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-/****************************************************************************
- *
- * Copyright (C) 2012 PX4 Development Team. All rights reserved.
- *
- * 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.
- *
- ****************************************************************************/
-
-/**
- * @file Matrix.h
- *
- * matrix code
- */
-
-#pragma once
-
-
-#include <inttypes.h>
-#include <assert.h>
-#include <stdlib.h>
-#include <string.h>
-#include <stdio.h>
-#include <math.h>
-
-#include "../Vector.hpp"
-#include "../Matrix.hpp"
-
-namespace math
-{
-
-class __EXPORT Matrix
-{
-public:
- // constructor
- Matrix(size_t rows, size_t cols) :
- _rows(rows),
- _cols(cols),
- _data((float *)calloc(rows *cols, sizeof(float))) {
- }
- Matrix(size_t rows, size_t cols, const float *data) :
- _rows(rows),
- _cols(cols),
- _data((float *)malloc(getSize())) {
- memcpy(getData(), data, getSize());
- }
- // deconstructor
- virtual ~Matrix() {
- delete [] getData();
- }
- // copy constructor (deep)
- Matrix(const Matrix &right) :
- _rows(right.getRows()),
- _cols(right.getCols()),
- _data((float *)malloc(getSize())) {
- memcpy(getData(), right.getData(),
- right.getSize());
- }
- // assignment
- inline Matrix &operator=(const Matrix &right) {
-#ifdef MATRIX_ASSERT
- ASSERT(getRows() == right.getRows());
- ASSERT(getCols() == right.getCols());
-#endif
-
- if (this != &right) {
- memcpy(getData(), right.getData(),
- right.getSize());
- }
-
- return *this;
- }
- // element accessors
- inline float &operator()(size_t i, size_t j) {
-#ifdef MATRIX_ASSERT
- ASSERT(i < getRows());
- ASSERT(j < getCols());
-#endif
- return getData()[i * getCols() + j];
- }
- inline const float &operator()(size_t i, size_t j) const {
-#ifdef MATRIX_ASSERT
- ASSERT(i < getRows());
- ASSERT(j < getCols());
-#endif
- return getData()[i * getCols() + j];
- }
- // output
- inline void print() const {
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- float sig;
- int exp;
- float num = (*this)(i, j);
- float2SigExp(num, sig, exp);
- printf("%6.3fe%03.3d,", (double)sig, exp);
- }
-
- printf("\n");
- }
- }
- // boolean ops
- inline bool operator==(const Matrix &right) const {
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- if (fabsf((*this)(i, j) - right(i, j)) > 1e-30f)
- return false;
- }
- }
-
- return true;
- }
- // scalar ops
- inline Matrix operator+(const float &right) const {
- Matrix result(getRows(), getCols());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(i, j) = (*this)(i, j) + right;
- }
- }
-
- return result;
- }
- inline Matrix operator-(const float &right) const {
- Matrix result(getRows(), getCols());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(i, j) = (*this)(i, j) - right;
- }
- }
-
- return result;
- }
- inline Matrix operator*(const float &right) const {
- Matrix result(getRows(), getCols());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(i, j) = (*this)(i, j) * right;
- }
- }
-
- return result;
- }
- inline Matrix operator/(const float &right) const {
- Matrix result(getRows(), getCols());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(i, j) = (*this)(i, j) / right;
- }
- }
-
- return result;
- }
- // vector ops
- inline Vector operator*(const Vector &right) const {
-#ifdef MATRIX_ASSERT
- ASSERT(getCols() == right.getRows());
-#endif
- Vector result(getRows());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(i) += (*this)(i, j) * right(j);
- }
- }
-
- return result;
- }
- // matrix ops
- inline Matrix operator+(const Matrix &right) const {
-#ifdef MATRIX_ASSERT
- ASSERT(getRows() == right.getRows());
- ASSERT(getCols() == right.getCols());
-#endif
- Matrix result(getRows(), getCols());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(i, j) = (*this)(i, j) + right(i, j);
- }
- }
-
- return result;
- }
- inline Matrix operator-(const Matrix &right) const {
-#ifdef MATRIX_ASSERT
- ASSERT(getRows() == right.getRows());
- ASSERT(getCols() == right.getCols());
-#endif
- Matrix result(getRows(), getCols());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(i, j) = (*this)(i, j) - right(i, j);
- }
- }
-
- return result;
- }
- inline Matrix operator*(const Matrix &right) const {
-#ifdef MATRIX_ASSERT
- ASSERT(getCols() == right.getRows());
-#endif
- Matrix result(getRows(), right.getCols());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < right.getCols(); j++) {
- for (size_t k = 0; k < right.getRows(); k++) {
