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Difference between revisions of "cpp/algorithm/inner product"

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< cpp‎ | algorithm
(The parameter name is `value` rather than `init`)
(Undo revision 105672 by Vladimir Reshetnikov (talk))
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Computes inner product (i.e. sum of products) or performs ordered map/reduce operation on the range {{tt|[first1, last1)}} and the range beginning at {{tt|first2}}.  
 
Computes inner product (i.e. sum of products) or performs ordered map/reduce operation on the range {{tt|[first1, last1)}} and the range beginning at {{tt|first2}}.  
  
−
@1@ Initializes the accumulator {{tt|acc}} with the initial value {{tt|value}} and then
+
@1@ Initializes the accumulator {{tt|acc}} with the initial value {{tt|init}} and then
 
{{rrev multi|until1=c++20|rev1=
 
{{rrev multi|until1=c++20|rev1=
 
modifies it with the expression {{c|1=acc = acc + *first1 * *first2}}, then modifies again with the expression {{c|1=acc = acc + *(first1+1) * *(first2+1)}}, etc
 
modifies it with the expression {{c|1=acc = acc + *first1 * *first2}}, then modifies again with the expression {{c|1=acc = acc + *(first1+1) * *(first2+1)}}, etc
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}}
 
}}
 
until reaching {{tt|last1}}. For built-in meaning of + and *, this computes inner product of the two ranges.
 
until reaching {{tt|last1}}. For built-in meaning of + and *, this computes inner product of the two ranges.
−
@2@ Initializes the accumulator {{tt|acc}} with the initial value {{tt|value}} and then
+
@2@ Initializes the accumulator {{tt|acc}} with the initial value {{tt|init}} and then
 
{{rrev multi|until1=c++20|rev1=
 
{{rrev multi|until1=c++20|rev1=
 
modifies it with the expression {{c|1=acc = op1(acc, op2(*first1, *first2))}}, then modifies again with the expression {{c|1=acc = op1(acc, op2(*(first1+1), *(first2+1)))}}, etc
 
modifies it with the expression {{c|1=acc = op1(acc, op2(*first1, *first2))}}, then modifies again with the expression {{c|1=acc = op1(acc, op2(*(first1+1), *(first2+1)))}}, etc

Revision as of 13:34, 11 July 2018

 
C++
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
Batch operations
(C++17)
Search operations
(C++11)                (C++11)(C++11)

Modifying sequence operations
Copy operations
(C++11)
(C++11)
(C++11)
Swap operations
Transformation operations
Generation operations
Removing operations
Order-changing operations
(until C++17)(C++11)
(C++20)(C++20)
Sampling operations
(C++17)

Sorting and related operations
Partitioning operations
Sorting operations
Binary search operations
(on partitioned ranges)
Set operations (on sorted ranges)
Merge operations (on sorted ranges)
Heap operations
Minimum/maximum operations
(C++11)
(C++17)
Lexicographical comparison operations
(C++20)
Permutation operations
C library
Numeric operations
(C++11)
inner_product
  
Operations on uninitialized memory
 
Defined in header <numeric>
template< class InputIt1, class InputIt2, class T >

T inner_product( InputIt1 first1, InputIt1 last1,

                 InputIt2 first2, T value );
 (1)
template<class InputIt1, class InputIt2, class T,

         class BinaryOperation1, class BinaryOperation2>
T inner_product( InputIt1 first1, InputIt1 last1,
                 InputIt2 first2, T value,
                 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)

Contents

Parameters

first1, last1 - the first range of elements
first2 - the beginning of the second range of elements
value - 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 value)
{
    while (first1 != last1) {
         value = std::move(value) + *first1 * *first2; // std::move since C++20
         ++first1;
         ++first2;
    }
    return value;
}
Second version 
template<class InputIt1, class InputIt2,
         class T,
         class BinaryOperation1, class BinaryOperation2>
T inner_product(InputIt1 first1, InputIt1 last1,
                InputIt2 first2, T value,
                BinaryOperation1 op1
                BinaryOperation2 op2)
{
    while (first1 != last1) {
         value = op1(std::move(value), op2(*first1, *first2)); // std::move since C++20
         ++first1;
         ++first2;
    }
    return value;
}

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

(C++17)
 applies an invocable, then reduces out of order
(function template) [edit]
sums up or folds a range of elements
(function template) [edit]
computes the partial sum of a range of elements
(function template) [edit]
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