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Jackson smoothed chebyshev and (untested) completion of force terms

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for Cayley, Partial and Cont fraction dwf and overlap.
have even odd and unprec forces.
This commit is contained in:
Peter Boyle
2015-08-01 05:58:35 +09:00
parent 9ff0b2987c
commit 1d67d29183
13 changed files with 292 additions and 18 deletions
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31
lib/algorithms/approx/Chebyshev.h
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@ -58,7 +58,9 @@ namespace Grid {
}
};
// c.f. numerical recipes "chebft"/"chebev". This is sec 5.8 "Chebyshev approximation".
//
Chebyshev(double _lo,double _hi,int _order, double (* func)(double) ){
lo=_lo;
hi=_hi;
@ -77,7 +79,34 @@ namespace Grid {
Coeffs[j] = s * 2.0/order;
}
};
void JacksonSmooth(void){
double M=order;
double alpha = M_PI/(M+2);
double lmax = std::cos(alpha);
double sumUsq =0;
std::vector<double> U(M);
std::vector<double> a(M);
std::vector<double> g(M);
for(int n=0;n<=M;n++){
U[n] = std::sin((n+1)*std::acos(lmax))/std::sin(std::acos(lmax));
sumUsq += U[n]*U[n];
}
sumUsq = std::sqrt(sumUsq);
for(int i=1;i<=M;i++){
a[i] = U[i]/sumUsq;
}
g[0] = 1.0;
for(int m=1;m<=M;m++){
g[m] = 0;
for(int i=0;i<=M-m;i++){
g[m]+= a[i]*a[m+i];
}
}
for(int m=1;m<=M;m++){
Coeffs[m]*=g[m];
}
}
double approx(double x) // Convenience for plotting the approximation
{
double Tn;