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tim | 
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#include "Utility.hpp"
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#include <vector>
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#include <iostream>
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#include <math.h>
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using namespace std;
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double dotProduct(vector<double>& v1, vector<double>& v2){
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  double sum;
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  sum = 0;
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  if(v1.size() != v2.size()){
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    cerr << "Utility Error: dimension of two vectors are not matched" << endl;
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    exit(-1);
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  }
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   for(int  i = 0; i < v1.size(); i++)
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     sum += v1[i]*v2[i];
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   return sum;
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}
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double copysign(double sign, double value){
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  double result = fabs(value);
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  return sign >= 0 ? result : -result;
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}
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tim | 
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double norm2(vector<double>& x){
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  return sqrt(dotProduct(x, x));
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}       
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