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