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Working on adding efficient eigenvector and value calculations #2

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Cynopolis merged 11 commits from eigenvector-and-values into main 2025-06-06 22:32:19 +00:00
Conversation 4 Commits 11 Files Changed 9 +266 -195
6 changed files with 266 additions and 195 deletions
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3
.vscode/settings.json vendored
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@@ -75,5 +75,6 @@
}, },
"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
} }

4
CMakeLists.txt
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@@ -6,7 +6,9 @@ add_subdirectory(unit-tests)
set(CMAKE_CXX_STANDARD 11) 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) include(FetchContent)

8
README.md
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@@ -3,7 +3,7 @@ This matrix math library is focused on embedded development and avoids any heap
It uses templates to pre-allocate matrices on the stack. It uses templates to pre-allocate matrices on the stack.
There are still several operations that are works in progress such as: There are still several operations that are works in progress such as:
TODO: Add a function to calculate eigenvalues/vectors - Add a function to calculate eigenvalues/vectors
TODO: Add a function to compute RREF - Add a function to compute RREF
TODO: Add a function for SVD decomposition - Add a function for SVD decomposition
TODO: Add a function for LQ decomposition - Add a function for LQ decomposition

366
src/Matrix.cpp
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@@ -5,25 +5,22 @@
#include <algorithm> #include <algorithm>
#include <cmath> #include <cmath>
#include <cstdlib> #include <cstdlib>
#include <type_traits>
#include <cstring> #include <cstring>
#include <type_traits>
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns>::Matrix(float value) Matrix<rows, columns>::Matrix(float value) {
{
this->Fill(value); this->Fill(value);
} }
template <uint8_t rows, uint8_t columns> 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); this->setMatrixToArray(array);
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
template <typename... Args> template <typename... Args>
Matrix<rows, columns>::Matrix(Args... args) Matrix<rows, columns>::Matrix(Args... args) {
{
constexpr uint16_t arraySize{static_cast<uint16_t>(rows) * constexpr uint16_t arraySize{static_cast<uint16_t>(rows) *
static_cast<uint16_t>(columns)}; static_cast<uint16_t>(columns)};
@@ -35,22 +32,17 @@ Matrix<rows, columns>::Matrix(Args... args)
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
void Matrix<rows, columns>::Identity() void Matrix<rows, columns>::Identity() {
{
this->Fill(0); this->Fill(0);
for (uint8_t idx{0}; idx < rows; idx++) for (uint8_t idx{0}; idx < rows; idx++) {
{
this->matrix[idx * columns + idx] = 1; this->matrix[idx * columns + idx] = 1;
} }
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns>::Matrix(const Matrix<rows, columns> &other) Matrix<rows, columns>::Matrix(const Matrix<rows, columns> &other) {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
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 column_idx{0}; column_idx < columns; column_idx++)
{
this->matrix[row_idx * columns + column_idx] = this->matrix[row_idx * columns + column_idx] =
other.Get(row_idx, column_idx); other.Get(row_idx, column_idx);
} }
@@ -59,21 +51,15 @@ Matrix<rows, columns>::Matrix(const Matrix<rows, columns> &other)
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
void Matrix<rows, columns>::setMatrixToArray( void Matrix<rows, columns>::setMatrixToArray(
const std::array<float, rows * columns> &array) const std::array<float, rows * columns> &array) {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
