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jiri
2011-01-18 14:37:05 +00:00
parent 600b5b3abd
commit 4534c2e56a
21 changed files with 753 additions and 138 deletions
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125
nonclass.h
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@@ -88,8 +88,8 @@ extern const NRVec<T> diagofproduct(const NRMat<T> &a, const NRMat<T> &b,\
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 T trace2(const NRSMat<T> &a, const NRMat<T> &b, const bool diagscaled=0);\
extern void linear_solve(NRMat<T> &a, NRMat<T> *b, double *det=0,int n=0); /*solve Ax^T=b^T (b is nrhs x n) */ \
extern void linear_solve(NRSMat<T> &a, NRMat<T> *b, double *det=0, int n=0); /*solve Ax^T=b^T (b is nrhs x n) */\
extern void linear_solve(NRMat<T> &a, NRMat<T> *b, T *det=0,int n=0); /*solve Ax^T=b^T (b is nrhs x n) */ \
extern void linear_solve(NRSMat<T> &a, NRMat<T> *b, T *det=0, int n=0); /*solve Ax^T=b^T (b is nrhs x n) */\
extern void linear_solve(NRMat<T> &a, NRVec<T> &b, double *det=0, int n=0); \
extern void linear_solve(NRSMat<T> &a, NRVec<T> &b, double *det=0, int n=0); \
extern void diagonalize(NRMat<T> &a, NRVec<LA_traits<T>::normtype> &w, const bool eivec=1, const bool corder=1, int n=0, NRMat<T> *b=NULL, const int itype=1); \
@@ -104,36 +104,28 @@ declare_la(complex<double>)
// Separate declarations
//general nonsymmetric matrix and generalized diagonalization
//corder =0 ... C rows are eigenvectors, =1 ... C columns are eigenvectors
extern void gdiagonalize(NRMat<double> &a, NRVec<double> &wr, NRVec<double> &wi,
NRMat<double> *vl, NRMat<double> *vr, const bool corder=1, int n=0, const int sorttype=0, const int biorthonormalize=0,
NRMat<double> *b=NULL, NRVec<double> *beta=NULL);
extern void gdiagonalize(NRMat<double> &a, NRVec< complex<double> > &w,
NRMat<double> *b=NULL, NRVec<double> *beta=NULL); //this used real storage of eigenvectors like dgeev
template<typename T>
extern void gdiagonalize(NRMat<T> &a, NRVec< complex<double> > &w,
NRMat< complex<double> >*vl, NRMat< complex<double> > *vr,
const bool corder=1, int n=0, const int sorttype=0, const int biorthonormalize=0,
NRMat<double> *b=NULL, NRVec<double> *beta=NULL);
extern NRMat<double> matrixfunction(NRSMat<double> a, double (*f) (double));
extern NRMat<double> realmatrixfunction(NRMat<double> a, double (*f) (double)); //a has to by in fact symmetric
extern NRMat<complex<double> > complexmatrixfunction(NRMat<double> a, double (*fre) (double), double (*fim) (double)); //a has to by in fact symmetric
extern NRMat<double> matrixfunction(NRMat<double> a, complex<double> (*f)(const complex<double> &),const bool adjust=0);
NRMat<T> *b=NULL, NRVec<T> *beta=NULL); //eigenvectors are stored in complex matrices for T both double and complex
extern complex<double> sqrtinv(const complex<double> &);
extern double sqrtinv(const double);
//functions on matrices
inline NRMat<double> sqrt(const NRSMat<double> &a) { return matrixfunction(a,&std::sqrt); }
inline NRMat<double> sqrtinv(const NRSMat<double> &a) { return matrixfunction(a,&sqrtinv); }
inline NRMat<double> realsqrt(const NRMat<double> &a) { return realmatrixfunction(a,&std::sqrt); }
inline NRMat<double> realsqrtinv(const NRMat<double> &a) { return realmatrixfunction(a,&sqrtinv); }
inline NRMat<double> log(const NRSMat<double> &a) { return matrixfunction(a,&std::log); }
extern NRMat<double> log(const NRMat<double> &a);
extern NRMat<double> exp0(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>&);
extern const NRMat< complex<double> > complexmatrix (const NRMat<double>&, const NRMat<double>&);
