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Remove old matrix inversion routines
This commit is contained in:
Julian Kent
Lorenz Meier
parent
e96e028327
commit
e014954c91
@ -33,7 +33,6 @@
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px4_add_library(mathlib
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math/test/test.cpp
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math/matrix_alg.cpp
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math/filter/LowPassFilter2p.cpp
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math/filter/LowPassFilter2pVector3f.cpp
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)
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@ -1,390 +0,0 @@
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/****************************************************************************
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*
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* Copyright (C) 2013 PX4 Development Team. All rights reserved.
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* Author: Siddharth Bharat Purohit <sidbpurohit@gmail.com>
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* 3. Neither the name PX4 nor the names of its contributors may be
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* used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
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* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
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* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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****************************************************************************/
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/**
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* @file matrix_alg.cpp
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*
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* Matrix algebra on raw arrays
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*/
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#include "matrix_alg.h"
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#include <px4_platform_common/defines.h>
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/*
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* Does matrix multiplication of two regular/square matrices
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*
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* @param A, Matrix A
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* @param B, Matrix B
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* @param n, dimemsion of square matrices
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* @returns multiplied matrix i.e. A*B
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*/
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float *mat_mul(float *A, float *B, uint8_t n)
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{
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float *ret = new float[n * n];
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memset(ret, 0.0f, n * n * sizeof(float));
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for (uint8_t i = 0; i < n; i++) {
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for (uint8_t j = 0; j < n; j++) {
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for (uint8_t k = 0; k < n; k++) {
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ret[i * n + j] += A[i * n + k] * B[k * n + j];
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}
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}
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}
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return ret;
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}
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static inline void swap(float &a, float &b)
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{
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float c;
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c = a;
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a = b;
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b = c;
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}
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/*
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* calculates pivot matrix such that all the larger elements in the row are on diagonal
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*
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* @param A, input matrix matrix
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* @param pivot
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* @param n, dimenstion of square matrix
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* @returns false = matrix is Singular or non positive definite, true = matrix inversion successful
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*/
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static void mat_pivot(float *A, float *pivot, uint8_t n)
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{
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for (uint8_t i = 0; i < n; i++) {
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for (uint8_t j = 0; j < n; j++) {
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pivot[i * n + j] = (i == j);
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}
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}
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for (uint8_t i = 0; i < n; i++) {
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uint8_t max_j = i;
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for (uint8_t j = i; j < n; j++) {
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if (fabsf(A[j * n + i]) > fabsf(A[max_j * n + i])) {
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max_j = j;
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}
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}
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if (max_j != i) {
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for (uint8_t k = 0; k < n; k++) {
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swap(pivot[i * n + k], pivot[max_j * n + k]);
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}
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}
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}
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}
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/*
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* calculates matrix inverse of Lower trangular matrix using forward substitution
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*
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* @param L, lower triangular matrix
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* @param out, Output inverted lower triangular matrix
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* @param n, dimension of matrix
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*/
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static void mat_forward_sub(float *L, float *out, uint8_t n)
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{
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// Forward substitution solve LY = I
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for (int i = 0; i < n; i++) {
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out[i * n + i] = 1 / L[i * n + i];
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for (int j = i + 1; j < n; j++) {
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for (int k = i; k < j; k++) {
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out[j * n + i] -= L[j * n + k] * out[k * n + i];
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}
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out[j * n + i] /= L[j * n + j];
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}
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}
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}
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/*
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* calculates matrix inverse of Upper trangular matrix using backward substitution
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*
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* @param U, upper triangular matrix
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* @param out, Output inverted upper triangular matrix
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* @param n, dimension of matrix
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*/
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static void mat_back_sub(float *U, float *out, uint8_t n)
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{
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// Backward Substitution solve UY = I
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for (int i = n - 1; i >= 0; i--) {
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out[i * n + i] = 1 / U[i * n + i];
