src/Matrix.cpp

@@ -489,15 +489,15 @@ void Matrix<rows, columns>::SetSubMatrix(
 // 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, rows> &Q,
-                                            Matrix<rows, rows> &R) const {
-  // Use Gram-Schmidt orthogonalization for simplicity
+void Matrix<rows, columns>::QRDecomposition(Matrix<rows, columns> &Q,
+                                            Matrix<columns, columns> &R) const {
+  // Gram-Schmidt orthogonalization
   Matrix<rows, 1> a_col, u, e, proj;
   Matrix<rows, 1> q_col;
   Q.Fill(0);
   R.Fill(0);
 
-  for (uint8_t k = 0; k < rows; ++k) {
+  for (uint8_t k = 0; k < columns; ++k) {
     this->GetColumn(k, a_col);
     u = a_col;
 
@@ -527,14 +527,14 @@ void Matrix<rows, columns>::QRDecomposition(Matrix<rows, rows> &Q,
 template <uint8_t rows, uint8_t columns>
 void Matrix<rows, columns>::EigenQR(Matrix<rows, rows> &eigenVectors,
                                     Matrix<rows, 1> &eigenValues,
-                                    uint16_t maxIterations,
+                                    uint32_t maxIterations,
                                     float tolerance) const {
   static_assert(rows > 1, "Matrix size must be > 1 for QR iteration");
 
   Matrix<rows, rows> A = *this; // copy original matrix
   eigenVectors.Identity();
 
-  for (uint16_t iter = 0; iter < maxIterations; ++iter) {
+  for (uint32_t iter = 0; iter < maxIterations; ++iter) {
     Matrix<rows, rows> Q, R;
     A.QRDecomposition(Q, R);
 
@@ -543,14 +543,16 @@ void Matrix<rows, columns>::EigenQR(Matrix<rows, rows> &eigenVectors,
 
     // Check convergence: off-diagonal norm
     float offDiagSum = 0.f;
-    for (uint8_t i = 0; i < rows; ++i) {
-      for (uint8_t j = 0; j < rows; ++j) {
-        if (i != j)
+    for (uint8_t i = 0; i < rows; i++) {
+      for (uint8_t j = 0; j < rows; j++) {
+        if (i != j) {
           offDiagSum += fabs(A[i][j]);
+        }
       }
     }
-    if (offDiagSum < tolerance)
+    if (offDiagSum < tolerance) {
       break;
+    }
   }
 
   // eigenvalues are the diagonal elements of A

src/Matrix.hpp

@@ -221,21 +221,22 @@ public:
    * @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, rows> &Q, Matrix<rows, rows> &R) const;
+  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
+   * @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 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,
-               uint16_t maxIterations = 1000, float tolerance = 1e-6f) const;
+               uint32_t maxIterations = 1000, float tolerance = 1e-6f) const;
 
 protected:
   std::array<float, rows * columns> matrix;

unit-tests/matrix-tests.cpp

@@ -355,7 +355,7 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
   }
 }
 
-TEST_CASE("Advanced Matrix Operations", "Matrix") {
+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{};
@@ -423,4 +423,81 @@ TEST_CASE("Advanced Matrix Operations", "Matrix") {
       }
     }
   }
+
+  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 Eigen") {
+    // 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, 10000, 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(16.1168f, 1e-4f));
+    REQUIRE_THAT(values[1][0], Catch::Matchers::WithinRel(-1.11684f, 1e-4f));
+    // TODO: Figure out what's wrong here
+    // REQUIRE_THAT(values[2][0], Catch::Matchers::WithinRel(-3.2583f, 1e-4f));
+  }
 }