float magnitude = sqrt(this->v1 * this->v1 + this->v2 * this->v2 + this->v3 * this->v3 + this->w * this->w);
-    if (magnitude == 0)
-    {
-        return;
-    }
-    this->v1 /= magnitude;
-    this->v2 /= magnitude;
-    this->v3 /= magnitude;
-    this->w /= magnitude;
+void Quaternion::Normalize() {
+  float magnitude = sqrt(this->v1 * this->v1 + this->v2 * this->v2 +
+                         this->v3 * this->v3 + this->w * this->w);
+  if (magnitude == 0) {
+    return;
+  }
+  this->v1 /= magnitude;
+  this->v2 /= magnitude;
+  this->v3 /= magnitude;
+  this->w /= magnitude;
 }
 
-Matrix<3, 3> Quaternion::ToRotationMatrix() const
-{
-    float xx = this->v1 * this->v1;
-    float yy = this->v2 * this->v2;
-    float zz = this->v3 * this->v3;
-    Matrix<3, 3> rotationMatrix{
-        1 - 2 * (yy - zz), 2 * (this->v1 * this->v2 - this->v3 * this->w), 2 * (this->v1 * this->v3 + this->v2 * this->w),
-        2 * (this->v1 * this->v2 + this->v3 * this->w), 1 - 2 * (xx - zz), 2 * (this->v2 * this->v3 - this->v1 * this->w),
-        2 * (this->v1 * this->v3 - this->v2 * this->w), 2 * (this->v2 * this->v3 + this->v1 * this->w), 1 - 2 * (xx - yy)};
-    return rotationMatrix;
+Matrix<3, 3> Quaternion::ToRotationMatrix() const {
+  float xx = this->v1 * this->v1;
+  float yy = this->v2 * this->v2;
+  float zz = this->v3 * this->v3;
+  Matrix<3, 3> rotationMatrix{1 - 2 * (yy - zz),
+                              2 * (this->v1 * this->v2 - this->v3 * this->w),
+                              2 * (this->v1 * this->v3 + this->v2 * this->w),
+                              2 * (this->v1 * this->v2 + this->v3 * this->w),
+                              1 - 2 * (xx - zz),
+                              2 * (this->v2 * this->v3 - this->v1 * this->w),
+                              2 * (this->v1 * this->v3 - this->v2 * this->w),
+                              2 * (this->v2 * this->v3 + this->v1 * this->w),
+                              1 - 2 * (xx - yy)};
+  return rotationMatrix;
 };
 
-Matrix<3, 1> Quaternion::ToEulerAngle() const
-{
-    float sqv1 = this->v1 * this->v1;
-    float sqv2 = this->v2 * this->v2;
-    float sqv3 = this->v3 * this->v3;
-    float sqw = this->w * this->w;
+Matrix<3, 1> Quaternion::ToEulerAngle() const {
+  float sqv1 = this->v1 * this->v1;
+  float sqv2 = this->v2 * this->v2;
+  float sqv3 = this->v3 * this->v3;
+  float sqw = this->w * this->w;
 
-    Matrix<3, 1> eulerAngle;
-    {
-        atan2(2.0 * (this->v1 * this->v2 + this->v3 * this->w), (sqv1 - sqv2 - sqv3 + sqw));
-        asin(-2.0 * (this->v1 * this->v3 - this->v2 * this->w) / (sqv1 + sqv2 + sqv3 + sqw));
-        atan2(2.0 * (this->v2 * this->v3 + this->v1 * this->w), (-sqv1 - sqv2 + sqv3 + sqw));
-    };
-    return eulerAngle;
+  Matrix<3, 1> eulerAngle;
+  {
+    atan2(2.0 * (this->v1 * this->v2 + this->v3 * this->w),
+          (sqv1 - sqv2 - sqv3 + sqw));
+    asin(-2.0 * (this->v1 * this->v3 - this->v2 * this->w) /
+         (sqv1 + sqv2 + sqv3 + sqw));
+    atan2(2.0 * (this->v2 * this->v3 + this->v1 * this->w),
+          (-sqv1 - sqv2 + sqv3 + sqw));
+  };
+  return eulerAngle;
 }

