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jiri
2006-09-11 23:07:22 +00:00
parent e49b73e9e9
commit d55727cb83
5 changed files with 71 additions and 24 deletions
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45
matexp.h
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@@ -248,28 +248,43 @@ return r;
//this simple implementation seems not to be numerically stable enough
//and probably not efficient either
//@@@ make more efficient - for nilpotent mat at known power and
template<class M, class V>
const V exptimesnaive(const M &mat, V vec) //uses just matrix vector multiplication
void exptimesdestructive(const M &mat, V &result, V &rhs, bool transpose=false, const double scale=1. ) //uses just matrix vector multiplication
{
if(mat.nrows()!=mat.ncols()||(unsigned int) mat.nrows() != (unsigned int)vec.size()) laerror("inappropriate sizes in exptimes");
if(mat.nrows()!=mat.ncols()||(unsigned int) mat.nrows() != (unsigned int)rhs.size()) laerror("inappropriate sizes in exptimes");
int power;
//prepare the polynom of and effectively scale the matrix
NRVec<typename LA_traits<V>::elementtype> taylor2=exp_aux<M,typename LA_traits<V>::elementtype>(mat,power);
cerr <<"test power "<<power<<endl;
V tmp;
V result(mat.nrows());
for(int i=1; i<=(1<<power); ++i) //unfortunatelly, here we have to repeat it many times, unlike if the matrix is stored explicitly
{
if(i>1) vec=result; //apply again to the result of previous application
//apply polynom of the matrix to the vector iteratively
V y=vec;
result=y*taylor2[0];
if(i>1) rhs=result; //apply again to the result of previous application
else result=rhs;
tmp=rhs; //now rhs can be used as scratch
result*=taylor2[0];
for(int j=1; j<taylor2.size(); ++j)
{
y=mat*y;
result.axpy(taylor2[j],y);
mat.gemv(0.,rhs,transpose?'t':'n',scale,tmp);
tmp=rhs;
result.axpy(taylor2[j],tmp);
}
}
return;
}
template<class M, class V>
const V exptimes(const M &mat, V rhs, bool transpose=false, const double scale=1.)
{
V result;
exptimesdestructive(mat,result,rhs,transpose,scale);
return result;
}
@@ -279,8 +294,7 @@ return result;
#ifdef EXPOKIT
//this comes from dgexpv from expokit, it had to be translated to C to make a template
// dgexpv.f -- translated by f2c (version 20030320).
@@ -323,13 +337,13 @@ extern "C" void FORNAME(dnchbv)(int *, double *, double *, int *, double *, doub
//partial template specialization leaving still free room for generic matrix type
template<class M>
extern void exptimes(const M &mat, NRVec<double> &result, const NRVec<double> &rhs, bool transpose=false, const double t=1., int mxkrylov=0, double tol=1e-14, int mxstep=1000, int mxreject=0, int ideg=6)
extern void dgexpv(const M &mat, NRVec<double> &result, const NRVec<double> &rhs, bool transpose=false, const double t=1., int mxkrylov=0, double tol=1e-14, int mxstep=1000, int mxreject=0, int ideg=6)
{
if(mat.nrows()!= mat.ncols()) laerror("non-square matrix in exptimes");
int n=mat.nrows();
int m;
if(mxkrylov) m=mxkrylov; else m= n>100? 100: n-1;
if (m >= n || m <= 0) laerror("illegal mxkrylov");
if(mxkrylov) m=mxkrylov; else m= n>100? 100: (n>1?n-1:1);
if (m > n || m <= 0) laerror("illegal mxkrylov");
if(result.size()!=n || rhs.size()!=n) laerror("inconsistent vector and matrix size in exptimes");
const double *v=rhs;
@@ -766,6 +780,9 @@ return;
#undef FORNAME
#undef pow_dd
#endif
//EXPOKIT
//@@@ power series matrix logarithm?