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 column_idx{0}; column_idx < columns; column_idx++)
{
uint16_t array_idx = uint16_t array_idx =
static_cast<uint16_t>(row_idx) * static_cast<uint16_t>(columns) + static_cast<uint16_t>(row_idx) * static_cast<uint16_t>(columns) +
static_cast<uint16_t>(column_idx); 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]; this->matrix[row_idx * columns + column_idx] = array[array_idx];
} } else {
else
{
this->matrix[row_idx * columns + column_idx] = 0; this->matrix[row_idx * columns + column_idx] = 0;
} }
} }
@@ -83,12 +69,9 @@ void Matrix<rows, columns>::setMatrixToArray(
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> & Matrix<rows, columns> &
Matrix<rows, columns>::Add(const Matrix<rows, columns> &other, Matrix<rows, columns>::Add(const Matrix<rows, columns> &other,
Matrix<rows, columns> &result) const Matrix<rows, columns> &result) const {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
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 column_idx{0}; column_idx < columns; column_idx++)
{
result[row_idx][column_idx] = result[row_idx][column_idx] =
this->Get(row_idx, column_idx) + other.Get(row_idx, column_idx); this->Get(row_idx, column_idx) + other.Get(row_idx, column_idx);
} }
@@ -99,12 +82,9 @@ Matrix<rows, columns>::Add(const Matrix<rows, columns> &other,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> & Matrix<rows, columns> &
Matrix<rows, columns>::Sub(const Matrix<rows, columns> &other, Matrix<rows, columns>::Sub(const Matrix<rows, columns> &other,
Matrix<rows, columns> &result) const Matrix<rows, columns> &result) const {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
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 column_idx{0}; column_idx < columns; column_idx++)
{
result[row_idx][column_idx] = result[row_idx][column_idx] =
this->Get(row_idx, column_idx) - other.Get(row_idx, column_idx); this->Get(row_idx, column_idx) - other.Get(row_idx, column_idx);
} }
@@ -117,18 +97,15 @@ template <uint8_t rows, uint8_t columns>
template <uint8_t other_columns> template <uint8_t other_columns>
Matrix<rows, other_columns> & Matrix<rows, other_columns> &
Matrix<rows, columns>::Mult(const Matrix<columns, other_columns> &other, 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 // allocate some buffers for all of our dot products
Matrix<1, columns> this_row; Matrix<1, columns> this_row;
Matrix<columns, 1> other_column; 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 // get our row
this->GetRow(row_idx, this_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 < columns; column_idx++) {
{
// get the other matrix'ss column // get the other matrix'ss column
other.GetColumn(column_idx, other_column); other.GetColumn(column_idx, other_column);
@@ -143,12 +120,9 @@ Matrix<rows, columns>::Mult(const Matrix<columns, other_columns> &other,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> & Matrix<rows, columns> &
Matrix<rows, columns>::Mult(float scalar, Matrix<rows, columns> &result) const 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 row_idx{0}; row_idx < rows; row_idx++) for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
{
for (uint8_t column_idx{0}; column_idx < columns; column_idx++)
{
result[row_idx][column_idx] = this->Get(row_idx, column_idx) * scalar; result[row_idx][column_idx] = this->Get(row_idx, column_idx) * scalar;
} }
} }
@@ -157,9 +131,7 @@ Matrix<rows, columns>::Mult(float scalar, Matrix<rows, columns> &result) const
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> Matrix<rows, columns> Matrix<rows, columns>::Invert() const {
Matrix<rows, columns>::Invert() const
{
// since all matrix sizes have to be statically specified at compile time we // since all matrix sizes have to be statically specified at compile time we
// can do this // can do this
static_assert(rows == columns, static_assert(rows == columns,
