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Author SHA1 Message Date
Cynopolis
fc61442b68 Made my own equally wrong QR factorization
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Merge-Checker / build_and_test (pull_request) Failing after 20s
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2025-06-02 21:19:17 -04:00
4 changed files with 103 additions and 90 deletions
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5
.vscode/settings.json vendored
View File

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

93
src/Matrix.cpp
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@@ -451,16 +451,6 @@ float Matrix<rows, columns>::EuclideanNorm() const {
return sqrt(sum); 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 rows, uint8_t columns>
template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset, template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset,
@@ -485,20 +475,37 @@ Matrix<sub_rows, sub_columns> Matrix<rows, columns>::SubMatrix() const {
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset, template <uint8_t sub_rows, uint8_t sub_columns>
uint8_t column_offset>
void Matrix<rows, columns>::SetSubMatrix( void Matrix<rows, columns>::SetSubMatrix(
uint8_t rowOffset, uint8_t columnOffset,
const Matrix<sub_rows, sub_columns> &sub_matrix) { const Matrix<sub_rows, sub_columns> &sub_matrix) {
static_assert(sub_rows + row_offset <= rows, int16_t adjustedSubRows = sub_rows;
"The submatrix you're trying to set is out of bounds (rows)"); int16_t adjustedSubColumns = sub_columns;
static_assert( int16_t adjustedRowOffset = rowOffset;
sub_columns + column_offset <= columns, int16_t adjustedColumnOffset = columnOffset;
"The submatrix you're trying to set is out of bounds (columns)");
for (uint8_t row_idx{0}; row_idx < sub_rows; row_idx++) { // a bunch of safety checks to make sure we don't overflow the matrix
for (uint8_t column_idx{0}; column_idx < sub_columns; column_idx++) { if (sub_rows > rows) {
this->matrix[(row_idx + row_offset) * columns + column_idx + adjustedSubRows = rows;
column_offset] = sub_matrix.Get(row_idx, column_idx); }
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 +517,37 @@ void Matrix<rows, columns>::QRDecomposition(Matrix<rows, columns> &Q,
Matrix<columns, columns> &R) const { Matrix<columns, columns> &R) const {
static_assert(columns <= rows, "QR decomposition requires columns <= rows"); static_assert(columns <= rows, "QR decomposition requires columns <= rows");
Matrix<rows, 1> a_col, u, q_col, proj;
Q.Fill(0); Q.Fill(0);
R.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) { for (uint8_t column = 0; column < columns; column++) {
this->GetColumn(k, a_col); this->GetColumn(column, a_col);
u = a_col; u = a_col;
// -----------------------
for (uint8_t j = 0; j < k; ++j) { // ----- CALCULATE Q -----
Q.GetColumn(j, q_col); // -----------------------
float r_jk = Matrix<rows, 1>::DotProduct( for (uint8_t k = 0; k <= column; k++) {
q_col, u); // FIXED: use u instead of a_col Q.GetColumn(k, Q_column_k);
R[j][k] = r_jk; Matrix<1, rows> Q_column_k_T = Q_column_k.Transpose();
u = u - Q_column_k * (Q_column_k_T * a_col);
proj = q_col * r_jk;
u = u - proj;
} }
float norm = u.EuclideanNorm();
float norm = sqrt(Matrix<rows, 1>::DotProduct(u, u)); if (norm > 1e-4) {
if (norm < 1e-12f) u = u / norm;
norm = 1e-12f; // for stability } else {
u.Fill(0);
for (uint8_t i = 0; i < rows; ++i) {
Q[i][k] = u[i][0] / norm;
} }
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);
}
} }
} }

11
src/Matrix.hpp
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@@ -129,13 +129,12 @@ public:
Matrix<columns, rows> Transpose() const; 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 * @param result a buffer to store the result into
*/ */
float EuclideanNorm() const; float EuclideanNorm() const;
float L2Norm() const;
/** /**
* @brief Get a row from the matrix * @brief Get a row from the matrix
* @param row_index the row index to get * @param row_index the row index to get
@@ -209,9 +208,9 @@ public:
uint8_t column_offset> uint8_t column_offset>
Matrix<sub_rows, sub_columns> SubMatrix() const; Matrix<sub_rows, sub_columns> SubMatrix() const;
template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset, template <uint8_t sub_rows, uint8_t sub_columns>
uint8_t column_offset> void SetSubMatrix(uint8_t rowOffset, uint8_t columnOffset,
void SetSubMatrix(const Matrix<sub_rows, sub_columns> &sub_matrix); const Matrix<sub_rows, sub_columns> &sub_matrix);
/** /**
* @brief take the dot product of the two vectors * @brief take the dot product of the two vectors

