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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