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jiri
2006-09-04 20:12:34 +00:00
parent 50dcdd2c17
commit 74ac2998b0
3 changed files with 20 additions and 5 deletions
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18
matexp.h
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@@ -8,7 +8,7 @@
#include "la_traits.h"
template<class T,class R>
const T polynom2(const T &x, const NRVec<R> &c)
const T polynom0(const T &x, const NRVec<R> &c)
{
int order=c.size()-1;
T z,y;
@@ -30,13 +30,14 @@ return y;
}
//algorithm which minimazes number of multiplications, at the cost of storage
template<class T,class R>
const T polynom(const T &x, const NRVec<R> &c)
{
int n=c.size()-1;
int i,j,k,m=0,t;
if(n<=4) return polynom2(x,c); //here the horner scheme is optimal
if(n<=4) return polynom0(x,c); //here the horner scheme is optimal
//first find m which minimizes the number of multiplications
j=10*n;
@@ -50,6 +51,7 @@ for(i=2;i<=n+1;i++)
}
}
//allocate array for powers up to m
T *xpows = new T[m];
xpows[0]=x;
@@ -65,7 +67,10 @@ for(i=0; i<=n/m;i++)
{
k++;
if(k>n) break;
if(j==0) {if(i==0) s=x; /*just to get the dimensions of the matrix*/ s=c[k]; /*create diagonal matrix*/}
if(j==0) {
if(i==0) s=x; /*just to get the dimensions of the matrix*/
s=c[k]; /*create diagonal matrix*/
}
else
LA_traits<T>::axpy(s,xpows[j-1],c[k]); //general s+=xpows[j-1]*c[k]; but more efficient for matrices
}
@@ -196,6 +201,7 @@ do {
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++)
@@ -209,14 +215,16 @@ return taylor2;
template<class T>
const T exp(const T &x)
const T exp(const T &x, const bool simple=false)
{
int power;
//prepare the polynom of and effectively scale T
NRVec<typename LA_traits<T>::elementtype> taylor2=exp_aux(x,power);
T r=polynom(x,taylor2); //for accuracy summing from the smallest terms up would be better, but this is more efficient for matrices
T r= simple?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
for(int i=0; i<power; i++) r=r*r;