.dot() product for VectorXcd in Eigen c++ - c++

Question

I'm trying to figure out if this is a bug in Eigen or something I'm doing wrong. I simply want the dot product of two complex vectors [ 1 , i] and [1 , -i]. The answer is 1*1 + i*(-i) = 2. But Eigen gives zero as answer. See code below:
#include <iostream>
#include <sstream>
#include <vector>
#include <fstream>
#include <stdlib.h>
#include <time.h>
#include <stdio.h>
#include <map>
#include <sys/sysinfo.h>
#include <algorithm>
#include <Eigen/Dense>
using namespace Eigen;
using namespace std;
int main( void ){
VectorXcd xd0(2);
complex<double> c_i( 0.0 , 1.0 );
xd0[0] = 1.0 ;
xd0[1] = c_i;
VectorXcd xd0conj = xd0.conjugate();
cout <<" vec is \n" << xd0 <<endl;
cout <<" conj vec is \n" << xd0conj <<endl;
cout << "eigen dot = " << (xd0conj).dot(xd0 ) <<endl;
complex<double> outVal = 0.0;
for( int a=0; a<xd0.size(); a++){
outVal += xd0[a]*xd0conj[a];
}
cout << "naive dot = " << outVal<<endl;
};

Answer 1

From the documentation:
"
If the scalar type is complex numbers, then this function returns the hermitian (sesquilinear) dot product, conjugate-linear in the first variable and linear in the second variable.
"
This product is often used, for example in quantum mechanics.
It computes conj(x)*y which is what you are seeing. I guess you want the simple / ordinary dot:
cout << "eigen dot = " << xd0conj.transpose()*xd0 <<endl;
This outputs
eigen dot = (2,0)