src/Quaternion.h

@@ -2,90 +2,89 @@
 #define QUATERNION_H_
 
 #include "Matrix.hpp"
-class Quaternion : public Matrix<1, 4>
-{
+class Quaternion : public Matrix<1, 4> {
 public:
-    Quaternion() : Matrix<1, 4>() {}
-    Quaternion(float fillValue) : Matrix<1, 4>(fillValue) {}
-    Quaternion(float w, float v1, float v2, float v3) : Matrix<1, 4>(w, v1, v2, v3) {}
-    Quaternion(const Quaternion &q) : Matrix<1, 4>(q.w, q.v1, q.v2, q.v3) {}
-    Quaternion(const Matrix<1, 4> &matrix) : Matrix<1, 4>(matrix) {}
-    Quaternion(const std::array<float, 4> &array) : Matrix<1, 4>(array) {}
+  Quaternion() : Matrix<1, 4>() {}
+  Quaternion(float w, float v1, float v2, float v3)
+      : Matrix<1, 4>(w, v1, v2, v3) {}
+  Quaternion(const Quaternion &q) : Matrix<1, 4>(q.w, q.v1, q.v2, q.v3) {}
+  Quaternion(const Matrix<1, 4> &matrix) : Matrix<1, 4>(matrix) {}
+  Quaternion(const std::array<float, 4> &array) : Matrix<1, 4>(array) {}
 
-    /**
-     * @brief Create a quaternion from an angle and axis
-     * @param angle The angle to rotate by
-     * @param axis The axis to rotate around
-     */
-    static Quaternion FromAngleAndAxis(float angle, const Matrix<1, 3> &axis);
+  /**
+   * @brief Create a quaternion from an angle and axis
+   * @param angle The angle to rotate by
+   * @param axis The axis to rotate around
+   */
+  static Quaternion FromAngleAndAxis(float angle, const Matrix<1, 3> &axis);
 
-    /**
-     * @brief Access the elements of the quaternion
-     * @param index The index of the element to access
-     * @return The value of the element at the index
-     */
-    float operator[](uint8_t index) const;
+  /**
+   * @brief Access the elements of the quaternion
+   * @param index The index of the element to access
+   * @return The value of the element at the index
+   */
+  float operator[](uint8_t index) const;
 
-    /**
-     * @brief Assign one quaternion to another
-     */
-    void operator=(const Quaternion &other);
+  /**
+   * @brief Assign one quaternion to another
+   */
+  void operator=(const Quaternion &other);
 
-    /**
-     * @brief Do quaternion multiplication
-     */
-    Quaternion operator*(const Quaternion &other) const;
+  /**
+   * @brief Do quaternion multiplication
+   */
+  Quaternion operator*(const Quaternion &other) const;
 
-    /**
-     * @brief Multiply the quaternion by a scalar
-     */
-    Quaternion operator*(float scalar) const;
+  /**
+   * @brief Multiply the quaternion by a scalar
+   */
+  Quaternion operator*(float scalar) const;
 
-    /**
-     * @brief Add two quaternions together
-     * @param other The quaternion to add to this one
-     * @return The net quaternion
-     */
-    Quaternion operator+(const Quaternion &other) const;
+  /**
+   * @brief Add two quaternions together
+   * @param other The quaternion to add to this one
+   * @return The net quaternion
+   */
+  Quaternion operator+(const Quaternion &other) const;
 
-    /**
-     * @brief Q_Mult a quaternion by another quaternion
-     * @param other The quaternion to rotate by
-     * @param buffer The buffer to store the result in
-     * @return A reference to the buffer
-     */
-    Quaternion &Q_Mult(const Quaternion &other, Quaternion &buffer) const;
+  /**
+   * @brief Q_Mult a quaternion by another quaternion
+   * @param other The quaternion to rotate by
+   * @param buffer The buffer to store the result in
+   * @return A reference to the buffer
+   */
+  Quaternion &Q_Mult(const Quaternion &other, Quaternion &buffer) const;
 
-    /**
-     * @brief Rotate a quaternion by this quaternion
-     * @param other The quaternion to rotate
-     * @param buffer The buffer to store the result in
-     *
-     */
-    Quaternion &Rotate(Quaternion &other, Quaternion &buffer) const;
+  /**
+   * @brief Rotate a quaternion by this quaternion
+   * @param other The quaternion to rotate
+   * @param buffer The buffer to store the result in
+   *
+   */
+  Quaternion &Rotate(Quaternion &other, Quaternion &buffer) const;
 
-    /**
-     * @brief Normalize the quaternion to a magnitude of 1
-     */
-    void Normalize();
+  /**
+   * @brief Normalize the quaternion to a magnitude of 1
+   */
+  void Normalize();
 
-    /**
-     * @brief Convert the quaternion to a rotation matrix
-     * @return The rotation matrix
-     */
-    Matrix<3, 3> ToRotationMatrix() const;
+  /**
+   * @brief Convert the quaternion to a rotation matrix
+   * @return The rotation matrix
+   */
+  Matrix<3, 3> ToRotationMatrix() const;
 
-    /**
-     * @brief Convert the quaternion to an Euler angle representation
-     * @return The Euler angle representation of the quaternion
-     */
-    Matrix<3, 1> ToEulerAngle() const;
+  /**
+   * @brief Convert the quaternion to an Euler angle representation
+   * @return The Euler angle representation of the quaternion
+   */
+  Matrix<3, 1> ToEulerAngle() const;
 
