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Working on getting the QR decomposition to compile

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This commit is contained in:
Quinn Henthorne
2024-12-18 16:30:53 -05:00
parent 0f76e8511e
commit 0b55d29376
4 changed files with 162 additions and 19 deletions
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3
.vscode/settings.json vendored
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@@ -70,7 +70,8 @@
"thread": "cpp",
"typeinfo": "cpp",
"variant": "cpp",
"shared_mutex": "cpp"
"shared_mutex": "cpp",
"complex": "cpp"
},
"clangd.enable": false,
"C_Cpp.dimInactiveRegions": false

97
Matrix.cpp
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@@ -17,6 +17,16 @@ Matrix<rows, columns>::Matrix(const std::array<float, rows * columns> &array) {
this->setMatrixToArray(array);
}
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++) {
this->matrix[row_idx * columns + column_idx] =
other.Get(row_idx, column_idx);
}
}
}
template <uint8_t rows, uint8_t columns>
template <typename... Args>
Matrix<rows, columns>::Matrix(Args... args) {
@@ -30,16 +40,6 @@ Matrix<rows, columns>::Matrix(Args... args) {
memcpy(this->matrix.begin(), initList.begin(), minSize * sizeof(float));
}
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++) {
this->matrix[row_idx * columns + column_idx] =
other.Get(row_idx, column_idx);
}
}
}
template <uint8_t rows, uint8_t columns>
void Matrix<rows, columns>::setMatrixToArray(
const std::array<float, rows * columns> &array) {
@@ -86,7 +86,7 @@ Matrix<rows, columns>::Sub(const Matrix<rows, columns> &other,
template <uint8_t rows, uint8_t columns>
template <uint8_t other_columns>
Matrix<rows, columns> &
Matrix<rows, other_columns> &
Matrix<rows, columns>::Mult(const Matrix<columns, other_columns> &other,
Matrix<rows, other_columns> &result) const {
// allocate some buffers for all of our dot products
@@ -353,11 +353,7 @@ 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++) {
this->matrix[row_idx * columns + column_idx] = value;
}
}
this->matrix.fill(value);
}
template <uint8_t rows, uint8_t columns>
@@ -440,4 +436,73 @@ Matrix<rows, columns>::Normalize(Matrix<rows, columns> &result) const {
return result;
}
template <uint8_t rows, uint8_t columns>
Matrix<rows, rows> Matrix<rows, columns>::Eye() {
Matrix<rows, rows> i_matrix;
i_matrix.Fill(0);
for (uint8_t i{0}; i < rows; i++) {
i_matrix[i][i] = 1;
}
return i_matrix;
}
template <uint8_t rows, uint8_t columns>
void Matrix<rows, columns>::QR_Decomposition(Matrix<rows, columns> &Q,
Matrix<rows, columns> &R) const {
Q = Matrix<rows, columns>::Eye(); // Q starts as the identity matrix
R = *this; // R starts as a copy of this matrix (For this algorithm we'll call
// this matrix A)
for (uint8_t row{0}; row < rows; row++) {
// compute the householder vector
const uint8_t houseHoldVectorSize{rows - row};
const uint8_t subMatrixSize{columns - row};
Matrix<houseHoldVectorSize, 1> x{};
this->SubMatrix(row, row, x);
Matrix<houseHoldVectorSize, 1> e1{};
e1.Fill(0);
if (x[0][0] >= 0) {
e1[0][0] = x.Norm();
} else {
e1[0][0] = -x.Norm();
}
Matrix<houseHoldVectorSize, 1> v = x + e1;
v = v * (1 / v.Norm()); // normalize V
// ************************************
// Apply the reflection to the R matrix
// ************************************
// initialize R's submatrix
Matrix<houseHoldVectorSize, subMatrixSize> R_subMatrix{};
R.SubMatrix(row, row, R_subMatrix);
// create some temporary buffers
Matrix<1, subMatrixSize> vR{};
Matrix<1, houseHoldVectorSize> v_T{};
v.Transpose(v_T);
Matrix<houseHoldVectorSize, subMatrixSize> vR_outer{};
// calculate the reflection
R_subMatrix =
R_subMatrix - 2 * Matrix<rows, columns>::OuterProduct(
v_T, v_T.Mult(R_subMatrix, vR), vR_outer);
// save the reflection back to R
R.CopySubMatrixInto(row, row, R_subMatrix);
// ************************************
// Apply the reflection to the Q matrix
// ************************************
// initialize Q's submatrix
Matrix<rows, houseHoldVectorSize> Q_subMatrix{};
Q.SubMatrix(0, row, Q_subMatrix);
// create some temporary buffers
Matrix<rows, 1> Qv{};
Matrix<rows, houseHoldVectorSize> Qv_outer{};
Q_subMatrix = Q_subMatrix - 2 * Matrix<rows, columns>::OuterProduct(
Q_subMatrix.Mult(v, Qv), v, Qv_outer);
Q.CopySubMatrixInto(0, row, Q_subMatrix);
}
}
#endif // MATRIX_H_

