# inner_product

 Category: algorithms Component type: function

### Prototype

Inner_product is an overloaded name; there are actually two inner_product functions.
```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 BinaryFunction1, class BinaryFunction2>
T inner_product(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, T init, BinaryFunction1 binary_op1,
BinaryFunction2 binary_op2);
```

### Description

Inner_product calculates a generalized inner product of the ranges [first1, last1) and [first2, last2).

The first version of inner_product returns init plus the inner product of the two ranges [1]. That is, it first initializes the result to init and then, for each iterator i in [first1, last1), in order from the beginning to the end of the range, updates the result by result = result + (*i) * *(first2 + (i - first1)).

The second version of inner_product is identical to the first, except that it uses two user-supplied function objects instead of operator+ and operator*. That is, it first initializes the result to init and then, for each iterator i in [first1, last1), in order from the beginning to the end of the range, updates the result by result = binary_op1(result, binary_op2(*i, *(first2 + (i - first1))). [2]

### Definition

Defined in algo.h.

### Requirements on types

For the first version:
• InputIterator1 is a model of Input Iterator.
• InputIterator2 is a model of Input Iterator.
• T is a model of Assignable.
• If x is an object of type T, y is an object of InputIterator1's value type, and z is an object of InputIterator2's value type, then x + y * z is defined.
• The type of x + y * z is convertible to T.
For the second version:
• InputIterator1 is a model of Input Iterator.
• InputIterator2 is a model of Input Iterator.
• T is a model of Assignable.
• BinaryFunction1 is a model of Binary Function.
• BinaryFunction2 is a model of Binary Function.
• InputIterator1's value type is convertible to BinaryFunction2's first argument type.
• InputIterator2's value type is convertible to BinaryFunction2's second argument type.
• T is convertible to BinaryFunction1's first argument type.
• BinaryFunction2's return type is convertible to BinaryFunction1's second argument type.
• BinaryFunction1's return type is convertible to T.

### Preconditions

• [first1, last1) is a valid range.
• [first2, first2 + (last1 - first1)) is a valid range.

### Complexity

Linear. Exactly last1 - first1 applications of each binary operation.

### Example

```int main()
{
int A1[] = {1, 2, 3};
int A2[] = {4, 1, -2};
const int N1 = sizeof(A1) / sizeof(int);

cout << "The inner product of A1 and A2 is "
<< inner_product(A1, A1 + N1, A2, 0)
<< endl;
}
```

### Notes

[1] There are several reasons why it is important that inner_product starts with the value init. One of the most basic is that this allows inner_product to have a well-defined result even if [first1, last1) is an empty range: if it is empty, the return value is init. The ordinary inner product corresponds to setting init to 0.

[2] Neither binary operation is required to be either associative or commutative: the order of all operations is specified.