@@ -169,8 +141,7 @@ Matrix<rows, columns>::Invert() const
// unfortunately we can't calculate this at compile time so we'll just reurn // unfortunately we can't calculate this at compile time so we'll just reurn
// zeros // zeros
float determinant{this->Det()}; float determinant{this->Det()};
if (determinant == 0) if (determinant == 0) {
{
// you can't invert a matrix with a negative determinant // you can't invert a matrix with a negative determinant
result.Fill(0); result.Fill(0);
return result; return result;
@@ -195,14 +166,10 @@ Matrix<rows, columns>::Invert() const
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<columns, rows> Matrix<columns, rows> Matrix<rows, columns>::Transpose() const {
Matrix<rows, columns>::Transpose() const
{
Matrix<columns, rows> result{}; Matrix<columns, rows> result{};
for (uint8_t column_idx{0}; column_idx < rows; column_idx++) 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 row_idx{0}; row_idx < columns; row_idx++)
{
result[row_idx][column_idx] = this->Get(column_idx, row_idx); result[row_idx][column_idx] = this->Get(column_idx, row_idx);
} }
} }
@@ -214,24 +181,19 @@ Matrix<rows, columns>::Transpose() const
// the fastest way to calculate a 2x2 matrix determinant // the fastest way to calculate a 2x2 matrix determinant
// template <> // template <>
// inline float Matrix<0, 0>::Det() const { return 1e+6; } // inline float Matrix<0, 0>::Det() const { return 1e+6; }
template <> template <> inline float Matrix<1, 1>::Det() const { return this->matrix[0]; }
inline float Matrix<1, 1>::Det() const { return this->matrix[0]; } template <> inline float Matrix<2, 2>::Det() const {
template <>
inline float Matrix<2, 2>::Det() const
{
return this->matrix[0] * this->matrix[3] - this->matrix[1] * this->matrix[2]; return this->matrix[0] * this->matrix[3] - this->matrix[1] * this->matrix[2];
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
float Matrix<rows, columns>::Det() const float Matrix<rows, columns>::Det() const {
{
static_assert(rows == columns, static_assert(rows == columns,
"You can't take the determinant of a non-square matrix."); "You can't take the determinant of a non-square matrix.");
Matrix<rows - 1, columns - 1> MinorMatrix{}; Matrix<rows - 1, columns - 1> MinorMatrix{};
float determinant{0}; 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 // for odd indices the sign is negative
float sign = (column_idx % 2 == 0) ? 1 : -1; float sign = (column_idx % 2 == 0) ? 1 : -1;
determinant += sign * this->matrix[column_idx] * determinant += sign * this->matrix[column_idx] *
@@ -244,12 +206,9 @@ float Matrix<rows, columns>::Det() const
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> & Matrix<rows, columns> &
Matrix<rows, columns>::ElementMultiply(const Matrix<rows, columns> &other, Matrix<rows, columns>::ElementMultiply(const Matrix<rows, columns> &other,
Matrix<rows, columns> &result) const Matrix<rows, columns> &result) const {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
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 column_idx{0}; column_idx < columns; column_idx++)
{
result[row_idx][column_idx] = result[row_idx][column_idx] =
this->Get(row_idx, column_idx) * other.Get(row_idx, column_idx); this->Get(row_idx, column_idx) * other.Get(row_idx, column_idx);
} }
@@ -261,12 +220,9 @@ Matrix<rows, columns>::ElementMultiply(const Matrix<rows, columns> &other,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> & Matrix<rows, columns> &
Matrix<rows, columns>::ElementDivide(const Matrix<rows, columns> &other, Matrix<rows, columns>::ElementDivide(const Matrix<rows, columns> &other,
Matrix<rows, columns> &result) const Matrix<rows, columns> &result) const {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
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 column_idx{0}; column_idx < columns; column_idx++)