67
Matrix.hpp
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@@ -35,6 +35,7 @@ public:
* @brief Initialize a matrix directly with any number of arguments
*/
template <typename... Args> Matrix(Args... args);
/**
* @brief Set all elements in this to value
*/
@@ -64,7 +65,7 @@ public:
* @param result A buffer to store the result into
*/
template <uint8_t other_columns>
Matrix<rows, columns> &Mult(const Matrix<columns, other_columns> &other,
Matrix<rows, other_columns> &Mult(const Matrix<columns, other_columns> &other,
Matrix<rows, other_columns> &result) const;
/**
@@ -125,6 +126,66 @@ public:
*/
Matrix<rows, columns> &Normalize(Matrix<rows, columns> &result) const;
/**
* @brief return an identity matrix of the specified size
*/
static Matrix<rows, rows> Eye();
/**
* @brief write a copy of a sub matrix into the given result matrix.
* @param rowIndex The row index to start the copy from
* @param columnIndex the column index to start the copy from
* @param result the matrix buffer to write the sub matrix into. The size of
* the matrix buffer allows the function to determine the end indices of the
* sub matrix
*/
template <uint8_t subRows, uint8_t subColumns>
Matrix<subRows, subColumns> &
SubMatrix(uint8_t rowIndex, uint8_t columnIndex,
Matrix<subRows, subColumns> &result) const {
return result;
}
/**
* @brief write a copy of a sub matrix into this matrix starting at the given
* idnex.
* @param rowIndex The row index to start the copy from
* @param columnIndex the column index to start the copy from
* @param subMatrix The submatrix to copy into this matrix. The size of
* the matrix buffer allows the function to determine the end indices of the
* sub matrix
*/
template <uint8_t subRows, uint8_t subColumns>
void CopySubMatrixInto(uint8_t rowIndex, uint8_t columnIndex,
const Matrix<subRows, subColumns> &subMatrix) {}
/**
* @brief Returns the norm of the matrix
*/
float Norm() { return 0; }
template <uint8_t vec1Length, uint8_t vec2Length>
static Matrix<vec1Length, vec2Length> &
OuterProduct(const Matrix<1, vec1Length> &vec1,
const Matrix<1, vec2Length> &vec2,
Matrix<vec1Length, vec2Length> &result) {
return result;
}
template <uint8_t vec1Length, uint8_t vec2Length>
static Matrix<vec1Length, vec2Length> &
OuterProduct(const Matrix<vec1Length, 1> &vec1,
const Matrix<vec2Length, 1> &vec2,
Matrix<vec1Length, vec2Length> &result) {
return result;
}
/**
* @brief Calulcate the QR decomposition of a matrix
* @param Q the
*/
void QR_Decomposition(Matrix<rows, columns> &Q,
Matrix<rows, columns> &R) const;
/**
* @brief Get a row from the matrix
* @param row_index the row index to get
@@ -160,6 +221,10 @@ public:
*/
float Get(uint8_t row_index, uint8_t column_index) const;
// *******************************************************
// ************** OPERATOR OVERRIDES *********************
// *******************************************************
/**
* @brief get the specified row of the matrix returned as a reference to the
* internal array

12
unit-tests/matrix-tests.cpp
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@@ -182,6 +182,18 @@ TEST_CASE("Elementary Matrix Operations", "Matrix") {
REQUIRE(minorMat4.Get(1, 0) == 4);
REQUIRE(minorMat4.Get(1, 1) == 5);
}
SECTION("Identity Matrix") {
Matrix<3, 3> mat4{Matrix<3, 3>::Eye()};
REQUIRE(mat4.Get(0, 0) == 1);
REQUIRE(mat4.Get(0, 1) == 0);
REQUIRE(mat4.Get(0, 2) == 0);
REQUIRE(mat4.Get(1, 0) == 0);
REQUIRE(mat4.Get(1, 1) == 1);
REQUIRE(mat4.Get(1, 2) == 0);
REQUIRE(mat4.Get(2, 0) == 0);
REQUIRE(mat4.Get(2, 1) == 0);
REQUIRE(mat4.Get(2, 2) == 1);
}
SECTION("Determinant") {
float det1 = mat1.Det();