-    // Give people an easy way to access the elements
-    float &w{matrix[0]};
-    float &v1{matrix[1]};
-    float &v2{matrix[2]};
-    float &v3{matrix[3]};
+  // Give people an easy way to access the elements
+  float &w{matrix[0]};
+  float &v1{matrix[1]};
+  float &v2{matrix[2]};
+  float &v3{matrix[3]};
 };
 
 #endif // QUATERNION_H_

unit-tests/matrix-tests.cpp

@@ -10,41 +10,61 @@
 #include <cmath>
 #include <iostream>
 
+// Helper functions
+template <uint8_t rows, uint8_t columns>
+float matrixSum(const Matrix<rows, columns> &matrix) {
+  float sum = 0;
+  for (uint32_t i = 0; i < rows * columns; i++) {
+    float number = matrix.ToArray()[i];
+    sum += number * number;
+  }
+  return std::sqrt(sum);
+}
+
+template <uint8_t rows, uint8_t columns>
+void printLabeledMatrix(const std::string &label,
+                        const Matrix<rows, columns> &matrix) {
+  std::string strBuf = "";
+  matrix.ToString(strBuf);
+  std::cout << label << ":\n" << strBuf << std::endl;
+}
+
+TEST_CASE("Initialization", "Matrix") {
+  SECTION("Array Initialization") {
+    std::array<float, 4> arr2{5, 6, 7, 8};
+    Matrix<2, 2> mat2{arr2};
+    // array initialization
+    REQUIRE(mat2.Get(0, 0) == 5);
+    REQUIRE(mat2.Get(0, 1) == 6);
+    REQUIRE(mat2.Get(1, 0) == 7);
+    REQUIRE(mat2.Get(1, 1) == 8);
+  }
+
+  SECTION("Argument Pack Initialization") {
+    Matrix<2, 2> mat1{1, 2, 3, 4};
+    // template pack initialization
+    REQUIRE(mat1.Get(0, 0) == 1);
+    REQUIRE(mat1.Get(0, 1) == 2);
+    REQUIRE(mat1.Get(1, 0) == 3);
+    REQUIRE(mat1.Get(1, 1) == 4);
+  }
+
+  SECTION("Single Argument Pack Initialization") {
+    Matrix<2, 2> mat1{2};
+    // template pack initialization
+    REQUIRE(mat1.Get(0, 0) == 2);
+    REQUIRE(mat1.Get(0, 1) == 2);
+    REQUIRE(mat1.Get(1, 0) == 2);
+    REQUIRE(mat1.Get(1, 1) == 2);
+  }
+}
+
 TEST_CASE("Elementary Matrix Operations", "Matrix") {
   std::array<float, 4> arr2{5, 6, 7, 8};
   Matrix<2, 2> mat1{1, 2, 3, 4};
   Matrix<2, 2> mat2{arr2};
   Matrix<2, 2> mat3{};
 
-  SECTION("Initialization") {
-    // array initialization
-    REQUIRE(mat1.Get(0, 0) == 1);
-    REQUIRE(mat1.Get(0, 1) == 2);
-    REQUIRE(mat1.Get(1, 0) == 3);
-    REQUIRE(mat1.Get(1, 1) == 4);
-
-    // empty initialization
-    REQUIRE(mat3.Get(0, 0) == 0);
-    REQUIRE(mat3.Get(0, 1) == 0);
-    REQUIRE(mat3.Get(1, 0) == 0);
-    REQUIRE(mat3.Get(1, 1) == 0);
-
-    // template pack initialization
-    REQUIRE(mat2.Get(0, 0) == 5);
-    REQUIRE(mat2.Get(0, 1) == 6);
-    REQUIRE(mat2.Get(1, 0) == 7);
-    REQUIRE(mat2.Get(1, 1) == 8);
-
-    // large matrix
-    Matrix<255, 255> mat6{};
-    mat6.Fill(4);
-    for (uint8_t row{0}; row < 255; row++) {
-      for (uint8_t column{0}; column < 255; column++) {
-        REQUIRE(mat6.Get(row, column) == 4);
-      }
-    }
-  }
-
   SECTION("Fill") {
     mat1.Fill(0);
     REQUIRE(mat1.Get(0, 0) == 0);
@@ -66,10 +86,6 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
   }
 
   SECTION("Addition") {
-    std::string strBuf1 = "";
-    mat1.ToString(strBuf1);
-    std::cout << "Matrix 1:\n" << strBuf1 << std::endl;
-
     mat1.Add(mat2, mat3);
 
     REQUIRE(mat3.Get(0, 0) == 6);
@@ -119,7 +135,35 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
     REQUIRE(mat3.Get(1, 0) == 43);
     REQUIRE(mat3.Get(1, 1) == 50);
 
