46 lines
879 B
C++
46 lines
879 B
C++
#include <cmath>
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#include "nr.h"
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using namespace std;
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void NR::gauher(Vec_O_DP &x, Vec_O_DP &w)
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{
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const DP EPS=1.0e-14,PIM4=0.7511255444649425;
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const int MAXIT=10;
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int i,its,j,m;
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DP p1,p2,p3,pp,z,z1;
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int n=x.size();
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m=(n+1)/2;
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for (i=0;i<m;i++) {
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if (i == 0) {
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z=sqrt(DP(2*n+1))-1.85575*pow(DP(2*n+1),-0.16667);
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} else if (i == 1) {
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z -= 1.14*pow(DP(n),0.426)/z;
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} else if (i == 2) {
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z=1.86*z-0.86*x[0];
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} else if (i == 3) {
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z=1.91*z-0.91*x[1];
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} else {
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z=2.0*z-x[i-2];
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}
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for (its=0;its<MAXIT;its++) {
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p1=PIM4;
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p2=0.0;
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for (j=0;j<n;j++) {
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p3=p2;
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p2=p1;
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p1=z*sqrt(2.0/(j+1))*p2-sqrt(DP(j)/(j+1))*p3;
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}
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pp=sqrt(DP(2*n))*p2;
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z1=z;
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z=z1-p1/pp;
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if (fabs(z-z1) <= EPS) break;
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}
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if (its >= MAXIT) nrerror("too many iterations in gauher");
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x[i]=z;
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x[n-1-i] = -z;
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w[i]=2.0/(pp*pp);
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w[n-1-i]=w[i];
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}
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}
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