{
result[row_idx][column_idx] = result[row_idx][column_idx] =
this->Get(row_idx, column_idx) / other.Get(row_idx, column_idx); this->Get(row_idx, column_idx) / other.Get(row_idx, column_idx);
} }
@@ -277,10 +233,8 @@ Matrix<rows, columns>::ElementDivide(const Matrix<rows, columns> &other,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
float Matrix<rows, columns>::Get(uint8_t row_index, float Matrix<rows, columns>::Get(uint8_t row_index,
uint8_t column_index) const uint8_t column_index) const {
{ if (row_index > rows - 1 || column_index > columns - 1) {
if (row_index > rows - 1 || column_index > columns - 1)
{
return 1e+10; // TODO: We should throw something here instead of failing return 1e+10; // TODO: We should throw something here instead of failing
// quietly // quietly
} }
@@ -290,8 +244,7 @@ float Matrix<rows, columns>::Get(uint8_t row_index,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<1, columns> & Matrix<1, columns> &
Matrix<rows, columns>::GetRow(uint8_t row_index, 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, memcpy(&(row[0]), this->matrix.begin() + row_index * columns,
columns * sizeof(float)); columns * sizeof(float));
@@ -301,10 +254,8 @@ Matrix<rows, columns>::GetRow(uint8_t row_index,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, 1> & Matrix<rows, 1> &
Matrix<rows, columns>::GetColumn(uint8_t column_index, Matrix<rows, columns>::GetColumn(uint8_t column_index,
Matrix<rows, 1> &column) const Matrix<rows, 1> &column) const {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
{
column[row_idx][0] = this->Get(row_idx, column_index); column[row_idx][0] = this->Get(row_idx, column_index);
} }
@@ -312,17 +263,13 @@ Matrix<rows, columns>::GetColumn(uint8_t column_index,
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
void Matrix<rows, columns>::ToString(std::string &stringBuffer) const void Matrix<rows, columns>::ToString(std::string &stringBuffer) const {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
for (uint8_t row_idx{0}; row_idx < rows; row_idx++)
{
stringBuffer += "|"; stringBuffer += "|";
for (uint8_t column_idx{0}; column_idx < columns; column_idx++) for (uint8_t column_idx{0}; column_idx < columns; column_idx++) {
{
stringBuffer += stringBuffer +=
std::to_string(this->matrix[row_idx * columns + column_idx]); std::to_string(this->matrix[row_idx * columns + column_idx]);
if (column_idx != columns - 1) if (column_idx != columns - 1) {
{
stringBuffer += "\t"; stringBuffer += "\t";
} }
} }
@@ -331,11 +278,9 @@ void Matrix<rows, columns>::ToString(std::string &stringBuffer) const
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
std::array<float, columns> &Matrix<rows, columns>:: std::array<float, columns> &
operator[](uint8_t row_index) Matrix<rows, columns>::operator[](uint8_t row_index) {
{ if (row_index > rows - 1) {
if (row_index > rows - 1)
{
// TODO: We should throw something here instead of failing quietly. // TODO: We should throw something here instead of failing quietly.
row_index = 0; row_index = 0;
} }
@@ -346,9 +291,8 @@ operator[](uint8_t row_index)
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> &Matrix<rows, columns>:: Matrix<rows, columns> &
operator=(const Matrix<rows, columns> &other) Matrix<rows, columns>::operator=(const Matrix<rows, columns> &other) {
{
memcpy(this->matrix.begin(), other.matrix.begin(), memcpy(this->matrix.begin(), other.matrix.begin(),
rows * columns * sizeof(float)); rows * columns * sizeof(float));
@@ -357,18 +301,16 @@ operator=(const Matrix<rows, columns> &other)
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> Matrix<rows, columns>:: Matrix<rows, columns>
operator+(const Matrix<rows, columns> &other) const Matrix<rows, columns>::operator+(const Matrix<rows, columns> &other) const {
{
Matrix<rows, columns> buffer{}; Matrix<rows, columns> buffer{};
