inner_product

Article
07/11/2012

Computes the sum of the element-wise product of two ranges and adds it to a specified initial value or computes the result of a generalized procedure where the sum and product binary operations are replaced by other specified binary operations.

template<class InputIterator1, class InputIterator2, class Type> 
   Type inner_product( 
      InputIterator1 _First1,  
      InputIterator1 _Last1, 
      InputIterator2 _First2,  
      Type _Val 
   ); 

template<class InputIterator1, class InputIterator2, class Type, 
   class BinaryOperation1, class BinaryOperation2> 
   Type inner_product( 
      InputIterator1 _First1,  
      InputIterator1 _Last1, 
      InputIterator2 _First2,  
      Type _Val,  
      BinaryOperation1 _Binary_op1,  
      BinaryOperation2 _Binary_op2 
   );

Parameters

_First1
An input iterator addressing the first element in the first range whose inner product or generalized inner product with the second range is to be computed.
_Last1
An input iterator addressing the last element in the first range whose inner product or generalized inner product with the second range is to be computed.
_First2
An input iterator addressing the first element in the second range whose inner product or generalized inner product with the first range is to be computed.
_Val
An initial value to which the inner product or generalized inner product between the ranges is to be added.
_Binary_op1
The binary operation that replaces the inner product operation of sum applied to the element-wise products in the generalization of the inner product.
_Binary_op2
The binary operation that replaces the inner product element-wise operation of multiply in the generalization of the inner product.

Return Value

The first member function returns the sum of the element-wise products and adds to it the specified initial value. So for ranges of values ai and bi, it returns:

_Val + ( a1 * b1 ) + ( a2 * b2 ) +

by iteratively replacing _Val with _Val + (*ai * *bi ).

The second member function returns:

_Val _Binary_op1 ( a1 _Binary_op2 b1 ) _Binary_op1 ( a2 _Binary_op2 b2 ) _Binary_op1

by iteratively replacing _Val with _Val _Binary_op1 (*ai _Binary_op2 *bi ).

Remarks

The initial value ensures that there will be a well-defined result when the range is empty, in which case _Val is returned. The binary operations do not need to be associative or commutative. The range must be valid and the complexity is linear with the size of the range. The return type of the binary operator must be convertible to Type to ensure closure during the iteration.

Example

// numeric_inner_prod.cpp
// compile with: /EHsc
#include <vector>
#include <list>
#include <numeric>
#include <functional>
#include <iostream>

int main()
{
   using namespace std;

   vector <int> v1, v2(7), v3(7);
   vector <int>::iterator iter1, iter2, iter3;

   int i;
   for (i = 1; i <= 7; i++)
   {
      v1.push_back(i);
   }

   cout << "The original vector v1 is:\n ( " ;
   for (iter1 = v1.begin(); iter1 != v1.end(); iter1++)
      cout << *iter1 << " ";
   cout << ")." << endl;

   list <int> l1, l2(7);
   list <int>::iterator lIter1, lIter2;

   int t;
   for (t = 1; t <= 7; t++)
   {
      l1.push_back(t);
   }

   cout << "The original list l1 is:\n ( " ;
   for (lIter1 = l1.begin(); lIter1 != l1.end(); lIter1++)
      cout << *lIter1 << " ";
   cout << ")." << endl;

   // The first member function for the inner product
   int inprod;
   inprod = inner_product(v1.begin(), v1.end(), l1.begin(), 0);

   cout << "The inner_product of the vector v1 and the list l1 is: "
        << inprod << "." << endl;

   // Constructing a vector of partial inner_products between v1 & l1
   int j = 0, parinprod;
   for (iter1 = v1.begin(); iter1 != v1.end(); iter1++) {
      parinprod = inner_product(v1.begin(), iter1 + 1, l1.begin(), 0);
      v2[j] = parinprod;
      j++;
   }

   cout << "Vector of partial inner_products between v1 & l1 is:\n ( " ;
   for (iter2 = v2.begin(); iter2 != v2.end(); iter2++)
      cout << *iter2 << " ";
   cout << ")." << endl << endl;

   // The second member function used to compute
   // the product of the element-wise sums
   int inprod2;
   inprod2 = inner_product (v1.begin(), v1.end(),
      l1.begin(), 1, multiplies<int>(), plus<int>());

   cout << "The sum of the element-wise products of v1 and l1 is: "
        << inprod2 << "." << endl;

   // Constructing a vector of partial sums of element-wise products
   int k = 0, parinprod2;
   for (iter1 = v1.begin(); iter1 != v1.end(); iter1++)
   {
      parinprod2 =
         inner_product(v1.begin(), iter1 + 1, l1.begin(), 1,
         multiplies<int>(), plus<int>());
      v3[k] = parinprod2;
      k++;
   }

   cout << "Vector of partial sums of element-wise products is:\n ( " ;
   for (iter3 = v3.begin(); iter3 != v3.end(); iter3++)
      cout << *iter3 << " ";
   cout << ")." << endl << endl;
}

Output

The original vector v1 is:
 ( 1 2 3 4 5 6 7 ).
The original list l1 is:
 ( 1 2 3 4 5 6 7 ).
The inner_product of the vector v1 and the list l1 is: 140.
Vector of partial inner_products between v1 & l1 is:
 ( 1 5 14 30 55 91 140 ).

The sum of the element-wise products of v1 and l1 is: 645120.
Vector of partial sums of element-wise products is:
 ( 2 8 48 384 3840 46080 645120 ).

Requirements

Header: <numeric>

Namespace: std

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