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R2917/Amplitude.h
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Amplitude.h
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#ifndef _AMPLITUDE_H
#define _AMPLITUDE_H
#include "BigDouble.h"
#include "BigComplex.h"
#include "WaveFunction.h"
#include "SpinState.h"
/*! \brief scalar product \f$\langle \{R_i,\sigma_i\}|\Psi\rangle\f$
*
* Class to calculate the scalar product between the real space spin state
* \f$|{R_i,\sigma_i}\rangle\f$ (represented by the class SpinState) and the
* trial wave function \f$|\Psi\rangle\f$ (represented by classes inheriting
* from the class WaveFunction). The class uses the determinant and inverse
* matrix update technique.
* For a column vector \f$u\f$ update (hop in the trial wavefunction space):
* \f[\frac{det(A')}{det(A)}=\frac{det(A+(u-Ae_k)e_k^T)}{det(A)}
* =e_k^TA^{-1}u\f]
* and
* \f[(A')^{-1}=(A+(u-Ae_k)e_k^T)^{-1}=A^{-1}-\frac{(A^{-1}u-e_k)e_k^TA^{-1}}
* {e_k^TA^{-1}u}\f]
* For a row vector \f$v^T\f$ update (hop in the real space):
* \f[\frac{det(A')}{det(A)}=\frac{det(A+e_r(v^T-e_r^TA))}{det(A)}
* =v^TA^{-1}e_r\f]
* and
* \f[(A')^{-1}=(A+e_r(v^T-e_r^TA))^{-1}=
* A^{-1}-\frac{A^{-1}e_r(v^TA^{-1}-e_r^T)}
* {v^TA^{-1}e_r}.\f]
* For a successive \f$r\f$ row and \f$k\f$ column update by repsectively
* \f$v^T\f$ and \f$u\f$ vectors:
* \f[\frac{det(A)}{det(A')}=\left|\begin{array}{cc}
* e_k^TA^{-1}u+A^{-1}_{kr}A_{rk} & A^{-1}_{kr}\\
* v^TA^{-1}u+A_{rk}v^TA^{-1}e_r-u_r+v_k(e_k^TA^{-1}u+A_{rk}A^{-1}_{kr}) &
* v^TA^{-1}e_r-v_kA^{-1}_{kr}\end{array}\right|,\f]
* and for a successive \f$k\f$ column and \f$r\f$ row update by repsectively
* \f$u\f$ and \f$v^T\f$ vectors:
* \f[\frac{det(A)}{det(A')}=\left|\begin{array}{cc}
* e_k^TA^{-1}u-u_rA^{-1}_{kr} & A^{-1}_{kr}\\
* v^TA^{-1}u-v_k+A_{rk}e_k^TA^{-1}u-u_r(v^TA^{-1}e_r+A_{rk}A^{-1}_{kr})
* & v^TA^{-1}e_r+A_{rk}A^{-1}_{kr}\end{array}\right|.\f]
*/
class Amplitude {
public:
Amplitude(SpinState* sp, WaveFunction* wav);//!< Constructor
~Amplitude();//!< Destructor
/*! Initialize or reinitialize the matrices
* Calculate determinant and inverse matrices.*/
void Init();
//! update matrices after a spin swap.
void ColUpdate(const size_t& idup,
const size_t& iddo);
/*! calculate the new determinant without updating
* the inverse matrices*/
BigComplex VirtColUpdate(const size_t& idup,
const size_t& fup,
const size_t& iddo,
const size_t& fdo) const;
//! update matrices after a hop in reciprocal space.
void RowUpdate(const size_t& idup,
const size_t& iddo);
/*! calculate the new determinant without updating
* the inverse matrices*/
BigComplex VirtRowUpdate(const size_t& idup,
const size_t& rup,
const size_t& iddo,
const size_t& rdo) const;
/*! gives the new determinants after the row update
* specified by r(...) for all subsequent column updates
* specified by k(...)*/
void VirtUpdate(const std::vector<hop_path_t> rhopup,
const std::vector<hop_path_t> rhopdo,
const std::vector<hop_path_t> khopup,
const std::vector<hop_path_t> khopdo,
BigComplex* qs) const;
void Update(const hop_path_t rhopup,
const hop_path_t rhopdo,
const hop_path_t khopup,
const hop_path_t khopdo);
//! returns \f$\langle \{R_i,\sigma\}|\Psi\rangle\f$.
BigComplex Amp() const;
const SpinState* GetSpinState() const {return m_sp;}
SpinState* GetSpinState() {return m_sp;}
const WaveFunction* GetWaveFunction() const {return m_wav;}
WaveFunction* GetWaveFunction() {return m_wav;}
private:
SpinState* m_sp;
WaveFunction* m_wav;
std::complex<double>* m_matup;
std::complex<double>* m_matiup;
std::complex<double>* m_matdo;
std::complex<double>* m_matido;
BigComplex m_amp;
bool m_amp_ok;
size_t m_Nup; //!< size of the up (square) matrices.
size_t m_Ndo; //!< size of the down (square) matrices.
};
#endif//_AMPLITUDE_H
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