this->Add(other, buffer); this->Add(other, buffer);
return buffer; return buffer;
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> Matrix<rows, columns>:: Matrix<rows, columns>
operator-(const Matrix<rows, columns> &other) const Matrix<rows, columns>::operator-(const Matrix<rows, columns> &other) const {
{
Matrix<rows, columns> buffer{}; Matrix<rows, columns> buffer{};
this->Sub(other, buffer); this->Sub(other, buffer);
return buffer; return buffer;
@@ -376,17 +318,15 @@ operator-(const Matrix<rows, columns> &other) const
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
template <uint8_t other_columns> template <uint8_t other_columns>
Matrix<rows, other_columns> Matrix<rows, columns>:: Matrix<rows, other_columns> Matrix<rows, columns>::operator*(
operator*(const Matrix<columns, other_columns> &other) const const Matrix<columns, other_columns> &other) const {
{
Matrix<rows, other_columns> buffer{}; Matrix<rows, other_columns> buffer{};
this->Mult(other, buffer); this->Mult(other, buffer);
return buffer; return buffer;
} }
template <uint8_t rows, uint8_t columns> 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{}; Matrix<rows, columns> buffer{};
this->Mult(scalar, buffer); this->Mult(scalar, buffer);
return buffer; return buffer;
@@ -395,11 +335,9 @@ Matrix<rows, columns> Matrix<rows, columns>::operator*(float scalar) const
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
template <uint8_t vector_size> template <uint8_t vector_size>
float Matrix<rows, columns>::DotProduct(const Matrix<1, vector_size> &vec1, 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}; 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); sum += vec1.Get(0, i) * vec2.Get(0, i);
} }
@@ -409,11 +347,9 @@ float Matrix<rows, columns>::DotProduct(const Matrix<1, vector_size> &vec1,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
template <uint8_t vector_size> template <uint8_t vector_size>
float Matrix<rows, columns>::DotProduct(const Matrix<vector_size, 1> &vec1, 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}; 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); sum += vec1.Get(i, 0) * vec2.Get(i, 0);
} }
@@ -421,12 +357,9 @@ float Matrix<rows, columns>::DotProduct(const Matrix<vector_size, 1> &vec1,
} }
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
void Matrix<rows, columns>::Fill(float value) void Matrix<rows, columns>::Fill(float value) {
{ for (uint8_t row_idx{0}; row_idx < rows; row_idx++) {
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 column_idx{0}; column_idx < columns; column_idx++)
{
this->matrix[row_idx * columns + column_idx] = value; this->matrix[row_idx * columns + column_idx] = value;
} }
} }
@@ -434,14 +367,11 @@ void Matrix<rows, columns>::Fill(float value)
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, 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{}; Matrix<rows - 1, columns - 1> MinorMatrix{};
for (uint8_t row_idx{0}; row_idx < rows; row_idx++) 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 column_idx{0}; column_idx < columns; column_idx++)
{
this->MinorMatrix(MinorMatrix, row_idx, column_idx); this->MinorMatrix(MinorMatrix, row_idx, column_idx);
result[row_idx][column_idx] = MinorMatrix.Det(); result[row_idx][column_idx] = MinorMatrix.Det();
} }
@@ -453,20 +383,15 @@ Matrix<rows, columns>::MatrixOfMinors(Matrix<rows, columns> &result) const
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows - 1, columns - 1> & Matrix<rows - 1, columns - 1> &
Matrix<rows, columns>::MinorMatrix(Matrix<rows - 1, columns - 1> &result, 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{}; std::array<float, (rows - 1) * (columns - 1)> subArray{};
uint16_t array_idx{0}; uint16_t array_idx{0};
for (uint8_t row_iter{0}; row_iter < rows; row_iter++) for (uint8_t row_iter{0}; row_iter < rows; row_iter++) {
{ if (row_iter == row_idx) {
