261 lines
7.3 KiB
C++
261 lines
7.3 KiB
C++
/**
|
|
******************************************************************************
|
|
* @file matrix.cpp/h
|
|
* @brief Matrix/vector calculation. 矩阵/向量运算
|
|
* @author Spoon Guan
|
|
******************************************************************************
|
|
* Copyright (c) 2023 Team JiaoLong-SJTU
|
|
* All rights reserved.
|
|
******************************************************************************
|
|
*/
|
|
|
|
#ifndef MATRIX_H
|
|
#define MATRIX_H
|
|
|
|
|
|
//#include "arm_math.h"
|
|
#include "user_lib.h"
|
|
// Matrix class
|
|
template <int _rows, int _cols>
|
|
class Matrixf {
|
|
public:
|
|
// Constructor without input data
|
|
Matrixf(void) : rows_(_rows), cols_(_cols) {
|
|
arm_mat_init_f32(&arm_mat_, _rows, _cols, this->data_);
|
|
}
|
|
// Constructor with input data
|
|
Matrixf(float data[_rows * _cols]) : Matrixf() {
|
|
memcpy(this->data_, data, _rows * _cols * sizeof(float));
|
|
}
|
|
// Copy constructor
|
|
Matrixf(const Matrixf<_rows, _cols>& mat) : Matrixf() {
|
|
memcpy(this->data_, mat.data_, _rows * _cols * sizeof(float));
|
|
}
|
|
// Destructor
|
|
~Matrixf(void) {}
|
|
|
|
// Row size
|
|
int rows(void) { return _rows; }
|
|
// Column size
|
|
int cols(void) { return _cols; }
|
|
|
|
// Element
|
|
float* operator[](const int& row) { return &this->data_[row * _cols]; }
|
|
|
|
// Operators
|
|
Matrixf<_rows, _cols>& operator=(const Matrixf<_rows, _cols> mat) {
|
|
memcpy(this->data_, mat.data_, _rows * _cols * sizeof(float));
|
|
return *this;
|
|
}
|
|
Matrixf<_rows, _cols>& operator+=(const Matrixf<_rows, _cols> mat) {
|
|
arm_status s;
|
|
s = arm_mat_add_f32(&this->arm_mat_, &mat.arm_mat_, &this->arm_mat_);
|
|
return *this;
|
|
}
|
|
Matrixf<_rows, _cols>& operator-=(const Matrixf<_rows, _cols> mat) {
|
|
arm_status s;
|
|
s = arm_mat_sub_f32(&this->arm_mat_, &mat.arm_mat_, &this->arm_mat_);
|
|
return *this;
|
|
}
|
|
Matrixf<_rows, _cols>& operator*=(const float& val) {
|
|
arm_status s;
|
|
s = arm_mat_scale_f32(&this->arm_mat_, val, &this->arm_mat_);
|
|
return *this;
|
|
}
|
|
Matrixf<_rows, _cols>& operator/=(const float& val) {
|
|
arm_status s;
|
|
s = arm_mat_scale_f32(&this->arm_mat_, 1.f / val, &this->arm_mat_);
|
|
return *this;
|
|
}
|
|
Matrixf<_rows, _cols> operator+(const Matrixf<_rows, _cols>& mat) {
|
|
arm_status s;
|
|
Matrixf<_rows, _cols> res;
|
|
s = arm_mat_add_f32(&this->arm_mat_, &mat.arm_mat_, &res.arm_mat_);
|
|
return res;
|
|
}
|
|
Matrixf<_rows, _cols> operator-(const Matrixf<_rows, _cols>& mat) {
|
|
arm_status s;
|
|
