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/**
* @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 <systemlib/math/Vector.hpp>
#include <systemlib/math/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