# std::inner_product

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< cpp‎ | algorithm

Defined in header `<numeric>` |  |
template< class InputIt1, class InputIt2, class T > T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init ); | (1) |
template<class InputIt1, class InputIt2, class T, class BinaryOperation1, class BinaryOperation2> T inner_product( InputIt1 first1, InputIt1 last1, InputIt2 first2, T init, BinaryOperation1 op1, BinaryOperation2 op2 ); | (2) |

Computes inner product (i.e. sum of products) or performs ordered map/reduce operation on the range `[first1, last1)` and the range beginning at `first2`.

1) Initializes the accumulator `acc` with the initial value `init` and then

modifies it with the expression acc = acc + *first1 * *first2, then modifies again with the expression acc = acc + *(first1+1) * *(first2+1), etc | (until C++20)
modifies it with the expression acc = std::move(acc) + *first1 * *first2, then modifies again with the expression acc = std::move(acc) + *(first1+1) * *(first2+1), etc | (since C++20)

until reaching `last1`. For built-in meaning of + and *, this computes inner product of the two ranges.
2) Initializes the accumulator `acc` with the initial value `init` and then

modifies it with the expression acc = op1(acc, op2(*first1, *first2)), then modifies again with the expression acc = op1(acc, op2(*(first1+1), *(first2+1))), etc | (until C++20)
modifies it with the expression acc = op1(std::move(acc), op2(*first1, *first2)), then modifies again with the expression acc = op1(std::move(acc), op2(*(first1+1), *(first2+1))), etc | (since C++20)

until reaching `last1`.

`op1` or `op2` must not have side effects. | (until C++11)
`op1` or `op2` must not invalidate any iterators, including the end iterators, or modify any elements of the range involved. | (since C++11)

### Parameters

first1, last1 | - | the first range of elements
first2 | - | the beginning of the second range of elements
init | - | initial value of the sum of the products

op1

-

binary operation function object that will be applied. This "sum" function takes a value returned by op2 and the current value of the accumulator and produces a new value to be stored in the accumulator.

The signature of the function should be equivalent to the following:

Ret fun(const Type1 &a, const Type2 &b);

The signature does not need to have const &.
The types Type1 and Type2 must be such that objects of types T and Type3 can be implicitly converted to Type1 and Type2 respectively. The type Ret must be such that an object of type T can be assigned a value of type Ret. ​

op2

-

binary operation function object that will be applied. This "product" function takes one value from each range and produces a new value.

The signature of the function should be equivalent to the following:

Ret fun(const Type1 &a, const Type2 &b);

The signature does not need to have const &.
The types Type1 and Type2 must be such that objects of types InputIt1 and InputIt2 can be dereferenced and then implicitly converted to Type1 and Type2 respectively. The type Ret must be such that an object of type Type3 can be assigned a value of type Ret. ​

Type requirements
- `InputIt1, InputIt2` must meet the requirements of LegacyInputIterator.
- `ForwardIt1, ForwardIt2` must meet the requirements of LegacyForwardIterator.
- `T` must meet the requirements of CopyAssignable and CopyConstructible.

### Return value

The final value of `acc` as described above.

### Possible implementation

First version

    template<class InputIt1, class InputIt2, class T>
    T inner_product(InputIt1 first1, InputIt1 last1,
                    InputIt2 first2, T init)
    {
        while (first1 != last1) {
             init = std::move(init) + *first1 * *first2; // std::move since C++20
             ++first1;
             ++first2;
        }
        return init;
    }

Second version

    template<class InputIt1, class InputIt2,
             class T,
             class BinaryOperation1, class BinaryOperation2>
    T inner_product(InputIt1 first1, InputIt1 last1,
                    InputIt2 first2, T init,
                    BinaryOperation1 op1
                    BinaryOperation2 op2)
    {
        while (first1 != last1) {
             init = op1(std::move(init), op2(*first1, *first2)); // std::move since C++20
             ++first1;
             ++first2;
        }
        return init;
    }

### Notes

The parallelizable version of this algorithm, std::transform_reduce, requires `op1` and `op2` to be commutative and associative, but `std::inner_product` makes no such requirement, and always performs the operations in the order given.

### Example

Run this code

    #include <numeric>
    #include <iostream>
    #include <vector>
    #include <functional>
    int main()
    {
        std::vector<int> a{0, 1, 2, 3, 4};
        std::vector<int> b{5, 4, 2, 3, 1};

        int r1 = std::inner_product(a.begin(), a.end(), b.begin(), 0);
        std::cout << "Inner product of a and b: " << r1 << '\n';

        int r2 = std::inner_product(a.begin(), a.end(), b.begin(), 0,
                                    std::plus<>(), std::equal_to<>());
        std::cout << "Number of pairwise matches between a and b: " <<  r2 << '\n';
    }

Output:

    Inner product of a and b: 21
    Number of pairwise matches between a and b: 2

### See also

transform_reduce (C++17) | applies a functor, then reduces out of order (function template)
accumulate | sums up a range of elements (function template)
partial_sum | computes the partial sum of a range of elements (function template)

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