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#ifndef GFXSYMMAT2_INCLUDED // -*- C++ -*-
#define GFXSYMMAT2_INCLUDED
#if !defined(__GNUC__)
# pragma once
#endif
/************************************************************************
Symmetric 2x2 Matrix class
************************************************************************/
#include "mat2.h"
namespace gfx
{
class SymMat2
{
private:
double elt[3];
inline int index(int i, int j) const
{
// if n=dim(), and if i<=j:
// index = ( n*(n+1)/2 - (n-i)*(n-i+1)/2 ) + (j-i)
//
if( i<=j ) return 3 - (2-i)*(3-i)/2 + (j-i);
else return 3 - (2-j)*(3-j)/2 + (i-j);
}
public:
// Standard constructors
//
SymMat2(double s=0.0) { *this = s; }
SymMat2(const SymMat2& m) { *this = m; }
double& operator()(int i, int j) { return elt[index(i,j)]; }
double operator()(int i, int j) const { return elt[index(i,j)]; }
static int size() { return 3; }
static int dim() { return 2; }
typedef Vec2 vector_type;
typedef Mat2 inverse_type;
typedef double value_type;
operator double*() { return elt; }
operator const double*() { return elt; }
operator const double*() const { return elt; }
inline Vec2 row(int i) const;
inline Vec2 col(int j) const;
Mat2 fullmatrix() const;
inline SymMat2& operator=(const SymMat2& m);
inline SymMat2& operator=(double s);
inline SymMat2& operator+=(const SymMat2& m);
inline SymMat2& operator-=(const SymMat2& m);
inline SymMat2& operator*=(double s);
inline SymMat2& operator/=(double s);
static SymMat2 I();
static SymMat2 outer_product(const Vec2& v);
};
////////////////////////////////////////////////////////////////////////
//
// Methods definitions
//
inline Vec2 SymMat2::row(int i) const
{ return Vec2((*this)(i, 0), (*this)(i, 1)); }
inline Vec2 SymMat2::col(int j) const
{ return Vec2((*this)(0, j), (*this)(1, j)); }
inline SymMat2& SymMat2::operator=(const SymMat2& m)
{ for(int i=0; i<size(); i++) elt[i]=m.elt[i]; return *this; }
inline SymMat2& SymMat2::operator=(double s)
{ for(int i=0; i<size(); i++) elt[i]=s; return *this; }
inline SymMat2& SymMat2::operator+=(const SymMat2& m)
{ for(int i=0; i<size(); i++) elt[i]+=m.elt[i]; return *this; }
inline SymMat2& SymMat2::operator-=(const SymMat2& m)
{ for(int i=0; i<size(); i++) elt[i]-=m.elt[i]; return *this; }
inline SymMat2& SymMat2::operator*=(double s)
{ for(int i=0; i<size(); i++) elt[i]*=s; return *this; }
inline SymMat2& SymMat2::operator/=(double s)
{ for(int i=0; i<size(); i++) elt[i]/=s; return *this; }
////////////////////////////////////////////////////////////////////////
//
// Operator definitions
//
inline SymMat2 operator+(SymMat2 n, const SymMat2& m) { n += m; return n; }
inline SymMat2 operator-(SymMat2 n, const SymMat2& m) { n -= m; return n; }
inline SymMat2 operator*(double s, SymMat2 m) { m*=s; return m; }
inline SymMat2 operator*(SymMat2 m, double s) { m*=s; return m; }
inline SymMat2 operator/(SymMat2 m, double s) { m/=s; return m; }
inline Vec2 operator*(const SymMat2& m, const Vec2& v)
{ return Vec2(m.row(0)*v, m.row(1)*v); }
extern SymMat2 operator*(const SymMat2& n, const SymMat2& m);
extern std::ostream &operator<<(std::ostream &out, const SymMat2& M);
////////////////////////////////////////////////////////////////////////
//
// Misc. function definitions
//
inline double det(const SymMat2& m) { return m(0,0)*m(1,1) - 2*m(0,1); }
inline double trace(const SymMat2& m) { return m(0,0) + m(1,1); }
inline SymMat2 transpose(const SymMat2& m) { return m; }
extern double invert(Mat2& m_inv, const SymMat2& m);
extern bool eigen(const SymMat2& m, Vec2& eig_vals, Vec2 eig_vecs[2]);
} // namespace gfx
// GFXSYMMAT2_INCLUDED
#endif
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