- result(i, j) += (*this)(i, k) * right(k, j);
- }
- }
- }
-
- return result;
- }
- inline Matrix operator/(const Matrix &right) const {
-#ifdef MATRIX_ASSERT
- ASSERT(right.getRows() == right.getCols());
- ASSERT(getCols() == right.getCols());
-#endif
- return (*this) * right.inverse();
- }
- // other functions
- inline Matrix transpose() const {
- Matrix result(getCols(), getRows());
-
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- result(j, i) = (*this)(i, j);
- }
- }
-
- return result;
- }
- inline void swapRows(size_t a, size_t b) {
- if (a == b) return;
-
- for (size_t j = 0; j < getCols(); j++) {
- float tmp = (*this)(a, j);
- (*this)(a, j) = (*this)(b, j);
- (*this)(b, j) = tmp;
- }
- }
- inline void swapCols(size_t a, size_t b) {
- if (a == b) return;
-
- for (size_t i = 0; i < getRows(); i++) {
- float tmp = (*this)(i, a);
- (*this)(i, a) = (*this)(i, b);
- (*this)(i, b) = tmp;
- }
- }
- /**
- * inverse based on LU factorization with partial pivotting
- */
- Matrix inverse() const {
-#ifdef MATRIX_ASSERT
- ASSERT(getRows() == getCols());
-#endif
- size_t N = getRows();
- Matrix L = identity(N);
- const Matrix &A = (*this);
- Matrix U = A;
- Matrix P = identity(N);
-
- //printf("A:\n"); A.print();
-
- // for all diagonal elements
- for (size_t n = 0; n < N; n++) {
-
- // if diagonal is zero, swap with row below
- if (fabsf(U(n, n)) < 1e-8f) {
- //printf("trying pivot for row %d\n",n);
- for (size_t i = 0; i < N; i++) {
- if (i == n) continue;
-
- //printf("\ttrying row %d\n",i);
- if (fabsf(U(i, n)) > 1e-8f) {
- //printf("swapped %d\n",i);
- U.swapRows(i, n);
- P.swapRows(i, n);
- }
- }
- }
-
-#ifdef MATRIX_ASSERT
- //printf("A:\n"); A.print();
- //printf("U:\n"); U.print();
- //printf("P:\n"); P.print();
- //fflush(stdout);
- ASSERT(fabsf(U(n, n)) > 1e-8f);
-#endif
-
- // failsafe, return zero matrix
- if (fabsf(U(n, n)) < 1e-8f) {
- return Matrix::zero(n);
- }
-
- // for all rows below diagonal
- for (size_t i = (n + 1); i < N; i++) {
- L(i, n) = U(i, n) / U(n, n);
-
- // add i-th row and n-th row
- // multiplied by: -a(i,n)/a(n,n)
- for (size_t k = n; k < N; k++) {
- U(i, k) -= L(i, n) * U(n, k);
- }
- }
- }
-
- //printf("L:\n"); L.print();
- //printf("U:\n"); U.print();
-
- // solve LY=P*I for Y by forward subst
- Matrix Y = P;
-
- // for all columns of Y
- for (size_t c = 0; c < N; c++) {
- // for all rows of L
- for (size_t i = 0; i < N; i++) {
- // for all columns of L
- for (size_t j = 0; j < i; j++) {
- // for all existing y
- // subtract the component they
- // contribute to the solution
- Y(i, c) -= L(i, j) * Y(j, c);
- }
-
- // divide by the factor
- // on current
- // term to be solved
- // Y(i,c) /= L(i,i);
- // but L(i,i) = 1.0
- }
- }
-
- //printf("Y:\n"); Y.print();
-
- // solve Ux=y for x by back subst
- Matrix X = Y;
-
- // for all columns of X
- for (size_t c = 0; c < N; c++) {
- // for all rows of U
- for (size_t k = 0; k < N; k++) {
- // have to go in reverse order
- size_t i = N - 1 - k;
-
- // for all columns of U
- for (size_t j = i + 1; j < N; j++) {
- // for all existing x
- // subtract the component they
- // contribute to the solution
- X(i, c) -= U(i, j) * X(j, c);
- }
-
- // divide by the factor
- // on current
- // term to be solved
- X(i, c) /= U(i, i);
- }
- }
-
- //printf("X:\n"); X.print();
- return X;
- }
- inline void setAll(const float &val) {
- for (size_t i = 0; i < getRows(); i++) {
- for (size_t j = 0; j < getCols(); j++) {
- (*this)(i, j) = val;
- }
- }
- }
- inline void set(const float *data) {
- memcpy(getData(), data, getSize());
- }
- inline size_t getRows() const { return _rows; }
- inline size_t getCols() const { return _cols; }
- inline static Matrix identity(size_t size) {
- Matrix result(size, size);
-
- for (size_t i = 0; i < size; i++) {
- result(i, i) = 1.0f;
- }
-
- return result;
- }
- inline static Matrix zero(size_t size) {
- Matrix result(size, size);
- result.setAll(0.0f);
- return result;
- }
- inline static Matrix zero(size_t m, size_t n) {
- Matrix result(m, n);
- result.setAll(0.0f);
- return result;
- }
-protected:
- inline size_t getSize() const { return sizeof(float) * getRows() * getCols(); }
- inline float *getData() { return _data; }
- inline const float *getData() const { return _data; }
- inline void setData(float *data) { _data = data; }
-private:
- size_t _rows;
- size_t _cols;
- float *_data;
-};
-
-} // namespace math
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