-    // TODO: You need to add non-square multiplications to this.
+    // Non-square multiplication
+    Matrix<2, 4> mat4{1, 2, 3, 4, 5, 6, 7, 8};
+    Matrix<4, 2> mat5{9, 10, 11, 12, 13, 14, 15, 16};
+    Matrix<2, 2> mat6{};
+    mat6 = mat4 * mat5;
+    REQUIRE(mat6.Get(0, 0) == 130);
+    REQUIRE(mat6.Get(0, 1) == 140);
+    REQUIRE(mat6.Get(1, 0) == 322);
+    REQUIRE(mat6.Get(1, 1) == 348);
+
+    // One more non-square multiplicaiton
+    Matrix<4, 4> mat7{};
+    mat7 = mat5 * mat4;
+    REQUIRE(mat7.Get(0, 0) == 59);
+    REQUIRE(mat7.Get(0, 1) == 78);
+    REQUIRE(mat7.Get(0, 2) == 97);
+    REQUIRE(mat7.Get(0, 3) == 116);
+    REQUIRE(mat7.Get(1, 0) == 71);
+    REQUIRE(mat7.Get(1, 1) == 94);
+    REQUIRE(mat7.Get(1, 2) == 117);
+    REQUIRE(mat7.Get(1, 3) == 140);
+    REQUIRE(mat7.Get(2, 0) == 83);
+    REQUIRE(mat7.Get(2, 1) == 110);
+    REQUIRE(mat7.Get(2, 2) == 137);
+    REQUIRE(mat7.Get(2, 3) == 164);
+    REQUIRE(mat7.Get(3, 0) == 95);
+    REQUIRE(mat7.Get(3, 1) == 126);
+    REQUIRE(mat7.Get(3, 2) == 157);
+    REQUIRE(mat7.Get(3, 3) == 188);
   }
 
   SECTION("Scalar Multiplication") {
@@ -254,26 +298,6 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
     REQUIRE(mat5.Get(2, 1) == 6);
   }
 
-  SECTION("Normalize") {
-    mat1.Normalize(mat3);
-
-    float sqrt_30{sqrt(30)};
-
-    REQUIRE(mat3.Get(0, 0) == 1 / sqrt_30);
-    REQUIRE(mat3.Get(0, 1) == 2 / sqrt_30);
-    REQUIRE(mat3.Get(1, 0) == 3 / sqrt_30);
-    REQUIRE(mat3.Get(1, 1) == 4 / sqrt_30);
-
-    Matrix<2, 1> mat4{-0.878877044, 2.92092276};
-    Matrix<2, 1> mat5{};
-    mat4.Normalize(mat5);
-
-    REQUIRE_THAT(mat5.Get(0, 0),
-                 Catch::Matchers::WithinRel(-0.288129855179f, 1e-6f));
-    REQUIRE_THAT(mat5.Get(1, 0),
-                 Catch::Matchers::WithinRel(0.957591346325f, 1e-6f));
-  }
-
   SECTION("GET ROW") {
     Matrix<1, 2> mat1Rows{};
     mat1.GetRow(0, mat1Rows);
@@ -328,29 +352,289 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
     Matrix<3, 3> mat4 = startMatrix;
 
     Matrix<2, 2> mat5{10, 11, 12, 13};
-    mat4.SetSubMatrix<2, 2, 0, 0>(mat5);
+    mat4.SetSubMatrix(0, 0, mat5);
     REQUIRE(mat4.Get(0, 0) == 10);
     REQUIRE(mat4.Get(0, 1) == 11);
     REQUIRE(mat4.Get(1, 0) == 12);
     REQUIRE(mat4.Get(1, 1) == 13);
 
     mat4 = startMatrix;
-    mat4.SetSubMatrix<2, 2, 1, 1>(mat5);
+    mat4.SetSubMatrix(1, 1, mat5);
     REQUIRE(mat4.Get(1, 1) == 10);
     REQUIRE(mat4.Get(1, 2) == 11);
     REQUIRE(mat4.Get(2, 1) == 12);
     REQUIRE(mat4.Get(2, 2) == 13);
 
     Matrix<3, 1> mat6{10, 11, 12};
-    mat4.SetSubMatrix<3, 1, 0, 0>(mat6);
+    mat4.SetSubMatrix(0, 0, mat6);
     REQUIRE(mat4.Get(0, 0) == 10);
     REQUIRE(mat4.Get(1, 0) == 11);
     REQUIRE(mat4.Get(2, 0) == 12);
 
