86 lines
3.2 KiB
C
86 lines
3.2 KiB
C
|
#include "vec.h"
|
||
|
|
#include "smat.h"
|
||
|
|
#include "mat.h"
|
||
|
|
|
||
|
|
//MISC
|
||
|
|
template <class T> extern const NRMat<T> diagonalmatrix(const NRVec<T> &x);
|
||
|
|
template <class T> extern const NRVec<T> lineof(const NRMat<T> &x, const int i);
|
||
|
|
template <class T> extern const NRVec<T> columnof(const NRMat<T> &x, const int i);
|
||
|
|
template <class T> extern const NRVec<T> diagonalof(const NRMat<T> &x);
|
||
|
|
|
||
|
|
//more efficient commutator for a special case of full matrices
|
||
|
|
template<class T>
|
||
|
|
inline const NRMat<T> commutator ( const NRMat<T> &x, const NRMat<T> &y, const bool trx=0, const bool tryy=0)
|
||
|
|
{
|
||
|
|
NRMat<T> r(trx?x.ncols():x.nrows(), tryy?y.nrows():y.ncols());
|
||
|
|
r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
|
||
|
|
r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)-1);
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
//more efficient commutator for a special case of full matrices
|
||
|
|
template<class T>
|
||
|
|
inline const NRMat<T> anticommutator ( const NRMat<T> &x, const NRMat<T> &y, const bool trx=0, const bool tryy=0)
|
||
|
|
{
|
||
|
|
NRMat<T> r(trx?x.ncols():x.nrows(), tryy?y.nrows():y.ncols());
|
||
|
|
r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
|
||
|
|
r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)1);
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
//////////////////////
|
||
|
|
// LAPACK interface //
|
||
|
|
//////////////////////
|
||
|
|
|
||
|
|
#define declare_la(T) \
|
||
|
|
extern const NRVec<T> diagofproduct(const NRMat<T> &a, const NRMat<T> &b,\
|
||
|
|
bool trb=0, bool conjb=0); \
|
||
|
|
extern T trace2(const NRMat<T> &a, const NRMat<T> &b, bool trb=0); \
|
||
|
|
extern T trace2(const NRSMat<T> &a, const NRSMat<T> &b, const bool diagscaled=0);\
|
||
|
|
extern void linear_solve(NRMat<T> &a, NRMat<T> *b, double *det=0); \
|
||
|
|
extern void linear_solve(NRSMat<T> &a, NRMat<T> *b, double *det=0); \
|
||
|
|
extern void diagonalize(NRMat<T> &a, NRVec<T> &w, const bool eivec=1,\
|
||
|
|
const bool corder=1); \
|
||
|
|
extern void diagonalize(NRSMat<T> &a, NRVec<T> &w, NRMat<T> *v, const bool corder=1);\
|
||
|
|
extern void singular_decomposition(NRMat<T> &a, NRMat<T> *u, NRVec<T> &s,\
|
||
|
|
NRMat<T> *v, const bool corder=1);
|
||
|
|
|
||
|
|
declare_la(double)
|
||
|
|
declare_la(complex<double>)
|
||
|
|
|
||
|
|
// Separate declarations
|
||
|
|
extern void gdiagonalize(NRMat<double> &a, NRVec<double> &wr, NRVec<double> &wi,
|
||
|
|
NRMat<double> *vl, NRMat<double> *vr, const bool corder=1);
|
||
|
|
extern void gdiagonalize(NRMat<double> &a, NRVec< complex<double> > &w,
|
||
|
|
NRMat< complex<double> >*vl, NRMat< complex<double> > *vr);
|
||
|
|
extern NRMat<double> matrixfunction(NRSMat<double> a, double (*f) (double));
|
||
|
|
extern NRMat<double> matrixfunction(NRMat<double> a, complex<double> (*f)(const complex<double> &),const bool adjust=0);
|
||
|
|
|
||
|
|
//functions on matrices
|
||
|
|
inline NRMat<double> sqrt(const NRSMat<double> &a) { return matrixfunction(a,&sqrt); }
|
||
|
|
inline NRMat<double> log(const NRSMat<double> &a) { return matrixfunction(a,&log); }
|
||
|
|
extern NRMat<double> log(const NRMat<double> &a);
|
||
|
|
|
||
|
|
|
||
|
|
extern const NRMat<double> realpart(const NRMat< complex<double> >&);
|
||
|
|
extern const NRMat<double> imagpart(const NRMat< complex<double> >&);
|
||
|
|
extern const NRMat< complex<double> > realmatrix (const NRMat<double>&);
|
||
|
|
extern const NRMat< complex<double> > imagmatrix (const NRMat<double>&);
|
||
|
|
|
||
|
|
//inverse by means of linear solve, preserving rhs intact
|
||
|
|
template<typename T>
|
||
|
|
const NRMat<T> inverse(NRMat<T> a, T *det=0)
|
||
|
|
{
|
||
|
|
#ifdef DEBUG
|
||
|
|
if(a.nrows()!=a.ncols()) laerror("inverse() for non-square matrix");
|
||
|
|
#endif
|
||
|
|
NRMat<T> result(a.nrows(),a.nrows());
|
||
|
|
result = (T)1.;
|
||
|
|
linear_solve(a, &result, det);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|