//complex,real,imaginary parts of various entities
template<typename T>
extern const typename LA_traits<T>::realtype realpart(const T&);
template<typename T>
extern const typename LA_traits<T>::realtype imagpart(const T&);
template<typename T>
extern const typename LA_traits<T>::complextype realmatrix (const T&);
template<typename T>
extern const typename LA_traits<T>::complextype imagmatrix (const T&);
template<typename T>
extern const typename LA_traits<T>::complextype complexmatrix (const T&, const T&);
//Cholesky decomposition
extern void cholesky(NRMat<double> &a, bool upper=1);
@@ -315,5 +307,84 @@ return r;
}
//matrix functions via diagonalization
extern NRMat<double> realmatrixfunction(NRMat<double> a, double (*f) (double)); //a has to by in fact symmetric
extern NRMat<complex<double> > complexmatrixfunction(NRMat<double> a, double (*fre) (double), double (*fim) (double)); //a has to by in fact symmetric
template<typename T>
NRMat<T> matrixfunction(NRSMat<T> a, double (*f) (double)) //of symmetric/hermitian matrix
{
int n = a.nrows();
NRVec<double> w(n);
NRMat<T> v(n, n);
diagonalize(a, w, &v, 0);
for (int i=0; i<a.nrows(); i++) w[i] = (*f)(w[i]);
NRMat<T> u = v;
NRVec<T> ww=w; //diagmultl needs same type
v.diagmultl(ww);
NRMat<T> r(n, n);
r.gemm(0.0, u, 't', v, 'n', 1.0); //gemm will use 'c' for complex ones
return r;
}
template<typename T>
extern NRMat<T> matrixfunction(NRMat<T> a, complex<double> (*f)(const complex<double> &)) //of a general real/complex matrix
{
int n = a.nrows();
NRVec<complex<double> > w(n);
NRMat<complex<double> > u(n,n),v(n,n);
#ifdef debugmf
NRMat<complex<double> > a0=a;
#endif
gdiagonalize<T>(a, w, &u, &v, false,n,0,false,NULL,NULL);//a gets destroyed, eigenvectors are rows
NRVec< complex<double> > z = diagofproduct(u, v, 1, 1);
#ifdef debugmf
std::cout <<"TEST matrixfunction\n"<<w<<u<<v<<z;
std::cout <<"TEST matrixfunction1 "<< u*a0 - diagonalmatrix(w)*u<<std::endl;
std::cout <<"TEST matrixfunction2 "<< a0*v.transpose(1) - v.transpose(1)*diagonalmatrix(w)<<std::endl;
std::cout <<"TEST matrixfunction3 "<< u*v.transpose(1)<<diagonalmatrix(z)<<std::endl;
#endif
NRVec< complex<double> > wz(n);
for (int i=0; i<a.nrows(); i++) wz[i] = w[i]/z[i];
#ifdef debugmf
std::cout <<"TEST matrixfunction4 "<< a0<< v.transpose(true)*diagonalmatrix(wz)*u<<std::endl;
#endif
for (int i=0; i<a.nrows(); i++) w[i] = (*f)(w[i])/z[i];
u.diagmultl(w);
NRMat< complex<double> > r(n, n);
r.gemm(0.0, v, 'c', u, 'n', 1.0);
return (NRMat<T>) r; //convert back to real if applicable by the explicit decomplexifying constructor; it is NOT checked to which accuracy the imaginary part is actually zero
}
extern complex<double> sqrtinv(const complex<double> &);
extern double sqrtinv(const double);
//functions on matrices
inline NRMat<double> sqrt(const NRSMat<double> &a) { return matrixfunction(a,&std::sqrt); }
inline NRMat<double> sqrtinv(const NRSMat<double> &a) { return matrixfunction(a,&sqrtinv); }
inline NRMat<double> realsqrt(const NRMat<double> &a) { return realmatrixfunction(a,&std::sqrt); }
inline NRMat<double> realsqrtinv(const NRMat<double> &a) { return realmatrixfunction(a,&sqrtinv); }
inline NRMat<double> log(const NRSMat<double> &a) { return matrixfunction(a,&std::log); }
extern NRMat<double> log(const NRMat<double> &a);
extern NRMat<complex<double> > log(const NRMat<complex<double> > &a);
extern NRMat<complex<double> > exp0(const NRMat<complex<double> > &a);
extern NRMat<complex<double> > copytest(const NRMat<complex<double> > &a);
extern NRMat<double> copytest(const NRMat<double> &a);
extern NRMat<double> exp0(const NRMat<double> &a);
}//namespace
#endif