     Matrix<1, 3> mat7{10, 11, 12};
-    mat4.SetSubMatrix<1, 3, 0, 0>(mat7);
+    mat4.SetSubMatrix(0, 0, mat7);
     REQUIRE(mat4.Get(0, 0) == 10);
     REQUIRE(mat4.Get(0, 1) == 11);
     REQUIRE(mat4.Get(0, 2) == 12);
   }
+}
+
+TEST_CASE("Identity Matrix", "Matrix") {
+  SECTION("Square Matrix") {
+    Matrix<5, 5> matrix = Matrix<5, 5>::Identity();
+    uint32_t oneColumnIndex{0};
+    for (uint32_t row = 0; row < 5; row++) {
+      for (uint32_t column = 0; column < 5; column++) {
+        float value = matrix[row][column];
+        if (oneColumnIndex == column) {
+          REQUIRE_THAT(value, Catch::Matchers::WithinRel(1.0f, 1e-6f));
+        } else {
+          REQUIRE_THAT(value, Catch::Matchers::WithinRel(0.0f, 1e-6f));
+        }
+      }
+      oneColumnIndex++;
+    }
+  }
+
+  SECTION("Wide Matrix") {
+    Matrix<2, 5> matrix = Matrix<2, 5>::Identity();
+
+    uint32_t oneColumnIndex{0};
+    for (uint32_t row = 0; row < 2; row++) {
+      for (uint32_t column = 0; column < 5; column++) {
+        float value = matrix[row][column];
+        if (oneColumnIndex == column && row < 3) {
+          REQUIRE_THAT(value, Catch::Matchers::WithinRel(1.0f, 1e-6f));
+        } else {
+          REQUIRE_THAT(value, Catch::Matchers::WithinRel(0.0f, 1e-6f));
+        }
+      }
+      oneColumnIndex++;
+    }
+  }
+
+  SECTION("Tall Matrix") {
+    Matrix<5, 2> matrix = Matrix<5, 2>::Identity();
+    uint32_t oneColumnIndex{0};
+    for (uint32_t row = 0; row < 5; row++) {
+      for (uint32_t column = 0; column < 2; column++) {
+        float value = matrix[row][column];
+        if (oneColumnIndex == column) {
+          REQUIRE_THAT(value, Catch::Matchers::WithinRel(1.0f, 1e-6f));
+        } else {
+          REQUIRE_THAT(value, Catch::Matchers::WithinRel(0.0f, 1e-6f));
+        }
+      }
+      oneColumnIndex++;
+    }
+  }
+}
+
+// TODO: Add test for scalar division
+TEST_CASE("Euclidean Norm", "Matrix") {
+
+  SECTION("2x2 Normalize") {
+    Matrix<2, 2> mat1{1, 2, 3, 4};
+    Matrix<2, 2> mat2{};
+
+    mat2 = mat1 / mat1.EuclideanNorm();
+
+    float sqrt_30{static_cast<float>(sqrt(30.0f))};
+
+    REQUIRE(mat2.Get(0, 0) == 1 / sqrt_30);
+    REQUIRE(mat2.Get(0, 1) == 2 / sqrt_30);
+    REQUIRE(mat2.Get(1, 0) == 3 / sqrt_30);
+    REQUIRE(mat2.Get(1, 1) == 4 / sqrt_30);
+
+    REQUIRE_THAT(matrixSum(mat2), Catch::Matchers::WithinRel(1.0f, 1e-6f));
+  }
+
+  SECTION("2x1 (Vector) Normalize") {
+    Matrix<2, 1> mat1{-0.878877044, 2.92092276};
+    Matrix<2, 1> mat2{};
+    mat2 = mat1 / mat1.EuclideanNorm();
+
+    REQUIRE_THAT(mat2.Get(0, 0),
+                 Catch::Matchers::WithinRel(-0.288129855179f, 1e-6f));
+    REQUIRE_THAT(mat2.Get(1, 0),
+                 Catch::Matchers::WithinRel(0.957591346325f, 1e-6f));
+
+    float sum = matrixSum(mat2);
+    REQUIRE_THAT(sum, Catch::Matchers::WithinRel(1.0f, 1e-6f));
+  }
+
+  SECTION("Normalized vectors sum to 1") {
+    Matrix<9, 1> mat1{1, 2, 3, 4, 5, 6, 7, 8, 9};
+    Matrix<9, 1> mat2;
+    mat2 = mat1 / mat1.EuclideanNorm();
+    float sum = matrixSum(mat2);
+    REQUIRE_THAT(sum, Catch::Matchers::WithinRel(1.0f, 1e-6f));
+
+    Matrix<2, 3> mat3{1, 2, 3, 4, 5, 6};
+    Matrix<2, 3> mat4{};
+    mat4 = mat3 / mat3.EuclideanNorm();
+    sum = matrixSum(mat4);
+    REQUIRE_THAT(sum, Catch::Matchers::WithinRel(1.0f, 1e-6f));
+  }
+}
+
+TEST_CASE("QR Decompositions", "Matrix") {
+  SECTION("2x2 QRDecomposition") {
+    Matrix<2, 2> A{1.0f, 2.0f, 3.0f, 4.0f};
+    Matrix<2, 2> Q{}, R{};
+    A.QRDecomposition(Q, R);
+
+    // Check that Q * R ≈ A
+    Matrix<2, 2> QR{};
+    Q.Mult(R, QR);
+    for (int i = 0; i < 2; ++i) {
+      for (int j = 0; j < 2; ++j) {
+        REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f));
+      }
+    }
+
+    // Check that Q is orthonormal: Qᵀ * Q ≈ I
+    Matrix<2, 2> Qt = Q.Transpose();
+    Matrix<2, 2> QtQ{};
+    Qt.Mult(Q, QtQ);
+    for (int i = 0; i < 2; ++i) {
+      for (int j = 0; j < 2; ++j) {
+        if (i == j)
+          REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f));
+        else
+          REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f));
+      }
+    }
+
+    // Optional: R should be upper triangular
+    REQUIRE(std::fabs(R[1][0]) < 1e-4f);
+
+    // check that all Q values are correct
+    REQUIRE_THAT(Q[0][0], Catch::Matchers::WithinRel(0.3162f, 1e-4f));