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for (int j = i - 1; j >= 0; j--) {
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for (int k = i; k > j; k--) {
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out[j * n + i] -= U[j * n + k] * out[k * n + i];
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}
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out[j * n + i] /= U[j * n + j];
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}
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}
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}
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/*
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* Decomposes square matrix into Lower and Upper triangular matrices such that
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* A*P = L*U, where P is the pivot matrix
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* ref: http://rosettacode.org/wiki/LU_decomposition
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* @param U, upper triangular matrix
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* @param out, Output inverted upper triangular matrix
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* @param n, dimension of matrix
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*/
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static void mat_LU_decompose(float *A, float *L, float *U, float *P, uint8_t n)
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{
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memset(L, 0, n * n * sizeof(float));
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memset(U, 0, n * n * sizeof(float));
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memset(P, 0, n * n * sizeof(float));
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mat_pivot(A, P, n);
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float *APrime = mat_mul(P, A, n);
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for (uint8_t i = 0; i < n; i++) {
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L[i * n + i] = 1;
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}
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for (uint8_t i = 0; i < n; i++) {
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for (uint8_t j = 0; j < n; j++) {
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if (j <= i) {
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U[j * n + i] = APrime[j * n + i];
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for (uint8_t k = 0; k < j; k++) {
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U[j * n + i] -= L[j * n + k] * U[k * n + i];
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}
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}
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if (j >= i) {
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L[j * n + i] = APrime[j * n + i];
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for (uint8_t k = 0; k < i; k++) {
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L[j * n + i] -= L[j * n + k] * U[k * n + i];
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}
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L[j * n + i] /= U[i * n + i];
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}
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}
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}
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delete[] APrime;
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}
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/*
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* matrix inverse code for any square matrix using LU decomposition
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* inv = inv(U)*inv(L)*P, where L and U are triagular matrices and P the pivot matrix
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* ref: http://www.cl.cam.ac.uk/teaching/1314/NumMethods/supporting/mcmaster-kiruba-ludecomp.pdf
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* @param m, input 4x4 matrix
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* @param inv, Output inverted 4x4 matrix
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* @param n, dimension of square matrix
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* @returns false = matrix is Singular, true = matrix inversion successful
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*/
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bool mat_inverse(float *A, float *inv, uint8_t n)
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{
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float *L, *U, *P;
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bool ret = true;
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L = new float[n * n];
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U = new float[n * n];
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P = new float[n * n];
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mat_LU_decompose(A, L, U, P, n);
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float *L_inv = new float[n * n];
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float *U_inv = new float[n * n];
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memset(L_inv, 0, n * n * sizeof(float));
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mat_forward_sub(L, L_inv, n);
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memset(U_inv, 0, n * n * sizeof(float));
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mat_back_sub(U, U_inv, n);
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// decomposed matrices no longer required
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delete[] L;
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delete[] U;
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float *inv_unpivoted = mat_mul(U_inv, L_inv, n);
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float *inv_pivoted = mat_mul(inv_unpivoted, P, n);
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//check sanity of results
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for (uint8_t i = 0; i < n; i++) {
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for (uint8_t j = 0; j < n; j++) {
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if (!PX4_ISFINITE(inv_pivoted[i * n + j])) {
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ret = false;
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}
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}
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}
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memcpy(inv, inv_pivoted, n * n * sizeof(float));
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//free memory
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delete[] inv_pivoted;
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delete[] inv_unpivoted;
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delete[] P;
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delete[] U_inv;
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delete[] L_inv;
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return ret;
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}
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bool inverse4x4(float m[], float invOut[])
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{
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float inv[16], det;
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uint8_t i;
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inv[0] = m[5] * m[10] * m[15] -
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m[5] * m[11] * m[14] -
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m[9] * m[6] * m[15] +
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m[9] * m[7] * m[14] +
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m[13] * m[6] * m[11] -
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m[13] * m[7] * m[10];
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inv[4] = -m[4] * m[10] * m[15] +
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m[4] * m[11] * m[14] +
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m[8] * m[6] * m[15] -
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m[8] * m[7] * m[14] -
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m[12] * m[6] * m[11] +
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m[12] * m[7] * m[10];
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inv[8] = m[4] * m[9] * m[15] -
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m[4] * m[11] * m[13] -
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m[8] * m[5] * m[15] +
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m[8] * m[7] * m[13] +
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m[12] * m[5] * m[11] -
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m[12] * m[7] * m[9];
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inv[12] = -m[4] * m[9] * m[14] +
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m[4] * m[10] * m[13] +
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m[8] * m[5] * m[14] -