if (row_iter == row_idx)
{
continue; continue;
} }
for (uint8_t column_iter{0}; column_iter < columns; column_iter++) for (uint8_t column_iter{0}; column_iter < columns; column_iter++) {
{ if (column_iter == column_idx) {
if (column_iter == column_idx)
{
continue; continue;
} }
subArray[array_idx] = this->Get(row_iter, column_iter); subArray[array_idx] = this->Get(row_iter, column_iter);
@@ -480,12 +405,9 @@ Matrix<rows, columns>::MinorMatrix(Matrix<rows - 1, columns - 1> &result,
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> & Matrix<rows, columns> &
Matrix<rows, columns>::adjugate(Matrix<rows, columns> &result) const Matrix<rows, columns>::adjugate(Matrix<rows, columns> &result) const {
{ for (uint8_t row_iter{0}; row_iter < rows; row_iter++) {
for (uint8_t row_iter{0}; row_iter < rows; row_iter++) for (uint8_t column_iter{0}; column_iter < columns; column_iter++) {
{
for (uint8_t column_iter{0}; column_iter < columns; column_iter++)
{
float sign = ((row_iter + 1) % 2) == 0 ? -1 : 1; float sign = ((row_iter + 1) % 2) == 0 ? -1 : 1;
sign *= ((column_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; result[column_iter][row_iter] = this->Get(row_iter, column_iter) * sign;
@@ -497,20 +419,16 @@ Matrix<rows, columns>::adjugate(Matrix<rows, columns> &result) const
template <uint8_t rows, uint8_t columns> template <uint8_t rows, uint8_t columns>
Matrix<rows, columns> & Matrix<rows, columns> &
Matrix<rows, columns>::Normalize(Matrix<rows, columns> &result) const Matrix<rows, columns>::Normalize(Matrix<rows, columns> &result) const {
{
float sum{0}; float sum{0};
for (uint8_t row_idx{0}; row_idx < rows; row_idx++) 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 column_idx{0}; column_idx < columns; column_idx++)
{
float val{this->Get(row_idx, column_idx)}; float val{this->Get(row_idx, column_idx)};
sum += val * val; sum += val * val;
} }
} }
if (sum == 0) if (sum == 0) {
{
// this wouldn't do anything anyways // this wouldn't do anything anyways
result.Fill(1e+6); result.Fill(1e+6);
return result; return result;
@@ -518,10 +436,8 @@ Matrix<rows, columns>::Normalize(Matrix<rows, columns> &result) const
sum = sqrt(sum); sum = sqrt(sum);
for (uint8_t row_idx{0}; row_idx < rows; row_idx++) 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 column_idx{0}; column_idx < columns; column_idx++)
{
result[row_idx][column_idx] = this->Get(row_idx, column_idx) / sum; result[row_idx][column_idx] = this->Get(row_idx, column_idx) / sum;
} }
} }
@@ -530,21 +446,20 @@ Matrix<rows, columns>::Normalize(Matrix<rows, columns> &result) 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, uint8_t column_offset> template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset,
Matrix<sub_rows, sub_columns> Matrix<rows, columns>::SubMatrix() const 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_rows + row_offset <= rows
// static assert that sub_columns + column_offset <= columns // static assert that sub_columns + column_offset <= columns
static_assert(sub_rows + row_offset <= rows, static_assert(sub_rows + row_offset <= rows,
"The submatrix you're trying to get is out of bounds (rows)"); "The submatrix you're trying to get is out of bounds (rows)");
static_assert(sub_columns + column_offset <= columns, static_assert(
"The submatrix you're trying to get is out of bounds (columns)"); sub_columns + column_offset <= columns,
"The submatrix you're trying to get is out of bounds (columns)");
Matrix<sub_rows, sub_columns> buffer{}; Matrix<sub_rows, sub_columns> buffer{};
for (uint8_t row_idx{0}; row_idx < sub_rows; row_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++) {
for (uint8_t column_idx{0}; column_idx < sub_columns; column_idx++)
{
buffer[row_idx][column_idx] = buffer[row_idx][column_idx] =
this->Get(row_idx + row_offset, column_idx + column_offset); this->Get(row_idx + row_offset, column_idx + column_offset);
