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ardupilot/libraries/AP_Math/matrix_alg.cpp

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/*
* matrix3.cpp
* Copyright (C) Siddharth Bharat Purohit, 3DRobotics Inc. 2015
*
* This file is free software: you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This file is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
* See the GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <AP_HAL/AP_HAL.h>
#include "AP_Math.h"
#include <stdio.h>
#if CONFIG_HAL_BOARD == HAL_BOARD_SITL
#include <fenv.h>
#endif
/*
* Does matrix multiplication of two regular/square matrices
*
* @param A, Matrix A
* @param B, Matrix B
* @param n, dimemsion of square matrices
* @returns multiplied matrix i.e. A*B
*/
template<typename T>
static T* matrix_multiply(const T *A, const T *B, uint16_t n)
{
T* ret = new T[n*n];
memset(ret,0.0f,n*n*sizeof(T));
for(uint16_t i = 0; i < n; i++) {
for(uint16_t j = 0; j < n; j++) {
for(uint16_t k = 0;k < n; k++) {
ret[i*n + j] += A[i*n + k] * B[k*n + j];
}
}
}
return ret;
}
template<typename T>
static inline void swap(T &a, T &b)
{
T c;
c = a;
a = b;
b = c;
}
/*
* calculates pivot matrix such that all the larger elements in the row are on diagonal
*
* @param A, input matrix matrix
* @param pivot
* @param n, dimenstion of square matrix
* @returns false = matrix is Singular or non positive definite, true = matrix inversion successful
*/
template<typename T>
static void mat_pivot(const T* A, T* pivot, uint16_t n)
{
for(uint16_t i = 0;i<n;i++){
for(uint16_t j=0;j<n;j++) {
pivot[i*n+j] = static_cast<T>(i==j);
}
}
for(uint16_t i = 0;i < n; i++) {
uint16_t max_j = i;
for(uint16_t j=i;j<n;j++){
if (std::is_same<T, double>::value) {
if(fabsf(A[j*n + i]) > fabsf(A[max_j*n + i])) {
max_j = j;
}
} else {
if(fabsf(A[j*n + i]) > fabsf(A[max_j*n + i])) {
max_j = j;
}
}
}
if(max_j != i) {
for(uint16_t k = 0; k < n; k++) {
swap(pivot[i*n + k], pivot[max_j*n + k]);
}
}
}
}
/*
* calculates matrix inverse of Lower trangular matrix using forward substitution
*
* @param L, lower triangular matrix
* @param out, Output inverted lower triangular matrix
* @param n, dimension of matrix
*/
template<typename T>
static void mat_forward_sub(const T *L, T *out, uint16_t n)
{
// Forward substitution solve LY = I
for(int i = 0; i < n; i++) {
out[i*n + i] = 1/L[i*n + i];
for (int j = i+1; j < n; j++) {
for (int k = i; k < j; k++) {
out[j*n + i] -= L[j*n + k] * out[k*n + i];
}
out[j*n + i] /= L[j*n + j];
}
}
}
/*
* calculates matrix inverse of Upper trangular matrix using backward substitution
*
* @param U, upper triangular matrix
* @param out, Output inverted upper triangular matrix
* @param n, dimension of matrix
*/
template<typename T>
static void mat_back_sub(const T *U, T *out, uint16_t n)
{
// Backward Substitution solve UY = I
for(int i = n-1; i >= 0; i--) {
out[i*n + i] = 1/U[i*n + i];
for (int j = i - 1; j >= 0; j--) {
for (int k = i; k > j; k--) {
out[j*n + i] -= U[j*n + k] * out[k*n + i];
}
out[j*n + i] /= U[j*n + j];
}
}
}
/*
* Decomposes square matrix into Lower and Upper triangular matrices such that
* A*P = L*U, where P is the pivot matrix
* ref: http://rosettacode.org/wiki/LU_decomposition
* @param U, upper triangular matrix
* @param out, Output inverted upper triangular matrix
* @param n, dimension of matrix
*/
template<typename T>
static void mat_LU_decompose(const T* A, T* L, T* U, T *P, uint16_t n)
{
memset(L,0,n*n*sizeof(T));
memset(U,0,n*n*sizeof(T));
memset(P,0,n*n*sizeof(T));
mat_pivot(A,P,n);
T *APrime = matrix_multiply(P,A,n);
for(uint16_t i = 0; i < n; i++) {
L[i*n + i] = 1;
}
for(uint16_t i = 0; i < n; i++) {
