=====inner_product=====
Syntax:

<code>
    #include <numeric>
    TYPE inner_product( input_iterator start1, input_iterator end1, input_iterator2 start2, TYPE val );
    TYPE inner_product( input_iterator start1, input_iterator end1, input_iterator2 start2, TYPE val, BinaryFunction f1, BinaryFunction2 f2 );
</code>

The inner_product function computes the inner product of ''[start1,end1)'' and a
range of the same size starting at ''start2''.

inner_product() runs in [[/complexity|linear time]].

For example, the following code shows how inner_product (or, alternatively, [[accumulate]]) can be used to compute the sums of squares of some data:

<code>
// Examples of std::accumulate and std::inner_product from wordaligned.org
#include <functional>
#include <iostream>
#include <numeric>
#include <string>
#include <valarray>
#include <vector>

typedef std::valarray<double> xyz;

// Xyz output operator
std::ostream & operator<<(std::ostream & os, xyz const & pt) {
    os << '(';
    char const * sep = "";
    for( size_t i = 0; i != pt.size(); sep = ", ", ++i ) {
        os << sep << pt[i];
    }
    os << ')';
    return os;
}

// Bitwise or function, for use in reductions
unsigned bit_or(unsigned u, unsigned v) {
    return u | v;
}

// Create and return a triangle
std::vector<xyz> create_triangle() {
    std::vector<xyz> pts;
    double const p[9] = {1.,1.,0.,1.,0.,1.,0.,1.,1.};
    pts.push_back(xyz(p + 0, 3));
    pts.push_back(xyz(p + 3, 3));
    pts.push_back(xyz(p + 6, 3));
    return pts;
}

// Set up some test arrays, accumulate them and print the results to stdout.
int main() {
    int const a[3] = { 1, 2, 3 };
    int const b[3] = { 3, 2, 1 };
    std::string const s[3] = { "http://", "wordaligned", ".org" };
    bool const t[3] = { false, true, false };
    std::vector<xyz> tri = create_triangle();
    unsigned m[3] = { 1<<1, 1<<3, 1<<5 };
    
    std::cout
        << "sum(a) "
        << std::accumulate(a, a + 3, 0)
        << "\nprod(a) "
        << std::accumulate(a, a + 3, 1, std::multiplies<int>())
        << "\nsum_sqs(a) "
        << std::inner_product(a, a + 3, a, 0)
        << "\ndot(a, b) "
        << std::inner_product(a, a + 3, b, 0)
        << "\nconcat(s) "
        << std::accumulate(s, s + 3, std::string(""))
        << "\nany(t) " << std::boolalpha
        << std::accumulate(t, t + 3, false, std::logical_or<bool>())
        << "\ncentroid(tri) "
        << std::accumulate(tri.begin(), tri.end(), xyz(0., 3)) / 3.
        << "\nbitor(m) " << std::hex << "0x"
        << std::accumulate(m, m + 3, 0, bit_or)
        << '\n';
    
    return 0;
}
</code>

When run, this code generates the following output:

<code terminal>
sum(a) 6
prod(a) 6
sum_sqs(a) 14
dot(a, b) 10
concat(s) http://wordaligned.org
any(t) true
centroid(tri) (0.666667, 0.666667, 0.666667)
bitor(m) 0x2a
</code>


Related Topics: [[accumulate]], [[adjacent_difference]], [[count]], [[partial_sum]]