} }
@@ -553,21 +468,94 @@ 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, uint8_t column_offset> template <uint8_t sub_rows, uint8_t sub_columns, uint8_t row_offset,
void Matrix<rows, columns>::SetSubMatrix(const Matrix<sub_rows, sub_columns> &sub_matrix) uint8_t column_offset>
{ void Matrix<rows, columns>::SetSubMatrix(
const Matrix<sub_rows, sub_columns> &sub_matrix) {
static_assert(sub_rows + row_offset <= rows, static_assert(sub_rows + row_offset <= rows,
"The submatrix you're trying to set is out of bounds (rows)"); "The submatrix you're trying to set is out of bounds (rows)");
static_assert(sub_columns + column_offset <= columns, static_assert(
"The submatrix you're trying to set is out of bounds (columns)"); sub_columns + column_offset <= columns,
"The submatrix you're trying to set is out of bounds (columns)");
for (uint8_t row_idx{0}; row_idx < sub_rows; row_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++) {
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);
this->matrix[(row_idx + row_offset) * columns + column_idx + column_offset] = 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, rows> &Q,
Matrix<rows, rows> &R) const {
// Use Gram-Schmidt orthogonalization for simplicity
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) {
this->GetColumn(k, 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, a_col);
R[j][k] = r_jk;
// proj = r_jk * q_j
proj = q_col * r_jk;
u = u - proj;
}
float norm = sqrt(Matrix<rows, 1>::DotProduct(u, u));
if (norm < 1e-12f)
norm = 1e-12f; // avoid div by zero
for (uint8_t i = 0; i < rows; ++i)
Q[i][k] = u[i][0] / norm;
R[k][k] = norm;
}
}
// Compute eigenvalues and eigenvectors by QR iteration
// maxIterations: safety limit, tolerance: stop criteria
template <uint8_t rows, uint8_t columns>
void Matrix<rows, columns>::EigenQR(Matrix<rows, rows> &eigenVectors,
Matrix<rows, 1> &eigenValues,
uint16_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) {
Matrix<rows, rows> Q, R;
A.QRDecomposition(Q, R);
A = R * Q;
eigenVectors = eigenVectors * Q;
// 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)
offDiagSum += fabs(A[i][j]);
}
}
if (offDiagSum < tolerance)
break;
}
// eigenvalues are the diagonal elements of A
for (uint8_t i = 0; i < rows; ++i)
eigenValues[i][0] = A[i][i];
}
#endif // MATRIX_H_ #endif // MATRIX_H_

5
src/Matrix.hpp
View File

@@ -216,6 +216,11 @@ public:
return vec1.Get(0, 0) * vec2.Get(0, 0); return vec1.Get(0, 0) * vec2.Get(0, 0);
} }
void QRDecomposition(Matrix<rows, rows> &Q, Matrix<rows, rows> &R) const;
void EigenQR(Matrix<rows, rows> &eigenVectors, Matrix<rows, 1> &eigenValues,
uint16_t maxIterations = 1000, float tolerance = 1e-6f) const;
protected: protected:
std::array<float, rows * columns> matrix; std::array<float, rows * columns> matrix;

75
unit-tests/matrix-tests.cpp
View File

@@ -353,4 +353,79 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
REQUIRE(mat4.Get(0, 1) == 11); REQUIRE(mat4.Get(0, 1) == 11);
REQUIRE(mat4.Get(0, 2) == 12); REQUIRE(mat4.Get(0, 2) == 12);
} }
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);
}
SECTION("3x3 QRDecomposition") {
// this symmetrix tridiagonal matrix is well behaved for testing
Matrix<3, 3> A{3.0f, -1.0f, 0.0f, -1.0f, 3.0f, -1.0f, 0.0f, -1.0f, 3.0f};
Matrix<3, 3> Q{}, R{};
A.QRDecomposition(Q, R);
std::string strBuf1 = "";
Q.ToString(strBuf1);
std::cout << "Matrix Q:\n" << strBuf1 << std::endl;
strBuf1 = "";
R.ToString(strBuf1);
std::cout << "Matrix R:\n" << strBuf1 << std::endl;
// Check that Q * R ≈ A
Matrix<3, 3> QR{};
Q.Mult(R, QR);
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
Matrix<3, 3> Qt = Q.Transpose();
Matrix<3, 3> QtQ{};
Qt.Mult(Q, QtQ);
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++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);
}
}
}
} }