Matrixf<_rows, _cols> res;
|
|
s = arm_mat_sub_f32(&this->arm_mat_, &mat.arm_mat_, &res.arm_mat_);
|
|
return res;
|
|
}
|
|
Matrixf<_rows, _cols> operator*(const float& val) {
|
|
arm_status s;
|
|
Matrixf<_rows, _cols> res;
|
|
s = arm_mat_scale_f32(&this->arm_mat_, val, &res.arm_mat_);
|
|
return res;
|
|
}
|
|
friend Matrixf<_rows, _cols> operator*(const float& val,
|
|
const Matrixf<_rows, _cols>& mat) {
|
|
arm_status s;
|
|
Matrixf<_rows, _cols> res;
|
|
s = arm_mat_scale_f32(&mat.arm_mat_, val, &res.arm_mat_);
|
|
return res;
|
|
}
|
|
Matrixf<_rows, _cols> operator/(const float& val) {
|
|
arm_status s;
|
|
Matrixf<_rows, _cols> res;
|
|
s = arm_mat_scale_f32(&this->arm_mat_, 1.f / val, &res.arm_mat_);
|
|
return res;
|
|
}
|
|
// Matrix multiplication
|
|
template <int cols>
|
|
friend Matrixf<_rows, cols> operator*(const Matrixf<_rows, _cols>& mat1,
|
|
const Matrixf<_cols, cols>& mat2) {
|
|
arm_status s;
|
|
Matrixf<_rows, cols> res;
|
|
s = arm_mat_mult_f32(&mat1.arm_mat_, &mat2.arm_mat_, &res.arm_mat_);
|
|
return res;
|
|
}
|
|
|
|
// Submatrix
|
|
template <int rows, int cols>
|
|
Matrixf<rows, cols> block(const int& start_row, const int& start_col) {
|
|
Matrixf<rows, cols> res;
|
|
for (int row = start_row; row < start_row + rows; row++) {
|
|
memcpy((float*)res[0] + (row - start_row) * cols,
|
|
(float*)this->data_ + row * _cols + start_col,
|
|
cols * sizeof(float));
|
|
}
|
|
return res;
|
|
}
|
|
// Specific row
|
|
Matrixf<1, _cols> row(const int& row) { return block<1, _cols>(row, 0); }
|
|
// Specific column
|
|
Matrixf<_rows, 1> col(const int& col) { return block<_rows, 1>(0, col); }
|
|
|
|
// Transpose
|
|
Matrixf<_cols, _rows> trans(void) {
|
|
Matrixf<_cols, _rows> res;
|
|
arm_mat_trans_f32(&arm_mat_, &res.arm_mat_);
|
|
return res;
|
|
}
|
|
// Trace
|
|
float trace(void) {
|
|
float res = 0;
|
|
for (int i = 0; i < fmin(_rows, _cols); i++) {
|
|
res += (*this)[i][i];
|
|
}
|
|
return res;
|
|
}
|
|
// Norm
|
|
float norm(void) { return sqrtf((this->trans() * *this)[0][0]); }
|
|
|
|
public:
|
|
// arm matrix instance
|
|
arm_matrix_instance_f32 arm_mat_;
|
|
|
|
protected:
|
|
// size
|
|
int rows_, cols_;
|
|
// data
|
|
float data_[_rows * _cols];
|
|
};
|
|
|
|
// Matrix funtions
|
|
namespace matrixf {
|
|
|
|
// Special Matrices
|
|
// Zero matrix
|
|
template <int _rows, int _cols>
|
|
Matrixf<_rows, _cols> zeros(void) {
|
|
float data[_rows * _cols] = {0};
|
|
return Matrixf<_rows, _cols>(data);
|
|
}
|
|
// Ones matrix
|
|
template <int _rows, int _cols>
|
|
Matrixf<_rows, _cols> ones(void) {
|
|
float data[_rows * _cols] = {0};
|
