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                       Standard C++ Library
             Copyright 1998, Rogue Wave Software, Inc.


NAME
     inner_product

      - Computes the inner product A X B of two ranges A and B.



SYNOPSIS
     #include <numeric>
     template <class InputIterator1, class InputIterator2,
              class T>
     T inner_product (InputIterator1 first1,
                     InputIterator1 last1,
                     InputIterator2 first2, T init);
     template <class InputIterator1, class InputIterator2,
              class T,
              class BinaryOperation1,
              class BinaryOperation2>
     T inner_product (InputIterator1 first1,
                     InputIterator1 last1,
                     InputIterator2 first2, T init,
                     BinaryOperation1 binary_op1,
                     BinaryOperation2 binary_op2);



DESCRIPTION
     There are two versions of inner_product. The first  computes
     an  inner product using the default multiplication and addi-
     tion operators, while  the  second  allows  you  to  specify
     binary operations to use in place of the default operations.

     The first version of the function  computes  its  result  by
     initializing the accumulator acc with the initial value init
     and then modifying it with:

     acc = acc + ((*i1) * (*i2))

     for every iterator i1  in  the  range  [first1,  last1)  and
     iterator  i2  in  the  range  [first2,  first2  +  (last1  -
     first1)). The algorithm returns acc.

     The second version of  the  function  initializes  acc  with
     init, then computes:

     acc  =  binary_op1(acc, binary_op2(*i1,  *i2))
     for every iterator i1  in  the  range  [first1,  last1)  and
     iterator  i2  in  the  range  [first2,  first2  +  (last1  -
     first1)).



COMPLEXITY
     The  inner_product  algorithm  computes  exactly  (last1   -
     first1) applications of either:

     acc + (*i1) * (*i2)

      or

     binary_op1(acc, binary_op2(*i1, *i2)).



EXAMPLE
     //
     // inr_prod.cpp
     //
      #include <numeric>       //For inner_product
      #include <list>          //For list
      #include <vector>        //For vectors
      #include <functional>    //For plus and minus
      #include <iostream>
     using namespace std;
     int main()
      {
        //Initialize a list and an int using arrays of ints
       int a1[3] = {6, -3, -2};
       int a2[3] = {-2, -3, -2};
       list<int>   l(a1, a1+3);
       vector<int> v(a2, a2+3);
        //Calculate the inner product of the two sets of values
       int inner_prod =
             inner_product(l.begin(), l.end(), v.begin(), 0);
        //Calculate a wacky inner product using the same values
       int wacky =
              inner_product(l.begin(), l.end(), v.begin(), 0,
                           plus<int>(), minus<int>());
        //Print the output
       cout << "For the two sets of numbers: " << endl
             << "     ";
       copy(v.begin(),v.end(),
            ostream_iterator<int,char>(cout," "));
       cout << endl << " and  ";
       copy(l.begin(),l.end(),
            ostream_iterator<int,char>(cout," "));

       cout << "," << endl << endl;
       cout << "The inner product is: " << inner_prod << endl;
       cout << "The wacky result is: " << wacky << endl;
       return 0;
      }

     Program Output



     For the two sets of numbers:
          -2 -3 -2
     and  6 -3 -2 ,
     The inner product is: 1
     The wacky result is: 8



WARNINGS
     If your compiler does not support default  template  parame-
     ters,  then you always need to supply the Allocator template
     argument. For instance, you have to write:

     list<int, allocator<int> > and vector<int, allocator<int> >

     instead of

     list<int> and vector<int>

     If your compiler does not support namespaces,  then  you  do
     not need the using declaration for std.

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