for(uint16_t j = 0; j < n; j++) {
if(j <= i) {
U[j*n + i] = APrime[j*n + i];
for(uint16_t k = 0; k < j; k++) {
U[j*n + i] -= L[j*n + k] * U[k*n + i];
}
}
if(j >= i) {
L[j*n + i] = APrime[j*n + i];
for(uint16_t k = 0; k < i; k++) {
L[j*n + i] -= L[j*n + k] * U[k*n + i];
}
L[j*n + i] /= U[i*n + i];
}
}
}
delete[] APrime;
}
/*
* matrix inverse code for any square matrix using LU decomposition
* inv = inv(U)*inv(L)*P, where L and U are triagular matrices and P the pivot matrix
* ref: http://www.cl.cam.ac.uk/teaching/1314/NumMethods/supporting/mcmaster-kiruba-ludecomp.pdf
* @param m, input 4x4 matrix
* @param inv, Output inverted 4x4 matrix
* @param n, dimension of square matrix
* @returns false = matrix is Singular, true = matrix inversion successful
*/
template<typename T>
static bool mat_inverseN(const T* A, T* inv, uint16_t n)
{
T *L, *U, *P;
bool ret = true;
L = new T[n*n];
U = new T[n*n];
P = new T[n*n];
mat_LU_decompose(A,L,U,P,n);
T *L_inv = new T[n*n];
T *U_inv = new T[n*n];
memset(L_inv,0,n*n*sizeof(T));
mat_forward_sub(L,L_inv,n);
memset(U_inv,0,n*n*sizeof(T));
mat_back_sub(U,U_inv,n);
// decomposed matrices no longer required
delete[] L;
delete[] U;
T *inv_unpivoted = matrix_multiply(U_inv,L_inv,n);
T *inv_pivoted = matrix_multiply(inv_unpivoted, P, n);
//check sanity of results
for(uint16_t i = 0; i < n; i++) {
for(uint16_t j = 0; j < n; j++) {
if(isnan(inv_pivoted[i*n+j]) || isinf(inv_pivoted[i*n+j])){
ret = false;
}
}
}
memcpy(inv,inv_pivoted,n*n*sizeof(T));
//free memory
delete[] inv_pivoted;
delete[] inv_unpivoted;
delete[] P;
delete[] U_inv;
delete[] L_inv;
return ret;
}
/*
* fast matrix inverse code only for 3x3 square matrix
*
* @param m, input 4x4 matrix
* @param invOut, Output inverted 4x4 matrix
* @returns false = matrix is Singular, true = matrix inversion successful
*/
template<typename T>
static bool inverse3x3(const T m[], T invOut[])
{
T inv[9];
// computes the inverse of a matrix m
T det = m[0] * (m[4] * m[8] - m[7] * m[5]) -
m[1] * (m[3] * m[8] - m[5] * m[6]) +
m[2] * (m[3] * m[7] - m[4] * m[6]);
if (is_zero(det) || isinf(det)) {
return false;
}
T invdet = 1 / det;
inv[0] = (m[4] * m[8] - m[7] * m[5]) * invdet;
inv[1] = (m[2] * m[7] - m[1] * m[8]) * invdet;
inv[2] = (m[1] * m[5] - m[2] * m[4]) * invdet;
inv[3] = (m[5] * m[6] - m[3] * m[8]) * invdet;
inv[4] = (m[0] * m[8] - m[2] * m[6]) * invdet;
inv[5] = (m[3] * m[2] - m[0] * m[5]) * invdet;
inv[6] = (m[3] * m[7] - m[6] * m[4]) * invdet;
inv[7] = (m[6] * m[1] - m[0] * m[7]) * invdet;
inv[8] = (m[0] * m[4] - m[3] * m[1]) * invdet;
for(uint16_t i = 0; i < 9; i++){
invOut[i] = inv[i];
}
return true;
}
/*
* fast matrix inverse code only for 4x4 square matrix copied from
* gluInvertMatrix implementation in opengl for 4x4 matrices.
*
* @param m, input 4x4 matrix
* @param invOut, Output inverted 4x4 matrix
* @returns false = matrix is Singular, true = matrix inversion successful
*/
template<typename T>
static bool inverse4x4(const T m[],T invOut[])
{
T inv[16], det;
uint16_t i;
#if CONFIG_HAL_BOARD == HAL_BOARD_SITL
//disable FE_INEXACT detection as it fails on mac os runs
int old = fedisableexcept(FE_INEXACT | FE_OVERFLOW);
if (old < 0) {
// hal.console->printf("inverse4x4(): warning: error on disabling FE_OVERFLOW floating point exception\n");
}
#endif
inv[0] = m[5] * m[10] * m[15] -
m[5] * m[11] * m[14] -
m[9] * m[6] * m[15] +
m[9] * m[7] * m[14] +
m[13] * m[6] * m[11] -
m[13] * m[7] * m[10];
inv[4] = -m[4] * m[10] * m[15] +
m[4] * m[11] * m[14] +
m[8] * m[6] * m[15] -
m[8] * m[7] * m[14] -
m[12] * m[6] * m[11] +
m[12] * m[7] * m[10];
inv[8] = m[4] * m[9] * m[15] -
m[4] * m[11] * m[13] -
