std::inner_product

Defined in header <numeric>

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)

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; }

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

#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

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)