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

Reviewed-on: #7

.vscode/settings.json

@@ -76,5 +76,8 @@
     "clangd.enable": true,
     "C_Cpp.dimInactiveRegions": false,
     "editor.defaultFormatter": "xaver.clang-format",
-    "clangd.inactiveRegions.useBackgroundHighlight": true
+    "clangd.inactiveRegions.useBackgroundHighlight": false,
+    "clangd.arguments": [
+        "--compile-commands-dir=${workspaceFolder}/build"
+    ],
 }

README.md

@@ -2,8 +2,11 @@
 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.
 
-There are still several operations that are works in progress such as:
-- Add a function to calculate eigenvalues/vectors
-- Add a function to compute RREF
-- Add a function for SVD decomposition
-- Add a function for LQ decomposition
+# 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"
@@ -6,12 +13,6 @@
 #include <cmath>
 #include <cstdlib>
 #include <cstring>
-#include <type_traits>
-
-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) {
@@ -25,6 +26,14 @@ Matrix<rows, columns>::Matrix(Args... args) {
                                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()));
@@ -32,11 +41,13 @@ 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>
@@ -451,16 +462,6 @@ float Matrix<rows, columns>::EuclideanNorm() const {
 
   return sqrt(sum);
 }
-template <uint8_t rows, uint8_t columns>
-float Matrix<rows, columns>::L2Norm() const {
-  float sum{0};
-  Matrix<rows, 1> columnMatrix{};
-  for (uint8_t column = 0; column < columns; column++) {
-    this.GetColumn(column, columnMatrix);
-    sum += columnMatrix.EuclideanNorm();
-  }
-  return sqrt(sum);
-}
 
 template <uint8_t rows, uint8_t columns>
 template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset,
@@ -485,20 +486,37 @@ 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>
+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) {
-  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)");
+  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);
     }
   }
 }
@@ -510,33 +528,37 @@ void Matrix<rows, columns>::QRDecomposition(Matrix<rows, columns> &Q,
                                             Matrix<columns, columns> &R) const {
   static_assert(columns <= rows, "QR decomposition requires columns <= rows");
 
-  Matrix<rows, 1> a_col, u, q_col, proj;
   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 k = 0; k < columns; ++k) {
-    this->GetColumn(k, a_col);
+  for (uint8_t column = 0; column < columns; column++) {
+    this->GetColumn(column, a_col);
     u = a_col;
-
-    for (uint8_t j = 0; j < k; ++j) {
-      Q.GetColumn(j, q_col);
-      float r_jk = Matrix<rows, 1>::DotProduct(
-          q_col, u); // FIXED: use u instead of a_col
-      R[j][k] = r_jk;
-
-      proj = q_col * r_jk;
-      u = u - proj;
+    // -----------------------
+    // ----- 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 = sqrt(Matrix<rows, 1>::DotProduct(u, u));
-    if (norm < 1e-12f)
-      norm = 1e-12f; // for stability
-
-    for (uint8_t i = 0; i < rows; ++i) {
-      Q[i][k] = u[i][0] / norm;
+    float norm = u.EuclideanNorm();
+    if (norm > 1e-4) {
+      u = u / norm;
+    } else {
+      u.Fill(0);
     }
+    Q.SetSubMatrix(0, column, u);
 
-    R[k][k] = norm;
+    // -----------------------
+    // ----- CALCULATE R -----
+    // -----------------------
+    for (uint8_t k = 0; k <= column; k++) {
+      Q.GetColumn(k, e);
+      R[k][column] = (a_col.Transpose() * e).Get(0, 0);
+    }
   }
 }
 
@@ -546,16 +568,19 @@ void Matrix<rows, columns>::EigenQR(Matrix<rows, rows> &eigenVectors,
                                     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{};
-  QQ.Identity();
+  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;
-    Ak.QRDecomposition(Q, R);
 
-    Ak = R * Q;
+    // // 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

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
@@ -129,13 +123,12 @@ 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
    */
   float EuclideanNorm() const;
 
-  float L2Norm() const;
-
   /**
    * @brief Get a row from the matrix
    * @param row_index the row index to get
@@ -209,9 +202,9 @@ public:
             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
@@ -259,6 +252,6 @@ private:
   void setMatrixToArray(const std::array<float, rows * columns> &array);
 };
 
+#ifndef MATRIX_H_
 #include "Matrix.cpp"
-
 #endif // MATRIX_H_

src/Quaternion.h

@@ -2,12 +2,11 @@
 #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(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) {}

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);
@@ -336,46 +352,86 @@ 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);
   }
 }
 
-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;
+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++;
+    }
   }
-  return std::sqrt(sum);
 }
 
 // TODO: Add test for scalar division
-
-TEST_CASE("Normalization", "Matrix") {
+TEST_CASE("Euclidean Norm", "Matrix") {
 