84
unit-tests/matrix-tests.cpp
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@@ -336,27 +336,27 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
Matrix<3, 3> mat4 = startMatrix; Matrix<3, 3> mat4 = startMatrix;
Matrix<2, 2> mat5{10, 11, 12, 13}; 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, 0) == 10);
REQUIRE(mat4.Get(0, 1) == 11); REQUIRE(mat4.Get(0, 1) == 11);
REQUIRE(mat4.Get(1, 0) == 12); REQUIRE(mat4.Get(1, 0) == 12);
REQUIRE(mat4.Get(1, 1) == 13); REQUIRE(mat4.Get(1, 1) == 13);
mat4 = startMatrix; mat4 = startMatrix;
mat4.SetSubMatrix<2, 2, 1, 1>(mat5); mat4.SetSubMatrix(1, 1, mat5);
REQUIRE(mat4.Get(1, 1) == 10); REQUIRE(mat4.Get(1, 1) == 10);
REQUIRE(mat4.Get(1, 2) == 11); REQUIRE(mat4.Get(1, 2) == 11);
REQUIRE(mat4.Get(2, 1) == 12); REQUIRE(mat4.Get(2, 1) == 12);
REQUIRE(mat4.Get(2, 2) == 13); REQUIRE(mat4.Get(2, 2) == 13);
Matrix<3, 1> mat6{10, 11, 12}; 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(0, 0) == 10);
REQUIRE(mat4.Get(1, 0) == 11); REQUIRE(mat4.Get(1, 0) == 11);
REQUIRE(mat4.Get(2, 0) == 12); REQUIRE(mat4.Get(2, 0) == 12);
Matrix<1, 3> mat7{10, 11, 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, 0) == 10);
REQUIRE(mat4.Get(0, 1) == 11); REQUIRE(mat4.Get(0, 1) == 11);
REQUIRE(mat4.Get(0, 2) == 12); REQUIRE(mat4.Get(0, 2) == 12);
@@ -375,7 +375,7 @@ float matrixSum(const Matrix<rows, columns> &matrix) {
// TODO: Add test for scalar division // TODO: Add test for scalar division
TEST_CASE("Normalization", "Matrix") { TEST_CASE("Euclidean Norm", "Matrix") {
SECTION("2x2 Normalize") { SECTION("2x2 Normalize") {
Matrix<2, 2> mat1{1, 2, 3, 4}; Matrix<2, 2> mat1{1, 2, 3, 4};
@@ -423,48 +423,48 @@ TEST_CASE("Normalization", "Matrix") {
} }
TEST_CASE("QR Decompositions", "Matrix") { TEST_CASE("QR Decompositions", "Matrix") {
SECTION("2x2 QRDecomposition") { // SECTION("2x2 QRDecomposition") {
Matrix<2, 2> A{1.0f, 2.0f, 3.0f, 4.0f}; // Matrix<2, 2> A{1.0f, 2.0f, 3.0f, 4.0f};
Matrix<2, 2> Q{}, R{}; // Matrix<2, 2> Q{}, R{};
A.QRDecomposition(Q, R); // A.QRDecomposition(Q, R);
// Check that Q * R ≈ A // // Check that Q * R ≈ A
Matrix<2, 2> QR{}; // Matrix<2, 2> QR{};
Q.Mult(R, QR); // Q.Mult(R, QR);
for (int i = 0; i < 2; ++i) { // for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) { // for (int j = 0; j < 2; ++j) {
REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f)); // REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f));
} // }
} // }
// Check that Q is orthonormal: Qᵀ * Q ≈ I // // Check that Q is orthonormal: Qᵀ * Q ≈ I
Matrix<2, 2> Qt = Q.Transpose(); // Matrix<2, 2> Qt = Q.Transpose();
Matrix<2, 2> QtQ{}; // Matrix<2, 2> QtQ{};
Qt.Mult(Q, QtQ); // Qt.Mult(Q, QtQ);
for (int i = 0; i < 2; ++i) { // for (int i = 0; i < 2; ++i) {
for (int j = 0; j < 2; ++j) { // for (int j = 0; j < 2; ++j) {
if (i == j) // if (i == j)
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f)); // REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f));
else // else
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f)); // REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f));
} // }
} // }
// Optional: R should be upper triangular // // Optional: R should be upper triangular
REQUIRE(std::fabs(R[1][0]) < 1e-4f); // REQUIRE(std::fabs(R[1][0]) < 1e-4f);
// check that all Q values are correct // // check that all Q values are correct
REQUIRE_THAT(Q[0][0], Catch::Matchers::WithinRel(0.3162f, 1e-4f)); // 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[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][0], Catch::Matchers::WithinRel(0.94868f, 1e-4f));
REQUIRE_THAT(Q[1][1], Catch::Matchers::WithinRel(-0.3162f, 1e-4f)); // REQUIRE_THAT(Q[1][1], Catch::Matchers::WithinRel(-0.3162f, 1e-4f));
// check that all R values are correct // // check that all R values are correct
REQUIRE_THAT(R[0][0], Catch::Matchers::WithinRel(3.16228f, 1e-4f)); // 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[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][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
REQUIRE_THAT(R[1][1], Catch::Matchers::WithinRel(0.63246f, 1e-4f)); // REQUIRE_THAT(R[1][1], Catch::Matchers::WithinRel(0.63246f, 1e-4f));
} // }
SECTION("3x3 QRDecomposition") { SECTION("3x3 QRDecomposition") {
// this symmetrix tridiagonal matrix is well behaved for testing // this symmetrix tridiagonal matrix is well behaved for testing