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m[8] * m[6] * m[13] -
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m[12] * m[5] * m[10] +
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m[12] * m[6] * m[9];
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inv[1] = -m[1] * m[10] * m[15] +
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m[1] * m[11] * m[14] +
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m[9] * m[2] * m[15] -
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m[9] * m[3] * m[14] -
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m[13] * m[2] * m[11] +
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m[13] * m[3] * m[10];
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inv[5] = m[0] * m[10] * m[15] -
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m[0] * m[11] * m[14] -
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m[8] * m[2] * m[15] +
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m[8] * m[3] * m[14] +
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m[12] * m[2] * m[11] -
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m[12] * m[3] * m[10];
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inv[9] = -m[0] * m[9] * m[15] +
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m[0] * m[11] * m[13] +
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m[8] * m[1] * m[15] -
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m[8] * m[3] * m[13] -
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m[12] * m[1] * m[11] +
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m[12] * m[3] * m[9];
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inv[13] = m[0] * m[9] * m[14] -
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m[0] * m[10] * m[13] -
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m[8] * m[1] * m[14] +
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m[8] * m[2] * m[13] +
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m[12] * m[1] * m[10] -
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m[12] * m[2] * m[9];
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inv[2] = m[1] * m[6] * m[15] -
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m[1] * m[7] * m[14] -
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m[5] * m[2] * m[15] +
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m[5] * m[3] * m[14] +
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m[13] * m[2] * m[7] -
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m[13] * m[3] * m[6];
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inv[6] = -m[0] * m[6] * m[15] +
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m[0] * m[7] * m[14] +
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m[4] * m[2] * m[15] -
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m[4] * m[3] * m[14] -
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m[12] * m[2] * m[7] +
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m[12] * m[3] * m[6];
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inv[10] = m[0] * m[5] * m[15] -
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m[0] * m[7] * m[13] -
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m[4] * m[1] * m[15] +
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m[4] * m[3] * m[13] +
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m[12] * m[1] * m[7] -
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m[12] * m[3] * m[5];
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inv[14] = -m[0] * m[5] * m[14] +
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m[0] * m[6] * m[13] +
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m[4] * m[1] * m[14] -
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m[4] * m[2] * m[13] -
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m[12] * m[1] * m[6] +
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m[12] * m[2] * m[5];
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inv[3] = -m[1] * m[6] * m[11] +
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m[1] * m[7] * m[10] +
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m[5] * m[2] * m[11] -
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m[5] * m[3] * m[10] -
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m[9] * m[2] * m[7] +
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m[9] * m[3] * m[6];
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inv[7] = m[0] * m[6] * m[11] -
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m[0] * m[7] * m[10] -
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m[4] * m[2] * m[11] +
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m[4] * m[3] * m[10] +
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m[8] * m[2] * m[7] -
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m[8] * m[3] * m[6];
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inv[11] = -m[0] * m[5] * m[11] +
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m[0] * m[7] * m[9] +
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m[4] * m[1] * m[11] -
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m[4] * m[3] * m[9] -
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m[8] * m[1] * m[7] +
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m[8] * m[3] * m[5];
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inv[15] = m[0] * m[5] * m[10] -
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m[0] * m[6] * m[9] -
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m[4] * m[1] * m[10] +
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m[4] * m[2] * m[9] +
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m[8] * m[1] * m[6] -
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m[8] * m[2] * m[5];
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det = m[0] * inv[0] + m[1] * inv[4] + m[2] * inv[8] + m[3] * inv[12];
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if (fabsf(det) < 1.1755e-38f) {
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return false;
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}
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det = 1.0f / det;
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for (i = 0; i < 16; i++) {
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invOut[i] = inv[i] * det;
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}
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return true;
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}
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@ -1,50 +0,0 @@
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/****************************************************************************
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*
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* Copyright (C) 2013 PX4 Development Team. All rights reserved.
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* Author: Siddharth Bharat Purohit <sibpurohit@gmail.com>
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*
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* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
*
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in
|
||||
* the documentation and/or other materials provided with the
|
||||
* distribution.
|
||||
* 3. Neither the name PX4 nor the names of its contributors may be
|
||||
* used to endorse or promote products derived from this software
|
||||
* without specific prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
||||
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
||||
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
||||
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
||||
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
|
||||
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
|
||||
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
||||
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
* POSSIBILITY OF SUCH DAMAGE.
|
||||
*
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****************************************************************************/
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/**
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* @file matrix_alg.h
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*
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* Matrix algebra on raw arrays
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*/
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#pragma once
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#include <inttypes.h>
|
||||
#include <string.h>
|
||||
#include <math.h>
|
||||
|
||||
float *mat_mul(float *A, float *B, uint8_t n);
|
||||
bool mat_inverse(float *A, float *inv, uint8_t n);
|
||||
bool inverse4x4(float m[], float invOut[]);
|
||||
@ -43,7 +43,6 @@
|
||||
|
||||
#include "math/Limits.hpp"
|
||||
#include "math/Functions.hpp"
|
||||
#include "math/matrix_alg.h"
|
||||
#include "math/SearchMin.hpp"
|
||||
#include "math/TrajMath.hpp"
|
||||
|
||||
|
||||
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Reference in New Issue
Block a user