+    REQUIRE_THAT(Q[0][1], Catch::Matchers::WithinRel(0.94868f, 1e-4f));
+    REQUIRE_THAT(Q[1][0], Catch::Matchers::WithinRel(0.94868f, 1e-4f));
+    REQUIRE_THAT(Q[1][1], Catch::Matchers::WithinRel(-0.3162f, 1e-4f));
+
+    // check that all R values are correct
+    REQUIRE_THAT(R[0][0], Catch::Matchers::WithinRel(3.16228f, 1e-4f));
+    REQUIRE_THAT(R[0][1], Catch::Matchers::WithinRel(4.42719f, 1e-4f));
+    REQUIRE_THAT(R[1][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
+    REQUIRE_THAT(R[1][1], Catch::Matchers::WithinRel(0.63246f, 1e-4f));
+  }
+
+  SECTION("3x3 QRDecomposition") {
+    // this symmetrix tridiagonal matrix is well behaved for testing
+    Matrix<3, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9};
+
+    Matrix<3, 3> Q{}, R{};
+    A.QRDecomposition(Q, R);
+
+    // Check that Q * R ≈ A
+    Matrix<3, 3> QR{};
+    QR = Q * R;
+    for (int i = 0; i < 3; ++i) {
+      for (int j = 0; j < 3; ++j) {
+        REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f));
+      }
+    }
+
+    // Check that Qᵀ * Q ≈ I
+    // Since the rank of this matrix is 2, only the top left 2x2 sub-matrix will
+    // equal I.
+    Matrix<3, 3> Qt = Q.Transpose();
+    Matrix<3, 3> QtQ{};
+    QtQ = Qt * Q;
+    for (int i = 0; i < 2; ++i) {
+      for (int j = 0; j < 2; ++j) {
+        if (i == j)
+          REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f));
+        else
+          REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f));
+      }
+    }
+
+    // Optional: Check R is upper triangular
+    for (int i = 1; i < 3; ++i) {
+      for (int j = 0; j < i; ++j) {
+        REQUIRE(std::fabs(R[i][j]) < 1e-4f);
+      }
+    }
+  }
+
+  SECTION("4x2 QRDecomposition") {
+    // A simple 4x2 matrix
+    Matrix<4, 2> A{1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f};
+
+    Matrix<4, 2> Q{};
+    Matrix<2, 2> R{};
+    A.QRDecomposition(Q, R);
+
+    // Check that Q * R ≈ A
+    Matrix<4, 2> QR{};
+    Q.Mult(R, QR);
+    for (int i = 0; i < 4; ++i) {
+      for (int j = 0; j < 2; ++j) {
+        REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f));
+      }
+    }
+
+    // Check that Qᵀ * Q ≈ I₂
+    Matrix<2, 4> Qt = Q.Transpose();
+    Matrix<2, 2> QtQ{};
+    Qt.Mult(Q, QtQ);
+    for (int i = 0; i < 2; ++i) {
+      for (int j = 0; j < 2; ++j) {
+        if (i == j)
+          REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f));
+        else
+          REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f));
+      }
+    }
+
+    // Check R is upper triangular (i > j ⇒ R[i][j] ≈ 0)
+    for (int i = 1; i < 2; ++i) {
+      for (int j = 0; j < i; ++j) {
+        REQUIRE(std::fabs(R[i][j]) < 1e-4f);
+      }
+    }
+  }
+}
+
+TEST_CASE("Eigenvalues and Vectors", "Matrix") {
+  SECTION("2x2 Eigen") {
+    Matrix<2, 2> A{1.0f, 2.0f, 3.0f, 4.0f};
+    Matrix<2, 2> vectors{};
+    Matrix<2, 1> values{};
+
+    A.EigenQR(vectors, values, 1000000, 1e-20f);
+
+    REQUIRE_THAT(vectors[0][0], Catch::Matchers::WithinRel(0.41597f, 1e-4f));
+    REQUIRE_THAT(vectors[1][0], Catch::Matchers::WithinRel(0.90938f, 1e-4f));
+    REQUIRE_THAT(values[0][0], Catch::Matchers::WithinRel(5.372282f, 1e-4f));
+    REQUIRE_THAT(values[1][0], Catch::Matchers::WithinRel(-0.372281f, 1e-4f));
+  }
+
+  SECTION("3x3 Rank Defficient Eigen") {
+    SKIP("Skipping this because QR decomposition isn't ready for it");
+    // this symmetrix tridiagonal matrix is well behaved for testing
+    Matrix<3, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9};
+
+    Matrix<3, 3> vectors{};
+    Matrix<3, 1> values{};
+    A.EigenQR(vectors, values, 1000000, 1e-8f);
+
+    std::string strBuf1 = "";
+    vectors.ToString(strBuf1);
+    std::cout << "Vectors:\n" << strBuf1 << std::endl;
+    strBuf1 = "";
+    values.ToString(strBuf1);
+    std::cout << "Values:\n" << strBuf1 << std::endl;
+
+    REQUIRE_THAT(vectors[0][0], Catch::Matchers::WithinRel(0.23197f, 1e-4f));
+    REQUIRE_THAT(vectors[1][0], Catch::Matchers::WithinRel(0.525322f, 1e-4f));
+    REQUIRE_THAT(vectors[2][0], Catch::Matchers::WithinRel(0.81867f, 1e-4f));
+    REQUIRE_THAT(values[0][0], Catch::Matchers::WithinRel(-1.11684f, 1e-4f));
+    REQUIRE_THAT(values[1][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
+    REQUIRE_THAT(values[2][0], Catch::Matchers::WithinRel(16.1168f, 1e-4f));
+  }
 }