|
for (int i = 0; i < _rows * _cols; i++) {
|
|
data[i] = 1;
|
|
}
|
|
return Matrixf<_rows, _cols>(data);
|
|
}
|
|
// Identity matrix
|
|
template <int _rows, int _cols>
|
|
Matrixf<_rows, _cols> eye(void) {
|
|
float data[_rows * _cols] = {0};
|
|
for (int i = 0; i < fmin(_rows, _cols); i++) {
|
|
data[i * _cols + i] = 1;
|
|
}
|
|
return Matrixf<_rows, _cols>(data);
|
|
}
|
|
// Diagonal matrix
|
|
template <int _rows, int _cols>
|
|
Matrixf<_rows, _cols> diag(Matrixf<_rows, 1> vec) {
|
|
Matrixf<_rows, _cols> res = matrixf::zeros<_rows, _cols>();
|
|
for (int i = 0; i < fmin(_rows, _cols); i++) {
|
|
res[i][i] = vec[i][0];
|
|
}
|
|
return res;
|
|
}
|
|
|
|
// Inverse
|
|
template <int _dim>
|
|
Matrixf<_dim, _dim> inv(Matrixf<_dim, _dim> mat) {
|
|
arm_status s;
|
|
// extended matrix [A|I]
|
|
Matrixf<_dim, 2 * _dim> ext_mat = matrixf::zeros<_dim, 2 * _dim>();
|
|
for (int i = 0; i < _dim; i++) {
|
|
memcpy(ext_mat[i], mat[i], _dim * sizeof(float));
|
|
ext_mat[i][_dim + i] = 1;
|
|
}
|
|
// elimination
|
|
for (int i = 0; i < _dim; i++) {
|
|
// find maximum absolute value in the first column in lower right block
|
|
float abs_max = fabs(ext_mat[i][i]);
|
|
int abs_max_row = i;
|
|
for (int row = i; row < _dim; row++) {
|
|
if (abs_max < fabs(ext_mat[row][i])) {
|
|
abs_max = fabs(ext_mat[row][i]);
|
|
abs_max_row = row;
|
|
}
|
|
}
|
|
if (abs_max < 1e-12f) { // singular
|
|
return matrixf::zeros<_dim, _dim>();
|
|
s = ARM_MATH_SINGULAR;
|
|
}
|
|
if (abs_max_row != i) { // row exchange
|
|
float tmp;
|
|
Matrixf<1, 2 * _dim> row_i = ext_mat.row(i);
|
|
Matrixf<1, 2 * _dim> row_abs_max = ext_mat.row(abs_max_row);
|
|
memcpy(ext_mat[i], row_abs_max[0], 2 * _dim * sizeof(float));
|
|
memcpy(ext_mat[abs_max_row], row_i[0], 2 * _dim * sizeof(float));
|
|
}
|
|
float k = 1.f / ext_mat[i][i];
|
|
for (int col = i; col < 2 * _dim; col++) {
|
|
ext_mat[i][col] *= k;
|
|
}
|
|
for (int row = 0; row < _dim; row++) {
|
|
if (row == i) {
|
|
continue;
|
|
}
|
|
k = ext_mat[row][i];
|
|
for (int j = i; j < 2 * _dim; j++) {
|
|
ext_mat[row][j] -= k * ext_mat[i][j];
|
|
}
|
|
}
|
|
}
|
|
// inv = ext_mat(:,n+1:2n)
|
|
s = ARM_MATH_SUCCESS;
|
|
Matrixf<_dim, _dim> res;
|
|
for (int i = 0; i < _dim; i++) {
|
|
memcpy(res[i], &ext_mat[i][_dim], _dim * sizeof(float));
|
|
}
|
|
return res;
|
|
}
|
|
|
|
} // namespace matrixf
|
|
|
|
namespace vector3f {
|
|
|
|
// hat of vector
|
|
Matrixf<3, 3> hat(Matrixf<3, 1> vec);
|
|
|
|
// cross product
|
|
Matrixf<3, 1> cross(Matrixf<3, 1> vec1, Matrixf<3, 1> vec2);
|
|
|
|
} // namespace vector3f
|
|
|
|
#endif // MATRIX_H
|