Computing the Norm of a Vector

Problem

You want to find the norm (i.e., the length) of a numerical vector.

Solution

You can use the inner_product function from the <numeric> header to multiply a vector with itself as shown in Example 11-21.

Example 11-21. Computing the norm of a vector

#include <numeric>
#include <vector>
#include <cmath>
#include <iostream>

using namespace std;

template<typename Iter_T>
long double vectorNorm(Iter_T first, Iter_T last) {
  return sqrt(inner_product(first, last, first, 0.0L));
}

int main( ) {
  int v[] = { 3, 4 };
  cout << "The length of the vector (3,4) is ";
  cout << vectorNorm(v, v + 2) << endl;
}

The program in Example 11-21 produces the following output:

The length of the vector (3,4) is 5

Discussion

Example 11-21 uses the inner_product function from the <numeric> header to find the dot product of the numerical vector with itself. The square root of this is known as the vector norm or the length of a vector.

Rather than deduce the result type in the vectorNorm function, I chose to return a long double to lose as little data as possible. If a vector is a series of integers, it is unlikely that in a real example, that the distance can be meaningfully represented as an integer as well.