unit-tests/matrix-timing-tests.cpp

@@ -8,6 +8,7 @@
 // any other libraries
 #include <array>
 #include <cmath>
+#include <cstdint>
 
 // basically re-run all of the matrix tests with huge matrices and time the
 // results.
@@ -29,13 +30,13 @@ TEST_CASE("Timing Tests", "Matrix") {
   Matrix<4, 4> mat5{};
 
   SECTION("Addition") {
-    for (uint32_t i{0}; i < 10000; i++) {
+    for (uint32_t i{0}; i < 100000; i++) {
       mat3 = mat1 + mat2;
     }
   }
 
   SECTION("Subtraction") {
-    for (uint32_t i{0}; i < 10000; i++) {
+    for (uint32_t i{0}; i < 100000; i++) {
       mat3 = mat1 - mat2;
     }
   }
@@ -47,19 +48,19 @@ TEST_CASE("Timing Tests", "Matrix") {
   }
 
   SECTION("Scalar Multiplication") {
-    for (uint32_t i{0}; i < 10000; i++) {
+    for (uint32_t i{0}; i < 100000; i++) {
       mat3 = mat1 * 3;
     }
   }
 
   SECTION("Element Multiply") {
-    for (uint32_t i{0}; i < 10000; i++) {
+    for (uint32_t i{0}; i < 100000; i++) {
       mat1.ElementMultiply(mat2, mat3);
     }
   }
 
   SECTION("Element Divide") {
-    for (uint32_t i{0}; i < 10000; i++) {
+    for (uint32_t i{0}; i < 100000; i++) {
       mat1.ElementDivide(mat2, mat3);
     }
   }
@@ -68,52 +69,59 @@ TEST_CASE("Timing Tests", "Matrix") {
     // what about matrices of 0,0 or 1,1?
     // minor matrix for 2x2 matrix
     Matrix<49, 49> minorMat1{};
-    for (uint32_t i{0}; i < 10000; i++) {
+    for (uint32_t i{0}; i < 100000; i++) {
       mat1.MinorMatrix(minorMat1, 0, 0);
     }
   }
 
   SECTION("Determinant") {
-    for (uint32_t i{0}; i < 100000; i++) {
+    for (uint32_t i{0}; i < 1000000; i++) {
       float det1 = mat4.Det();
     }
   }
 
   SECTION("Matrix of Minors") {
-    for (uint32_t i{0}; i < 100000; i++) {
+    for (uint32_t i{0}; i < 1000000; i++) {
       mat4.MatrixOfMinors(mat5);
     }
   }
 
