58 lines
1.1 KiB
C++
58 lines
1.1 KiB
C++
#ifndef BESSEL_H
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#define BESSEL_H
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namespace Distribution {
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/** helper class */
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template <typename T> class Bessel {
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public:
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/**
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* calculation for I_v(z)
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* https://en.wikipedia.org/wiki/Bessel_function
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* http://www.boost.org/doc/libs/1_35_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html
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*/
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T getModified(const int v, const T z) const {
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// running factorials (updated within for-loops)
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uint64_t runFac1 = 1;
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uint64_t runFac2 = factorial(v); // Delta(k+v+1) = (k+v+1-1)! = (k+v)! [k starts at 0] -> (v)!
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// running potential
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T runPot = 1;
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const T pot = T(0.25) * z * z;
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// start for-loop at k=1 instead of k=0. allows for running factorial without using if (k==0)
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T sum = 0;
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for (int k = 0; k < 16; ) {
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sum += runPot / runFac1 / runFac2;
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++k;
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runFac1 *= k;
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runFac2 *= k;
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runPot *= pot;
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}
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// done
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return std::pow( (T(0.5) * z), v) * sum;
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}
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private:
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static uint64_t factorial(const int n) {
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uint64_t res = 1;
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for (int i = 2; i <= n; ++i) {res *= i;}
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return res;
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}
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};
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}
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#endif // BESSEL_H
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