Index C++ Code Documentation mrbubblelab::kernel::MrBubble File: LAB/mrbubblelab/kernel/MrBubble.H public: MrBubble( Complex const &coefficient, Real exponent, Real u0, Real uprime0 ); constructor typical values: coefficient = 1 exponent = 1 (three-legged; legs=exponent+2) u0 = 1 uprime0 = 0 virtual ~MrBubble(); destructor struct Data; void start( Data &X, Complex const &z, uint count ); void step( Data &X, Complex const &z1, uint count ); void step( Data &X, Complex const &z2 ); protected: private: void integrate_metric( Data &X, Complex const &dz ); INTEGRATION STEP 1 compute the metric void metric_integration_function( Real &du, Real &dv, Real u, Real v, Real r ); void integrate_frame( Data &X, Complex const &dz ); INTEGRATION STEP 2: computing the frame from the maurer-cartan form Integrate the frame differentials to get the frame for the surface. Integrate the differential equation dF = F T where F is the frame for the surface in SU(2), and T is the Maurer-Cartan form. The corresponding difference equation is F_new = F_old + F_old T or equivalently, F_new = F_old ( I + T ) void frame_integration_function( Complex4 &dF, Complex4 const &F, Data const &X, Complex const &dz ); void integrate_surface( Data &X, Complex const &dz ); INTEGRATION STEP 3: computing the surface from the frame Integrate the frame to get the surface. Compute f_z = exp(u/2) dz F.e1.Finv f_zb = exp(u/2) dzb F.e2.Finv = -conj(trans(f_z)) where f is the surface in R^3 and e1 = {{0,1},{0,0}} e2 = {{0,0},{-1,0}} void compute_df( Complex4 &df, Data const &X, Complex const &dz ); static void su2_to_r3( base::ArrayX<Real, 3U> &f, Complex4 const &X ); utility routines static void make_unitary( Complex4 &F ); Complex _coefficient; Real _exponent; Real _u0; Real _uprime0; Real H; Complex Q( Complex const & ); struct Real2; base::vector<Real2> _metric; static Complex const I; Complex4 e1, e2, e3; inline MrBubble( MrBubble const & ); disabled copy constructor inline MrBubble &operator=( MrBubble const & ); disabled assigment operator
	mrbubblelab::kernel::MrBubble GANG