m[8] * m[5] * m[15] +
m[8] * m[7] * m[13] +
m[12] * m[5] * m[11] -
m[12] * m[7] * m[9];
inv[12] = -m[4] * m[9] * m[14] +
m[4] * m[10] * m[13] +
m[8] * m[5] * m[14] -
m[8] * m[6] * m[13] -
m[12] * m[5] * m[10] +
m[12] * m[6] * m[9];
inv[1] = -m[1] * m[10] * m[15] +
m[1] * m[11] * m[14] +
m[9] * m[2] * m[15] -
m[9] * m[3] * m[14] -
m[13] * m[2] * m[11] +
m[13] * m[3] * m[10];
inv[5] = m[0] * m[10] * m[15] -
m[0] * m[11] * m[14] -
m[8] * m[2] * m[15] +
m[8] * m[3] * m[14] +
m[12] * m[2] * m[11] -
m[12] * m[3] * m[10];
inv[9] = -m[0] * m[9] * m[15] +
m[0] * m[11] * m[13] +
m[8] * m[1] * m[15] -
m[8] * m[3] * m[13] -
m[12] * m[1] * m[11] +
m[12] * m[3] * m[9];
inv[13] = m[0] * m[9] * m[14] -
m[0] * m[10] * m[13] -
m[8] * m[1] * m[14] +
m[8] * m[2] * m[13] +
m[12] * m[1] * m[10] -
m[12] * m[2] * m[9];
inv[2] = m[1] * m[6] * m[15] -
m[1] * m[7] * m[14] -
m[5] * m[2] * m[15] +
m[5] * m[3] * m[14] +
m[13] * m[2] * m[7] -
m[13] * m[3] * m[6];
inv[6] = -m[0] * m[6] * m[15] +
m[0] * m[7] * m[14] +
m[4] * m[2] * m[15] -
m[4] * m[3] * m[14] -
m[12] * m[2] * m[7] +
m[12] * m[3] * m[6];
inv[10] = m[0] * m[5] * m[15] -
m[0] * m[7] * m[13] -
m[4] * m[1] * m[15] +
m[4] * m[3] * m[13] +
m[12] * m[1] * m[7] -
m[12] * m[3] * m[5];
inv[14] = -m[0] * m[5] * m[14] +
m[0] * m[6] * m[13] +
m[4] * m[1] * m[14] -
m[4] * m[2] * m[13] -
m[12] * m[1] * m[6] +
m[12] * m[2] * m[5];
inv[3] = -m[1] * m[6] * m[11] +
m[1] * m[7] * m[10] +
m[5] * m[2] * m[11] -
m[5] * m[3] * m[10] -
m[9] * m[2] * m[7] +
m[9] * m[3] * m[6];
inv[7] = m[0] * m[6] * m[11] -
m[0] * m[7] * m[10] -
m[4] * m[2] * m[11] +
m[4] * m[3] * m[10] +
m[8] * m[2] * m[7] -
m[8] * m[3] * m[6];
inv[11] = -m[0] * m[5] * m[11] +
m[0] * m[7] * m[9] +
m[4] * m[1] * m[11] -
m[4] * m[3] * m[9] -
m[8] * m[1] * m[7] +
m[8] * m[3] * m[5];
inv[15] = m[0] * m[5] * m[10] -
m[0] * m[6] * m[9] -
m[4] * m[1] * m[10] +
m[4] * m[2] * m[9] +
m[8] * m[1] * m[6] -
m[8] * m[2] * m[5];
det = m[0] * inv[0] + m[1] * inv[4] + m[2] * inv[8] + m[3] * inv[12];
if (is_zero(det) || isinf(det)){
return false;
}
det = 1.0f / det;
for (i = 0; i < 16; i++)
invOut[i] = inv[i] * det;
#if CONFIG_HAL_BOARD == HAL_BOARD_SITL
if (old >= 0 && feenableexcept(old) < 0) {
// hal.console->printf("inverse4x4(): warning: error on restoring floating exception mask\n");
}
#endif
return true;
}
/*
* generic matrix inverse code
*
* @param x, input nxn matrix
* @param y, Output inverted nxn matrix
* @param n, dimension of square matrix
* @returns false = matrix is Singular, true = matrix inversion successful
*/
template<typename T>
bool mat_inverse(const T x[], T y[], uint16_t dim)
{
switch(dim){
case 3: return inverse3x3(x,y);
case 4: return inverse4x4(x,y);
default: return mat_inverseN(x,y,dim);
}
}
template <typename T>
void mat_mul(const T *A, const T *B, T *C, uint16_t n)
{
memset(C, 0, sizeof(T)*n*n);
for(uint16_t i = 0; i < n; i++) {
for(uint16_t j = 0; j < n; j++) {
for(uint16_t k = 0;k < n; k++) {
C[i*n + j] += A[i*n + k] * B[k*n + j];
}
}
}
}
template <typename T>
void mat_identity(T *A, uint16_t n)
{
memset(A, 0, sizeof(T)*n*n);
for (uint16_t i=0; i<n; i++) {
A[i*n+i] = 1;
}
}
template bool mat_inverse<float>(const float x[], float y[], uint16_t dim);
template void mat_mul<float>(const float *A, const float *B, float *C, uint16_t n);
template void mat_identity<float>(float x[], uint16_t dim);
template bool mat_inverse<double>(const double x[], double y[], uint16_t dim);
template void mat_mul<double>(const double *A, const double *B, double *C, uint16_t n);
template void mat_identity<double>(double x[], uint16_t dim);
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