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// Demonstrates usage of the Gauss-Hermite nodes and weights
// generated by our program GaussHermite_NodesWeights.cpp.
//
// Joachim Wuttke, 2023, public domain
#include "GaussHermiteConstants.cpp"
#include <cmath>
#include <iostream>
#include <iomanip>
// With f(x)=cos(x), analytical integration yields exp(-1/4).
// See https://www.chebfun.org/examples/quad/HermiteQuad.html, with different normalization.
double f(double x)
{
return cos(x);
}
int main(int argc, char* argv[])
{
std::cout << std::setprecision(15);
for (int n=0; n<12; ++n) {
double sum = 0;
for (int i = 0; i<n; ++i) {
int k = n * (n-1) + 2*i;
sum += GaussHermiteNodesWeights[k+1] * f(GaussHermiteNodesWeights[k]);
}
std::cout << sum << "\n";
}
}
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