Hi Damir,
You are unfortunately right.
We had to clean recently the ROOT source from code imported from
Numerical Recipees (3.05/02 only)
Rene Brun
On Thu, 20
Feb 2003, Damir Buskulic wrote:
> Since Numerical Recipes is not free software, in the sense that you have
> to pay a minimal fee, I don't think that it is possible to include this
> code in ROOT. Am I wrong ?
>
> Cheers
>
> Damir
>
> =====================================================================
> | Damir Buskulic | Universite de Savoie/LAPP |
> | | Chemin de Bellevue, B.P. 110 |
> | Tel : +33 (0)450091600 | F-74941 Annecy-le-Vieux Cedex |
> | e-mail: buskulic@lapp.in2p3.fr | FRANCE |
> =====================================================================
> mailto:buskulic@lapp.in2p3.fr
>
> On Fri, 21 Feb 2003, Allister Levi Sanchez wrote:
>
> > Hi Rooters,
> >
> > I was working on some integrals lately and I stumbled on "exponential
> > integrals". I was surprised that they were not implemented in TMath.
> > Anyway, I decided to look them up from the online Numerical Recipes in
> > C. I simply copied the codes for E_{n}(x) and Ei(x), where x>0. By the
> > way,
> >
> > E_{n}(x) = \int_{1}^{infty} { exp(-xt)/t^{n} } dt and
> > Ei(x) = -\int_{-x}^{infty} { exp(-t)/t } dt
> >
> > However, since I needed to input negative values for Ei(x), I used the
> > fact that
> > E_{1}(x) = -Ei(-x)
> > and placed it into the code.
> >
> > Anyway, here's the code, just in case someone else will need them like I
> > did.
> >
> > //************** EXPONENTIAL INTEGRAL Ei ******
> > // define: ei(x) = -\int_{-x}^{\infty}{exp(-t)/t}dt, for x>0
> > // power series: ei(x) = eulerconst + ln(x) + x/(1*1!) + x^2/(2*2!) + ...
> > double ei(double x)
> > { // taken from Numerical Recipes in C
> > const double euler = 0.57721566; // Euler's constant, gamma
> > const int maxit = 100; // max. no. of iterations allowed
> > const double fpmin = 1.0e-40; // close to smallest floating-point
> > number
> > const double eps = 1.0e-30; // relative error, or absolute error
> > near
> > // the zero of Ei at x=0.3725
> > // I actually changed fpmin and eps into smaller values than in NR
> >
> > int k;
> > double fact, prev, sum, term;
> >
> > // special case
> > if(x < 0) return -expint(1,-x);
> >
> > if(x == 0.0) { cout << "Bad argument for ei(x)" << endl; return -1; }
> > if(x < fpmin) return log(x)+euler;
> > if(x <= -log(eps)) {
> > sum = 0;
> > fact = 1;
> > for(k=1; k<=maxit; k++) {
> > fact *= x/k;
> > term = fact/k;
> > sum += term;
> > if(term < eps*sum) break;
> > }
> > if(k>maxit) { cout << "Series failed in ei(x)" << endl; return -1; }
> > return sum+log(x)+euler;
> > } else {
> > sum = 0;
> > term = 1;
> > for(k=1; k<=maxit; k++) {
> > prev = term;
> > term *= k/x;
> > if(term<eps) break;
> > if(term<prev) sum+=term;
> > else {
> > sum -= prev;
> > break;
> > }
> > }
> > return exp(x)*(1.0+sum)/x;
> > }
> > }
> > //*********************************************
> >
> > //************** EXPONENTIAL INTEGRALS En *****
> > // define: E_n(x) = \int_1^infty{exp(-xt)/t^n}dt, x>0, n=0,1,...
> > double expint(int n, double x) {
> > // based on Numerical Recipes in C
> > const double euler = 0.57721566; // Euler's constant, gamma
> > const int maxit = 100; // max. no. of iterations allowed
> > const double fpmin = 1.0e-30; // close to smallest floating-point
> > number
> > const double eps = 6.0e-8; // relative error, or absolute error near
> > // the zero of Ei at x=0.3725
> >
> > int i, ii, nm1;
> > double a,b,c,d,del,fact,h,psi,ans;
> >
> > nm1=n-1;
> > if(n<0 || x<0 || (x==0 && (n==0 || n==1))) {
> > cout << "Bad argument for expint(n,x)" << endl; return -1;
> > }
> > else {
> > if(n==0) ans=exp(-x)/x;
> > else {
> > if(x==0) ans=1.0/nm1;
> > else {
> > if(x>1) {
> > b=x+n;
> > c=1.0/fpmin;
> > d=1.0/b;
> > h=d;
> > for(i=1; i<maxit; i++) {
> > a = -i*(nm1+i);
> > b += 2.0;
> > d=1.0/(a*d+b);
> > c=b+a/c;
> > del=c*d;
> > h *= del;
> > if(fabs(del-1.0)<eps) {
> > ans=h*exp(-x);
> > return ans;
> > }
> > }
> > cout << "***continued fraction failed in expint(n,x)!!!" << endl;
> > return -1;
> > } else {
> > ans = (nm1!=0 ? 1.0/nm1 : -log(x)-euler);
> > fact=1;
> > for(i=1; i<=maxit; i++) {
> > fact *= -x/i;
> > if(i!=nm1) del = -fact/(i-nm1);
> > else {
> > psi = -euler;
> > for(ii=1; ii<=nm1; ii++) psi += 1.0/ii;
> > del = fact*(-log(x)+psi);
> > }
> > ans += del;
> > if(fabs(del)<fabs(ans)*eps) return ans;
> > }
> > cout << "***series failed in expint!!!" << endl;
> > return -1;
> > }
> > }
> > }
> > }
> >
> > return ans;
> > }
> > //*********************************************
> >
> >
> >
> >
>
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