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jiri
2005-02-14 00:10:07 +00:00
parent ac8afe89ad
commit 6150e1b9c6
14 changed files with 513 additions and 62 deletions
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15
matexp.h
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@@ -6,7 +6,6 @@
// is defined containing definition of an element type, norm and axpy operation
#include "la_traits.h"
#include "sparsemat_traits.h"
template<class T,class R>
const T polynom2(const T &x, const NRVec<R> &c)
@@ -68,7 +67,7 @@ for(i=0; i<=n/m;i++)
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*/}
else
NRMat_traits<T>::axpy(s,xpows[j-1],c[k]); //general s+=xpows[j-1]*c[k]; but more efficient for matrices
LA_traits<T>::axpy(s,xpows[j-1],c[k]); //general s+=xpows[j-1]*c[k]; but more efficient for matrices
}
if(i==0) {r=s; f=xpows[m-1];}
@@ -125,7 +124,7 @@ template<class T>
const T ipow( const T &x, int i)
{
if(i<0) laerror("negative exponent in ipow");
if(i==0) {T r=x; r=(T)1; return r;}//trick for matrix dimension
if(i==0) {T r=x; r=(typename LA_traits<T>::elementtype)1; return r;}//trick for matrix dimension
if(i==1) return x;
T y,z;
z=x;
@@ -153,7 +152,7 @@ return int(ceil(log(n)/log2-log(.75)));
template<class T>
NRVec<typename NRMat_traits<T>::elementtype> exp_aux(const T &x, int &power)
NRVec<typename LA_traits<T>::elementtype> exp_aux(const T &x, int &power)
{
//should better be computed by mathematica to have accurate last digits, chebyshev instead, see exp in glibc
static double exptaylor[]={
@@ -179,7 +178,7 @@ static double exptaylor[]={
8.2206352466243294955e-18,
4.1103176233121648441e-19,
0.};
double mnorm= NRMat_traits<T>::norm(x);
double mnorm= LA_traits<T>::norm(x);
power=nextpow2(mnorm);
double scale=exp(-log(2.)*power);
@@ -198,7 +197,7 @@ 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 NRMat_traits<T>::elementtype> taylor2(n+1);
NRVec<typename LA_traits<T>::elementtype> taylor2(n+1);
for(i=0,t=1.;i<=n;i++)
{
taylor2[i]=exptaylor[i]*t;
@@ -215,7 +214,7 @@ const T exp(const T &x)
int power;
//prepare the polynom of and effectively scale T
NRVec<typename NRMat_traits<T>::elementtype> taylor2=exp_aux(x,power);
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
@@ -233,7 +232,7 @@ const V exptimes(const M &mat, V vec) //uses just matrix vector multiplication
if(mat.nrows()!=mat.ncols()||(unsigned int) mat.nrows() != (unsigned int)vec.size()) laerror("inappropriate sizes in exptimes");
int power;
//prepare the polynom of and effectively scale the matrix
NRVec<typename NRMat_traits<M>::elementtype> taylor2=exp_aux(mat,power);
NRVec<typename LA_traits<M>::elementtype> taylor2=exp_aux(mat,power);
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