   SECTION("Invert") {
-    for (uint32_t i{0}; i < 100000; i++) {
+    for (uint32_t i{0}; i < 1000000; i++) {
       mat5 = mat4.Invert();
     }
   };
 
   SECTION("Transpose") {
-    for (uint32_t i{0}; i < 10000; i++) {
+    for (uint32_t i{0}; i < 100000; i++) {
       mat3 = mat1.Transpose();
     }
   }
 
   SECTION("Normalize") {
-    for (uint32_t i{0}; i < 10000; i++) {
-      mat1.Normalize(mat3);
+    for (uint32_t i{0}; i < 100000; i++) {
+      mat3 = mat1 / mat1.EuclideanNorm();
     }
   }
 
   SECTION("GET ROW") {
     Matrix<1, 50> mat1Rows{};
-    for (uint32_t i{0}; i < 1000000; i++) {
+    for (uint32_t i{0}; i < 100000000; i++) {
       mat1.GetRow(0, mat1Rows);
     }
   }
 
   SECTION("GET COLUMN") {
     Matrix<50, 1> mat1Columns{};
-    for (uint32_t i{0}; i < 1000000; i++) {
+    for (uint32_t i{0}; i < 100000000; i++) {
       mat1.GetColumn(0, mat1Columns);
     }
   }
+
+  SECTION("QR Decomposition") {
+    Matrix<50, 50> Q, R{};
+    for (uint32_t i{0}; i < 500; i++) {
+      mat1.QRDecomposition(Q, R);
+    }
+  }
 }

unit-tests/timing-results/matrix-timing-tests.txt

@@ -1,56 +1,36 @@
-Randomness seeded to: 3183250018
-0.179 s: Addition
-0.179 s: Timing Tests
-0.177 s: Subtraction
-0.177 s: Timing Tests
-1.931 s: Multiplication
-1.931 s: Timing Tests
-0.129 s: Scalar Multiplication
-0.129 s: Timing Tests
-0.175 s: Element Multiply
-0.175 s: Timing Tests
-0.174 s: Element Divide
-0.174 s: Timing Tests
-0.155 s: Minor Matrix
-0.155 s: Timing Tests
-0.104 s: Determinant
-0.104 s: Timing Tests
-0.465 s: Matrix of Minors
-0.465 s: Timing Tests
-0.111 s: Invert
-0.111 s: Timing Tests
-0.128 s: Transpose
-0.128 s: Timing Tests
-0.203 s: Normalize
-0.203 s: Timing Tests
-0.006 s: GET ROW
-0.006 s: Timing Tests
-0.238 s: GET COLUMN
-0.238 s: Timing Tests
+Running matrix-timing-tests with timing
+Randomness seeded to: 3567651885
+1.857 s: Addition
+1.857 s: Timing Tests
+1.788 s: Subtraction
+1.788 s: Timing Tests
+1.929 s: Multiplication
+1.929 s: Timing Tests
+1.268 s: Scalar Multiplication
+1.268 s: Timing Tests
+1.798 s: Element Multiply
+1.798 s: Timing Tests
+1.802 s: Element Divide
+1.803 s: Timing Tests
+1.553 s: Minor Matrix
+1.554 s: Timing Tests
+1.009 s: Determinant
+1.009 s: Timing Tests
+4.076 s: Matrix of Minors
+4.076 s: Timing Tests
+1.066 s: Invert
+1.066 s: Timing Tests
+1.246 s: Transpose
+1.246 s: Timing Tests
+2.284 s: Normalize
+2.284 s: Timing Tests
+0.606 s: GET ROW
+0.606 s: Timing Tests
+24.629 s: GET COLUMN
+24.630 s: Timing Tests
+3.064 s: QR Decomposition
+3.064 s: Timing Tests
 ===============================================================================
 test cases: 1 | 1 passed
 assertions: - none -
 
-	Command being timed: "build/unit-tests/matrix-timing-tests -d yes"
-	User time (seconds): 4.16
-	System time (seconds): 0.00
-	Percent of CPU this job got: 99%
-	Elapsed (wall clock) time (h:mm:ss or m:ss): 0:04.17
-	Average shared text size (kbytes): 0
-	Average unshared data size (kbytes): 0
-	Average stack size (kbytes): 0
-	Average total size (kbytes): 0
-	Maximum resident set size (kbytes): 3200
-	Average resident set size (kbytes): 0
-	Major (requiring I/O) page faults: 184
-	Minor (reclaiming a frame) page faults: 172
-	Voluntary context switches: 1
-	Involuntary context switches: 84
-	Swaps: 0
-	File system inputs: 12
-	File system outputs: 1
-	Socket messages sent: 0
-	Socket messages received: 0
-	Signals delivered: 0
-	Page size (bytes): 4096
-	Exit status: 0