   SECTION("2x2 Normalize") {
     Matrix<2, 2> mat1{1, 2, 3, 4};
@@ -473,13 +529,6 @@ TEST_CASE("QR Decompositions", "Matrix") {
     Matrix<3, 3> Q{}, R{};
     A.QRDecomposition(Q, R);
 
-    std::string strBuf1 = "";
-    Q.ToString(strBuf1);
-    std::cout << "Q:\n" << strBuf1 << std::endl;
-    strBuf1 = "";
-    R.ToString(strBuf1);
-    std::cout << "R:\n" << strBuf1 << std::endl;
-
     // Check that Q * R ≈ A
     Matrix<3, 3> QR{};
     QR = Q * R;
@@ -490,11 +539,13 @@ TEST_CASE("QR Decompositions", "Matrix") {
     }
 
     // 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 < 3; ++i) {
-      for (int j = 0; j < 3; ++j) {
+    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
@@ -508,28 +559,6 @@ TEST_CASE("QR Decompositions", "Matrix") {
         REQUIRE(std::fabs(R[i][j]) < 1e-4f);
       }
     }
-
-    // check that all Q values are correct
-    REQUIRE_THAT(Q[0][0], Catch::Matchers::WithinRel(0.1231f, 1e-4f));
-    REQUIRE_THAT(Q[0][1], Catch::Matchers::WithinRel(0.904534f, 1e-4f));
-    REQUIRE_THAT(Q[0][2], Catch::Matchers::WithinRel(0.0f, 1e-4f));
-    REQUIRE_THAT(Q[1][0], Catch::Matchers::WithinRel(0.49237f, 1e-4f));
-    REQUIRE_THAT(Q[1][1], Catch::Matchers::WithinRel(0.301511f, 1e-4f));
-    REQUIRE_THAT(Q[1][2], Catch::Matchers::WithinRel(0.0f, 1e-4f));
-    REQUIRE_THAT(Q[2][0], Catch::Matchers::WithinRel(0.86164f, 1e-4f));
-    REQUIRE_THAT(Q[2][1], Catch::Matchers::WithinRel(-0.30151f, 1e-4f));
-    REQUIRE_THAT(Q[2][2], Catch::Matchers::WithinRel(0.0f, 1e-4f));
-
-    // check that all R values are correct
-    REQUIRE_THAT(R[0][0], Catch::Matchers::WithinRel(8.124038f, 1e-4f));
-    REQUIRE_THAT(R[0][1], Catch::Matchers::WithinRel(9.60114f, 1e-4f));
-    REQUIRE_THAT(R[0][2], Catch::Matchers::WithinRel(11.07823f, 1e-4f));
-    REQUIRE_THAT(R[1][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
-    REQUIRE_THAT(R[1][1], Catch::Matchers::WithinRel(0.90453f, 1e-4f));
-    REQUIRE_THAT(R[1][2], Catch::Matchers::WithinRel(1.80907f, 1e-4f));
-    REQUIRE_THAT(R[2][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
-    REQUIRE_THAT(R[2][1], Catch::Matchers::WithinRel(0.0f, 1e-4f));
-    REQUIRE_THAT(R[2][2], Catch::Matchers::WithinRel(1.0f, 1e-4f));
   }
 
   SECTION("4x2 QRDecomposition") {
@@ -571,42 +600,41 @@ TEST_CASE("QR Decompositions", "Matrix") {
   }
 }
 
-// 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{};
+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);
+    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));
-//   }
+    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 Eigen") {
-//     // this symmetrix tridiagonal matrix is well behaved for testing
-//     Matrix<3, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9};
+  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);
+    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;
+    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));
-//   }
-// }
+    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++) {
+    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: 2444679151
-0.180 s: Addition
-0.180 s: Timing Tests
-0.177 s: Subtraction
-0.177 s: Timing Tests
-1.868 s: Multiplication
-1.868 s: Timing Tests
-0.127 s: Scalar Multiplication
-0.127 s: Timing Tests
-0.173 s: Element Multiply
-0.173 s: Timing Tests
-0.178 s: Element Divide
-0.178 s: Timing Tests
-0.172 s: Minor Matrix
-0.172 s: Timing Tests
-0.103 s: Determinant
-0.103 s: Timing Tests
-0.411 s: Matrix of Minors
-0.411 s: Timing Tests
-0.109 s: Invert
-0.109 s: Timing Tests
-0.122 s: Transpose
-0.122 s: Timing Tests
-0.190 s: Normalize
-0.190 s: Timing Tests
-0.006 s: GET ROW
-0.006 s: Timing Tests
-0.235 s: GET COLUMN
-0.235 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): 4.05
-	System time (seconds): 0.00
-	Percent of CPU this job got: 100%
-	Elapsed (wall clock) time (h:mm:ss or m:ss): 0:04.05
-	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: 171
-	Voluntary context switches: 1
-	Involuntary context switches: 26
-	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