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jiri
2006-09-10 20:06:44 +00:00
parent 04b4ef9f72
commit b0a83b6d6e
10 changed files with 130 additions and 74 deletions
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14
matexp.h
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@@ -109,7 +109,7 @@ return z;
//general BCH expansion (can be written more efficiently in a specialization for matrices)
template<class T>
const T BCHexpansion (const T &h, const T &t, const int n, const bool verbose=1)\
const T BCHexpansion (const T &h, const T &t, const int n, const bool verbose=0)\
{
T result=h;
double factor=1.;
@@ -118,7 +118,7 @@ for(int i=1; i<=n; ++i)
{
factor/=i;
z= z*t-t*z;
if(verbose) cerr << "BCH contribution at order "<<i<<" : "<<z.norm()<<endl;
if(verbose) cerr << "BCH contribution at order "<<i<<" : "<<z.norm()*factor<<endl;
result+= z*factor;
}
return result;
@@ -184,12 +184,12 @@ static double exptaylor[]={
4.1103176233121648441e-19,
0.};
double mnorm= LA_traits<T>::norm(x);
power=nextpow2(mnorm);
power=nextpow2(mnorm);
double scale=exp(-log(2.)*power);
//find how long taylor expansion will be necessary
const double precision=1e-16;
const double precision=1e-14; //decreasing brings nothing
double s,t;
s=mnorm*scale;
int n=0;
@@ -202,6 +202,7 @@ while(t*exptaylor[n]>precision);//taylor 0 will terminate in any case
int i; //adjust the coefficients in order to avoid scaling the argument
NRVec<typename LA_traits<T>::elementtype> taylor2(n+1);
for(i=0,t=1.;i<=n;i++)
@@ -214,8 +215,9 @@ return taylor2;
//it seems that we do not gain anything by polynom vs polynom0, check the m-optimization!
template<class T>
const T exp(const T &x, const bool simple=false)
const T exp(const T &x, const bool horner=true)
{
int power;
@@ -223,7 +225,7 @@ int power;
NRVec<typename LA_traits<T>::elementtype> taylor2=exp_aux(x,power);
T r= simple?polynom0(x,taylor2):polynom(x,taylor2);
T r= horner?polynom0(x,taylor2):polynom(x,taylor2);
//for accuracy summing from the smallest terms up would be better, but this is more efficient for matrices
//power the result back