149 lines
5.0 KiB
C++
149 lines
5.0 KiB
C++
#ifndef _LA_NONCLASS_H_
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#define _LA_NONCLASS_H_
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#include "vec.h"
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#include "smat.h"
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#include "mat.h"
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#include "la_traits.h"
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//MISC
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export template <class T>
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const NRMat<T> diagonalmatrix(const NRVec<T> &x)
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{
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int n=x.size();
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NRMat<T> result((T)0,n,n);
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T *p = result[0];
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for(int j=0; j<n; j++) {*p = x[j]; p+=(n+1);}
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return result;
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}
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//more efficient commutator for a special case of full matrices
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template<class T>
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inline const NRMat<T> commutator ( const NRMat<T> &x, const NRMat<T> &y, const bool trx=0, const bool tryy=0)
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{
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NRMat<T> r(trx?x.ncols():x.nrows(), tryy?y.nrows():y.ncols());
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r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
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r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)-1);
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return r;
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}
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//more efficient commutator for a special case of full matrices
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template<class T>
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inline const NRMat<T> anticommutator ( const NRMat<T> &x, const NRMat<T> &y, const bool trx=0, const bool tryy=0)
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{
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NRMat<T> r(trx?x.ncols():x.nrows(), tryy?y.nrows():y.ncols());
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r.gemm((T)0,x,trx?'t':'n',y,tryy?'t':'n',(T)1);
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r.gemm((T)1,y,tryy?'t':'n',x,trx?'t':'n',(T)1);
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return r;
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}
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//////////////////////
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// LAPACK interface //
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//////////////////////
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#define declare_la(T) \
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extern const NRVec<T> diagofproduct(const NRMat<T> &a, const NRMat<T> &b,\
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bool trb=0, bool conjb=0); \
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extern T trace2(const NRMat<T> &a, const NRMat<T> &b, bool trb=0); \
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extern T trace2(const NRSMat<T> &a, const NRSMat<T> &b, const bool diagscaled=0);\
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extern void linear_solve(NRMat<T> &a, NRMat<T> *b, double *det=0,int n=0); \
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extern void linear_solve(NRSMat<T> &a, NRMat<T> *b, double *det=0, int n=0); \
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extern void linear_solve(NRMat<T> &a, NRVec<T> &b, double *det=0, int n=0); \
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extern void linear_solve(NRSMat<T> &a, NRVec<T> &b, double *det=0, int n=0); \
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extern void diagonalize(NRMat<T> &a, NRVec<T> &w, const bool eivec=1, const bool corder=1, int n=0, NRMat<T> *b=NULL, const int itype=1); \
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extern void diagonalize(NRSMat<T> &a, NRVec<T> &w, NRMat<T> *v, const bool corder=1, int n=0, NRSMat<T> *b=NULL, const int itype=1);\
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extern void singular_decomposition(NRMat<T> &a, NRMat<T> *u, NRVec<T> &s,\
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NRMat<T> *v, const bool corder=1, int m=0, int n=0);
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declare_la(double)
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declare_la(complex<double>)
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// Separate declarations
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//general nonsymmetric matrix and generalized diagonalization
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extern void gdiagonalize(NRMat<double> &a, NRVec<double> &wr, NRVec<double> &wi,
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NRMat<double> *vl, NRMat<double> *vr, const bool corder=1, int n=0, const int sorttype=0, const bool biorthonormalize=0,
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NRMat<double> *b=NULL, NRVec<double> *beta=NULL);
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extern void gdiagonalize(NRMat<double> &a, NRVec< complex<double> > &w,
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NRMat< complex<double> >*vl, NRMat< complex<double> > *vr,
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const bool corder=1, int n=0, const int sorttype=0, const bool biorthonormalize=0,
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NRMat<double> *b=NULL, NRVec<double> *beta=NULL);
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extern NRMat<double> matrixfunction(NRSMat<double> a, double (*f) (double));
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extern NRMat<double> matrixfunction(NRMat<double> a, complex<double> (*f)(const complex<double> &),const bool adjust=0);
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//functions on matrices
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inline NRMat<double> sqrt(const NRSMat<double> &a) { return matrixfunction(a,&sqrt); }
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inline NRMat<double> log(const NRSMat<double> &a) { return matrixfunction(a,&log); }
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extern NRMat<double> log(const NRMat<double> &a);
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extern const NRMat<double> realpart(const NRMat< complex<double> >&);
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extern const NRMat<double> imagpart(const NRMat< complex<double> >&);
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extern const NRMat< complex<double> > realmatrix (const NRMat<double>&);
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extern const NRMat< complex<double> > imagmatrix (const NRMat<double>&);
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//inverse by means of linear solve, preserving rhs intact
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template<typename T>
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const NRMat<T> inverse(NRMat<T> a, T *det=0)
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{
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#ifdef DEBUG
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if(a.nrows()!=a.ncols()) laerror("inverse() for non-square matrix");
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#endif
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NRMat<T> result(a.nrows(),a.nrows());
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result = (T)1.;
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linear_solve(a, &result, det);
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return result;
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}
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//general determinant
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template<class MAT>
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const typename LA_traits<MAT>::elementtype determinant(MAT a)//passed by value
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{
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typename LA_traits<MAT>::elementtype det;
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if(a.nrows()!=a.ncols()) laerror("determinant of non-square matrix");
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linear_solve(a,NULL,&det);
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return det;
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}
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//general determinant destructive on input
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template<class MAT>
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const typename LA_traits<MAT>::elementtype determinant_destroy(MAT &a) //passed by reference
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{
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typename LA_traits<MAT>::elementtype det;
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if(a.nrows()!=a.ncols()) laerror("determinant of non-square matrix");
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linear_solve(a,NULL,&det);
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return det;
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}
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//general submatrix
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template<class MAT, class INDEX>
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const NRMat<typename LA_traits<MAT>::elementtype> submatrix(const MAT a, const INDEX rows, const INDEX cols, int indexshift=0, bool ignoresign=false)
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{
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NRMat<typename LA_traits<MAT>::elementtype> r(rows.size(),cols.size());
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if(ignoresign)
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{
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for(int i=0; i<rows.size(); ++i)
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for(j=0; j<cols.size(); ++j)
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r(i,j) = a(abs(rows[i])+indexshift,abs(cols[j])+indexshift);
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}
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else
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{
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for(int i=0; i<rows.size(); ++i)
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for(j=0; j<cols.size(); ++j)
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r(i,j) = a(rows[i]+indexshift,cols[j]+indexshift);
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}
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return r;
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}
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//auxiliary routine to adjust eigenvectors to guarantee real logarithm
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extern void adjustphases(NRMat<double> &v);
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#endif
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